Seismic Behavior of Sheathed Cold-Formed Steel Stud Shear Walls ...

Seismic Behavior of Sheathed Cold-Formed Steel Stud Shear Walls: An Experimental Investigation – Luigi Fiorino - 2003avSeismic Behavior of SheathedCold-Formed Steel StudShear Walls:An Experimental InvestigationtLuigi FiorinoRotational-hingeSliding-hingeDottorato di Ricerca in Ingegneria delle Strutture

Università degli Studi di Napoli Federico IIPolo delle Scienze e delle TecnologieLuigi FiorinoSeismic Behavior of Sheathed Cold-FormedSteel Stud Shear Walls:An Experimental InvestigationTesi di dottoratoXVI CicloDottorato di ricerca in Ingegneria delle Strutture

I would like to express my sincere gratitude to my tutor Prof. FedericoM. Mazzolani, who has guided me during the doctoral activity. Hisenthusiasm and determination have represented a clear example for myresearch activity and not only for it.I am much thankful to Prof. Raffaele Landolfo who offered and madepossible my studies in the field of cold-formed steel structures. This researchwould not have been possible without his supervision and support.Thanks to Dr. Gaetano Della Corte for his assistance in this study,particularly in the field of seismic engineering. I appreciate a lot of useful helpthat I received from His.I would like to thank to Dr. Beatrice Faggiano for her aid. She alwayssomehow found time to help me and all-working group.The suggestion and constructive criticism of Dr. Gianfranco De Matteisis also gratefully acknowledged.I thank my fellow engineers, Ettore de Cesbron de la Grennellais,Gianmaria Di Lorenzo, Maurizio Manganiello, Simeone Panico, FrancescoPortioli, who shared with me the experiences of the PhD period.I respectfully acknowledge the financial support given to the researchproject by the Italian Ministry for University and Research. Also I extend theacknowledgements to the BPB Italia for the furniture of gypsum wall boardsheathings and the assembling of the specimens, the GUERRASIO for thefurniture of cold-formed steel profiles, the TECFI s.r.l. for the furniture ofscrews, and the HILTI Italia for the furniture of anchors.I also wish to thank my family for their affection, and encouragement aswell as their appreciation of my studies.Last, but not least thanks to my wife Stefania for his love, patience,emotional and material support.

To my grandmother Assuntina

iContentsForeword 1Chapter ILow-rise residential buildings built with cold-formedlightweight steel members 51.1 BASIC CONSTRUCTION SYSTEMS…………………………………………………………….. 61.2 STICK-BUILT CONSTRUCTIONS………...………………………………………...…………... 81.3 PROFILES…...………….……………………………………………………………………………151.4 SHEATHINGS.……………………………………………………………………………………… 181.4.1 Wood-based panels…………………………………………………………………………………... 181.4.2 Gypsum-based boards………………………………………………………………………………... 201.5 CONNECTIONS…………………………………………………………………………………….. 211.5.1 Screws………………………………………………………………………………………………... 221.5.2 Welding………………………………………………...…………………………………………….. 241.5.3 Pins…..……………………………………………………………………………………………….. 241.5.4 Nails………………………………………………………………………………………………….. 261.5.5 Bolts………………………………………………………………………………………………….. 261.5.6 Anchors………………………………………………………………...…………………………….. 261.5.7 Adhesives…………………………………………………………………………………………….. 301.5.8 Hold-down...………………………………………………………………………………………….. 301.6 THE BUILDING PROCESS………………………………………………………………………... 311.7 BASIC PROBLEMS OF STRUCTURAL DESIGN………………………………………………. 341.7.1 Vertical loads………………………………………………………………………………………… 341.7.2 Horizontal loads……………………………………………………………………………………… 351.8 ADDITIONAL CONSIDERATIONS……………………………………………………………… 381.8.1 Fire resistance………………………………………………………………………………………… 381.8.2 Durability…………………………………………………………………………………………….. 391.8.3 Thermal and acoustic insulation, air and moisture permeability…………………………………….. 401.9 ADVANTAGES AND LIMITATIONS……………………………………………………………. 41REFERENCES…………………………………………………………………………………………… 42Chapter IIDesign of cold-formed steel stud shear walls 452.1 MAIN DESIGN METHODOLOGIES FOR SHEAR STRENGTH OF CFSSSWS……………... 46

Contentsii2.2 SEMI-ANALYTICAL EVALUATION OF SHEAR STRENGTH ………………………………. 482.2.1 Strength of the sheathing-to-frame connections (S-F)……………………………………………….. 502.2.2 Strength of the frame (stud buckling strength) (F)…………………………………………………… 552.2.3 Strength of the frame-to-foundation connections (F-F)……………………………………………… 672.3 UNITS SHEAR DESIGN VALUES FOR CFSSSWS…………………………………………….. 762.3.1 UBC and IBC design tables………………………………………………………………………….. 762.3.2 IRC provisions on the PSW method utilizations…………………………………………………….. 83REFERENCES…………………………………………………………………………………………… 84Chapter IIITesting of cold-formed steel stud shear walls: review ofexisting literature 893.1 SUMMARY OF MAIN EXISTING TEST PROGRAMS……………………………………. 893.1.1 McCreless & Tarpy (1978)…………………………………………………………………………... 903.1.2 Tarpy & Hauenstein (1978)………………………………………………………………………….. 923.1.3 Tarpy (1980)………………………………………………………………………….………………. 923.1.4 Tarpy & Girard (1982)……………………………………………………………….………………. 943.1.5 Tissell (1993)………………………………………………………………………………………… 963.1.6 Serrette (1994)……………………………………………………………………….……………….. 973.1.7 Serrette & Ogunfunmi (1996)……………………………………………………….……………….. 973.1.8 Serrette et al. (1996a,b)………………………………………………………………………………. 993.1.9 Serrette et al. (1997a)………………………………………………………………………………… 1013.1.10 Serrette et al. (1997b)………………………………………………………………………………… 1043.1.11 NAHB Research Center (1997)……………………………………………………………………… 1073.1.12 Gad et al. (1999a, b)………………………………………………………………………………….. 1083.1.13 Selenikovich et al. (1999)……………………………………………………………………………. 1113.1.14 COLA-UCI (2001)…………………………………………………………………………………… 1123.1.15 Dubina & Fulop (2002)………………………………………………………………………………. 1143.1.16 Branston et al. (2003)………………………………………………………………………………… 1163.2 FACTOR AFFECTING CFSSSW BEHAVIOR UNDER LATERAL LOADING: THEYINDIVIDUATION AND ANALYSIS…………………………………………………………. 1183.2.1 Sheathing (type, thickness, orientation)……………………………………………………………… 1183.2.2 Framing (stud size, thickness and spacing, presence of X-bracing)…………………………………. 1203.2.3 Fastener (type, size, spacing)………………………………………………………………………… 1203.2.4 Geometry (wall aspect ratio, openings)……………………………………………………………… 1213.2.5 Type of loading (monotonic or cyclic)……………………………………………………………….. 1233.2.6 Construction techniques and anchorage details……………………………………………………… 124REFERENCES…………………………………………………………………………………………… 124Chapter IVEvaluation of seismic capacity: the monotonic test 1274.1 THE STUDY CASE: BASIC ASSUMPTIONS…………………………………………………… 1284.2 GENERAL DESIGN PRINCIPLES………………………………………………………………... 1314.3 TEST PROGRAM…………………………………………………………………………………… 1334.3.1 Description of test specimens………………………………………………………………………… 1344.3.2 Test set-up ……………………………………………………………………………………………. 1404.3.3 Instrumentation………………………………………………………………………………………. 1424.3.4 Test procedure for the monotonic test………………………………………………………………... 1434.4 TEST RESULTS…………………………………………………………………………………….. 144REFERENCES…………………………………………………………………………………………… 152

ContentsiiiChapter VEvaluation of seismic demand 1535.1 MODEL OF THE HYSTERETIC BEHAVIOR OF CFSSSW SYSTEMS………………………. 1545.1.1 The loading branch without pinching………………………………………………………………... 1555.1.2 The loading branch with pinching…………………………………………………………………… 1565.1.3 The unloading branch ………………………………………………………………………………... 1585.1.4 Calibration of the model……………………………………………………………………………… 1595.2 ASSESSMENT OF DEFORMATION DEMAND………………………………………………… 1665.2.1 Data-base of considered earthquake ground motions………………………………………………... 1665.2.2 Displacement demand evaluation……………………………………………………………………. 1715.3 DEFINITION OF A LOAD HISTORY FOR A CYCLIC TESTING……………………………. 1805.3.1 Loading histories in quasi-static cyclic loading tests: basic procedures for Multiple Step Test……... 1805.3.2 Definition of the deformation history for the cyclic testing………………………………………….. 185REFERENCES…………………………………………………………………………………………… 191Chapter VIThe cyclic test 1936.1 TEST PROCEDURE………………………………………………………………………………… 1946.2 TEST RESULTS…………………………………………………………………………………….. 197REFERENCES…………………………………………………………………………………………… 205Conclusions 207AppendicesAppendix A: Summary of existing experimental results….. 15 ppAppendix B: Summary of objectives and results of existingexperimental studies…………………………….. 6 ppAppendix C: Evaluation of seismic action and wall shear strength forthe study case…………………………………….. 14 ppAppendix D: Construction details of the sub-assembly specimen………………………………………………………. 10 ppAppendix E: Monotonic test results………………………….. 11 ppAppendix F: Cyclic test results……………………………….. 11 pp

vIndex of figuresFIGURE 1.1: STICK-BUILT CONSTRUCTION……………………………………………………... 6FIGURE 1.2: PANELIZED CONSTRUCTION……………………………………………………….. 7FIGURE 1.3: MODULAR CONSTRUCTION………………………………………………………… 8FIGURE 1.4: STRUCTURE OF TYPICAL STICK-BUILT CONSTRUCTION (NASFA 2000)…. 9FIGURE 1.5: WALL FRAMING OF TYPICAL STICK-BUILT CONSTRUCTION (NASFA 2000)…………………………………..………………………………………………………… 11FIGURE 1.6: TYPICAL WALL FRAMING DETAILS (NASFA 2000)……………………………. 11FIGURE 1.7: FLOOR FRAMING OF TYPICAL STICK-BUILT CONSTRUCTION (NASFA 2000)…………………………………………………………………………………………….. 12FIGURE 1.8: ROOF FRAMING OF TYPICAL STICK-BUILT CONSTRUCTION (NASFA 2000)…………………………………………………………………………………………….. 14FIGURE 1.9: BASIC FRAMING SYSTEMS IN STICK-BUILT CONSTRUCTIONS (CSSBI 1991)…………………………………………………………………………………………….. 15FIGURE 1.10: CHANNEL SECTION DIMENSIONS……………………………………………….. 16FIGURE 1.11: ON SITE COLD FORMING OF PROFILES………………………………………… 17FIGURE 1.12: UN-REINFORCED HOLES IN WEBS OF STUDS…………………………………. 18FIGURE 1.13: WOOD-BASED PANELS PRIMARILY USED IN THE CONSTRUCTION MARKET…………………………………………………………………………………………….. 20FIGURE 1.14: SCREW POINT TYPES……………………………………………………………….. 23FIGURE 1.15: SCREW HEAD TYPES………………………………………………………………... 24FIGURE 1.16: PNEUMATICALLY DRIVEN AND POWDER-ACTUATED PINS………………. 25FIGURE 1.17: SPIRAL SHANK NAILS………………………………………………………………. 26FIGURE 1.18: LOAD-TRANSFER MECHANISMS…………………………………………………. 27FIGURE 1.19: CAST-IN-PLACE ANCHORS………………………………………………………… 27FIGURE 1.20: POST-INSTALLED ANCHORS - MECHANICAL SYSTEMS…….……………… 29FIGURE 1.21: POST-INSTALLED ANCHORS - ADHESIVE SYSTEMS………………………… 30FIGURE 1.22: HOLD-DOWN (BRANSTON ET AL. 2003)………………………………………… 31FIGURE 1.23: FOUNDATION…………………………………………………………………………. 32FIGURE 1.24: INSTALL GROUND FLOOR…………………………………………………………. 32FIGURE 1.25: ERECT WALLS…………………………………………………………………………33FIGURE 1.26: INSTALL FIRST FLOOR……………………………………………………………... 33FIGURE 1.27: INSTALL ROOF……………………………………………………………………….. 33FIGURE 1.28: DISTRIBUTION OF HORIZONTAL (WIND) LOADS IN A HOUSE CONSTRUCTION…………………………………………………………………………………………….. 37

Index of figuresviFIGURE 1.29: WALL BRACED WITH STEEL SHEET X-BRACING…………………………….. 37FIGURE 1.30: BLOCKING…………………………………………………………………………….. 38FIGURE 1.31: TYPICAL INSULATION DETAILS…………………………………………………. 41FIGURE 2.1: MODEL OF A SIMPLE SHEAR WALL………………………………………………. 47FIGURE 2.2: COMPARISON BETWEEN SEGMENT METHOD AND PSW METHOD……….... 48FIGURE 2.3: FACTORS AFFECTING CFSSSWS SHEAR BEHAVIOR………………………….. 49FIGURE 2.4: FAILURE MODES OF SHEATHING-TO-FRAME CONNECTIONS UNDER SHEARLOADING………………………………………………………………………………… 51FIGURE 2.5: ASSUMED SHEATHING FASTENER FORCES (EASLEY ET AL. 1982)……….. 54FIGURE 2.6: BUCKLING MODES OF AN UNSHEATHED STUD……………………………….. 56FIGURE 2.7: “FLANGE BUCKLING” MODEL FOR DISTORTIONAL COLUMN BUCKLING(LANDOLFO ET AL. 2002)……………………………………………………………. 58FIGURE 2.8: BUCKLING MODES OF A SHEATHED STUD (AISI 1996)………………………. 63FIGURE 2.9: FAILURE MODES OF SCREWED CONNECTIONS UNDER SHEAR LOADING. 68FIGURE 2.10: FAILURE MODES OF BOLTED CONNECTIONS UNDER SHEAR LOADING.. 70FIGURE 2.11: FAILURE MODES OF ANCHORS UNDER TENSION LOADING (HILTI 2001) 72FIGURE 2.12: FAILURE MODES OF ANCHORS UNDER SHEAR LOADING (HILTI 2001)… 74FIGURE 2.13: MONOTONIC SHEAR LOAD-LATERAL DISPLACEMENT RESPONSE……… 78FIGURE 2.14: REVERSED-CYCLIC SHEAR LOAD-LATERAL DISPLACEMENT RESPONSE 78FIGURE 3.1: INFLUENCE OF THE SHEATHING ORIENTATION………………………………. 120FIGURE 3.2: INFLUENCE OF THE ASPECT RATIO………………………………………………. 122FIGURE 3.3: INFLUENCE OF THE OPENINGS……………………………………………………. 122FIGURE 3.4: INFLUENCE OF CYCLIC LOADING………………………………………………… 123FIGURE 3.5: CYCLIC RESPONSE FOR OSB 4-8 US C-A TEST PERFORMED BY BRANSTON ETAL. (2003)………………………………………………………………………………... 124FIGURE 4.1: TYPICAL ANALYZED STICK-BUILT HOUSE……………………………………... 128FIGURE 4.2: EUROCODE 8 TYPE 1 ELASTIC SPECTRUM ACCELERATION………………... 133FIGURE 4.3: GLOBAL 3D VIEW OF THE GENERIC SUB-ASSEMBLY………………………… 135FIGURE 4.4: A CLOSE-UP VIEW OF THE CONNECTION BETWEEN END STUDS ANDFOUNDATION…………………………………………………………………………… 135FIGURE 4.5: A CLOSE-UP VIEW OF THE CONNECTION BETWEEN THE FLOOR JOISTS ANDTHE WALL STUDS……………………………………………………………………... 135FIGURE 4.6: CFS PROFILES (MANIFACTURED BY GUERRASIO)……………………………. 137FIGURE 4.7: SHEATHINGS…………………………………………………………………………… 137FIGURE 4.8: SELF DRILLING SCREWS (MANIFACTURED BY TECFI S.R.L.)………………. 137FIGURE 4.9: HOLD-DOWN CONNECTOR………………………………………………………….. 138FIGURE 4.10: (A) SHEAR AND (B) HOLD-DOWN ANCHORS (MANUFACTURED BY HILTI

Index of figuresviiITALIA)…………………………………………………………………………………... 138FIGURE 4.11: LOAD TRANSFER SYSTEM…………………………………………………………. 141FIGURE 4.12: TEST SET-UP………………………………………………………………………….. 142FIGURE 4.13: INSTRUMENT ARRANGEMENT…………………………………………………… 143FIGURE 4.14: UNIT SHEAR RESISTANCE VS. MEAN DISPLACEMENT CURVE………….... 145FIGURE 4.15: SPECIMEN CONDITION AT STEP 1(D=10MM)………………………………….. 146FIGURE 4.16: SPECIMEN CONDITION AT STEP 2 (MAXIMUM SHEAR RESISTENCE -D=36MM)………………………………………………………………………………… 147FIGURE 4.17: SPECIMEN CONDITION AT STEP 3 (D=80MM)…………………………………. 148FIGURE 4.18: SPECIMEN CONDITION AT STEP 4 (D=130MM)………………………………... 149FIGURE 4.19: SHEAR VS. DISPLACEMENT CURVES FOR WALL 1 AND WALL 2…………. 151FIGURE 4.20: SHEAR VS. DISPLACEMENT MEASURED BY HORIZONTAL LVDTS .…….. 151FIGURE 4.21: SHEAR VS. DISPLACEMENT MEASURED BY VERTICAL LVDTS…………... 152FIGURE 5.1: BASIC DEFINITIONS (DELLA CORTE ET AL. 1999)…………………………….. 155FIGURE 5.2: THE LOADING BRANCH WITHOUT PINCHING………………………………….. 156FIGURE 5.3: THE LOADING BRANCH WITHOUT PINCHING (DELLA CORTE ET AL. 1999)………………………………………………..…………………………………………… 157FIGURE 5.4: THE LOADING BRANCH WITHOUT PINCHING (DELLA CORTE ET AL. 1999)…………………………………………………………………………………………….. 158FIGURE 5.5: THE UNLOADING BRANCH (DELLA CORTE ET AL. 1999)……………………..159FIGURE 5.6: CYCLIC TEST PROTOCOLS………………………………………………………….. 163FIGURE 5.7: CYCLIC RESPONSE……………………………………………………………………. 164FIGURE 5.8: NUMERICAL VS. EXPERIMENTAL CYCLIC RESPONSE FOR THE C01-4(A)SPECIMEN……………………………………………………………………………….. 164FIGURE 5.9: NUMERICAL VS. EXPERIMENTAL MONOTONIC RESPONSE…………………. 165FIGURE 5.10: GEOGRAPHICAL DISTRIBUTION OF THE SELECTED STRONG-MOTIONRECORDS………………………………………………………………………………… 169FIGURE 5.11A: ELASTIC SPECTRA OF EARTHQUAKE RECORDS FOR TYPE A SOIL……. 169FIGURE 5.11B: ELASTIC SPECTRA OF EARTHQUAKE RECORDS FOR TYPE B SOIL……. 170FIGURE 5.11C: ELASTIC SPECTRA OF EARTHQUAKE RECORDS FOR TYPE C SOIL……. 170FIGURE 5.11D: ELASTIC SPECTRA OF EARTHQUAKE RECORDS FOR TYPE D SOIL……. 170FIGURE 5.11E: ELASTIC SPECTRA OF EARTHQUAKE RECORDS FOR TYPE E SOIL…….. 171FIGURE 5.12: NUMERIC MODEL SCHEMATIZATION…………………………………………... 171FIGURE 5.13: IDA PROCEDURE EXAMPLE……………………………………………………….. 174FIGURE 5.14A: IDA CURVES FOR “LAZIO-ABRUZZO” EARTHQUAKE……………………... 175FIGURE 5.14B: IDA CURVES FOR “UMBRO-MARCHIGIANO” EARTHQUAKE…………….. 176FIGURE 5.15A: IDA CURVES FOR SOIL TYPE A…………………………………………………. 176FIGURE 5.15B: IDA CURVES FOR SOIL TYPE B…………………………………………………. 177FIGURE 5.15C: IDA CURVES FOR SOIL TYPE C…………………………………………………. 177FIGURE 5.15D: IDA CURVES FOR SOIL TYPE D…………………………………………………. 178FIGURE 5.15E: IDA CURVES FOR SOIL TYPE E………………………………………...……….. 178FIGURE 5.16: DETERIORATION OF A CFSSSW SYSTEM (BRANSTON ET AL. 2003)……... 180FIGURE 5.17: BASIC PARAMETERS IN A TYPICAL CYCLIC OF LOADING (ATC 1992)….. 181

Index of figuresviiiFIGURE 5.18: DEPENDENCE OF MEAN NUMBER OF INELASTIC EXCURSIONS ON NATURALPERIOD AND DUCTILITY RATIO (KRAWINKLER 1996)……………………….. 183FIGURE 5.19: DEPENDENCE OF MEAN NUMBER OF THE SUM OF NORMALIZED PLASTICDEFORMATION RANGES ON NATURAL PERIOD AND DUCTILITY RATIO(KRAWINKLER 1996)………………………………………………………………….. 183FIGURE 5.20: LOADING HISTORY FOR MULTIPLE STEP TEST (KRAWINKLER 1996)…… 184FIGURE 5.21: ASSUMED DEFINITIONS OF INDIVIDUAL PLASTIC DEFORMATION RANGE…………………………………………………………………………………………….. 186FIGURE 5.22A: RESULTS OF THE STATISTIC CHARACTERIZATION OF THE DEFORMATIONDEMAND IN TERMS OF MAXIMUM NORMALIZED DEFORMATION………… 188FIGURE 5.22B: RESULTS OF THE STATISTIC CHARACTERIZATION OF THE DEFORMATIONDEMAND IN TERMS OF NUMBER OF INELASTIC EXCURSION………………. 188FIGURE 5.22C: RESULTS OF THE STATISTIC CHARACTERIZATION OF THE DEFORMATIONDEMAND IN TERMS OF SUM OF NORMALIZED PLASTIC DEFORMATIONRANGES…………………………………………………………………………….……. 189FIGURE 5.22D: RESULTS OF THE STATISTIC CHARACTERIZATION OF THE DEFORMATIONDEMAND IN TERMS OF RATION BETWEEN THE MEAN VALUE AND THEMAXIMUM VALUE OF THE PLASTIC DEFORMATION RANGE……………….. 189FIGURE 6.1: CYCLIC TEST PROTOCOL……………………………………………………………. 196FIGURE 6.2: NUMERICAL CYCLIC RESPONSE…………………………………………………... 196FIGURE 6.3: UNIT SHEAR RESISTANCE VS. MEAN DISPLACEMENT CURVE…………..… 198FIGURE 6.4: BEHAVIOR OF OSB SHEATHING-TO-FRAME CONNECTIONS………………... 200FIGURE 6.5: BEHAVIOR OF GWB SHEATHING-TO-FRAME CONNECTIONS………………. 200FIGURE 6.6: FAILURE OF SHEATHING-TO-FRAME CONNECTIONS DUE TO SCREW HEADSPULL THROUGH………………………………………………………………………... 201FIGURE 6.7: FAILURE OF SHEATHING-TO-FRAME CONNECTIONS DUE TO RUPTURE OFSHEATHING EDGES…………………………………………………………………… 201FIGURE 6.8: UNZIPPING OF SHEATHINGS……………………………………………………….. 202FIGURE 6.9: BUCKLING OF END STUDS………………………………………………………….. 202FIGURE 6.10: DEFORMATION OF WALLS FOR LATERAL DISPLACEMENT MORE THAN 36MM…………………………………………………………………………………………….. 202FIGURE 6.11: CYCLIC VS. MONOTONIC BEHAVIOR…………………………………………… 204FIGURE 6.12: SHEAR VS. DISPLACEMENT CURVES FOR WALL 1 AND WALL 2……….... 205

ixIndex of tablesTABLE 2.1: FAILURE MODES IN A CFSSSW BRACED LATERALLY WITH WOOD BASEDPANELS………………………………………………………………………………….. 50TABLE 2.2: INDICATIVE SHEAR RESISTANCE OF SCREWS……………….…………………. 52TABLE 2.3: 1997 UBC NOMINAL SHEAR STRENGTH VALUES FOR SEISMIC ACTIONS... 79TABLE 2.4: 2000 IBC NOMINAL SHEAR STRENGTH VALUES FOR SEISMIC ACTIONS .... 80TABLE 2.5A: 1997 UBC NOMINAL SHEAR STRENGTH VALUES FOR WIND ACTIONS .... 80TABLE 2.5B: 1997 UBC NOMINAL SHEAR STRENGTH VALUES FOR WIND ACTIONS….. 81TABLE 2.6A: 2000 IBC NOMINAL SHEAR STRENGTH VALUES FOR WIND ACTIONS.….. 81TABLE 2.6B: 2000 IBC NOMINAL SHEAR STRENGTH VALUES FOR WIND ACTIONS…... 82TABLE 2.7: SAFETY AND RESISTANCE FACTORS PER 1997 UBC AND 2000 IBC………… 82TABLE 2.8: MAXIMUM UNRESTRAINED OPENING HEIGHT PER 2000 IRC……..………… 83TABLE 2.9: ADJUSTMENT FACTORS FOR APPLICATION OF THE PSW METHOD PER 2000IRC………………………………………………………………………………………... 84TABLE 3.1: LISTING OF TESTS OF CFSSSW……………………………………………………… 90TABLE 3.2: NORMALIZED SHEAR CAPACITY FOR DIFFERENT SHEATHING TYPE ANDTHICKNESS……………………………………………………………………………… 119TABLE 4.1: MAIN STRUCTURAL DIMENSION 129TABLE 4.2: UNIT DEAD LOADS 129TABLE 4.3: VALUES OF PARAMETERS DESCRIBING THE EUROCODE 8 TYPE 1 ELASTICRESPONSE SPECTRUM 130TABLE 4.4: MAXIMUM ELASTIC SPECTRUM ACCELERATION AND CORRESPONDINGLATERAL FORCE VALUES 133TABLE 4.5: FULL-SCALE SPECIMEN MATERIALS AND CONSTRUCTION DATA 139TABLE 5.1: WALL GEOMETRY AND MATERIAL DATA 160TABLE 5.2: CYCLIC TEST PROTOCOLS 162

Index of tablesxTABLE 5.3: RESULTS OF CALIBRATION OF LOWER BOUND CURVE AND TRANSITIONPARAMETERS OBTAINED ON THE BASIS OF EXISTING CYCLIC TESTS 165TABLE 5.4: RESULTS OF CALIBRATION OF UPPER AND LOWER BOUND CURVEPARAMETERS OBTAINED ON THE BASIS OF MONOTONIC TESTS CARRIED-OUTIN THE CURRENT RESEARCH 165TABLE 5.5: DATA-BASE OF SELECTED EARTHQUAKE RECORDS 168TABLE 5.6: IDA RESULTS 179TABLE 5.7: PREDICTED AND EXPERIMENTAL DEMANDS FOR A BILINEAR SDOF(KRAWINKLER 1996) 185TABLE 5.8: RESULTS OF THE STATISTIC CHARACTERIZATION OF THE DEFORMATIONDEMAND 190TABLE 6.1: CYCLIC TEST PROTOCOL 195TABLE 6.2: COMPARISON BETWEEN THE DEFORMATION DEMAND PARAMETERSOBTAINED FROM THE STATISTIC CHARACTERIZATION AND THE ADOPTEDLOADING HISTORY 197

1ForewordIn recent years, the use of cold-formed steel members in low-rise buildingshas increased significantly in North-America, North-Europe and Australia.The cold-formed steel products, traditionally used as secondary structures(profiles and decks) of industrial buildings, have had in such countries abrilliant and diffused application as main structures of residential (housing)and commercial constructions, mainly thanks to the expected economicadvantages deriving from the significant reduction of the construction time.The structural typologies, where cold-formed steel profiles are adopted asmain structural elements, according to the prefabrication level, can beclassified in: “stick – built” (lowest prefabrication degree); “panelized”(intermediate prefabrication degree); and “modular” (highest prefabricationdegree) constructions. They are generally made of steel profiles andsheathings assembled together by means of mechanical fasteners. The profilesare generally cold-formed lightweight galvanized steel with C (lippedchannel), U (unlipped channel), Z, and L sections. The most widely usedstructural sheathings are wood-based and gypsum-based panels, but also steelsheet sheathing may be used. Due to the presence of different structuralmaterials various connection typologies, as screws, welding, pins, nails, bolts,anchors and adhesives, may be employed.For the design of these structural systems under both vertical andhorizontal loads two approaches can by used, which are different as respect tocommon structures. In the first approach, named “all-steel design”, thecontribution of the attached sheathings is neglected and the profiles areconsidered as free-standing members. In the second, named “sheathingbraced design”, the interaction between profiles and sheathings is taken in-to

2account in the evaluation of the load bearing capacity. As a consequence, inthe case of horizontal loads two basic lateral load resisting systems may beconsidered. Following the “all-steel design” approach, the in-plane stability inroofs, floors and walls should be provided by the use of diagonal steel flatstrap bracings. While, considering the “sheathing braced design” approach, ifsheathing elements have adequate strength and stiffness, and if there areadequate connections to the profiles, then roofs, floors and walls can performas diaphragms.Although today the utilization of the cold-formed steel profiles in Italy isstill limited to secondary structure, the aptitude of such constructive systemsto be quickly and easily assembled makes this structural system an interestingalternative solution to the use of prefabricated modules (containers) for theefficient management of emergency situations. One important example, forthe national territory, is the management of post-earthquake emergencysituations.Such an employment of the cold-formed steel housing obviously requiresan accurate study of the seismic behavior of this structural system. The studymust be carried out according to modern and advanced knowledge ofearthquake engineering, using the recently developed performance-baseddesign and analysis approach. In fact, over the last decade, great emphasis hasbeen placed on the need to overcome limitations of current codified, forcebasedand prescriptive, seismic design procedures and to implement aprobabilistic performance-based approach. The latter is based on the couplingof multiple performance levels and ground motion intensities, thus generatingperformance objectives to be satisfied. While the application of theperformance-based methodology has long been tested for classic reinforcedconcrete and steel structures, its application to light cold-formed steel housingremains largely unexplored.The design of classic building structures is based on force-reduction factorsthat, exploiting the structure own ductility, avoids collapse, safeguards humanlives and allows a relatively less expensive structural design. In case of lightgaugecold-formed steel framed structures, the seismic weight of the buildingand its content is significantly smaller, allowing the design to be carried outwith relatively very low values of the force reduction factors. This event isparticularly favorable, because of the relatively small ductility of the light-

Foreword 3gauge structure. Consequently, cold-formed structures are more damagetolerantthan classic structures under earthquakes having the design intensity(i.e. earthquakes having a 10% probability of being exceeded in 50 yearsaccording to modern design standards). However, the ability of this type ofstructure to survive more violent earthquakes (rare earthquakes, for example,those having a 2% probability of being exceeded in 50 years according tocurrent research trends) is currently unexplored and need to be clarified. Thisrequires the evaluation of seismic performance through the comparisonbetween the seismic demand and the seismic capacity. In fact, adequateperformance implies that the capacity exceed the imposed demand with anadequate margin of safety. For a structural component or sub-assembly, thismeans that its capacities as well as the demands imposed by earthquakes needto be quantified.The main objective of this dissertation is to give a contribution to theevaluation of seismic performance of low-rise residential buildings built withcold-formed steel members through the evaluation of the seismic demand, theseismic capacity and their comparison.The same reason motivates a joint research effort between the University“Federico II” of Naples and the University “Gabriele D’Annunzio” of Chieti-Pescara, Italy. Namely, the research project, entitled “A theoretical andexperimental study on the feasibility of using cold-formed steel members inseismic zones” is supported by the Italian Ministry of University and Research(MIUR) as a part of a more comprehensive research program, devoted tostudy innovative steel structures for the seismic protection of buildings.Although the study had general purpose, with regard to low-rise residentialbuildings built with cold-formed steel members, the attention has beenfocused on the stick-built construction system because it represents the basicsystem for the development of more industrialized constructions (panelizedand modular constructions). In particular, considering this construction systemespecially advantageous when the members-to-sheathing interaction is takesin-to account (sheathing braced design), the research has been concerned onthe seismic behavior of cold-formed steel stud shear walls (CFSSSWs)laterally braced with sheathings (sheathed).

4The dissertation, as well as the research program, has been articulated in sixmain phases.The first phase of the research has been particularly devoted to study theconstruction system, the building process and the basic aspects of structuraldesign under vertical and horizontal loads (Chapter I). The second part of thestudy has been dedicated to analyze the available main design methodologiesfor the evaluation of shear capacity for CFSSSW systems (Chapter II). Thereview of existing literature focused on the critical examination of previoustests on CFSSSWs, together with the definition of basic factors that influencetheir lateral load response, have been the objects of the third phase (ChapterIII).The forth phase of the research (Chapter IV) represented the fist step of theexperimental activity. In fact, it has been dedicated to evaluate the seismiccapacity for small building made by a stick-built construction system. Inparticular, the design and the monotonic testing of a full-scale CFSSSW subassemblyspecimen, it representing a realistic model of typical lateral loadresisting systems of stick-built house structures, has been included.The fifth phase (Chapter V) of the research activity has been a theoreticalone. It has been articulated in the following three main steps: (1) developmentof reliable mathematical models calibrated using the experimental results ofthe monotonic test, in order to capture the complex hysteretic response ofCFSSSWs; (2) evaluation of the deformation demand to stud shear wallsystems obtained on the basis of a large database of acceleration records; and(3) definition of a load history for a successive cyclic testing.Finally, in the sixth phase (Chapter VI) the second step of the experimentalprogram was performed. In fact, in this stage a specimen nominally identicalto that tested under monotonic loading has been subjected to fully reversingcyclic horizontal displacements according to the definition of the deformationhistory parameters carried out in the theoretical phase.

Chapter ILow-rise residential buildings built withcold-formed lightweight steel members5The use of light steel framing as a method of low-rise house constructionhas increased significantly in industrialized countries in recent years. In someEuropean countries this is from a small base (Lawson & Ogden 2001). Inother countries, such as USA, Canada, Australia and Japan, there is a welldevelopedindustry with well-established practices. In fact, in the USA, 15000steel homes were built in 1993, 75000 were constructed in 1996 and it isexpected that in the year 2002 the steel house constructions will be about375000 (Yu 2000).The present generation of steel framed house construction systems has beenderived from traditional timber framed house construction systems withoutany significant change in either the architecture or the interior and exteriorfinishing materials.This Chapter describes the construction system (Sections 1.1 through 1.5);the erection procedure (Section 1.6); the fundamental problems of structuraldesign (Section 1.7); the additional considerations on fire resistance, durabilityand insulation (Section 1.8); the advantages and the limitations of the low-riseresidential buildings built with cold-formed lightweight steel members(Section 1.9).

Low-rise residential buildings built with cold-formed lightweight steel members 61.1 BASIC CONSTRUCTION SYSTEMSThere are three basic systems of constructions for low-rise house which arenamed (Landolfo et al. 2002): stick-built constructions; panelized constructions; modular constructions.Stick-built constructionsThe stick-built construction (see Fig. 1.1) is characterized by the lowestprefabrication degree and it is the most common method used for built coldformedsteel (CFS) frames, because it is the same as the familiar stick-builtwood construction method. In fact, in these systems the wood members havereplaced with appropriate CFS members. In general, the steel members maybe cut to length on job-site with a hand-held saw. Similar to woodconstruction, steel components are fastened together on the floor surface intowall sections and tilted into positions. Once the wall sections are structurallyconnected together, exterior and interior sheathing materials are applied. Theconstruction time is short, the steel structure of a typical detached houserequiring between 2 and 4 days.The advantages of stick constructions are (Grubb and Lawson 1997): the system can accommodate larger constructions tolerances; the workshop facilities associated with modular constructions are notnecessary; simple constructions techniques without heavy lifting equipment maybe used; members can be densely packed for transport.Figure 1.1: Stick-built construction.

Low-rise residential buildings built with cold-formed lightweight steel members 7Panelized constructionsIn panelized construction (see Fig. 1.2), wall and floor sub-frames and rooftrusses may be prefabricated in the factory. The panels are lifted into positionon the job-site and fastened together generally by bolting to form the requiredbuilding geometry. This method of construction is particularly efficient whenthere is repetition of panel types and dimensions. In contrast to stick-builtconstruction, in the panel construction exterior sheathings, thermal insulationand some of the lining and finishing materials may also be applied to the steelsub-frames in the factory.The main advantages of panel construction are (Grubb and Lawson 1997): speed of erection; factory standards of quality control during fabrication of the units; reduction of site labor costs, scope for automation in factory production.Figure 1.2: Panelized construction.Modular constructionsPrefabrication of wall, floor and roof units is taken a stage further inmodular construction (see Fig. 1.3). Here, lightweight steel boxes, which mayfor example be hotel room units, are completely prefabricated in the factorybefore being delivered to the site. It is usual for all internal finishes, fixturesand fittings, and even the carpets, curtains and furniture, to be fitted in the

Low-rise residential buildings built with cold-formed lightweight steel members 8factory. On job-site, the units are stacked side-by-side and up to severalstoreys high on prepared foundations and service connections made to formthe complete structure. Nowadays, many hotels and motels are built in thisway.This chapter is particularly focused on the stick-built construction systemthat certainly represents the more used structural solution. Besides, thisstructural solution is also the basic system for the development of moreindustrialized constructions, like the panelized construction and the modularconstruction.Figure 1.3: Modular construction.1.2 STICK-BUILT CONSTRUCTIONSFigure 1.4 shows typical stick-built construction (NASFA 2000).The basic elements of a stick-built construction are: foundations; walls framing; floors framing; roofs framing.

Low-rise residential buildings built with cold-formed lightweight steel members 9Figure 1.4: Structure of typical stick-built construction (NASFA 2000).FoundationsTwo kinds of foundations are typically used in a stick-built construction: poured concrete walls foundations; slab-on-grade foundations.For both foundation types, up-lift loads represent the critical problem. Infact, when the horizontal loads are large, the overturning moment is high, andthe tendency for the wall to overturn is elevated. Consequently, forcounterbalance the up-lift force the foundation must be capable of distributingthe load and the weight of the foundations itself must be exceeds that of up-liftforce.Walls framingWall framing generally have two and possibly three separate functions.Their primary function is to carry vertical load from the floors and roof above(load bearing wall). In external walls, they also have to resist the lateralpressure from the wind and transmit this to the floor and roof diaphragms andto the foundations. In addition, certain walls may also form part of the system

Low-rise residential buildings built with cold-formed lightweight steel members 10resisting in-plane forces from wind or seismic shear (bracing wall). A typicalwall framing system, component and terminology are shown in Figure 1.5 andsome constructional details are shown in Figure 1.6 (NASFA 2000).The main structural components of wall framing construction are:stud:vertical structural element of a wall assembly, which supportvertical loads and/or transfer lateral loads (typically lippedchannel sections).wall track: horizontal member used such as top and bottom plate for walls(typically unlipped channel sections).Wall studs are typically C-shaped galvanized CFS sections placed withtheir flanges in contact with the wall sheathing. The profiles are usually on amodule ranging approximately from 300mm to 600mm. The wall sheathingmay be, for example, a gypsum or wood fiber based board, plywood or, insome cases steel sheet or corrugated sheathings. If this wall sheathing hasadequate strength and stiffness and if there is adequate attachment to the studs,then the axial load bearing capacity may be substantially increased by theresulting structural interaction. This is mainly as a consequence of theresistance provided against lateral buckling modes.Evidently, wall studs can be designed as free-standing members withouttaking advantage of the influence of the other elements of the wallconstruction and modern codes of practice allow this on the basis ofcalculations alone. Inclusion of the stiffening influence of the walls has to besemi-empirical based on the interpretation of test results.

Low-rise residential buildings built with cold-formed lightweight steel members 11Figure 1.5: Wall framing of typical stick-built construction (NASFA 2000).Figure 1.6: Typical wall framing details (NASFA 2000).

Low-rise residential buildings built with cold-formed lightweight steel members 12Floors framingFloor framing construction is typically lightweight and dry. However, thereare circumstances where heavier constructions are specified, usually to meetrequirements for fire and/or sound isolations.Generally, the floor construction is constituted by cold-formed lightweightsteel profiles with a wood-based sheathing. The profiles are usually on amodule that coincides with studs on the supporting elevations. A typical steelfloor system, component and terminology are shown in Figure 1.7 (NASFA2000).Figure 1.7: Floor framing of typical stick-built construction (NASFA 2000).The main structural components of floor framing construction are:floor joists: horizontal member that supports floor loads (typicallylipped channel sections).floor track: horizontal member used as band or rim joists forflooring systems (typically unlipped channel sections).web stiffener: additional material that is attached to the web tostrengthen the member against web crippling. Alsocalled bearing stiffener.

Low-rise residential buildings built with cold-formed lightweight steel members 13Joist designs are rarely based on the bending resistance of the crosssections,in fact, normally the serviceability criteria of deflection and vibrationcontrol the design. Steel floors can sometimes resonate with the vibrationsinduced by human footsteps and, although this does not usually producestructural damages, it can be a source of discomforts. This problem tends tobecome more acute when lightweight construction is used.In some cases, the floor can be realized by trapezoidally profiled steel decksupported on primary beams and carrying a wood-based walking surface or,more infrequently, it can be realized by composite (steel-concrete) decksupported on primary beams.Roofs framingFor the roof framing construction, steel truss with similar proportions to aconventional gang-nailed timber truss is often about six times as strong as thetimber equivalent and is uneconomic at modest spans and load levels. For thisreason, when a habitable roof space is not required steel framed houses areoften completed with timber roof trusses. Steel trusses can, however, be usedeconomically when they are spaced at wider centers with purlins spanningbetween the trusses. All-steel solutions become much more favorable when ausable roof space is required. In Figure 1.8 (NASFA 2000) a typical solutionis shows, in which attic frames are connected in a conventional manner. Analternative system could use sandwich panels either spanning from caves toridge or supported on intermediate purlins.The main structural components of wall framing construction are:rafter:structural framing member (usually sloped) thatsupports roof loads (typically lipped channel sections).ceiling joist: horizontal structural cold-formed lightweight steelprofiles that supports a ceiling and attic loads (typicallylipped channel sections).ridge member: horizontal member placed at intersection between thetop edges of two sloping roof surfaces.fascia:member applied to the rafter ends as an edge memberfor attachment of roof sheathing, exterior finishes, orgutter.

Low-rise residential buildings built with cold-formed lightweight steel members 14Figure 1.8: Roof framing of typical stick-built construction (NASFA 2000).The others main structural components of floor, wall and roof framingconstructions are (NASFA 2000):header: horizontal built-up structural framing member used over wall,roof or floor openings to transfer loads above opening toadjacent framing member.blocking: solid block or piece of material placed between structuralmembers to provide lateral bracing as in bridging and/or edgesupport for sheathings.bridging: bracing or blocking placed between joist to provide lateralsupport.flat strap: sheet steel cut to a specified width without any bends. Typicallyused for bracing and transfer of loads by tension.There are two basic framing systems in stick-built constructions that areusually defined as (CSSBI 1991): platform system; balloon system.

Low-rise residential buildings built with cold-formed lightweight steel members 15In platform construction, as shown in Figure 1.9a, the structure is builtstorey by storey so that each floor can serve as a working platform for theconstruction of the floor above. The walls are not structurally continuous andloads from the walls above are generally transferred through the floorstructure to the walls below. The wall studs are connected to horizontal trackstop and bottom and the floor joists are seated on the top track of the studsbelow. Sufficient stiffening is incorporated in the connection to ensure thesafe transfer of vertical load though the floor construction.In balloon construction, as shown in Figure 1.9b, the wall panels arecontinuous over two or more storeys and the floors are attached to them. Itfollows that loads from the floors above pass down the load-bearing studswithout affecting the incoming floor construction.a: Platform framing system b: Balloon framing systemFigure 1.9: basic framing systems in stick-built constructions (CSSBI 1991).1.3 PROFILESSteel members used in residential buildings in the construction of floors,walls and roof are predominantly cold-formed lightweight galvanized steelmembers. The profiles are cold-formed from structural quality steel sheet witha yield strength ranging from 230MPa to 350MPa, an ultimate tensile strengthranging from 310MPa to 480MPa. Moreover, the ultimate tensile strength-toyieldstrength ratio shall be at least 1.10 and the total elongation shall be atleast 10%.

Low-rise residential buildings built with cold-formed lightweight steel members 16As illustrated previously, the main profiles are commonly divided intolipped and unlipped channel sections. The lipped channel sections are usuallyused for joist, stud and rafter profiles, while the unlipped channel sections arenormally utilized for track profiles. These profiles are identified using: web depth; flange width; thickness.In this dissertation a lipped channel section (see Fig. 1.10a) is identified as“C web depth x flange width x lip size x thickness” (all dimensions in mm),while a unlipped channel section (see Fig. 1.10b) is identified as “U web depthx flange width x thickness” (all dimensions in mm).a: Lipped channel section dimensions. b: Unlipped channel section dimensions.Figure 1.10: Channel section dimensions.In North America, stud type members typically range from about 90 to200mm in web depth, with an about 40mm flange width, and with thicknessesranging from 0.8 to 2.5mm. Joist type members have a flange width rangingfrom around 40 to 45mm and range in web depth approximately from 140 to310mm with thicknesses ranging from 0.8 to 2.5mm.In Europe, dimensions of studs and joists are similar to that used in NorthAmerica except for the thickness, which in European profiles ranges from 1.2to 3.2mm.

Low-rise residential buildings built with cold-formed lightweight steel members 17The profiles may by cold-formed and cut in the factory or on site.Generally, it is more convenient to order precut cold-formed members becausein this way it is possible to save time and material. But, if the exactdimensions of structure are unknown, it is usually preferable cut, and in somecase, cold form the profiles on site, as shown in Figure 1.11.Figure 1.11: On site cold forming of profiles.The profiles normally have holes in their webs for water lines, gas pipe,and electrical wiring, as shown in Figure 12. As far as concern the holedimension, it is possible to consider the following classification.Un-forced holes (small hole): if the depth of the hole, measured across theweb, does not exceed about 40mm, and the length of the hole, measured alongthe web, do not exceed about 100mm. In these cases, it is not necessary totake any precaution.Reinforced holes (intermediate holes): if web holes violates any of therequirements reported at the above point. In these cases, the web shall bestrengthened with an appropriate solid steel plate, stud section, or tracksection.Big holes: if the depth of the hole, measured across the web, exceeds about75% of the depth of the web, and/or, the length of the hole, measured along

Low-rise residential buildings built with cold-formed lightweight steel members 18the web, exceeds about 150mm. In these cases, the profiles shall be designedin accordance with accepted engineering practices taking in to account ofpresence of the hole.Figure 1.12: Un-reinforced holes in webs of studs.1.4 SHEATHINGSThe most widely used types of sheathing are: wood-based panels; gypsum-based boards, steel sheathings.Neglecting the well-known steel sheet sheathing, some discussion about onthe main types of wood-based and gypsum-based products used in steelframed house constructions are given hereafter.1.4.1 Wood-based panelsAll wood-based panels are composite materials made of wood elementssuch as veneer, particles, flakes, or fibers and some adhesive. The main typesof structural wood-based panels are (Faherty and Williamson 1999): veneer panels; particleboard panels.

Low-rise residential buildings built with cold-formed lightweight steel members 20Wood-based products are manufactured in sheets or panels with about 1.2 x2.4m as a generally standard size and with thickness varying from 8 to 30mm.Other sizes may be available for specific scopes, although widths other than1.2m are rare.The main product standards for wood-based panels, which describeminimum properties that the product must have to be acceptable, are: thePS1-95 (1983) and the ANSI A208.1-93 (1993) used in the USA, and theEN 313-1 (1997) and EN 313-2 (2000) for the plywood and the EN 309(1993) for the particleboard used in Europe.a. Plywood panel b. Oriented strand board panel c. FibreBoard panelFigure 1.13: Wood-based panels primarily used in the construction market.1.4.2 Gypsum-based boardsThe gypsum-based boards are a family of panel products consisting of anon-combustible core, primarily of gypsum, with a paper surfacing on theface, back and long edges. The main types of gypsum-based sheet productsused in building constructions are standard gypsum wallboard, water-resistantgypsum board, fire-resistant gypsum board, and foil-backed gypsum board.The water-resistant gypsum board is a wallboard specially processed foruse as a base for ceramic and other non-absorbent wall tiles in bath andshower areas. These products consist of a solid set, water-resistant gypsumcore covered with durable water-resistant backing paper and green-coloredface paper.The fire-resistant gypsum board is a wallboard that provides greater fireresistance. In fact, in this board type a specially formulated core provides fire

Low-rise residential buildings built with cold-formed lightweight steel members 21resistance ratings when used in tested assemblies. Facing paper is generallycolored pink.The foil-backed gypsum board is a wallboard panel consisting of a gypsumcore enclosed in heavy natural-side and strong liner paper on the backside towhich aluminum foil is laminated.Gypsum boards are manufactured with 1.2m generally standard widths,with lengths varying from 2 to 3.5m, and with thicknesses ranging from 6 to23mm.The main product standards for gypsum-based boards, which fix minimumproperties for these products, are the ISO 6308 (1980) and the ASTMC1396/C1396M-02 (2002).1.5 CONNECTIONSIn a residential CFS structure, taking into account the various structuralmaterials, it is possible to consider the following connections typology (AISI1993): steel-to-steel connections; steel-to-sheathing (wood-based and gypsum-based sheathings)connections; steel-to-concrete connections.For these connections typology the most common connector systems are: screws (steel-to-steel and steel-to-sheathing connections); welding (steel-to-steel connections); pins (steel-to-steel, steel-to-sheathing and steel-to-concreteconnections), nails (steel-to-sheathing connections), bolts (steel-to-steel connections); anchors (steel-to-concrete connections); adhesives (steel-to-sheathing connections).Moreover, a connection system named hold-down, typically used in thestick-built wood constructions for transferring the uplift loads, is alsoemployed in the stick-built CFS constructions for the same scope.

Low-rise residential buildings built with cold-formed lightweight steel members 22Others relatively new techniques, known a press-joining or clinching(Pedreschi and Sinha 1996) and rosette-joining (Machelainen et al. 1998) canadvantageously be used for steel-to-steel connections, particularly when theCFS systems are prefabricated in the factory (in the cases of panelized andmodular constructions).1.5.1 ScrewsThe most common fastener for steel framing is the self-tapping screw. Inone operation, it can drill the hole and fasten the material to steel framing.These screws come in a variety of styles to fit a vast range of requirements.For exterior applications, screws are available finished with zinc, cadmium orco-polymer coatings.Screws are available in diameters ranging from 3.5mm to 6.5mm. Lengthstypically vary from 12mm to as much as 75mm depending on the application.Screws are generally 10mm to 12mm longer than the thickness of theconnected materials so that a minimum of three threads shall extend beyondthe connected material. It is important that the drill point be as long as thematerial thickness to achieve an efficient drilling.Two specific point types are commonly used, as shown in Figure 1.14. Self-Drilling Screws: Externally threaded fasteners with the ability todrill their own hole and form their own internal threads withoutdeforming their own thread and without breaking during assembly.These screws are used with 0.8mm steel or thicker. Self-Piercing Screws: Externally threaded fasteners with the ability topierce relatively thin steel material. They are commonly used to attachrigid materials, such as gypsum wallboard, to 0.8mm or thinner steel.Self-drilling screws are manufactured in a variety of head configurations tomeet specific installation needs. The main head types, as shown in Figure1.15, are: pan head: This common head configuration generally fastens studs totrack, connects steel strapping or furring channels to studs or joists,and steel door frames to studs; modified truss head: An extremely low profile head commonly usedfor attaching metal lath to steel framing (also referred to as lath head);

Low-rise residential buildings built with cold-formed lightweight steel members 23hex washer head: This is also a common style for penetrating steel andis more commonly used on thicker steel materials. The washer faceprovides a bearing surface for the driver socket, assuring greaterstability during driving;oval head: Used when an accessory that will be attached to the framinghas oversized holes or requires a low profile appearance;flat head: Designed to countersink without causing splintering orsplitting of wood flooring and finishes;trim head: Used for fastening wood trim or other thick dense finishmaterials to steel studs. The small head pierces into the trim material,allowing easy finishing with minimal disturbance of the materialsurface;bugle head: Designed to countersink slightly in gypsum wallboard orsheathing, plywood or finish material without crushing the material ortearing the surface. Leaves a flat, smooth surface for easy finishing;low-profile head: Maintains a pleasing appearance at fastening pointswhere the application does not require jut heads. This style should beused when rigid sheathings or finish material is to be installed over topof the screw head;wafer head: Larger than the flat or bugle head, the wafer head is usedfor connecting soft materials to studs. The large head provides anample bearing surface to achieve a flat, clean, finished appearance.Figure 1.14: Screw point types.

Low-rise residential buildings built with cold-formed lightweight steel members 24Figure 1.15: Screw head types.1.5.2 WeldingWelding can be used to prefabricate steel framing components into panelassemblies and trusses. Welding is also commonly used in the attachment ofsite-fabricated or erected panels and for connecting shelf angles to steelframing.For helping assure quality installation, all work should be completed bywelders qualified in the welding of sheet steel. Where the studs, joists andframing accessories have been fabricated from galvanized or painted steel, thecoating will normally be burned away by the welding processes. Whererequired, weld areas should be re-touched with the appropriate paint or coldgalvanizing to maintain corrosion resistance.1.5.3 PinsTwo specific types are commonly used, as shown in Figure 1.16: pneumatically driven pins; powder-actuated pins.

Low-rise residential buildings built with cold-formed lightweight steel members 25Pneumatically driven pins are quite new to the CFS framing industry.They use techniques similar to nail guns for wood, and are commonly used fornailing plywood to steel. They are also available for fastening thicker coldformedsteel to concrete.These fasteners are available with mechanical or electro-zinc plating, or copolymercoatings, depending on corrosion resistance requirements. Headdiameters range from 6mm to 10mm, shank diameters vary from 2.5mm to8mm, and lengths from 12.5 to 200mm.The shanks may be step-down, knurled, or smooth, as shown in Figure1.16a. Step-down shanks are generally used on thicker materials for greaterload carrying capacities. Pins are typically supplied in bulk, in collated strips,or in coils, depending on tool requirements.Powder-actuated pins are frequently used to fasten CFS framing membersto concrete or to hot-rolled steel. For example, they are widely used to attachsteel track to concrete slabs and foundations. Powder-actuated pins systemscan be threaded, headed with a wisher or standard headed, as shown in Figure1.16b.The holding strength of fastener in concrete depends on the compressivestrength of the concrete, sank diameter, depth of penetration, and spacing andedge conditions. Headed or threaded drive pins are available with knurledshanks to increase holding power in structural steel. Fasteners loaded intension may require washers to prevent the fastener from prematurely pullingthrough the sheet steel.headed with astep-down knurled smooth threadedwishera: Pneumatically driven pins. b: Powder-actuated pins.standardheadedFigure 1.16: Pneumatically driven and powder-actuated pins.

Low-rise residential buildings built with cold-formed lightweight steel members 261.5.4 NailsCFS framing members may be also fastened to sheathing with nails.Generally, nails are spiral shank nails (see Fig. 1.17). They are case hardenedand phosphate treated to etch their surface for increased holding power. Theycan be used to fasten plywood subfloors and underlayment to steel.Figure 1.17: Spiral shank nails.1.5.5 BoltsBolts commonly used for connecting hot-rolled steel members can be alsoused to fasten CFS framing to other steel component. Generally, pre-drillingof holes is necessary for this fastening system. Washers should be providedfor oversized or slotted holes. When the bolt is loaded in tension, washers maybe required to prevent premature pull-through of the anchor.1.5.6 AnchorsAnchor commonly used for connecting concrete to steel can be separated intwo major categories (Hilti 2001): cast-in-place anchors, those are placed before the concrete is cast; post-installed or drilled-in anchors, those are installed into hardenedconcrete.Each of these categories is composed of a variety of different anchors, allof which transfer loads from the attachment to the concrete in a variety ofways. The primary load-transfer mechanisms (see Fig. 1.18) under tensionloading are friction, keying, and bonding as well as combinations. For shearloading, it is keying or direct bearing.

Low-rise residential buildings built with cold-formed lightweight steel members 27Figure 1.18: Load-transfer mechanisms.Generally, design engineers specify cast-in-place anchors (see Fig. 1.19) ifthey know beforehand where anchors are to be installed. The main cast-inplaceanchors are the standard fasteners (headed bolts, J bolts and L bolts,stud-welded plates), proprietary shapes (threaded inserts, proprietary anchorsand proprietary shapes), through bolts (usually sleeved), and special shapes(shear lugs, channel bars). All these anchors use keying as load transfermechanism. Many of these types of anchors have special uses. Stud-weldedplates and shear lugs provide large shear resistance, while channel bars givespecific attachment capability. J and L bolts are typically used for anchoringsill plates to foundations, but have a tendency to straighten and pull-out underhigher tension loading.Figure 1.19: Cast-in-place anchors.With the development and improvements of rotary hammer drills andcarbide-tipped bits, the user has the capability to install many different kindsof post-installed anchors (see Fig. 1.20) in hardened concrete virtually

Low-rise residential buildings built with cold-formed lightweight steel members 28anywhere that is accessible to the drill. Post-installed anchors can be dividedinto two major types, depending on the method of transferring load into theconcrete. They are mechanical systems and bonded or adhesive systems.Anchors can be also be cross-classified according to their load carryingcapability into heavy-duty, medium duty, and light-duty.The mechanical anchoring systems cover the range from heavy-duty tolight-duty capacities. The main kinds of mechanical anchors are undercutanchors and expansion anchors. The undercut anchors have been on themarket for about 20 years, they are excellent for use under both static anddynamic loads. They obtain their holding capacity through keying, that is,direct bearing on the concrete, and, under proper installation, can withstandvery high load without slipping out of the drilled hole. They are the preferredanchors for use where cracks in tension zones of the concrete can be expectedto occur. The expansion anchors have been available for at least 30 years.There are two basic types that are distinguished by their operating principles.The first, torque-controlled expansion anchors, are installed by inserting theanchor into the drilled hole, and applying the prescribed setting torque to thehead or nut. A cone at the bottom of the anchor is pulled up into the concretewith local crushing, and providing both friction and localized keying as loadtransfermechanism. There are several types available that vary significantly intheir ability to resist static and dynamic loads. The heavy-duty sleeve anchorcan resist dynamic loads as well as function well in expected cracks inconcrete. The second major type of expansion anchor is the displacementcontrolledexpansion anchor. Two primary examples are the drop-in and theself-driller. Drop-in anchors are installed in the predrilled hole by use of asetting tool that drives a plug into the expansion portion of the anchor. Thelower section of the anchor is expanded into concrete, which experiences localcrushing. The second type has cutting teeth on the lower end and drills its ownhole. The anchor is driven onto an expansion plug that expands the lowerportion of the anchor into the concrete. These anchors derive their holdingcapacity from friction and keying.

Low-rise residential buildings built with cold-formed lightweight steel members 29Figure 1.20: Post-installed anchors - mechanical systems.Bonded resin or adhesive anchors (see Fig. 1.21) were generally introducedinto the construction market about 20 years ago. Bonded systems use acombination of adhesive bond and micro keying into the pores of the concrete.Early systems used polyester resin, epoxies, and later, vinyl ester resins. Inrecent years, a larger variety of resins have been developed that haveindividual advantages, such as use in high temperatures, low temperatures,damp and wet holes, etc. For two component epoxy systems, the ratio to resinis critical. Prepackaged cartridge systems assure that the proper mixing isobtained.While a variety of installation methods are used, most are two componentresin systems that anchor threaded rod into predrilled holes. Most will resistsdynamic loads, both seismic and fatigue, but documentation in the form of testreports should be obtained. Bonded or adhesive anchoring systems are notwell suited for cracked tensile zones of concrete since about ½ the bonding islost.

Low-rise residential buildings built with cold-formed lightweight steel members 30Figure 1.21: Post-installed anchors - adhesive systems.1.5.7 AdhesivesAdhesives are generally optional when screws are used in attachingsubfloors or underlayment to steel joists, and are necessary when nails areemployed. The use of adhesives can provide for long-term bonding capacitythat contributes to a stable assembly. Adhesives are also utilized in attachingdrywall materials and paneling to steel studs or when laminating panelstogether, serving to eliminate some, but not all, of the mechanical fasteners.1.5.8 Hold-downUplift forces exist on shear walls because the horizontal forces are appliedto the top of the wall. These uplift forces try to lift up one end of the wall andpush the other end down. In some cases, the uplift force is large enough to tipthe wall over. Uplift forces are greater on tall short walls and less on low longwalls. Bearing walls have less uplift than non-bearing walls because gravityloads on shear walls help them resist uplift. Shear walls need hold-downdevices at each end when the gravity loads cannot resist all of the uplift. Thehold-down device then provides the necessary uplift resistance. In fact, holddownstransfer uplift forces from the end of the wall through a floor to a wallor foundation below.

Low-rise residential buildings built with cold-formed lightweight steel members 31Hold-downs that connect a shear wall to the foundation are bolted orscrewed to the end stud and they are anchored to the footings using cast-inplaceor post-installed anchors that are connected to the hold-down. Thisanchors transfer the uplift force from the wall down into the foundation. Thisminimizes the tendency of the wall to overturn (Fig. 1.22).Hold-downs that connect two walls through a floor come in pairs, oneabove and one below. The hold-downs are bolted or screwed their respectiveend stud. The uplift forces are then transferred from the wall above to the wallbelow through a threaded rod that is bolted to the hold-downs.Similar to bolted hold-downs, metal straps can be used as hold-downs. Thestrap must be long enough to pass through the floor framing and be attached tothe end studs so that the required number of screws or bolts is providedbetween the strap and the end stud. The strap should also be stiff and straightto reduce slippage.Figure 1.22: Hold-down (Branston et al. 2003).1.6 THE BUILDING PROCESSThe main phases of the building process for a stick-built structure as thatshown in Figure 1.4 are: foundation; install ground floor; erect ground walls; install first floor; erect first floor walls; install roof.

Low-rise residential buildings built with cold-formed lightweight steel members 32Some of these building phases are shown in Figures 1.23 through 1.27.These are considered to be self-explanatory.Slab-on-grade foundation.Poured concrete walls.Figure 1.23: Foundation.Floor joists are fastened to the top track of a steelframedwall with screws driven through the joistflanges. Additional web stiffeners fastened withself-drilling screws are added to each joist-to-trackconnections as required.Joist track is installed over the ends of the floorjoists. The track is fastened to each joist with selfdrillingscrews and is anchored to foundation withanchor bolt or other connection as required.Figure 1.24: Install ground floor.

Low-rise residential buildings built with cold-formed lightweight steel members 33Stud tracks are installed over the ends of thestuds. Each top and bottom tracks are fastenedto each studs with self-drilling screws.Sheathings are screwed to both studs and stud trackfor a secure connection between sheathing and coldformedframe.Figure 1.25: Erect walls.Floor joists are fastened to the track with thesame procedure reported in Figure 1.24.Floor decking is fastened to the floor joists and tracksgenerally using self-drilling screws.Figure 1.26: Install first floor.In roof framing structures pre-assembled steel truss can be used. Alternately, the profiles can be screwedwith the same procedure used for floor joists.Figure 1.27: Install roof.

Low-rise residential buildings built with cold-formed lightweight steel members 341.7 BASIC PROBLEMS OF STRUCTURAL DESIGNAs well as in a common structure, the basic requirements in a stick-builtstructure are two: the transmission of vertical loads to the foundation; the transmission of horizontal loads to the foundation.1.7.1 Vertical loadsThe design of a stick-built structure under vertical loads is relatively lesscomplicated. In fact, rafters and joists carry essentially bending loads, whereasstuds carry basically compression axial load.Rafters, joists and studs can be designed by using one of two differentapproaches, as follows: all-steel design; sheathing braced design.In the all-steel design, the contribution of the attached sheathings isneglected and the profile is considered as free-standing members withouttacking in to account of the influence of the interactions with the sheathingelements. In this way, the calculated resistance of the profile is based solely onthe condition of lateral bracing of the member. The advantage of this approachis that the load bearing capacity, being compression or bending, is determinedwithout having to rely on the structural bracing capability of the sheathingmaterial.In the sheathing braced design, the presence of attached sheathings istaken in-to account in the valuation of the compressive resistance calculation.In fact, if these elements have adequate strength and stiffness, and if there areadequate connections to the members, then the load bearing capacity may besignificantly improved. This is principally a result of the resistance providedagainst global buckling modes. In modern code (ENV 1993-1-3 1996, AISI1996, AS/NZS 4600 1996), it is allowed to take in-to account the members-tosheathingsinteraction with semi-empirical calculations based on theinterpretation of test results.

Low-rise residential buildings built with cold-formed lightweight steel members 351.7.2 Horizontal loadsThe design of a stick-built structure under horizontal loads (wind orseismic loads) is more problematic. The components of this problem are two(Davies 1998), as shown in Figure 1.28 for wind load. (1) The floor and roofframes must be able to act as diaphragms in plan to transmit horizontal loadson the wall frames parallel to the direction of the loads. (2) The wall framesmust be able to transmit the in-plane forces from the floor and roof framesdown to the foundations. It is found that significant uplift forces may arise atthe leeward end of the wind-frames. Providing an adequate tie to adequatefoundations is another aspect of this problem.There are two main methods existing for providing in-plane stability infloor, roof and wall: the use of diagonal bracings (X- and K-bracings); the use of floor, roof, or wall structure as diaphragms.When X-bracings are used (see Fig. 1.29), flat straps of thin steel passunder the bottom flange of the joists or rafters in the floor or roof and over theexternal faces of the studs in the walls. Due to their high slenderness, thesestraps act only in tension. They are connected to the primary structure at theirends in order to transfer the calculated tensile force and at their intersection inorder to reduce their tendency to sag.An alternative system is K-bracing which takes the form of C-sectionsfixed within the depth of the primary structure. These members act in eithertension or compression and, together with the adjacent members form a truss.As a result, adjacent members with a larger section than the norm andappropriate connections are required.Evidently, diagonal bracing should be used wherever possible and currentpractice is to use this method for the floor and roof and for walls where thereare few door and window openings. However, the currently popular housingstyle results in elevations that contain much opening. In such cases, diagonalbracing may not be possible and it is necessary to search for another solutions.Floor, roof or walls constructions often are made of panels supported bysteel joists, rafters or studs respectively. Only when the connections between

Low-rise residential buildings built with cold-formed lightweight steel members 36sheathings and supporting members are properly designed, these structurescan perform as a diaphragm and the structural system is termed a “boxsystem”. In this way, it is possible to take advantage of suitable sheathingsmaterials.Floors and roofs can be considered horizontal, simple supporteddiaphragms, whereas walls can be regarded as vertical, cantilevereddiaphragms. For full diaphragms design, it is necessary to analyze sheathings,connections, diaphragm edge members, and tie-down behavior. In fact, adiaphragm acts in a manner analogous to a deep beam, where the sheathingsact as a web, resisting shear, while the diaphragm edge members perform thefunction of flange, resisting bending. The diaphragm edge members arecommonly called chords, and may be joists, trusses, studs, etc.Due to the great depth of most diaphragms in the direction parallel to thatof load, and to their way of assembly, the behavior differs slightly from that ofthe usual beam.Shear stresses have been proven essentially uniform across the depth of thediaphragm, rather than showing significant parabolic distribution as in the webof a beam.Chords in a diaphragm carry all “flange" stresses acting in a simple tensionand compression, rather than devising these stresses significantly with theweb.As in any beam, consideration must be given to bearing stiffeners,continuity of webs and chords, and to web buckling, which is normallyresisted by the framing members.Diaphragms vary considerably in load-carrying capacity, depending onwhether they are blocked or unblocked. Blocking consists generally of lippedor unlipped channel sections placed between the joists or other primarystructural supports for the specific purpose of connecting the edges of thepanels (see Fig. 1.30). Systems that provide support framing at all sheathingedges are also considered blocked. The reason of blocking in diaphragms is toallow connection of sheathings at all edges for better shear transfer. Bucklingof unsupported sheathing edges, with consequent reduced load bearingcapacity, controls unblocked diaphragm behavior.The three main part of a diaphragm are the web, the chords, and theconnections. Since the individual pieces of web must be connected to form a

Low-rise residential buildings built with cold-formed lightweight steel members 37unit, since the chord members in all probability are not a single pieces, sinceweb and chords must be fixed so that they act together, and since the loadsmust have a path to other elements or to the foundation, connections arecritical to good diaphragm action. Their choice actually becomes a major partof the design procedure.Figure 1.28: Distribution of horizontal (wind) loads in a house construction.Figure 1.29: Wall braced with steel sheet X-bracing.

Low-rise residential buildings built with cold-formed lightweight steel members 38sheathingjoistflat strapblockingFigure 1.30: Blocking.1.8 ADDITIONAL CONSIDERATIONS1.8.1 Fire resistanceDue to several aspects, the issues of CFS structures in fire are muchdifferent in comparison to those for hot-rolled structures.Cold-formed members are generally used in low-rise constructions wherethe fire resistance requirements may be less onerous.In CFS profiles, the thin material produce more limited thermal capacity incomparison to that for hot-rolled members.For hot-rolled members, the critical steel temperature, at which structuralfailure may by anticipated, is in the region 450-700°C, depending on thestructural system and the load level in the vicinity of the fire. In absence ofany calculation model, a conservative approach for CFS profiles is to designthe fire protection systems to achieve a critical temperature of 350°C.In conventional hot-rolled construction, the fire resistance may be providedby protection applied to the members in the form of boards or sprayed onmaterials which delay the temperature increase in the steel by providingthermal insulation. Otherwise, CFS profiles in residential buildings are more

Low-rise residential buildings built with cold-formed lightweight steel members 39often part of a wall or floor structure such that they do not require speciallyapplied fire protection of this sort. In fact, walls and floors are usually built upof layers of materials such as mineral wool and gypsum board in order to meetthe requirements of sound and thermal insulation and these materials generallyalso have favorable properties of fire insulation. Thus, these elements of theconstruction can be built up in such a way that they meet all of theperformance requirements with regard to resistance to fire, sound and thermalloss in a consistent manner.1.8.2 DurabilityWith good quality detailing, the durability of a CFS structure should be thesame of traditional construction. There are two characteristics forguaranteeing good durability: avoid the accumulation of moisture in the external envelope; avoid bringing incompatible materials into contact with each other.These aspects are related because most types of material incompatibilityare aggravated in the presence of moisture. Main forms of materialincompatibility to avoid are the followings. Bimetallic contact: this is only likely if the cladding or fasteners are ofa different material to the main structure. Cementitious materials-to-steel contact: galvanized steel reacts withfresh cementitious materials with the formation of hydrogen bubbleson the surface of the zinc which reduce the bond with the steel. Thisreaction can be controlled by the addition of soluble chromates to thecementitious material but a more reliable solution is to chromate thesurface of the galvanized steel. Gypsum plaster-to-steel contact: moist gypsum plaster attacksgalvanized steel both in the fresh condition and if it dries out andsubsequently becomes wet. The G275 coating of normally galvanizedsteel will prevent corrosion of the metal. Wood-to-steel contact: wood is a corrosive material that can be mademore corrosive by the protective treatments given to it. Corrosion ofmetals in contact with timber is a function of the moisture content ofthe timber. Moreover, there is less risk with soft woods than with hard

Low-rise residential buildings built with cold-formed lightweight steel members 40woods. Correct seasoning of the wood significantly reduces theproblem.To limit the corrosion of steel and to improve the durability there aregeneral precautions which can be followed. To ensure that the cladding is sufficiently impermeable and to detail itin such a way that rainwater does not penetrate the structural frame ofthe building. To ensure that the external envelope performs thermally in such a waythat condensation of moisture from humid air is not possible.1.8.3 Thermal and acoustic insulation, air and moisture permeabilityIn the design of walls and roofs of lightweight construction thermal andacoustic insulation as well as air and moisture permeability are mostimportant.The need to achieve an adequate level of thermal insulation is now wellunderstood and the requirements seem to become more onerous year by year.A fundamental aspect is the need to avoid “thermal bridging”. It is less wellunderstood that this theoretical thermal performance can be reduced by airinfiltration, particularly at the roof space of a building. It is also wellunderstood that it is necessary to avoid condensation of moisture within thestructure and that a primary requirement is an appropriately placed vaporbarrier.Control of thermal insulation, air and moisture permeability is largely amatter of good detailing. For most climates, the first essential is a high level ofthermal insulation and this generally involves the provision of an appropriatethickness of insulation material as well as a cavity. The insulation material isgenerally mineral wool although a wide variety of suitable alternatives isavailable. It is also essential to avoid thermal bridges and moisturepenetration. Some insulation details of wall and roof construction are shownin Figure 1.31.Sound transmission and attenuation is an other most significant problembecause the occupants of buildings are rightly sensitive to noise intrusion fromother occupants of the same building or from outside. Fiberglass or celluloseinsulation installed in floor assemblies can significantly reduce the sound

Low-rise residential buildings built with cold-formed lightweight steel members 41transmission. Moreover, good construction practices can also result insignificant reduction in sound transmission through CFS floors.Insulation of a wall.Insulation of a roof.Figure 1.31: Typical insulation details.1.9 ADVANTAGES AND LIMITATIONSThere are numerous advantages that can be obtained by using CFSmembers in residential construction. The main benefits are the followings. High structural performance: The CFS members offer one of thehighest load capacity-to-weight ratio of any building componentcurrently on the market. The strength of steel permits the use of greaterspans than would be possible with wood components, often requiringless material. For example, joists and studs can be positioned 600mmon center and support the same load as wood framing 400mm oncenter. Lightweight: The lightweight of framing components reduces totalbuilding and seismic loads. Moreover, it is easy to handle, contributingto reduced labor costs and worker fatigue. High quality: The steel profiles are produced in factory, consequentlythey are more straight, uniform and consistent in quality than wood,hand-laid masonry and in-situ concrete elements. Design flexibility: The variety of size and thicknesses of steelcontribute to flexibility. For example, to obtain a desiderate design it

Low-rise residential buildings built with cold-formed lightweight steel members 42can reduce the width of a joist but compensate with a heavier gaugesteel and not change the spacing of members.Construction speed. It is possible to erect a CFS structure in much lesstime than a traditional structure.Dry constructions: Except for the foundation, the use of the CFSstructures allow dry constructions, therefore, dirt, dust and general lackof precision associated with hand-laid masonry, in-situ concrete areavoided.Ease of wiring installation: Holes are normally preformed simplifyingthe installation of the wirings.Recyclables: Cold-formed steel members are easily recycled.Common appearance: Once exterior and interior finishes are installed,a traditional and a CFS house are indistinguishable from each other.Incombustibility: Steel does not burn and prevents the spread of fire.The principal limitations that restraining the use of CFS framing inresidential house are the followings. Thermal performance: The thermal performance of steel usingstandard framing techniques is below that of traditional framing due tothermal conductivity of steel. Remedies, such as applying externalinsulation to the frame, add to the cost and the difficulty of fasteningwith screws. Fastening: The installation labor cost of CFS framing is higher thanfor wood framing. The primary labor component where productivitylags is the fastening of steel members using self-drilling screws.Development of pneumatic and clinching technology holds promise ofimproving fastening.REFERENCESAISI (1993) Fasteners for residential steel framing. AISI (American iron and SteelInstitute). Washington DC.AISI (1996) Cold-formed steel design manual. AISI (American Iron and SteelInstitute). Washington DC.

Low-rise residential buildings built with cold-formed lightweight steel members 43ANSI A208.1-93 (1993) Mat-formed wood particleboard. ANSI (American NationalStandards Institute). New York.ASTM C1396/C1396M-02 (2002) Standard specification for gypsum board. ASTM(American Society for Testing and Materials). West Conshohocken, PA, USA.AS/NZS 4600 (1996) Cold-formed steel structures. AS/NZS (AustralianStandards/New Zealand Standards). Sydney.Branston, A., Boudreault, F., Rogers, C.A. (2003) Testing on steel frame / woodpanels shear walls. Progress Report, Departement of Civil Engineering and AppliedMechanics, McGill University. Montreal.CSSBI (1991) Canadian Steel framing design manual, CSSBI (Canadian Sheet SteelBuilding Institute). Cambridge, Ontario.Davies J.M. (1998) Light gauge steel framing for housing construction. InProceedings of the 2nd International conference on thin-walled structures.Singapore.EN 309 (1993) Wood particleboards – Definition and classification. CEN (EuropeanCommittee for Standardization). Bruxelles.EN 313-1 (1997) Plywood. Classification and terminology - Classification. CEN(European Committee for Standardization). Bruxelles.EN 313-2 (2000) Plywood - Classification and terminology - Terminology. CEN(European Committee for Standardization). Bruxelles.ENV 1993-1-3 (1996) Eurocode 3: Design of steel structures – Part 1-3: Generalrules - Supplementary rules for cold formed thin gauge members and sheeting. CEN(European Committee for Standardization). Bruxelles.Faherty, K.F. and Williamson, T.G. (1999) Wood Engineering and constructionhandbook (Third edition). McGraw-Hill.Grubb, P.J. & Lawson, R.M. (1997) Building design using cold formed steel sections:construction detailing and practice. SCI Publication P165. The Steel ConstructionInstitute. Ascot, Berkshire, United Kingdom.Hilti (2001) Hilti North America product technical guide.ISO (1980) Gypsum plasterboard – Specification. ISO (International Organization forStandardization). Geneva.Landolfo, R., Di Lorenzo, G, Fiorino, L. (2002) Attualità e prospettive dei sistemicostruttivi cold-formed. Costruzioni metalliche No.1

Low-rise residential buildings built with cold-formed lightweight steel members 44Lawson, R.M. & Ogden, R.G. (2001) Recent developments in the light steel housingin the UK. In Proceedings of the 9th North steel conference of construction institute.Helsinki.Mkelinen, P., Kesti, J., Kaitila, O. (1998) Advanced method for light-weight steeltruss joining. In Proceedings of the Nordic steel construction conference '98. Bergen,Norway.NASFA (2000) Prescriptive Method For Residential Cold-Formed Steel Framing(Year 2000 Edition). NASFA (North American Steel Framing Alliance). Lexington,KY, USA.Pedreschi, R.F. & Sinha, B.P. (1996) The potential of press-joining in cold-formedsteel structures. Construction and building materials, Vol.10.PS1-95 (1983) Voluntary product standard PS1-95 for commercial and industrialplywood, U.S. Department of commerce, National institute of standard andtechnology. Gaithersburg, MD, USA.Schuster, R.M. (1996) Residential applications of cold-formed steel members inNorth America. In Proceedings of the 5th International Structural Stability ResearchConcilium – SSRC. Chicago.Yu, W.W. (2000) Cold Formed Design (3rd Edition). John Wiley & Sons. NewYork.

45Chapter IIDesign of cold-formed steel stud shearwallsCold-formed/light gauge steel (CFS/LGS) buildings typically use woodstructural panel sheathing fastened to repetitive member framing to provide anadequate lateral force resisting system (LFRS) to resist seismic and windloads. Therefore, the evaluation of the shear strength values used in the designof these systems are critical to the accuracy and efficiency of an engineeringanalysis and design for the cold-formed steel stud shear walls (CFSSSW).The objective of this Chapter is to provide a concise basic design referencefor CFS/LGS LFRSs. The Chapter is organized in three main parts. In the firstpart (Section 2.1) the main shear wall design methodologies are illustrated.The semi-analytical evaluation of shear strength for CFSSSWs is examined inthe second part (Section 2.2). In the third part (Section 2.3) the units sheardesign values for CFSSSWs reported in the main Codes (UBC 1997, IBC2000) are examined.

46 Chapter II2.1 MAIN DESIGN METHODOLOGIES FOR SHEARSTRENGTH OF CFSSSWsTwo main design methodologies for the evaluation of the shear capacity ofa CFSSSW exist, following methods similar to that used for wood-framedwalls: “segment” method; “perforated shear wall” method.The “segment” method is a traditional shear wall design methodology. Thebasic principles are demonstrated in the simple shear wall segment model ofFigure 2.1.This model is commonly used in current engineering practice to designwall segments in a wood frame building to resist lateral loads. In this simpleapproach, the effects of contributions from various connections and wallportions that are not part of the “designed” LFRS are neglected, as shown inFigure 2.2a. Therefore, while the method provides a simple analysis, itrequires greater amounts of connection for each shear wall segment thatdecreases the construction speed and increases the costs. This method of shearwall design is most appropriate for heavily loaded walls and those with manylarge openings that effectively break a wall line into segments. An examplewould be the design of shear wall segments to either side of a garage openingthat supports more than a roof load above. In other less demanding situationsthis process will tend to provide a conservative design with the largestamounts of hold-down connectors.This method is described in numerous technical resources on wood-framedshear wall design (Hoyle & Woeste 1986, Ambrose & Dimitry 1987, Beyer 1993,APA 1996, SSTD 10-97 1997).

Design of cold-formed steel stud shear walls 47unit shear vshearforce VBasic relations:htypicaloverturninganchorV = v wT = C = V h / wTvwCFigure 2.1: Model of a simple shear wall.In the “perforated shear wall” method the resistance of shear walls withun-restrained openings can be determined with reasonable accuracy (about ±5%) by an empirical method known as the Perforated Shear Wall (PSW)design method (Dolan & Heine 1997a, b, Dolan & Johnson 1997a, b, NAHBResearch Center 1997, 1998).The PSW design method is very simple, andonly requires that a fully-sheathed wall line with perforations for windows anddoors be restrained at the ends with a hold-down bracket or adequate cornerframing in lower capacity shear walls (Dolan & Heine 1997c), as shown inFigure 2.2b. For determining the shear wall capacity, all that is needed is theunit shear value for the shear wall construction, the area of wall openings, thelength of full-height wall segments, and the overall length of the wall. Thesevalues are inputs to a simple two-step equation that gives the overall wallcapacity without the use of internal connection detailing or hold-downs.In particular, the PSW design method for wood-frame shear wallsappearing in the IBC is based on the Sugiyama & Matsumoto’s (1994)equation. This equation gives the ratio of the strength of a shear wall withopenings to the strength of a fully sheathed shear wall without openings (F):

48 Chapter IIrF (2.1)3 2rwhere r is the sheathing area ratio as defined in the following equation:1r (2.2)Ao1h Liwhere Ao is the total area of openings, h is the height of the wall and Li is thelength of the full height wall segment.Wall 1 Wall 2 Wall 3Wallw 1 w 2 w 3w(a)V = v (w 1 + w 2 + w 3 )(b)V = F vwFigure 2.2: Comparison between Segment method (a) and PSW method (b).For both the Segment and the PSW methodology the evaluation of shearwall capacity of a fully sheathed shear wall without openings is required. Thisevaluation may be achieved by a semi-analytical approach based on the modelof a simple shear wall or by the nominal shear value tables for specific wallconfigurations obtained on the basis of experimental results.2.2 SEMI-ANALYTICAL EVALUATION OF SHEARSTRENGTHThe shear capacity of a CFSSSW is quite complex and depends by manyfactors. If a shear wall is laterally braced by sheathings this factors may bygrouped as follows (Fig. 2.3): strength of the sheathings; strength of the sheathing-to-frame connections;

Design of cold-formed steel stud shear walls 49strength of the frame (stud buckling strength);strength of the frame-to-foundation connections.FrameSheathing-to-frameconnectionsFrame-to-foundationconnectionsFigure 2.3: Factors affecting CFSSSWs shear behavior.A different failure mode is associated to each factor reported above.Following the limit states design philosophy, the smallest value obtained fromall of these possible failure modes will control the shear capacity of the wall(v), as defined by the following relation:v min vS; vSF; vF; vFF(2.3)in which v S , v S-F , v F and v F-F are the shear strengths associate to sheathing,sheathing-to-frame connections, frame and frame-to-foundation connectionsfailure, respectively.In most cases, a shear wall fails due to the sheathing-to-frame collapse. Infact, all the CFSSSW components are designed according to capacity designprinciples, in such a way to promote the development of the full shear strengthof sheathing-to-frame connections. For this reason, the studs (frame) aredesigned to avoid failure due to buckling in end studs. Analogously, the holddownand shear anchors (frame-to-foundation connections) are designed toprevent either shear failure at the base of the walls or failure due tooverturning. Moreover, the types of sheathings generally used in the

50 Chapter IICFSSSWs (wood-based and gypsum-based panels) are able to avoid thesheathing collapse. Consequently the evaluation of strength for the sheathingfailure usually is not performed (v S >> max {v S-F ; v F ; v F-F }).Strength calculations for the different failure modes of a CFSSSW laterallybraced with wood-based sheathings, as schematised in Table 2.1, are detailedbelow.CFSSSW ComponentsSheathingsSheathing-to-frame connections (S-F)Frame (F)Tension frame-to-foundation connections (F-F)NShear frame-to-foundation connections (F-F)VFailure modesNeglectedBearing in the steel frame (bs)Tilting of the screw (ts)Screw shear (ss)Bearing in the wood panels (bp)Stud buckling (sb)Hold-down (hd)Shear in hold-down-to-frame connection (hd-fr)Tension in the hold-down-to-foundation connection (hd-fo)Anchor-to-frame connection (a-fr)Anchor-to-foundation connection (a-fo)Table 2.1: Failure modes in a CFSSSW braced laterally with wood based panels.2.2.1 Strength of the sheathing-to-frame connections (S-F)The wood-based sheathing-to-steel frame screw connections are subjectedto shear forces consequently their failure limit modes include, as reported inFigure 2.4: bearing failure in the steel frame; tilting failure of the screw; screw shear failure; bearing failure in the wood panels.Therefore, the shear strength of a sheathing-to-frame connection (F S-F ) isequal to the minimum of the shear strengths associated to each failure mode,as defined by the following relation:FSF minFSF, bs;FSF, ts;FSF, ss;FSF, bp(2.4)where:F S-F,bs : is the bearing strength of the screws for steel members;

Design of cold-formed steel stud shear walls 51F S-F,ts : is the tilting strength of the screws;F S-F,ss : is the shear strength of the screws;F S-F,bp : is the bearing strength of the screws for wood panels.Bearing failure in the steel frametilting failure of the screwscrew shear failurebearing failure in the wood panelsFigure 2.4: Failure modes of sheathing-to-frame connections under shear loading.Bearing failure in the steel frame (F S-F,bs )Because cold formed steel frame are relatively thin (0.6÷1.5mm) comparedwith the thickness of wood-based sheathings (10÷20mm) normally used inCFSSSW structures, it is possible to calculate the bearing strength of thescrews for steel members (F S-F,bs ) with the following equation:FSF, bs tf d fu,s(2.5)where:: is a coefficient defined as follows: = 2.1 in Eurocode 3 - Part 1.3 (ENV 1993-1-3 1996) = 2.7 in AISI (1999)t f : is the thickness of the cold-formed steel member;d: is the nominal diameter of the screw;f u,s : is the tensile strength of the cold-formed steel member.Tilting failure of the screw (F S-F,ts )The tilting strength of the screws (F S-F,ts ) is defined as follows:3 0.5tf d fu s3 0.5tf d fusFS F , ts 3.2 ,for ENV 1993-1-3 (1996) (2.6)FS F , ts 4.2 ,for AISI (1996) (2.7)

52 Chapter IIScrew shear failure (F S-F,ss )The shear resistance of screws must be documented by testing andprovided by the manufacturer. For avoiding a brittle and sudden fracture of ascrew subjected to a shear force, the shear strength of the screws (F S-F,ss ) mustbe larger than the bearing strength (F S-F,bs ) and tilting strength (F S-F,ts ) of thescrews (F S-F,ss 1.2 F S-F,bs and F S-F,ss 1.2 F S-F,ts in ENV 1993-1-3 (1996) orF S-F,ss 1.25 F S-F,bs and F S-F,ss 1.25 F S-F,ts in AISI (1996)). Some indicativevalues of the characteristic shear resistance of screws made of hardened orstainless steel are reported in Table 2.2.Nominal diameter (mm) Hardened steel Stainless steel4.8 5.2 4.65.5 7.2 6.56.3 9.8 8.58.0 16.3 14.3Table 2.2: Indicative shear resistance of screws (kN/screw).Bearing failure in the wood panels (F S-F,bp )The bearing strength of the screws for wood panels (F S-F,bp ) is defined bythe following equation (Faherty & Williamson 1999):ts du fb,wFS F , bp 3. 5CDKD(2.8)where:C D : is the duration factor, which is equal to 1.6 for wind andearthquake loads;K D : is a coefficient that depends on the diameter of the screw:K D = 2.2 for D 4.3mm;K D = 10 D + 0.5 for 4.3mm < D < 6.4mm;K D = 3.0 for D > 6.4mm;t s : is the thickness of the wood-based sheathing;d u : is the unthreaded shank diameter of the screw;f b,w : is the dowel bearing strength of the wood-based sheathing.

Design of cold-formed steel stud shear walls 53Shear strength of the wall associated to sheathing-to-frame connectionsstrength (v S-F )Two methods exist to calculate the shear strength associated to sheathingto-frameconnections: Easley et al.’s method; simplified method.The Easley et al.’s method (Easley et al. 1982) is a design procedure thatrelates the shear capacity per unit length (v S-F ) with the shear strength of thesheathing-to-frame connections (F S-F ), based on equilibrium. Based on theresults of observation tests performed on wood-frame shear walls withplywood panels, the fasteners’ forces in a typical sheathing of a loaded shearwall were assumed to be directed as shown in Figure 2.5. In particular: The fastener forces in the sheathing ends were assumed to have both x-and y-components. The x-components (F ex ) were assumed uniform inthe x-direction. The y-components (F eyi ) were assumed proportional tothe distances of the fasteners from the sheathing center line (x ei ). The fastener forces in the sheathing sides (F s ) were assumed to beuniform and to act only in the y-direction (along the stud). The F sforces were assumed to be proportional to their distances from thesheathing center line. The fastener forces in the interior studs (F si ) were assumed to act onlyin the y-direction (along the stud) and to be proportional to thedistances x si .Indicating with:a: the length of the sheathing;h: the height of the wall;n e : the number of the end fasteners;n s :n si :the number of the side fasteners, excluding those at the end;the number of the fasteners in each interior stud, excluding thoseat the end;m: the number of the interior studs.

54 Chapter IIInteriorFastenersFigure 2.5: Assumed sheathing fastener forces (Easley et al. 1982).the relations between the side fastener forces (F s ), the end fastener forces (F ei )and the shear force per unit length acting on the shear wall (v a ) are thefollowings:Fshs (2.9)v where: nsn ei1m4I2I e x ei2I s x sii1ea22F ei a h ei 2xei (2.10)va ne a 2n2asiIs0.5

Design of cold-formed steel stud shear walls 55Defining with max the largest value between that obtained from s and ei ,the shear strength per unit length (v S-F ) is obtained as follow:1vSF FSF(2.11)maxin which F S-F is defined in Equation (2.4).With the simplified method it is assumed that only the end screws resisthorizontal load, and consequently, the contribution of side and interiorfasteners is ignored. According to this hypothesis the shear strength per unitlength (v S-F ) is obtained from the value of sheathing-to-frame connectionsshear strength (F S-F ), multiplied by the number of the end fasteners per unitlength (n’ e ):vSF n' eFSF(2.12)2.2.2 Strength of the frame (stud buckling strength) (F)Considering that the end studs are subjected to high compression force dueto overturning, it is possible that these members will fail due to stud buckling.The sheathing, usually connected to studs by screws, significantly restrainsthe buckling behavior of the studs. Therefore, the strength of the sheathed studwall system is significantly larger than that of unsheathed studs.Unsheathed studIn general, considering an unsheathed stud it can present three differenttypes of buckling: local, distortional and global (flexural and/or torsional)buckling or their coupling.When global buckling occurs, any cross-section of the stud moves as arigid body with a half-wavelength comparable to that of the stud. This type ofbuckling is governed by the global slenderness of the stud and normallyimplies the collapse of the structure.Local buckling is characterized by a relatively short half-wavelength of theorder of magnitude of individual plate elements, while the fold lines remainstraight.Distortional buckling implies the rotation and the translation of the multipleelements of the cross-section. This bucking mode occurs at a half-wavelength

56 Chapter IIintermediate to local and global mode buckling. Also, the cross section getsmuch more distorted than in the local one.Both local and distortional modes do not imply the collapse of thestructure. In fact, in these cases post-buckling strength is developed.Figure 2.6 illustrates these three modes of buckling for an unsheathed stud.Figure 2.6: Buckling modes of an unsheathed stud.The behavior of cold-formed steel members is characterized by high nonlinearity;consequently, its accurate prediction is feasible only through a finiteelement analysis that takes in to account both mechanical and geometricalnon-linearity (Della Corte et al. 2003, Fiorino et al. 2003). As a result of thisdifficulty, the design methodologies currently assumed in many Codes adoptsemi-empirical approaches that predict the ultimate strength through thedetermination of the elastic buckling load and considering a series of ultimatestrength curves (Fiorino & Landolfo 2001).LOCAL BUCKLINGLocal buckling is typically treated by ignoring any interaction betweenelements (flanges, web and lips). Each element is considered independentfrom the others and classical plate buckling equations based on isolatedsimply supported plates are generally used. In this approach, termed “element

Design of cold-formed steel stud shear walls 57model”, each element of the section is predicted to buckle at a different stress.The critical stress of each element is obtained by the well-known Eulerformula:2 E t cr k 2 (2.13)12(1 ) b where b and t are respectively the width and the thickness of the consideredelement, E and are respectively the Young’s modulus and the Poisson’s ratioof the material and k is the buckling factor which depends on the type ofelement (double or simply supported element) and on the stress distributionalong the element. The buckling factor k is equal to 4 for a stiffened element(double supported element) and to 0.43 for an unstiffened element (simplysupported element) under uniform compression.In order to better predict the actual local buckling stress, semi-empiricalmethods including elements interaction have been proposed by Batista (1988)and Shafer & Peköz (2001). In these approaches the expressions for k aredetermined by empirical close-fit solutions to finite strip analysis results.For the determination of the axial strength under local buckling (N b,l )effective widths and effective cross-section properties are generally used.According to the semi-empirical Von Karman’s approach, the non-uniformdistribution of stresses, which crop up in the post-buckling range, can bereplaced by an equivalent uniform stress distribution equal to the yield limitstress (f y ) acting on the effective width of the plate (b eff ). The effective widthformula usually adopted is the well-known semi-empirical formula proposedby Winter:b eff b(2.14)where: 1 if 0. 673 0.22 1 1 if p 0. 673(2.15) p pin which the normalized plate slenderness pis given by:fyp (2.16)crp2

58 Chapter IIThe reduced properties of effective plate elements in compression may becombined with the full width of plate element in tension to give an effectivecross-section for use in strength calculations.DISTORTIONAL BUCKLINGDistortional buckling usually involves rotation of each flange and lip aboutthe flange-web junction in opposite directions as shown in Figure 2.6. Theweb undergoes flexure at the same half-wavelength as the flange buckle andthe whole section may translate in a direction normal to the web also at thesame half-wavelength as the flange and web buckling deformations. The webbuckle involves single curvature transverse bending of the web.A general model for the determination of the elastic distortional bucklingstress under axial compression has been originally developed by Lau &Hancock (1987). Figure 2.7 shows this analytical model that is based on aflange buckling where the flange is treated as a compression memberrestrained by a rotational and a transational spring. The rotational springstiffness k , represents the torsional restraint from the web and the transationalspring stuffiness k x , represents the torsional restraint to transational movementof the cross-section. Lau & Hancock showed that the transational springstiffness k x , does not have much significance and the value of k x was assumedto be zero. The key to evaluating this model is to consider the rotational springstiffness k , and the half buckling wavelength , while taking account ofsymmetry.Figure 2.7: “Flange buckling” model for distortional column buckling (Landolfo et al. 2002).

Design of cold-formed steel stud shear walls 59The Authors gave a detailed analysis in which the effect of the localbuckling stress in the web and of shear and flange distortion were taken intoaccount in determining expressions for k and . This gives rise to a ratherlong and detailed series of explicit equations for the distortional bucklingstress that, not-withstanding their cumbersome nature, are included in theAustralian/New Zealand Code (AS/NZS 4600 1996).A similar set of explicit equations bas also proposed by Schafer (2001) andwill be incorporated in future AISI Specifications.For the determination of the axial strength under distortional buckling(N b,d ), Hancock (1985) developed expressions on the basis of effective widthsfor distortional buckling.COUPLED BUCKLINGFor taking in-to account the interaction between local and global buckling,the axial strength (N b ) has to be based upon the effective cross-section,calculated for uniform compression.In Eurocode 3 - Part 1.3 (ENV 1993-1-3 1996) a well-known Ayrton-Perryformula is used for the calculation of the axial strength:N A f(2.17)where:A eff :Afb effy1 1(2.18)2 2 0.5 2 0.51 0.2 (2.19)is the area of effective cross-section at uniformcompression at yield limit stress;eff y is the normalized slenderness;NcrN cr :is the minimum elastic critical axial force for global(flexural and/or torsional) buckling for the gross crosssection;: is the imperfection factor corresponding to theappropriate buckling curve:= 0.34 for lipped channel section (curve b);= 0.49 for unlipped channel section (curve c).

60 Chapter IIIn AISI (1996) the axial strength (N b ) for concentrically loadedcompression members is calculated with the following equation:N A f A f(2.20)where:A e :ncf 0.6582fy if c 1.50.877 f if c > 1.5fn 2cfybeneffyis the area of effective cross-section at uniformcompression at stress f n ;yc is the normalized slenderness;cr cr :is the minimum elastic critical stress for global(flexural and/or torsional) buckling considering thegross cross-section.NEW METHODOLOGIES: DIRECT STRENGTH METHOD AND “WHOLE SECTION”APPROACHSchafer & Peköz (1998) have recently proposed a new procedure whichworks only with the gross properties of a member and can take into accountthe interaction between local and global buckling and also the interactionbetween distortional and global buckling.Use of the Direct Strength Method for columns requires (1) thedetermination of the elastic buckling axial load (N cr ) of the member and (2)using that information in a series of ultimate strength curves to predict thestrength (N b ) (Fiorino 2000).For the determination of the elastic buckling load, as an alternative to thetraditional analytical solutions, numerical solutions based on the “wholesection” approach may be used to accurately calculate the elastic bucklingbehavior necessary for step (1). In fact, besides to the traditional finite elementmethod (FEM) some friendly computer programs, mainly based on the finitestrip method (FSM) (CU-FSM 2003, THIN-WALL 2003) or the generalized

Design of cold-formed steel stud shear walls 61beam theory (GBT) (Davies & Leach 1994a, b) have been purposely writtenfor the determination of the local, distortional and global elastic critical loads.The procedure employed to calculate the axial strength is the sameunderlying empirical assumptions as the effective width method used in themain Specification. In fact, the axial strength (N b ) is a function of the elasticbuckling load (N cr ) and the yield load (N y ).In particular, the axial strength (N b ) is the minimum of axial strength forglobal (flexural and/or torsional) buckling (N b,g ), local buckling (N b,l ) anddistortional buckling (N b,d ):N b minNb , g; N b , l; N b , d(2.21)The axial strength for global buckling (N b,g ) is:Nb, g g Ny(2.22)with:20.877gg 0.658if g 1. 5 or g if 1. 52 g(2.23)in whichNyg is the normalized global slenderness and N cr,g is theNcr,gminimum of elastic critical axial loads for flexural, torsional and flexuraltorsionalbuckling.The axial strength for local buckling (N b,l ) is:Nb, l l Nb,g(2.24)with:l 1 if l 0. 776 or 1 0.15 1l if l l 0. 776 (2.25)lin which N elastic critical axial load for local buckling.0.4b,ll is the normalized local slenderness and N cr,l is theNcr,lThe axial strength for distortional buckling (N b,d ) is:Nb, d d Ny(2.26)with:g

62 Chapter IId 1 if d 0. 561 or 1 0.25 1d if d d 0. 561 (2.27)d0.6 Nyin which dis the normalized distortional slenderness and N cr,d is Ncr,d the elastic critical axial load for distortional buckling.Sheathed studIn a sheathed stud the bending strength and diaphragm action due to thepresence of the sheathings increase the load-carrying capacity considerably(Miller and Peköz 1993, 1994).In Eurocode 3 - Part 1.3 (ENV 1993-1-3 1996) only the diaphragmsbracingeffect on buckling of beams is considered, while the AISI (1996)Specification considers the effect of sheathing material on buckling ofcolumns and beams. In particular, for the columns the AISI (1996) designrequirements are limited only to those studs that have identical wall materialattached to both flanges.In the evaluation of the axial strength (N b ) of a sheathed stud the AISI(1996) Specification follows the “Diaphragm stiffness” mechanical model.According to this approach the load-carrying capacity is governed by: column buckling of studs between fasteners in the plane of the wall(Fig. 2.4a); or overall column buckling of studs (Fig. 2.4b); or shear failure of the sheathing.Therefore, the axial strength (N b ) is equal to the minimum axial strengthassociated to the first two failure modes listed above, as defined by thefollowing relation:Nb minNbf; Nbo(2.28)where:N bf : is the axial strength associated to the column buckling of the studbetween fasteners;N bo : is the axial strength associated to the overall column buckling ofthe studs.

Design of cold-formed steel stud shear walls 63Moreover, it is needed to avoid the shear failure of the sheathing.(a) column buckling of studs between fasteners(b) overall column buckling of studsFigure 2.8: Buckling modes of a sheathed stud (AISI 1996).COLUMN BUCKLING OF STUDS BETWEEN FASTENERSIn case of column buckling of studs between fasteners in the plane of thewall, the failure mode can present local, distortional, global (flexural and/ortorsional) buckling or their coupling depending on the geometric configurationof the cross section and the spacing of fasteners. Consequently, in this case theevaluation of the axial strength (N bf ) is based on the same methodologiesillustrated for unsheathed studs without considering any interaction with thesheathing material in accordance with Equation 2.20 and considering anunbraced length equal to two times the distance between fasteners.OVERALL COLUMN BUCKLING OF STUDSThe overall column buckling of studs braced by sheathing material hasbeen mainly studied at Cornell University (Yu 2000). In particular, the earlierAISI provisions were developed on the basis of the Pincus & Fischer (1966),Errera et al. (1967), Apparao et al. (1969), Errera & Apparao (1976) andSimaan & Peköz (1976) research. In these studies, the sheathings wereattached either on both flanges or on one flange only of the studs. In addition,

64 Chapter IIboth the shear rigidity and the rotational restraint of the sheathings wereconsidered.For the purpose of simplicity, in the AISI Specification only the case ofidentical sheathings attached on both flanges is considered. Moreover, therotational restraint provided by sheathings is neglected.According to these hypotheses, in AISI (1996) the axial strength (N bo ) forconcentrically loaded compression members is calculated in accordance withEquation 2.20 with the elastic critical stress ( cr ) value obtained as follows: for singly symmetric C-sections, cr is the smallest of the followingelastic critical stresses: Q(2.29)crcr,ip a2, , ,,, ,4 ,, , cr op cr t Qcr op cr t Q cr opcr t Qcr(2.30)2 for doubly symmetric sections, cr is the smallest of the followingelastic critical stresses:cr cr,ip Qa(2.31)cr cr,op(2.32)In the above formulas: cr,ipis the elastic critical stress for flexural buckling in theplane of the wall considering the gross cross-sectionand an unbraced length equal to the length of the stud; cr,opis the elastic critical stress for flexural buckling in theout of plane of the wall considering the gross crosssectionand an unbraced length equal to the length ofthe stud; Qcr, t,Q cr,t cr,tQ a Q /Q tA2Qd 24Ar 0tis the elastic critical stress for torsional bucklingconsidering the gross cross-section and an unbracedlength equal to the length of the stud;

Design of cold-formed steel stud shear walls 65 s Q Q02 s'where:A: is the area of the gross cross-section;d: is the depth of the section;r 0 :is the polar radius of gyration of the cross sectionabout its shear center;s: is the fastener spacing (152mm s 305mm);s’ = 305mmQ0:is a parameter provided by AISI (1996) as function ofthe sheathing type; x 0 : x 1 0 r02is the distance from centroid to shear center.SHEAR FAILURE OF THE SHEATHINGTo prevent shear failure of the sheathing, a value of nominal strength(f bo =N bo / A) shall be used in the following equations so that the shear strain ofthe sheathing () does not exceed the permissible shear strain ( ) that isprovided by AISI (1996) as function of the sheathing type: E1d C1 (2.33)L 2 where: for singly symmetric C-sections:fbC0C1(2.34) f QE1fbcr,ipb2cr,op fbr0E0 x0D0fbx0D0 x0E02 f r f fx 2cr,opb0acr,t,Qbb0(2.35)for doubly symmetric sections:fbCC1 fcr,ip0b Qa(2.36)

66 Chapter IIE 1 = 0 (2.37)In the above formulas C 0 , E 0 , D 0 are initial column imperfections whichshall be assumed to be at least:C 0 = L/350in a direction parallel to the wall;E 0 = L/700in a direction perpendicular to the wall;D 0 = L/(10000 d) rad as measure of initial twist of the stud fromthe initial ideal, unbuckled shape.Moreover, if f b >0.5f y , then in the definitions for cr,ip , cr,op and cr,t , theYoung’s modulus (E) and the shear modulus (G) shall be replaced by E’ andG’, respectively, as defined below:fb fy fb E' 4 E(2.38)fysE'G' G(2.39)EShear strength of the wall associated to stud buckling strength (v F )Assuming F F = N b as the strength associated to stud buckling failure, theshear strength per unit length of the wall (v F ) associated to this failure mode isobtained as follows:FFvF (2.40)hwith h height of the wall.RESULTS OF CURRENT STUDIESRecent studies have been dedicated to study cold formed steel stud wallssheathed with gypsum board panels (Miller & Peköz 1993, 1994; Lee &Miller 2001a, b; Talue & Mahendran 20001; Schafer & Hiriyur 2002).From these studies result that the “diaphragm stiffness” mechanical modeladopted by AISI (1996) may be inaccurate at least for the gypsum sheathings.In particular, Lee & Miller (2001a) report that the axial strength isindependent of stud spacing, reflecting the localized nature of the wallboarddeformations rather than the shear diaphragm behavior assumed in the current

Design of cold-formed steel stud shear walls 67AISI (1996) Specification. Moreover, using the differential equation ofequilibrium the Authors derive an approach for determining the axial strengthof a cold-formed steel stud wall sheathed with gypsum sheathings. In thisapproach, it is assumed that the axial load is applied to the centroid of thegross cross section for each stud and the bracing from the wallboardconnected by screws is represented by elastic springs.Shafer & Hiriyur (2002) summarize the deficiencies of models currentlyadopted by AISI (1996, 2001) and of the approach proposed by Lee & Miller(2001a). In particular, Shafer & Hiriyur carried out numerical analyses ofsheathed wall systems using a plane stress FEM with imposed displacement,and a FSM with a discretized sheathing modeled. The Authors concludedfrom the numerical results that: (a) the “diaphragm stiffness” can be yet usedas basic mechanical model; (b) the diaphragm stiffness, per stud, is nonuniformand is not solely depended from stud spacing (as assumed in AISI1986) nor it is independent of stud spacing (as assumed in AISI 1996, 2001);(c) the sheathing resists against the weak axis buckling of the stud by meansof shear stiffness, either locally of the material or globally for the diaphragm;(d) the sheathing does not have much influence on local buckling of studs; (e)in cases of highly dissimilar sheathing, such as in case of one-side sheathing,distortional buckling of studs influences the behavior (moreover both codifiedcurrent (AISI 1996, 2001) and novel (Lee & Miller 2001a) approaches do nottake in-to account this aspect; (f) in cases of sheathing on both sides the axialstrength significantly increases in comparison with one-side sheathing even ifsheathings are dissimilar or relatively weak (gypsum board); (g) a simpleapproach to evaluate the buckling capacity of unperforated studs with one-sideand/or dissimilar sheathing may be the FSM.However, additional experimental and theoretical research is needed forincreasing the knowledge of the stud-to-sheathing interaction and to providedesign methodologies that can easily and correctly evaluate the axial strengthof cold-formed steel stud walls sheathed with panels.2.2.3 Strength of frame-to-foundation connections (F-F)The frame-to-foundation connections may by grouped in two types: tensionconnections and shear connections.

68 Chapter IIStrength of frame-to-foundation tension connections (F (F-F)N )Possible failure modes of tension connections are: failure in the hold-down (F (F-F)N,hd ); shear failure in the hold-down-to-frame connection (F (F-F)N,hd-fr ); tension failure in the hold-down-to-foundation connection(F (F-F)N,hd-fo ).Therefore, the strength of the tension frame-to-foundation connection(F (F-F)N ) is obtained by the minimum strength associated to each failure mode:F min F ; F F(2.41)( F F) N( F F) N , hd ( F F) N , hd fr;( F F) N , hd foFAILURE IN THE HOLD-DOWNThe strength corresponding to the failure in the hold-down (F (F-F)N,hd )regularly is not performed because the hold-down is normally purposelydesigned by the manufacturer to avoid its failure.SHEAR FAILURE IN THE HOLD-DOWN-TO-FRAME CONNECTIONThe strength corresponding to the shear failure in the hold-down-to-frameconnection (F (F-F)N,hd-fr ) depends on the type of connection used which isgenerally a bolted or screwed connection.In case of screwed connections, F (F-F)N,hd-fr is obtained by the minimum ofthe following values: the net section strength (F n ); the bearing/tilting strength (F b/t ); the screw shear strength (F s ).Figure 2.9 shows the failure mode associated to net section, bearing/tiltingand screw shear strengths.net section failurebearing / tilting failurescrew shear failureFigure 2.9: Failure modes of screwed connections under shear loading.

Design of cold-formed steel stud shear walls 69Because the hold down is thicker and stronger than the cold-formed steelstud, it is possible to calculate the strength by the equations reported below.The net section strength (F n ) is defined by the following equation:Fn Anet fu,s(2.42)where:A net is the net area of the cold-formed steel member;f u,s : is the tensile strength of the cold-formed steel member.The bearing/tilting strength (F b/t ) is defined as follows:Fb / t ns b / t tf d fu,s(2.43)where:n s : is the number of screws; b/t : is a coefficient defined as follows:if t hd = t f (tilting strength) 3.20.5/ d 2. in ENV 1993-1-3 (1996)t f 1 5b / tb / t 4.2t f/ d in AISI (1996)if t hd 2.5 t f (bearing strength) b/t = 2.1 in ENV 1993-1-3 (1996) b/t = 2.7 in AISI (1996)if t f < t hd < 2.5 t f b/t is obtained by linear interpolationt f : is the thickness of the cold-formed steel member;d: is the nominal diameter of the screw.The manufacturer usually provides the shear resistance (F s ). However,some indicative values of F s are given in Table 2.2 (see Section 2.2.1). Theshear strength of the screws (F s ) must be about 1.2 greater than thebearing/tilting strength (F b/t ) of the screws to avoid a brittle and suddenfracture of a screw.In case of bolted connections, F (F-F)N,hd-fr is obtained by the minimum of thefollowing values: the longitudinal shear strength of the sheet shear strength (F l );

70 Chapter II the net section strength (F n ); the bearing strength (F b ); the bolt shear strength (F v ).Figure 2.10 shows the above-introduced failure modes.Because the hold down is thicker and stronger than the cold-formed steelfame, it is possible to calculate the strength by the equations reported below.If the bolted part has a reduced edge distance in the direction of the appliedforce the connection can fails due to longitudinal shear collapse of the sheet.For this failure type, the nominal strength (F l ) is defined as follows:Fl e1 tf fu,s(2.44)where e 1 is the end distance from the center of the bolt to the adjacent end ofthe connected part, in the direction of load transfer (in ENV 1993-1-3 (1996)and AISI (1996)), or the distance from the center of the bolt to the nearestedge of an adjacent hole, in the direction of load transfer (in AISI (1996)only).longitudinal shear failure of the sheet shearbearing failurenet section failurebolt shear failureFigure 2.10: Failure modes of bolted connections under shear loading.For the net section strength (F n ) the ENV 1993-1-3 (1996) gives thefollowing formula: d Fn 1 3r Anet fu,s Anet fu,su (2.45)While, in case of channel sections having two or more bolts in the line ofthe force, the AISI (1996) defines F n as follows:

Design of cold-formed steel stud shear walls 71 x Fn1.0 0.36 Anet fu,s L(2.46)but F n 0.5 A net f u,s and F n < 0.9 A net f u,swhere:r: is the ratio between the number of bolts at the crosssection and the total number of bolts in the connection;u = 2e 2 p 2 with e 2 , the edge distance from the center of the bolt tothe adjacent edge of the connected part, in thedirection perpendicular to the load transfer and p 2 , thespacing center-to-center of bolts in the directionperpendicular to the direction of load transfer;x :is the distance from the shear plane to the centroid ofthe cross section;L: is the length of the connection.The bearing strength (F b ) is defined as follows:Fb nb be tf d fu,s(2.47)where:n b : is the number of bolts; be : is a coefficient defined as follows: be = 2.5, but be e 1 /1.2d in ENV 1993-1-3 (1996), where e 1 isthe end distance from the center of the bolt to the adjacent end ofthe connected part;in AISI (1996) be depends on the use of washers, thickness ofconnected part (t f ), type of joint, and f u,s /f y ; In particular, in case oft f < 4.76mm, for connections with washers under both bolt headand nut be ranges from 3.00 to 3.33, while for connectionswithout washers under both head and nut or with only one washer be ranges from 2.22 to 3.00.In ENV 1993-1-3 (1996), the bolt shear strength (F v ) is defined through thefollowing relation:Fv nb bo As fu,bo(2.48)in which:n b : is the number of bolts;

72 Chapter II bo :A s :f u,bo :is a coefficient that depends on the steel strength grade of the bolt: bo = 0.6 for strength grade 4.6, 5.6 and 8.8; bo = 0.5 for strength grade 4.8, 5.8, 6.8 and 10.9;is the tensile stress area of the bolt;is the ultimate tensile strength of the anchor steel.For the bolt shear strength (F v ) the AISI (1996) gives the followingformula:Fv nb Ab fv,bo(2.49)in which:n b : is the number of bolts;A b : is the gross cross-sectional area of the bolt;f v,bo : is the nominal unit shear strength of the bolt, provided by AISI(1996) as function of steel strength grade and diameter of bolt.TENSION FAILURE IN THE HOLD-DOWN-TO-FOUNDATION CONNECTIONThe failure mode in the connections between hold-down and foundationdepends on the type of anchor, depth of embedment, concrete strength, edgedistances and spacing between anchors (Hilti 2001).For both mechanical and adhesive-bonded anchors the main failure modesunder tension loading are concrete cone failure, pull-out (including anyexpansion sleeve), tension steel breakage. These different failure modes areshown in Figure 2.11.concrete cone failurepull-out failuresteel breakage failureFigure 2.11: Failure modes of anchors under tension loading (Hilti 2001).The tension strength of the hold-down-to-foundation connection(F (F-F)N,hd-fo ) is equal to the minimum strength associated to each differentfailure mode, as defined by the following relation:

Design of cold-formed steel stud shear walls 73F( F F ) N , hd fo min N c; N p; N s(2.50)where:N c : is the resistance against concrete cone failure;N p : is the resistance against pull-out failure;N s : is the tensile resistance of steel.The resistance against concrete cone failure (N c ) may be generally definedby the following relation: N r r(2.51)in which:N c,o :r N,s :r N,e :Nc c, o N , sN , eis the basic value of resistance against concrete cone failure, thatdepends on the type (AT) and diameter (d a ) of anchor, depth ofembedment (d e ) and concrete strength (f ck ):N c,o =f(AT, d a , d e , f ck )is the anchor spacing reduction factor, that depends on type (AT)and diameter (d a ) of anchor, depth of embedment (d e ) and anchorspacing (s):r N,s =f(AT, d a , d e , s)1is the edge distance reduction factor, that depends on type (AT)and diameter (d a ) of anchor, depth of embedment (d e ) and anchoredge distance (e):r N,s =f(AT, d a , d e , e)1The resistance against pull-out failure (N p ) depends on the type of anchor(AT), its diameter (d a ) and depth of embedment (d e ):N p =f(AT, d a , d e ) (2.52)The following relation may generally be used to obtain the tensileresistance against steel failure (N s ):Ns As fu,a(2.53)in which:A s : is the tensile stress area of the anchor;f u,a : is the ultimate tensile strength of the anchor steel.

74 Chapter IIStrength of frame-to-foundation shear connections (F (F-F)V )The failure modes of shear connections include: shear failure in the anchor-to-frame connection (F (F-F)V,a-fr ); shear failure in the anchor-to-foundation connection (F (F-F)V,a-fo ).The strength of the shear frame-to-foundation connection (F (F-F)V ) is equalto the minimum shear strength related to the failure mode previously defined:F min F F(2.54)( F F) V( F F) V , afr;( F F) V , afoFAILURE IN THE ANCHOR-TO-FRAME CONNECTIONThe shear strength of the anchor-to-frame connection (F (F-F)V,a-fr ) may bycalculate following the approach illustrated for the determination of the shearfailure in the hold-down-to-frame connection.SHEAR FAILURE IN THE ANCHOR-TO-FOUNDATION CONNECTION.As for the tension failure in the hold-down-to-foundation connection, alsothe failure mode in the connections between anchor and foundation dependson the type of anchor, depth of embedment, concrete strength, edge distancesand spacing between anchors (Hilti 2001).For both mechanical and adhesive-bonded anchors the main failure modesunder shear loading are concrete edge failure and shear steel breakage, asshown in Figure 2.12.concrete edge breakoutsteel breakage failureFigure 2.12: Failure modes of anchors under shear loading (Hilti 2001).The shear strength of the anchor-to-foundation connection (F (F-F)V,a-fo ) isequal to the minimum shear strength associated to failure modes introduced,as defined by the following relation:F( F F ) V , a fo minVc; V s(2.55)

Design of cold-formed steel stud shear walls 75where:V c :V s :is the resistance against concrete edge failure;is the shear resistance of steel.The following relation may generally define the resistance against concreteedge failure (V c ): V r f(2.56)in which:V c,o :r V,se :f V,d :Vc c, o V , seV , dis the basic value of resistance against concrete edge failure, thatdepends on the type (AT) and diameter (d a ) of anchor, depth ofembedment (d e ) and concrete strength (f ck ):V c,o =f(AT, d a , d e , f ck )is the anchor spacing and edge reduction factor, that depends ontype (AT) and diameter (d a ) of anchor, depth of embedment (d e ),anchor spacing (s) and edge distance (e):r N,s =f(AT, d a , d e , s, e)1is the loading direction factor, that depends on the direction ofshear force ():f V,d =f()The shear resistance against of steel failure (V s ) may be generally obtainedby the following relation:Vs s As fu,a(2.57)in which: s : is a coefficient that depends on the steel strength grade of theanchor ( = 0.5 ÷ 0.6);A s : is the tensile stress area of the anchor;f u,a : is the ultimate tensile strength of the anchor steel.Shear strength of wall associated to frame-to-foundation connectionsstrength (v F-F )The shear strength per unit length associated to frame-to-foundationconnections strength (v F-F ) is the minimum value between shear strength per

76 Chapter IIunit length associated to tension (v (F-F)N ) and shear (v (F-F)V ) connectionsstrength:vF F minv( F F) N; v(F F) V(2.58)in which (v (F-F)N ) is obtained form strength of the frame-to-foundation tensionconnections (F (F-F)N ) as follows:F(F F) Nv(F F) N (2.59)hwith h height of the wall and (v (F-F)V ) is obtained form strength of the frameto-foundationshear connections (F (F-F)V ):v( F F) V n' F(F F) V(2.60)with n’ number of the end fasteners per unit length.2.3 UNITS SHEAR DESIGN VALUES FOR CFSSSWsThe basic LFRSs used in CFSSSWs currently recognized by main buildingCodes are: shear sheathing and diagonal bracings.For the sheathed CFSSSWs the Codes include wall sheathed with woodbasedstructural panels (plywood and oriented strand board (OSB)), sheetsteel, gypsum wallboard (GWB) and gypsum sheathing board (GSB). In thiscase design values are provided in the Codes.For diagonally braced CFSSSWs a rational set of design procedures withspecific force and drift limitations imposed for seismic event are presented inbuilding Codes.The nominal shear design values given by the main building Codes used inthe United States, such as 1997 Uniform Building Code (UBC 1997) and 2000International Building Code (IBC 2000), are illustrated and commented inSection 2.3.1. Furthermore, the provisions reported by the 2000 InternationalResidential Code for One- and Two-Family Dwelling (IRC 2000), for theapplication of the PSW method, are synthesized in the Section 2.3.2.2.3.1 UBC and IBC design tablesBuilding Codes make a distinction between design for wind and seismicloading. This distinction is based on the type of testing that has been used todevelop the design values for the shear strength. In fact, for all sheathed

Design of cold-formed steel stud shear walls 77CFSSSWs currently permitted in the 1997 UBC and 2000 IBC (plywood,OSB, sheet steel, GWB, GSB), tabulated design values are based exclusivelyon physical testing which included monotonic loading for wind design valuesand reversed cyclic loading for seismic design values.Testing for development of Code design values occurred in two phases(Serrette et al. 1996a, b and Serrette et al. 1997a, b). The results of the firstphase of testing were incorporated in the 1997 UBC and the results of thesecond phase of testing (combined with the results of the first phase) wereincorporated in the 2000 IBC.The typical test assembly in both phases of testing comprised 8ft.(2440mm) high walls having a width of 2ft. (610mm), 4ft. (1220mm) or 8ft.(2440mm) corresponding to aspect ratios (ratio of the wall height to width) of4:1, 2:1 and 1:1. For the 1997 UBC (the first phase of testing), all walls were4ft. (1220mm) wide except for gypsum sheathed walls that were 8ft.(2440mm) wide. The 2ft. (610mm) wide walls were part of the second phaseof testing. For each test, the wall was anchored at both ends for overturningand between the ends for shear transfer. In the shear wall tests, the sheathingwas oriented parallel to framing (all edges blocked), except for the gypsumwallboard sheathing tests where the panels were installed perpendicular toframing with strap blocking the abutting edges (see Chapter 3, Section 3.2.5for details).The typical results for the monotonic and reversed cyclic load tests, and theinterpretation of these test results, are illustrated in Figures 2.13 and 2.14,respectively.Using the measured wall response, as illustrated in Figures 2.13 and 2.14,the Code tabulated nominal design strengths for the wall configurations testedwere determined as follows.For wind designThe nominal wall strength was taken as the smallest of (see Fig. 2.13): 3.0 times the strength (averaging positive and negative values) at 0.5in.(12.7mm) of lateral displacement. the maximum strength (averaging positive and negative values) of thewall.

78 Chapter IIFor seismic designThe nominal wall strength was taken as the smallest of (see Fig. 2.14): 2.5 times the second loop envelope strength (averaging positive andnegative values) at 0.5in. (12.7mm) of displacement the maximum second loop envelope strength (averaging positive andnegative values).maximum loadload at 12.7mm lateral displacement12.7mm lateral displacementFigure 2.13: Monotonic shear load-lateral displacement response.+ max. stable load+ 2 nd lood envelopestable load at +12.7mm-12.7mm+12.7mmstable load at -12.7mm- 2 nd lood envelope- max. stable loadFigure 2.14: Reversed-cyclic shear load-lateral displacement response.

Design of cold-formed steel stud shear walls 79In both the 1997 UBC and 2000 IBC, design values are tabulated in termsof a nominal capacity (R n ). Allowable Stress Design (ASD) and Load andResistance Factor Design (LRFD) capacities are computed as:R n / for ASD (2.61) R n for LRFD (2.62)where is a safety factor and is a resistance factor.The tabulated design values for seismic design under the 1997 UBC and2000 IBC are reproduced in Tables 2.3 and 2.4, respectively. The tabulateddesign values for wind action are reproduced in Tables 2.5 and 2.6 for designunder the 1997 UBC and 2000 IBC, respectively. The safety and resistancefactors for the UBC and IBC are summarized in Table 2.7.Comparing the 2000 IBC tables with the 1997 UBC tables, it is evident thata larger number of design options is permitted by IBC. This difference, asindicated earlier, is the result of additional testing (second phase) that wascompleted after publication of the 1997 UBC.The seismic and wind design values in Tables 2.5 and 2.6 assume thatwalls are fully sheathed and hold down anchors are provided at each end ofthe wall as required by calculation. All panel edges are assumed to be blockedfor the shear wall applications. Some monotonic test data has shown that oneunblocked edge may reduce the fully-blocked capacity by about 50%, asshown in Chapter 3 (Section 3.2.1).No. 8 screws = 4.2 mm nominal diameter screwsTable 2.3: 1997 UBC nominal shear strength (R n ) values for seismic actions (lbs./foot).

80 Chapter IINo. 8 screws = 4.2 mm nominal diameter screwsTable 2.4: 2000 IBC nominal shear strength (R n ) values for seismic actions (lbs./foot).No. 8 screws = 4.2 mm nominal diameter screwsTable 2.5a: 1997 UBC nominal shear strength (R n ) values for wind actions (lbs./foot).

Design of cold-formed steel stud shear walls 81Table 2.5b: 1997 UBC nominal shear strength (R n ) values for wind actions (lbs./foot).No. 8 screws = 4.2 mm nominal diameter screwsTable 2.6a: 2000 IBC nominal shear strength (R n ) values for wind actions (lbs./foot).

82 Chapter IITable 2.6b: 2000 IBC nominal shear strength (R n ) values for wind actions (lbs./foot).Table 2.7: Safety and resistance factors per 1997 UBC and 2000 IBC.Following the Serrette’s comments regarding the tabulated design values itis possible to extrapolate of the Code design values in a rational manner thatmeets the intent and overall safety implied by the Code.Serrette specifies that some unpublished data show that for walls with thesame material on both sides (and identically attached) the shear values listedin the tables may be doubled. Although these conclusions are encouraging,additional testing is needed to verify performance. As a provisional measure,the Author suggests that it may be adequate to use only 90% of the doubledvalue with special attention given to the design of the chords and anchorage ofthe wall.Both the 1997 UBC and 2000 IBC Codes for gypsum board suggest thatsheathings should be applied perpendicular to framing with strap blockingadjacent to panel edges and solid block in the end bays. This limitation isbased on the configuration used in the testing for development of the Code

Design of cold-formed steel stud shear walls 83values. Serrette indicates that the behavior of a shear wall suggests that itwould be rational and safe to allow the use of the Code values for gypsumboard applied parallel to framing provided that all edges are, as required,blocked.For gypsum board shear walls, the Codes require the use of both flat strapand solid end bay blocks at abutting panel edges (when the abutting edge doesnot occur at a stud). Serrette reports that, because of the mechanism of loadtransfer at the abutting panel edge, solid-blocked end bays are not structurallynecessary for the shear wall application. Moreover He notes that solidblocking may be required to avoid global buckling of studs.2.3.2 IRC provisions on the PSW method utilizationIn addition to the design data provide in the UBC and IBC, some basicresearch has been conducted on perforated CFSSSWs. Based on this research,the 2000 IRC (IRC 2000) permits the seismic capacity of long walls withopenings to be computed on the basis of PSW method. The IRC provision islimited to structures located in zones characterized by relatively low seismicintensity. For applying the PSW method, the maximum aspect ratio of all fullheight sheathed segments between openings must be 2:1, including the endsegments of the wall. Therefore, the maximum unrestrained opening heightmust respect the limits indicated in IRC provision (see Table 2.8). The valuesof the ratio of the strength of a shear wall with openings to the strength of afully sheathed shear wall without openings (F) reported by IRC are shown inTable 2.9. According to the PSW approach, the value of the adjustment factor(F) depends on sheathing area ratio (r).1 feet = 305 mmTable 2.8: Maximum unrestrained opening height (H) per 2000 IRC.

84 Chapter IITable 2.9: Adjustment factors (F) for application of the PSW method per 2000 IRC.REFERENCESAISI (1986) AISI Specification for the design of Cold-Formed Steel structuralmembers. AISI (American Iron and Steel Institute). Washington DC.AISI (1996) Cold-Formed Steel Design manual. AISI (American Iron and SteelInstitute). Washington DC.AISI (2001) North American Specification for the design of Cold-Formed Steelstructural members (November 9, 2001 draft edition). AISI (American Iron and SteelInstitute), Washington DC.Ambrose, J. & Dimitry, V. (1987) Design for Lateral Forces. John Wiley & Sons,Inc. New York.APA (1996) Use Panel Supplement. APA (The Engineered Wood Association).Tacoma, WA, USA.AS/NZS 4600 (1996) Cold-formed steel structures. AS/NZS (AustralianStandards/New Zealand Standards). Sydney.Apparao, T.V.S., Errera, S.J., Fischer, G.P. (1969) Columns braced by girts anddiaphragm. Journal of structural Division. ASCE, Vol.95:965-990Batista, E.M. (1988) Etude de la stabilité des profiles à parois minces et sectionsouverte de type U et C. Ph.D. Thesis, University of Liege. Liege.Beyer, D.E. (1993) Design of Wood Structures, Third Edition. McGraw-Hill, Inc.New York.CU-FSM (2003) http://www.ce.jhu.edu/bschafer/cufsm/index.htm. (UpgradedAugust 2003)Davies, J.M. & Leach, P. (1994a) First-order generalised beam theory. Journal ofconstruction steel research. Elsevier, Vol.31.

Design of cold-formed steel stud shear walls 85Davies, J.M. & Leach, P. (1994b) Second-order generalised beam theory. Journal ofconstruction steel research. Elsevier, Vol.31.Della Corte, G., De Martino, A., Fiorino, L., Landolfo, R. (2003) Numericalmodeling of thin-walled cold-formed steel C-sections in bending. In Proceedings ofthe Advances in Structures Steel, Concrete, Composite and Aluminum (ASSCCA'03).Sydney.Dolan, J.D. & Heine, C.P. (1997a) Monotonic Tests of Wood-frame Shear Walls withVarious Opening and Base Restraint Conditions. Report TE-1997-001, Brooks ForestProducts Research Center, Virginia Polytechnic Institute and State University.Blacksburg, VA, USA.Dolan, J.D. & Heine, C.P. (1997b) Sequential Phased Displacement Cyclic Tests ofWood-frame Shear Walls with Various Opening and Base Restraint Conditions.Report TE-1997-002, Brooks Forest Products Research Center, Virginia PolytechnicInstitute and State University. Blacksburg, VA, USA.Dolan, J.D. & Heine, C.P. (1997.) Sequential Phased Displacement Tests of WoodframedShear Walls with Corners. Report TE-1997-003, Brooks Forest ProductsResearch Center, Virginia Polytechnic Institute and State University. Blacksburg,VA, USA.Dolan, J.D. & Johnson, A.C. (1997a) Monotonic Tests of Long Shear Walls withOpenings. Report TE-1996-001, Brooks Forest Products Research Center, VirginiaPolytechnic Institute and State University. Blacksburg, VA, USA.Dolan, J.D. & Johnson, A.C. (1997b) Cyclic Tests of Long Shear Walls withOpenings. Report TE-1996-002, Brooks Forest Products Research Center, VirginiaPolytechnic Institute and State University. Blacksburg, VA, USA.Easley, J.T., Foomani, M., Dodds, R.H. (1982) Formulas for wood shear walls.Journal of structural Division. ASCE, Vol.105, No.11:2460-2478.Errera, S.J. & Apparao, T.V.S.R. (1976) Design of I-shaped columns with diaphragmbracing. Journal of structural Division. ASCE, Vol.102.Errera, S.J., Pincus, G., Fischer, G.P. (1967) Columns and beams braced bydiaphragms. Journal of Structural Division. ASCE, Vol.93:295-318.ENV 1993-1-3 (1996) Eurocode 3: Design of steel structures – Part 1-3: Generalrules - Supplementary rules for cold formed thin gauge members and sheeting. CEN(European Committee for Standardization). Bruxelles.Faherty, K.F. & Williamson, T.G. (1999) Wood Engineering and constructionhandbook (Third edition). McGraw-Hill.

86 Chapter IIFiorino, L. (2000) Il metodo “direct strength” per il progetto di profili “coldformed”in acciaio (Tesi di Laurea). Dipartimento di Analisi e ProgettazioneStrutturale, Facoltà di Ingegneria, Università di Napoli “Federico II”. Napoli.Fiorino, L. & Landolfo, R. (2001). Il metodo “direct strength” per la progettazione dimembrature in parete sottile formate a freddo in acciaio. In Proceedings of the XVIIICongresso CTA (CTA 2001), Vol.2. Venezia.Fiorino, L. & Landolfo, R. (2003) Il ruolo delle imperfezioni geometriche nellacalibrazione di modelli agli elementi finiti per profili sottili inflessi con sezione a Cformata a freddo. In Proceedings of the XIX Congresso CTA (CTA 2003). Genova.Hancock, G,J. (1985) Distortional buckling of storage rack columns. Journal ofstructural engineering. ASCE, Vol.111, No.12:2770-2783.Hilti (2001) Hilti North America product technical guide.Hoyle, R.J., Jr. & Woeste, F.E. (1986) Wood Technology in the Design of Structures,Fifth Edition. Iowa State University Press. Ames, IA, USA.IBC (2000) International Building Code: 2000. International Code Council, Inc. FallsChurch, VA, USA.IRC (2000) International Residential Code for One- and Two-Family Dwelling:2000. International Code Council, Inc. Falls Church, VA, USA.Landolfo, R., Di Lorenzo, G, Fiorino, L. (2002) Attualità e prospettive dei sistemicostruttivi cold-formed. Costruzioni metalliche No.1Lau, S.C.W. & Hancock, G.J. (1987) Distortional buckling formulas for channelcolumns. Journal of structural engineering. ASCE, Vol.113, No.5.Lee, Y. & Miller, T.H. (2001a) Axial strength determination for gypsum-sheathed,cold-formed steel wall stud composite panels. Journal of structural engineering.ASCE, Vol.127, No.6:608-615.Lee, Y. & Miller, T.H. (2001b) Limiting heights for gypsum-sheathed, cold-formedsteel wall studs. Practice periodical on structural design and construction. ASCE,Vol.6, No.2:83-89.Miller, T.H. & Peköz, T. (1993) Behavior of cold-formed steel wall stud assemblies.Journal of structural engineering. ASCE, Vol.119, No.2:641-651.Miller, T.H. & Peköz, T. (1994) Behavior of gypsum-sheathed cold-formed steel wallstuds. Journal of structural engineering. ASCE, Vol.120, No.5:1644-1650.NAHB Research Center (1997) Monotonic Tests of cold-formed steel shear wallswith openings. NAHB (National Association of Home Builders). Upper Marlboro,MD, USA.

Design of cold-formed steel stud shear walls 87NAHB Research Center (1998) The Performance of Perforated Shear Walls withNarrow Wall Segments, Reduced Base Restraint, and Alternative Framing Methods.NAHB (National Association of Home Builders). Upper Marlboro, MD, USA.Pincus, G. & Fischer, G.P. (1966) Behavior of diaphragm-braced columns andbeams. Journal of Structural Division. ASCE, Vol.92:323-350.prEN 1998-1 (2001) Eurocode 8: Design of structures for earthquake resistance –Part 1: General rules – Seismic actions and rules for buildings. CEN (EuropeanCommittee for Standardization). Bruxelles.Schafer, B.W. (2001) Thin-walled column design considering local, distorsional andEuler buckling. Proceedings of the Structural Stability Research Council, AnnualTechnical Session and Meeting.Schafer B.W. & Peköz T. (1998). Direct strength prediction of cold-formed steelmembers using numerical elastic buckling solution. In Proceedings of the 2thInternational conference on thin-walled structures. Singapore.Schafer, B.W. & Peköz T. (1999) Local distortional buckling of cold-formed steelmembers with edge stiffened flanges. In Proceedings of the 4th Internationalconference on steel and aluminium structures (ICSAS ’99). Helsinki.Schafer, B.W. & Hiriyur, B. (2002) Analysis of sheathed cold-formed steel wallstuds. In Proceedings of the 16 th International Specialty Conference on Cold-formedSteel Structures. St. Louis, MO, USA:501-513.Serrette, R., Nguyen, H., Hall, G. (1996a) Shear wall values for light weight steelframing. Report No. LGSRG-3-96, Light Gauge Steel Research Group, Departmentof Civil Engineering, Santa Clara University. Santa Clara, CA, USA.Serrette, R., Hall, G., Nguyen, H. (1996b) Dynamic performance of light gauge steelframed shear walls. In Proceedings of the 13 th International Specialty Conference onCold-formed Steel Structures. St. Louis, MO, USA:487-498.Serrette, R.L., Encalada, J., Juadines, M., Nguyen, H. (1997a) Static racking behaviorof plywood, OSB, gypsum, and fiberboard walls with metal framing. Journal ofStructural Engineering. ASCE, Vol.123, No.8:1079-1086.Serrette, R., Encalada, J., Matchen, B., Nguyen, H., Williams, A. (1997b) Additionalshear wall values for light weight steel framing. Report No. LGSRG-1-97, LightGauge Steel Research Group, Department of Civil Engineering, Santa ClaraUniversity. Santa Clara, CA, USA.Simaan, A. & Peköz, T. (1976) Diaphragm braced members and design of wall stud.Journal of structural Division. ASCE, Vol.102.

88 Chapter IISSTD 10-97 (1997) Standard for Hurricane Resistant Residential Construction.Southern Building Code Congress International, Inc. Birmingham, AL, USA.Sugiyama, H & Matsumoto, T. (1984) Empirical equations for the estimation ofracking strength of plywood-sheathed shear walls with openings. Summaries ofTechnical Papers of Annual Meeting, Transactions of the Architectural Institute ofJapan, No.338.Talue, Y. & Mahendran, M. (2000) Behaviour of cold-formed steel wall frames linedwith plasterboard. Journal of constructional steel research. Elsevier. Vol.57:435-452.THIN-WALL (2003) http://www.civil.usyd.edu.au/case/thinwall.php. (UpgradedAugust 2003)UBC (1997) Uniform Building Code: Volume 2. International Conference of BuildingOfficials. Whittier, CA. USA.Yu, W.W. (2000) Cold Formed Design (3rd Edition), John Wiley & Sons. NewYork.

89Chapter IIITesting of cold-formed steel stud shearwalls: review of existing literatureA large number of experimental research programs have been performed tostudy the structural behavior of cold-formed steel stud shear walls (CFSSSW)laterally braced with sheathings and/or with diagonal steel straps (McCreless& Tarpy 1978, Tarpy & Hauenstein 1978, Tarpy 1980, Tarpy & Girard 1982,Tissell 1993, Serrette 1994, Serrette & Ogunfunmi 1996, Serrette et al. 1996a,b, 1997a, b, NAHB Research Center 1997, Gad et al. 1999a, b, Selenikovichet al. 1999, COLA-UCI 2001, Dubina & Fulop 2002, Branston et al. 2003).This Chapter contains a review of the main tests concerning the structuralbehavior of CFSSSW carried out in Northern America, Europe and Australia.The main goal of the review has been to investigate the influence of the basicparameters on the lateral behavior of CFSSSW.The Chapter is organized in two main parts. In the first part (Section 3.1) asummary of the main existing test results is presented. The individuation ofbasic factors that influence the lateral load response of CFSSSWs and theanalysis of their influence are illustrated in the second part (Section 3.2).3.1 SUMMARY OF MAIN EXISTING TEST PROGRAMSA summary of the main research programs regarding the testing ofCFSSSW carried out in Northern America, Europe and Australia is describedin this Section. A general listing of the tests presented in this Section is

90 Chapter IIIreported in Table 3.1. A more complete listing of the test data is given inAppendix A.Author No of tests Bracing systemsMcCreless & Tarpy (1978) NA 16 M GWBTarpy & Hauenstein (1978) NA 18 M GWBTarpy (1980) NA 4 M , 8 C GWB, CPTarpy & Girard (1982) NA 14 M GWB, PLYTissell (1993) NA 8 M OSB, PLYSerrette (1994) NA 12 M GWB, GSB, OSB, PLY, X-BSerrette & Ogunfunmi (1996) NA 13 M GSB, GWB, X-BSerrette et al. (1996a, b) NA 24 M , 16 C GWB, OSB, PLYSerrette et al. (1997a) NA 33 M GWB, FBW, OSB, PLYSerrette et al. (1997b) NA 16 M , 28 C OSB, PLY, SSS, X-BNAHB Research Center (1997) NA 4 M OSB, GWBGad et al. (1999a, b) AX-BSelenikovich et al. (1999) NA 6 M , 10 C OSB, GWBCOLA-UCI (2001) NA 18 C OSB, PLYDubina & Fulop (2002) E 7 M , 9 C SCS, GWB, OSBBranston et al. (2003) NA 6 M , 6 C OSB, PLYNA : North American tests; A : Australian tests; E : European testsM : monotonic tests; C : cyclic testsCP: cement plaster; FBW: FiberBond wallboard; GSB: gypsum sheathing board; GWB: gypsumwallboard; OSB: oriented strand board; PLY: plywood; SCS: steel corrugated sheet; SSS: steelsheet sheathing; X-B: steel flat strap X-bracingTable 3.1: Listing of tests of CFSSSW.3.1.1 McCreless & Tarpy (1978)This experimental research consisted of the testing of sixteen shear wallsmade of steel studs and gypsum wallboard (GWB) with various aspect ratiosunder monotonic loads. The tests were carried out in accordance with ASTME 564-76 (1976). The wall construction used was representative of the type ofconstruction usually used for internal wall partitions.The objectives of the testing program were: To determine the variation of the shear strength when the aspect ratio(height/width) changing from 0.33 (2440/7320mm) to 2 (3660/3660). To establish the allowable degree of panel distortion before major wallpanel damage.

Testing of cold-formed steel stud shear walls: review of existing literature 91 To determine if the addition of a single horizontal stiffener located atmid-height in the plane of the wall could improve the shear behavior.The wall sizes of specimens were 3660x3660mm, 3660x4880mm,3660x7320mm, 3050x3660mm, 3050x4880mm, 3050x7320mm,2440x2440mm, 2440x3660mm, 2440x4880mm and 2440x7320mm (height xlength) with aspect ratios that ranges from 0.33 to 1.00. Each wall wasassembled with 89x0.84mm (web depth x thickness) C (lipped)-sections studsspaced at 610mm on center. Double back-to-back coupled studs were used atends of each wall. The studs were attached to 92x38x0.84mm (web depth xflange size x thickness) U (unlipped)-sections track with 4.8x13mm (diameterx length) low profile head screws. GWB, 12.7mm thick, was attached to bothsides of the stud assembly with 3.5x25mm bugle head screws spaced at305mm at the perimeter and in the field of the panel. Clip angles were used toanchor the specimens to the load frame.The Authors observed that for shorter walls bending deformationdominated. In this case, the bottom track deformed around the exterior cornertension anchorage point and then the screws in tension corner rotated throughthe GWB, followed by cracking separation of the wallboard. The final failurewas due to excessive rotation. For longer walls, where the shear deformationcontrolled the behavior, the edge screws rotated through the panel and thefinal failure was produced by the stud framing shearing through the GWBalong the top.McCreless & Tarpy concluded from the test results that: For the aspect ratio varying between 0.33 and 1.00 the shear strengthwas constant but the shear stiffness decreased; The first noticeable wallboard damage occurred at about 6 to 13mmtotal displacement (for the shorter walls) and at about 6mm (for thelonger walls). The real damage occurred at about 13 to 19mm totaldisplacement (for the shorter walls) and at about 6 to 13mm (for thelonger walls).

92 Chapter III3.1.2 Tarpy & Hauenstein (1978)The testing program performed by Tarpy & Hauenstein included eighteenfull-scale walls made of steel studs and GWB with seven different types ofwall panel construction and anchorage details.The main objectives of the experimental research were: To determine the effect of different construction and anchorage detailson shear resistance of stud shear walls. To evaluate the damage thresholds load levels. To provide a comparison between the performances of wood-framedand steel-framed shear walls.One wall type consisted of 51x102mm (width x depth) wood-studs, whileothers were constructed using 89x38x0.81mm (web depth x flange size xthickness) C-sections studs spaced at 610mm on center. GWB, 12.7mm thick,placed in horizontal position was attached to both sides of the specimens. Thefasteners to connect the panels to the steel frame were 3.5x25mm (diameter xlength) bugle head screws whereas to connect the panels to the wood frame35mm annular head nails were used.The Authors observed from the test results that: For avoiding uplift failure an adequate attachment should be adoptedto connect the track and floor framing systems. The reduction of the fasteners spacing around the wall perimeter couldprovide higher shear strength. For design purposes, a safety factor of 2.0 was recommended fordesign purposes to ensure that the design load level does not exceedthe damage threshold level.3.1.3 Tarpy (1980)Nine different types of GWB and cement plaster (CP) attached to lightgauge steel stud were tested under monotonic and cyclic loading protocol byTarpy. The tests were carried out in accordance with ASTM E 564-76 (1976)

Testing of cold-formed steel stud shear walls: review of existing literature 93The main test objectives were: To investigate the behavior of the different sheathing types. To study the effect of GWB fasteners spacing. To determine the effect of cyclic loading versus monotonic loading onthe shear behavior. To analyze the behavior of different construction techniques andanchorage details. To establish the thresholds for damage of the walls due to lateraldisplacement. To study the contribution to shear capacity of a 45° stud placed at thebottom corner between the chord members and the adjacent stud.The wall sizes of specimens were 2440x2440mm or 2440x3660mm (heightx length). The frame was made using 89x38x13x0.84mm (web depth x flangesize x lip size x thickness) C (lipped)-sections studs at 610mm on center. Thestuds, with a mean yield strength of 331MPa, were attached to 92x38x0.84mmU-sections track with 4.8x13mm (diameter x length) low profile head screws.GWB, 12.7mm thick and 22.2mm thick CP placed in vertical position wasconnected to the frame using different fastener type and spacing. In particular,the following fastener type and spacing were used: 3.5x25mm bugle headscrews spaced at 305mm; 3.5x25mm bugle head screws spaced at 610mm;3.5x25mm bugle head screws spaced at 152/305mm (perimeter/field);3.5x13mm pan washer head screws spaced at 197mm; 3.5x10mm bugle headscrews spaced at 305mm.Tarpy concluded from the test results that: The use of CP increased the shear strength and the stiffness. The use of two layer of GWB increased the shear capacity, whiledecreasing the shear stiffness, in comparison with single layer. The reduction of the fastener spacing increased the shear strength andstiffness. Cyclic load decreases shear strength and damage threshold level. The corner anchorage influenced the shear behavior dramatically.Hold-down exhibited higher shear strength than bolt and washer

94 Chapter IIIanchors. Densely spaced powder actuated fasteners (connected to asupporting concrete beam) provided similar restraint to the hold-down. The shear resistance did not vary extensively when using differenttypes of interior shear anchorage. The use of a 45° stud placed at the bottom corner between the chordmembers and the adjacent stud had little effect on the shear capacity.3.1.4 Tarpy & Girard (1982)The study of Tarpy & Girard was performed in response to a need todevelop design criteria for steel stud sear wall panels with differentconstruction details and sheathing materials. The materials used for thesheathings were GWB, gypsum sheathing board (GSB) and plywood (PLY).The experimental program was based on the testing of fourteen specimensunder monotonic load following the requirements of ASTM E 564-76 (1976).The objectives of the research were: To determine the effect of different construction techniques andanchorage details on the shear resistance of stud shear walls withdifferent types of sheathing. In particular, the parameters examinedwere: The effect of using light gage clip angles and powder-actuatedfasteners in place of bolts and washers to anchor the base of thewall and the effect of anchoring the wall through transverse floorjoists. The effect of PLY or gypsum exterior sheathing in place of GWB. The effect of using fillet welds instead of self drilling screws toattach the studs to the tracks. The effect of using a 406mm rather a 610mm stud spacing. To establish the thresholds for damage of the walls due to lateraldisplacement.All wall sizes were 2440x2440mm (height x length), except for onespecimen that had a wall size of 2440x3660mm. The stud wall systems wereconstructed using 89x25x13x0.84mm C-sections studs attached to92x38x0.84mm U-sections track. Double back-to-back coupled studs were

Testing of cold-formed steel stud shear walls: review of existing literature 95employed at the ends of each wall. GWB, 12.7mm thick, was attached to bothsides of the specimens, except for two specimens, that had GWB as internalpanel and PLY (12.7mm thick) or GSB (12.7mm thick), respectively, asexterior panels. The sheathing orientation was always horizontal. All panelswere connected to the frame with 3.5x25mm (diameter x length) bugle headscrews spaced at 305mm at the perimeter and in the field of the panel. Clipangles fixed with bolts or powder-actuated fasteners were used to connect thebase of some walls.Tarpy & Girard noted that all wall types had the same basic failure mode.The bottom track deformed around the anchorage device at the uplift corner ofthe wall and the cracking of the GWB happened at the same locations fromthe corner fasteners to the edge of the panel.They concluded that: When the bolt and washer anchorage details were used without clipangles the shear capacity decreased. Moreover, the use of closelyspaced powder actuated fasteners negligibly increased the shearbehavior in comparison to using corner clips. When the wall wasanchored through the floor joist it showed lower shear capacity thanwhen it was connected directly to the test frame. Therefore, it wassuggested a rigid attachment to connect the wall panel to the floor orroof framing systems and it was recommended the use of clip angles. The use of PLY increased the shear strength whereas the use of GSBdecreased it in comparison with the employ of GWB. The use of welded stud to track connections provided the same shearstrength as screw connections. The reduction of the stud spacing did not increase significantly theshear strength and stiffness. For design purposes, a safety factor of 2.0 was recommended todetermine the design shear strength from the ultimate shear strengthfor the type of stud shear walls examined.

96 Chapter III3.1.5 Tissell (1993)Tissell conducted for the American Plywood Association eight monotonicloading tests on walls that were sheathed with either oriented strand board(OSB) or PLY and that had various frame thicknesses.The tests were carried out to achieve the principal following goals: To examine the effect of fasteners size and spacing. To study the influence of frame thickness.All wall sizes were 2440x2440mm (height x length). The frame was madeusing 64x41x1.88mm (web depth x flange size x thickness) C-sections studsat 610mm on center attached to 64x41x1.88mm U-sections track for thespecimens 1, 7 and 8. The frame used for other specimens were made using89x41x1.50 studs at 610mm on center attached to 89x41x1.50 track(specimens 2 and 3) and 89x41x1.19 studs at 610mm on center attached to89x41x1.19 track (specimens 4, 5 and 6).Fasteners types were 4.2mm diameter screws for the 1.19mm framethickness and 4.8mm diameter screws or 3.7mm diameter pins for the 1.50and 1.88mm frame thickness. Different fasteners schedule was used. In fact,the edge fasteners spacing varied form 76 to 152mm while the field fastenersspacing was 305mm.The different sheathing types for tests included 9.5mm thick PLY(specimens 1, 2, 4 and 5), 15.9mm thick PLY (specimen 8), 11.1mm thickOSB (specimens 3 and 6) and 15.1mm thick OSB (specimen 7). The sheathingorientation was vertical in each case.The Author reported that in most cases failure occurred due to buckling ofthe single end studs or the bottom track at the anchor bolts. These prematurecollapses prevented the full development of the shear capacity of the panels.For this reason the test results did not offer a correct valuation of the behaviorof the sheathing panels.

Testing of cold-formed steel stud shear walls: review of existing literature 973.1.6 Serrette (1994)This experimental program consisted of the monotonic load testing oftwelve CFSSSW. The walls were laterally braced with 51x0.84mm (width xthickness) X-bracing steel flat strap (X-B) on one side only (specimen 1),12.7mm thick GWB on both sides (specimen 2), 12.7mm thick GWB and12.7mm thick GSB in combination with X-B (specimen 3), 11.9mm thickPLY (specimens from 4 to 8) or 11.1mm thick OSB (specimens from 9 to 12)on one side only. All sheathings were vertically oriented, except for specimens6 and 7 that had sheathings horizontally oriented.The 2440mm by 2440mm steel frame was identical for all walls. The framewas made using 152x41x0.84mm (web depth x flange size x thickness) C-sections studs at 610mm on center attached to 152x32x0.84mm U-sectionstrack. Double back-to-back coupled studs were used at ends of walls.The panels to frame connections were 3.5mm diameter screws forspecimens 2, 3, 4, and 12; 4.2mm diameter screws for the specimens 6, 7, 8and 11; and 2.9mm diameter pins for the specimens 5 and 9. All fastenerswere spaced at 152mm at the perimeter and at 305mm in the field.From the tests results, it is possible to conclude that: The PLY panels carried slightly higher loads in comparison with OSBpanels. The use of 2.9mm diameter pins decreased the maximum shearstrength in comparison with 3.5 and 4.2mm diameter screws. The walls with panels oriented vertically and with blocked panelsoriented horizontally provided essentially the same shear strength. When blocking is omitted for the walls with horizontal panels, theshear capacity of the wall was reduced by more than 50%.3.1.7 Serrette & Ogunfunmi (1996)A series of monotonic loading tests were conducted by Serrette &Ogunfunmi on 13 walls. These tests included three different shear resistingsystems: framed walls with X-B (type A); framed walls with GSB on the faceand GWB on the back (type B); and framed walls with GSB and X-B on theface and GWB on the back (type C).

98 Chapter IIIThe main objectives of the investigation were: To study the contribution of X-B, GSB and GWB, and thecombination of X-B, GSB, GWB to the in-plane shear resistance ofsteel stud walls.The 2440mm by 2440mm steel frame was identical for all walls. The framewas made using 152x32x0.84mm (web depth x flange size x thickness) C-sections studs at 610mm on center attached to 152x0.84mm (web depth xthickness) U-sections track. At the ends of each wall, double back-to-backcoupled studs were used to avoid chord buckling. The fasteners used for theframe connections were 4.2x13mm (diameter x length) wafer-head screws.Clip angles were used to connect each wall specimen to the base of the testframe.The different shear resisting systems included: Type A: framed walls with 51x0.84mm (width x thickness) X-B on theface. The straps were attached to the frame using gusset connectionsthat were designed for the yield strength of the strap. Type B: framed walls with 12.7mm thick GSB on the face and12.7mm thick GWB on the back. The gypsum panels were orientatedvertically and were attached to the frame using 3.5x25mm bugle headscrews spaced at 152mm at the perimeter and at 305mm in the field. Type C: framed walls with both Type A and B shear resisting systems.All specimens were raised with GSB and X-B on the face and GWBon the back except for one specimen that was built with X-B on bothsides.The Authors reported that for type A walls, failure resulted from excessivelateral deflections that followed the yielding of the tension X-B. For type Band C walls, at approximately half of the maximum load, screw rotationoccurred at the perimeter edge, and at the maximum load, the paper along theedges of the panels broke at the locations of the screws. Type B wallsprovided about 2.1 times the maximum load of type A walls, type C wallswith one X-B on one side increased the maximum load by approximately 1.3

Testing of cold-formed steel stud shear walls: review of existing literature 99times over type B walls, and type C wall with X-B on both sides amplified themaximum load by about 1.8 times in comparison with type B walls.Serrette & Ogunfunmi concluded that: The use of X-B plus gypsum board reduced the permanent deflectionof the wall and increased the shear strength without decreasing thestiffness. The use of X-B plus gypsum board is not practical due to the need topretension the straps and the need for additional screws to connect thestraps.3.1.8 Serrette et al. (1996a,b)Serrette conducted twenty-four monotonic loading tests and sixteen cyclicloading tests on walls with various sheathing types. All specimens weresheathed with OSB or PLY on a side, except for 10 specimens of themonotonic tests that were sheathed with OSB on a side and GWB on the otherside or with GWB on both sides. The tests were planned to generate designdata for specific wall constructions and also answer certain fundamentaldesign questions.The monotonic test program was divided in two phases with differentobjectives.The first phase included walls sheathing on one side only and wasaddressed to the following issues: To compare the differences in the behavior of OSB and PLY. To examine the effect on the shear strength of a variation of the aspectratio (height/width) from 1 (2440/2440) to 2 (2440/1220). To examine the effect of dense fasteners schedules.The second phase consisted of walls sheathing on both sides and wasaddressed to the following questions: To study the behavior of walls with OSB on a side and GWB on theother. To study the behavior of walls with GWB on both sides.The objectives of cyclic test program were the followings:

100 Chapter III To determine the relative strength of walls with OSB and with PLY. To study the effect of dense fasteners schedules. To determine the relative strength of walls in cyclic and in monotonictests.The wall sizes of specimens were 2440x2440mm or 2440x1220mm (heightx length) for monotonic tests and 2440x1220mm for cyclic tests. The framewas made using 89x41x10x0.84mm C-sections studs at 610mm on centerattached to 89x32x0.84mm U-sections track. Double back-to-back coupledstuds were employed at ends of each wall to avoid studs buckling. Holddowns(tie-downs) were used to connect each wall specimen to the base of thetest frame.The different sheathing types, sheathing orientations and screws spacingfor monotonic tests included: 2440x2440mm framed walls with 15.9mm thick PLY verticallyorientated with 152/305mm (perimeter/field) screw spacing. 2440x2440mm or 2440x1220mm framed walls with 11.1mm thickorientated strand board vertically or horizontally orientated withfasteners spacing varying between 152/305mm and 51/305mm. 2440x1220mm framed walls with 11.1mm thick orientated strandboard on one side with fasteners spacing varying between 152/305mmand 51/305mm and 12.7mm thick gypsum wallboard on the other sidewith 178/178mm screw spacing, both external and internal sheathingswere vertically orientated. 2440x2440mm framed walls with 12.7mm thick GWB on both sidewith fasteners spacing varying between 178/178mm and 102/102mm,both external and internal sheathings were horizontally orientated.For cyclic tests the sheathings used were 11.1mm thick orientated strandboard or 15.9mm thick PLY. The panels were always vertically orientated andthe screws spacing varying between 152/305mm and 51/305mm.For both monotonic and cyclic tests, the fasteners used were: 4.2x13mm(diameter x length) wafer-head screws for the frame connections; 4.2x25mmflat head screws for the PLY and OSB panel and 4.2x32mm bugle headscrews for gypsum wallboard.

Testing of cold-formed steel stud shear walls: review of existing literature 101From the monotonic tests results, the Authors concluded that: The overall behavior of the PLY and OSB panel assemblies waspractically identical. In particular the PLY walls carried slightly higherloads. The sheathings oriented horizontally exhibited slightly higher shearstrength than the panels oriented vertically. The shear strength was practically the same for the aspect ratio varyingbetween 1 and 2. The reduction of the fastener spacing increased significantly the shearstrength. The walls with OSB panels on one side and GWB on the other sideexhibited similar failure behavior, but degraded more gradually thanthe walls with OSB on one side alone in terms of shear capacity. The walls with GWB panels on both sides had much lower shearstrength than walls with OSB sheathing.Serrette et al. concluded form the results of the cyclic tests that: PLY and OSB panel assemblies sowed a little difference in the cyclicshear strength. As in the monotonic tests, the wall shear strength increasedsignificantly with the reduction of the fastener spacing. The shear behavior of walls observed in cyclic tests was somewhatlower than the shear behavior exhibited in monotonic tests for walls ofsimilar construction details.3.1.9 Serrette et al. (1997a)In this paper, the Authors presented the results of thirty-three full-scalemonotonic racking tests and twenty small-scale lateral shear tests on PLY,OSB, GWB and FiberBond wallboard (FBW) attached to light gauge steelstud.The main test objectives were: To investigate the behavior of the different sheathings material. To examine the effect of fasteners type and size.

102 Chapter III To examine the effect of fasteners spacing for gypsum and FBW. To compare the behavior of the panels oriented vertically and panelsoriented horizontally with steel flat strap and solid blocking attachedacross the mid-height. To compare the full-scale and small-scale test results.Two different frames were used in the full-scale tests: type A and type B.The type A frame was 2440x2440mm (height x length) in size constructedwith ASTM A446 Grade A galvanized steel members. The studs were152x41x10x0.84 C-sections spaced at 610mm on center and the tracks were152x25x0.84mm U-sections. The chord studs were two back-to-back coupledprofiles. The type B frame was identical to type A except that 51x0.84mm(width x thickness) steel flat strap was attached across the mid-height of thewall and that solid blocking was installed above the strap in the and bays. Thetype A and B frames were sheathed with: 11.9mm thick PLY; 11.1mm thickOSB; 12.7mm thick FBW; 12.7mm thick GWB. The panels were placedeither one side or both sides and they were oriented either vertically orhorizontally depending on the test. The frame fasteners were 4.2x13mm(diameter x length) wafer-head screws. Panels were attached to the frameusing either 3.5x25mm bugle-head screws, 4.2x32mm flat-head screws withcountersinking nibs, or 3.7mm diameter steel pins depending on the test.Hold-downs were used to connect each wall specimen to the base of testframe.The small-scale specimens consisting of single 610x610mm panelsattached to opposite flanges of the studs that were oriented horizontally with asingle stud on top and double studs placed back-to-back on the bottom. Thespecimens were sheathed with panels including 11.9mm thick PLY; 11.1mmthick OSB; 12.7mm thick FBW; 12.7mm thick GWB. The panels wereconnected with three 3.5x25mm bugle-head screws (152mm on centerspacing) to the top stud and with two rows of six screws (102mm on centerspacing) to the bottom studs.The full-scale tests failed initially by fasteners rotation (tilting) about theplane of the stud flange. In some tests the chord studs were subjected to local

Testing of cold-formed steel stud shear walls: review of existing literature 103crushing at the bearing end. Otherwise, generally the specimens failed eitherwhen the edges of the panels broke off at the screw fastener or when the panelpulled over the head of the screws. In some cases where 3.5mm diameterscrews were used in PLY and OSB panels, fracture of the screws occurred.The Authors reported for the full-scale tests the following conclusions: The behavior of the PLY and OSB panels was comparable, whereasthe strength of gypsum and FBW walls was relatively low. The use ofGWB on the interior of the wall and PLY on the exterior produced ahigher shear capacity, by approximately 18%, in comparison with thePLY wall. The use of 3.7mm diameter nails decreased the maximum shearstrength in comparison with 3.5 and 4.2mm diameters screws. Themaximum shear strength was not influenced by the size of the fastener.The failure mode for the specimens with 3.5mm diameter screws wasfracture of fasteners and thus walls with 3.5mm diameter screws mayfail at lower loads than walls with 4.2mm diameter screws. For gypsum and FBW the reduction of the fastener spacing increasedsignificantly the shear strength. The walls with blocked panels oriented horizontally providedessentially the same shear capacity but higher stiffness than acomparable wall with panels oriented vertically. When blocking wasomitted from the walls with horizontal panels, the shear capacity of thewall was reduced by more than 50%.For the small-scale tests the conclusions of the Authors were: Both the strength and stiffness of the PLY specimens were more thanthat of the OSB specimens. The strength of gypsum and FBW wallswas less than that of PLY and OSB specimens. The normalized shear strength for small-scale tests was similar asthose for full-scale tests, thus the small-scale tests were considered tobe useful in an evaluation of the relative resistance of different wallassemblies.

104 Chapter III3.1.10 Serrette et al. (1997b)The Authors illustrated in this work the results of sixteen monotonic andtwenty eight cyclic shear tests conducted on walls assembled with PLY, OSB,steel sheet sheathing (SSS) and X-B attached to light gauge steel frame ononly one side.The objectives of the test program were the followings: To obtain design data for walls with high aspect ratios (varying from 2to 4). To define limits for framing thickness for sheathing attached with4.2mm diameter screws. To study the behavior of different types of sheathings (PLY, OSB,SSS). To evaluated the performance of X-B. To examine the effect of various fastener schedules.Both monotonic and cyclic tests were conducted on walls with89x43x13mm (web depth x flange size x lip size) C-sections studs at 610mmon center and with 89x32 (web depth x flange size) U-sections track. Doublestuds (back-to-back) were used at the ends of the walls. All PLY and OSBpanels were orientated vertically. The fastener types used were 4.2x13mmmodified truss head screws for the frame connections, 4.2x25mm (diameter xlength) flat head screws for the PLY and OSB panels, and 4.2x13mmmodified truss head screws for the X-B and SSS. Hold-downs were used toconnect each wall specimen to the base of the test frame.For monotonic tests, the studs were 0.84mm thick except for one casewhere 1.09mm thick studs were used (tests 3-4). The following assemblieswere tested: 2440x1220mm walls with 114x0.84mm (width x thickness) and191x0.84mm X-B (tests 1-4). 2440x610mm walls with 11.1mm thick OSB attached to the frameusing screws spaced at 305mm in the field and at 152, 102 and 51mmat the perimeter (tests 5-10).

Testing of cold-formed steel stud shear walls: review of existing literature 1052440x610mm walls with 0.46 and 0.69mm thick SSS attached to theframe using screws spaced at 305mm in the field and at 152 and 102 atthe perimeter (tests 11-14).2440x1220mm walls with 0.46mm thick SSS attached to the frameusing screws spaced at 305mm in the field and at 152 at the perimeter(tests 15-16).For the cyclic tests, the studs were 0.84mm thick except for some cases. Infact, for A1-A8 tests the end studs were 1.09mm thick, while for B1-B2 andB3-B4 tests all studs were 1.09 and 1.37mm thick respectively. The differentshear resisting systems included: 2440x1220mm walls with 11.9mm thick PLY and 11.1mm thick OSBattached to the frame using screws spaced at 305mm in the field and at76 and 51mm at the perimeter (tests A1-A8). 2440x1220mm walls with 11.9mm thick PLY attached to the frameusing screws spaced at 305mm in the field and at 152mm at theperimeter (tests B1-B4). 2440x1220mm walls with 114x0.84mm (width x thickness) and191x0.84mm X-B (tests C1-C4). 2440x1220mm walls with 0.46mm thick SSS attached to the frameusing screws spaced at 305mm in the field and at 152 at the perimeter(tests D1-D2). 2440x1220mm walls with 0.46mm thick SSS attached to the frameusing screws spaced at 305mm in the field and at 152mm at theperimeter (tests D1-D2). 2440x610mm walls with 11.1mm thick OSB attached to the frameusing spaced at 305mm in the field and at 152, 102 and 51mm at theperimeter (tests E1-E6). 2440x610mm walls with 0.69mm thick SSS attached to the frameusing screws spaced at 305mm in the field and at 102 and 51mm at theperimeter (tests F1-F4).For the monotonic tests, Serette et al. reported that the walls with114x0.84mm X-B failed due to local buckling of the end studs, differently, the

106 Chapter IIIwalls with 191x0.84mm X-B failed due to local buckling in the top track andend studs, aggravated by bending due to the eccentricity of the strap force.For the walls with OSB panels with a 51mm edge screw spacing, the endstuds buckled just above the track. With a 102mm edge screw spacingdisplacements became excessive. With a 152mm edge screw spacing failurewas initiated by buckling of the end stud at the hold-down.Failure of walls with SSS resulted from rupture of the steel sheet along theline of the screws at the edges. Diagonal “tension field” patterns were notobserved.In the case of cyclic tests, for orientated strand board and PLY sheathingswith aspect ratio of 2, failure was initiated by screw heads pulling through thesheathing or screw pulling out of the framing in 1.09mm thick framing (testsA1-A8 and B1, B2), but in 1.37mm thick framing (tests B3, B4) some screwsfailed in shear.Failure modes in walls with X-B (C1-C4) were similar to those observed inmonotonic tests of similar specimens.Analogously, for orientated strand board sheathings with an aspect ratio of4 (tests E1-E6) failure modes were similar to those observed in monotonictests of similar specimens.Finally, failure modes for walls with SSS (D1, D2, F1-F4) resulted from acombination of screws pulling out of the framing, rupture of the steel sheetalong the line of screws at the edges, and in some cases local buckling of theend studs.From the tests results, the Authors concluded that: The shear strength appreciably decreased when the aspect ratioincreased from 2 to 4. The use of thicker and back-to-back coupled end studs for the wallswith PLY and OSB panels allowed to fully develop the shear strengthof the panels-to-frame connections also in the cases in which densefasteners schedules were used. 4.2mm screws should be limited to1.09mm thick framing. In fact, this screw behaved well in the 0.84 and1.09mm thick frames (screws pull-out or pull-through failure) butfractured in shear when 1.37mm thick frames were used.

Testing of cold-formed steel stud shear walls: review of existing literature 107 The walls sheathed with SSS had a ductile behavior without suddendecreases in shear load capacity; moreover, the use of thick sheathingsincreased the shear resistance, but the failure mode moved fromrupture at the edges of the sheathing to screw pull-out from theframing. In the design of walls with X-B, the designer must consider that theforce in the strap may be larger than that corresponding to the nominalyield strength; also, if X-Bs are installed on one side of the wall only,the effect of eccentricity should be considered. Decreasing the screws spacing result in the increased maximum shearload.3.1.11 NAHB Research Center (1997)In this paper, the National Association of Home Builders (NAHB)Research Center presented the results of four monotonic load tests of12190mm long, cold-formed steel (CFS) framed shear walls with openings.The goals of the experimental program were the followings: To study the capacity of steel-framed shear walls as influenced by thepresence of openings and, in particular, to investigate the suitability ofusing the “Perforated Shear Wall” (PSW) design method, originallydeveloped for wood structures (Sugiyama & Matsumoto, 1993), also incase of light-gauge steel-framed shear walls. To briefly investigate the effects of reduced anchoring constraints inview of future research to account for restraint provided by cornerswithout including hold-down brackets. To provide a direct comparison between the performances of woodframedand steel-framed shear walls.All shear walls specimens were 2440x12190mm (height x length) in size.The frames were constructed of 89x38x0.84mm (web depth x flange size xthickness) C-sections studs spaced at 610mm on center. Exterior sheathingsconsisted of 11.1mm thick OSB oriented vertically and fastened to the frameswith 4.2mm diameter screws spaced 152mm along the perimeter and 305mmin the field of the panels. Interior sheathings were 12.7mm thick GWB

108 Chapter IIIoriented vertically and attached to the frames with 3.5mm diameter screwsspaced 178mm along the perimeter and 254mm in the field.The wall 1 was fully sheathed, while the walls 2A and 2B had one2032x1219mm (height x length) door and one 1727x2400mm window.Besides the same openings present in the wall 2A and 2B, the wall 4 had one2032x3658mm door. The specimens 1, 2A and 4 were constructed withtypical details. In particular two hold-down anchors were used on each ofthese walls (one at each end). On the contrary, the specimen 2B wasconstructed without hold-down anchors.It was reported in the NAHB document that similar modes of failure wereobserved in the specimens with hold-down anchors. The initial loading waslinear until the screws began to pull through the GWB, then; it was observed aslight reduction in stiffness. As the load approached ultimate capacity theOSB panels cracked at the perimeter screw connections.The wall without hold-down anchors also showed failure of the interiorpanels, although the exterior panels and the bottom track were unable todistribute the uplift forces at the end of the wall. In fact, the bottom trackfailed in bending due to uplift at the location of the first anchor bolt.The NAHB presented the following conclusions: The calculation of the shear capacity using the PSW design methodappeared valid, but revealed a conservative prediction of ultimateshear strength. Hold-down reduced uplift and increased the ultimate shear capacity byallowing more sheathing-to-frame screws to resist shear. The lateral load resisting mechanism for both wood-framed and steelframedshear walls appeared to be similar.3.1.12 Gad et al. (1999a, b)The Authors illustrated in this work an important investigation in theseismic performance of residential structures with CFS frames. The researchinvolved an extensive racking and dynamic testing program on the both twoandtree-dimensional framing assemblies with X-B bracing.

Testing of cold-formed steel stud shear walls: review of existing literature 109The objectives of the experimental program were the followings: To study the interaction between the different components of a typicalwall assemblage. To quantify the lateral stiffness and strength contributions ofplasterboard and determine its reliability under cyclic loads. To investigate the inertial loading effect of brick veneer walls on theframing assembly. To develop guidelines that enable prediction of the behavior ofcomplete structures.The experimental program was divided into two steps: testing of twodimensionalunlined frames with different frame connection types and testingof a one-room-house at various stages of construction.The two-dimensional specimens measured 2400x2400mm (height x length)and were constructed from CFS channel sections with steel grade of G300.The section of the studs was 75x32x1.2mm (web depth x flange size xthickness), for the plates (stud track) the section was 78x31x1.2mm and forthe noggings (blocking placed between all studs) was 72x34x1.2mm. Each X-B was 1.0 thick and 25mm wide with steel grade of G250. For simulating themass of a steel sheet roof, a 350kg concrete beam was bolted to the top of theframe.The different connection types used were: Tab-in-slot connections, which are essentially pinned connections.These connections represent the lower bound response. Welded connections, which represent the upper bound response.On the walls with tab-in-slot connections were conducted slow cyclicracking and dynamic tests. In particular, the dynamic tests included pluck(applying a hammer blow on the concrete mass on the wall panel), swept sinewave and simulated earthquakes.The tests conducted on the welded frames were swept sine wave andsimulated earthquakes only.The one-room-house specimen measured 2300x2400x2400mm high andwas constructed from full-scale components. It represents a section of a

110 Chapter IIIrectangular house with plan dimensions of 11000x16000mm. The mass,applied on the test house through a concrete slab fixed to the joists, was2300kg. This mass corresponded to that due to roof tiles, battens, insulation,ceiling lining and trusses for a plan area of 11000x2400mm. The two walls inthe east-west direction were framing assemblies with X-B bracing while thetwo walls in the north-south direction were non-load bearing and had standard900x2100mm door openings.All construction details were standard except for the hold-down that wasover-designed to eliminate a potential uplift failure. All the framing memberswere 75x35x1.0mm CFS channel sections with steel grade of G550. Tab-inslotconnections were used for to connect the stud, plates and noggings.Plasterboard lining, 10mm thick, was used for the ceiling and the walls, andconnected to the frame with 4.1x25mm (diameter x length) bugle head selfdrilling screws spaced 200mm along the wall vertical edges, 600mm along thetop and bottom plates, 300mm in the field of the ceiling and 400mm in thefield of the walls. Skirting boards, 55mm ceiling cornices and set corner jointswere used in conjunction with the plasterboard lining. The brick veneer wallswere connected to the studs by metal clip-on brick ties.The house was tested in the east-west and north-south directions atdifferent stages of construction. The tests conducted were mainly slow cyclicracking, swept sine wave and simulated earthquakes.From the two-dimensional tests results, the Authors concluded that theimportant component in unlined single frames is the strap bracing system. Inparticular they reported that: The failure of the frame was governed by the failure of the X-B. The dynamic characteristics of the frame were governed by the initialtension in the straps. In fact, the welded frame had a lower naturalfrequency (7.0Hz) than the tab-in-slot frame (6.3Hz) and thiscontradicted the expectation that the welded frame would be stifferthan the frame with tab-in-slot. The type of connections between the framing members did not seem tohave an influence on the structural response of the braced frames.

Testing of cold-formed steel stud shear walls: review of existing literature 111Gad et al. concluded from the three-dimensional test results that residentialsteel frames used in the tests performed well under racking and earthquakeloads. In particular, the Authors reported their conclusions for each differentstage of construction.For unlined frames: The behavior was governed by the X-B system. The initial tension in the X-B increased the frame stiffness of theframe and when the X-B yield then the true stiffness of the X-B system(strap and its connections) defined the stiffness of the frame. The type of strap bracing-to-plate connections governed the failureload and mechanism.For the lined frames: Plasterboard fixed as non-structural component provided higherstiffness, load carrying capacity and damping than X-B. When X-B and plasterboard were combined, the overall stiffness andstrength of the system is simple addition of individual contributionsfrom X-B and plasterboard. The plasterboard combined with ceiling cornices, skirting board andset corner joints, resisted about 60-70% of the applied racking loadwhereas the X-B resisted 30-40%.For brick veneer walls: In-plane brick veneer walls attached to the frame via clip-on ties didnot contribute to the stiffness of the system. Different displacements between the frame and the out-of-plane brickveneer walls were mainly accommodated by deformation of the studflanges rather than deformation of brick ties.3.1.13 Selenikovich et al. (1999)Selenikovich et al. presented the results of monotonic and cyclic tests onsix-teen full-size shear walls with and without openings.The objectives of the study were: To establish the effect of size of openings on shear wall performance. To compare the shear strength of the walls with previsions of the PSWdesign method (Sugiyama & Matsumoto, 1993).

112 Chapter III To determine the effect of cyclic loading on shear behavior. To examine the effect of the addition of internal GWB.The specimens were built in accordance with the “Builder’s Steel-StudGuide” (AISI, 1996). All walls were 2440x12192mm (height x length) in sizewith the same type of framing, sheathing, fasteners, and fasteners schedules.The frames consisted in 89x38x0.84mm (web depth x flange size x thickness)C-sections studs at 610mm on center. Double studs (back-to-back) were usedat the ends of the walls and around doors and windows. Exterior sheathingswere 11.1mm thick OSB sheathing oriented vertically. Interior 12.7mm thickGWB sheathings oriented vertically were on an additional monotonic test. Thefasteners to connect the steel frame members were 4.2mm (diameter) lowprofile head screws whereas to connect the sheathing to the frame were used4.2mm bugle head screws. Sheathing screws were spaced 152mm onperimeter and 305mm in field to attach OSB panels, and 178mm on perimeterand 254mm in field for GWB. Hold-downs were used to connect each wallspecimen to the base of test frame.The Authors observed that the predominant failure mode was head pullthroughof sheathing screws and bending of frame elements. They concludedthe following: Long, fully sheathed walls were significantly stiffer and stronger butless ductile than walls with openings. The predictions of the PSW design method were conservative at alllevels of monotonic and cyclic loading. Cyclic loading did not influence the elastic behavior of the walls butreduced their deformation capacity. The strength of fully sheathed walls was affected more significantly bycyclic loading than walls with openings. Adding of GWB panels increased the shear strength and stiffness offully sheathed walls under monotonic load.3.1.14 COLA-UCI (2001)The City of Los Angeles – University of California (COLA – UCI) testswere carried out with the aim to develop an understanding of the probable

Testing of cold-formed steel stud shear walls: review of existing literature 113dynamic behavior of PLY and OSB panels attached to wood frame walls orlight-gauge steel frame by fasteners such as nails or screws.The main goals of the study were: To determine whether the shear wall system could be modeled in theirlinear displacement range as principally shear deforming systems. To determine the cyclic force-displacement relationships forcommonly used light-framed walls with shear panels. To provide data for the improvement of the design of lateral-loadresisting shear wall systems. To make recommendations to the City of Los Angeles if code changesare warranted by the data and data analysis.A total of thirty-six groups of 2440x2440mm (height x length) shear wallwith three specimens per group were tested under cyclic load. The groupsfrom 1 to 13 and from 20 to 36 had wood frame walls, whereas the groupsfrom 14 to 19 had light-gauge steel frame.The specimens with steel frame included 11.1mm thick OSB or 11.9 thickPLY, which were attached to frame with 4.2x25mm (diameter x length) buglehead screws spaced 305mm in the field and 51, 102, or 152 at the perimeter.The 89x41x10x0.84 C-sections studs were spaced at 610mm on center andwere connected to the 89x38mm (web depth x thickness) U-sections track.Double studs were coupled back-to-back at the end of the wall to prevent localand flexural buckling in the chords. Strap hold-down anchors were used toconnect each wall specimen to the base of test frame.Tests results showed that: A reduction of the fastener spacing nonlinearly increased the shearstrength and stiffness for both the light-gauge steel framed and woodframed stud walls. With the same sheathing types and fastener spacing, steel-framed wallsexhibited somewhat higher shear strength and ductility but lesshysteretic damping than wood-framed walls.

114 Chapter III3.1.15 Dubina & Fulop (2002)The experimental program presented by Dubina & Fulop was based on sixseries of full-scale tests with different cladding arrangements. Each seriesconsisted of identical wall panels, tested statically both monotonic and cyclic.The objectives of test program were the followings: To compare monotonic and cyclic behavior of wall-stud shear walls. To confirm the previous results about the effect of interior gypsumcladding. To study the effect of openings. To compare the behavior of different cladding materials and crossbracing. To provide experimental information for the calibration of finiteelement models.All shear walls specimens were 2440x3600mm (height x length) in size.The CFS frames consisted in 600S175-62 studs (150x1.5mm (web depth xthickness) C-sections) at 600mm on center, while the tracks were 600T225-62(154x1.5 (web depth x thickness) U-sections). Double studs (back-to-back)were used at the ends of the walls and around openings.The different wall specimen series included: Series 0: constituted by one wall specimen consisting of CFS frameswithout some shear resisting system. Series I: represented by three wall specimens with exterior claddingconsisting of steel corrugated sheet (SCS) LTP20/0.5 placed inhorizontal position and fixed to the frame using SL2-T-A14(4.8x22mm (diameter x length)) self-tapping screws spaced at 114mmat sheet ends and at 229mm in the field. Series II: composed by three wall specimens with exterior claddingsimilar to those of the series I and with interior cladding consisting of12.5mm thick GWB placed in vertical position and fixed to the frameat 250mm in the field and at the perimeter of the panel. Series III: constituted by two wall specimens braced by means of110x1.5mm (width x thickness) steel straps on both sides of the frame.

Testing of cold-formed steel stud shear walls: review of existing literature 115The straps were fixed to the wall structures using SPEDEC SL4-F-4.8x16 (4.8x16mm (diameter x length)) and SD6-T16-6.3x25(6.3x25mm (diameter x length)) self-drilling screws. The numbers ofscrews were designed for the yield strength of the strap.Series IV: composed by three wall specimens similar to those of theseries II except for the presence of the one 1200mm wide door.Series OSB I: composed by two wall specimens with exteriorconsisting of 10mm thick OSB placed in vertical position and fixed tothe frame using bugle head self-drilling screws of 4.2mm diameterspaced at 250mm in the field and at 105mm at the perimeter of thepanel.Series OSB II: composed by three wall specimens similar to those ofthe series OSB I except for the presence of the one 1200mm widedoor.The Authors reported that for Series I and II local deformation in theuplifted corners was followed by profile-end distortion, gradual deformationin connections and failure occurred in seam lines. The behavior of Series IVwas very similar to the ones in Series I and II, with much stronger cornersuplift. For the Series III after buckling of compressed straps in the early stage,the local deformation of the lower track followed. Important plastic elongationof the straps was observed, but because of this unexpected failure of thecorner occurred. In the case of Series OSB I the failure mechanism of thespecimens was different from SCS specimens due to different sheetingorientation. Failure of the specimens was sudden when one vertical row ofscrews unzipped from the stud and both pull over the screw head, and failureof OSB margin was observed. For the Series OSB II important inclination ofthe screws developed in the OSB panels-to-lower track connection, followedby sudden rupture of this connection line.The Authors concluded that: Very significant pinching, and reduced energy dissipation characterizethe hysteretic behavior.

116 Chapter III The behavior of gypsum panels was satisfactory. In fact they couldfollow even extreme deformation of the wall without significantdamage.3.1.16 Branston et al. (2003)In an attempt to draw a link between the existing database of steel frame /wood panel shear tests carried out in the USA and any future experiment withCanadian products, a series of 12 match tests was conducted by Branston etal..The goal of the research project was to reproduce the results of some testscompleted by Serrette et al. (1996a) and COLA-UCI (2001) using steel andwood panel products purchased in the USA and following the procedures setup by previous researchers. In particular, the overall long-term objective of theshear wall research is to investigate the performance of, and to provideguidelines for the design of the light gauge steel structures when subjected toearthquake loading.In this research program, twelve full-scale steel frame shear walls, witheither OSB or PLY sheathing, were tested (6 monotonic load tests and 6 cyclicload tests).The frame was made using 89x41x10x0.84 C-sections studs spaced at610mm on center attached to the 89x38mm (web depth x thickness) U-sections track. Double studs were coupled back-to-back at the end of the wallto prevent local and flexural buckling in the chords. The fasteners used for theframe connections were 4.2x13mm wafer-head screws. The panels wereconnected to the frame with 4.2x38mm bugle head screws. Wall specimenswere connected to the base of test frame with hold-downs (tie-downs) forspecimens OSB 4-8 US M-, OSB 4-8 US C- and PLY 8-8 US M- and withstrap hold-down anchors for specimens PLY 8-8 US C-.The different tests included: OSB 4-8 US M- A, B, C: Monotonic tests of 1220x2440mm (height xlength) walls with 0.84mm thick steel framing sheathed on one sidewith 11mm thick OSB. Self-drilling sheathing screws were spaced at

Testing of cold-formed steel stud shear walls: review of existing literature 117102mm at the perimeter and at 305mm in the field. (Previous tests:Serrette et al. (1996a) OSB – 1D3, 1D4).OSB 4-8 US C- A, B, C: Cyclic tests of 1220x2440mm (height xlength) walls with 0.84mm thick steel framing sheathed on one sidewith 11mm thick OSB. Self-drilling sheathing screws were spaced at102mm at the perimeter and at 305mm in the field. (Previous tests:Serrette et al. (1996a) AISI OSB – 3, 4).PLY 8-8 US M- A, B, C: Monotonic tests of 2440x2440mm (height xlength) walls with 0.84mm thick steel framing sheathed on one sidewith 12mm thick PLY. Self-drilling sheathing screws were spaced at152mm at the perimeter and at 305mm in the field. (Previous tests:Serrette et al. (1996a) PLY – 1A6, 1A7).PLY 8-8 US C- A, B, C: Cyclic tests of 2440x2440mm (height xlength) walls with 0.84mm thick steel framing sheathed on one sidewith 12mm thick PLY. Self-drilling sheathing screws were spaced at152mm at the perimeter and at 305mm in the field. (Previous tests:COLA-UCI (2001) 14A. 14B, 14C).In general, the failure of all wall specimens was restricted to the wood tosteel connections and the studs did not fail in compression, nor did the holddownssuffer any type of failure.From the monotonic tests results, the Authors concluded that a variation inthe performance of the walls from the different research programs wasobserved. In a number of instances the shear capacity and stiffness of the testsspecimens differed by a substantial amount. The variation in strength of thewalls can be attributed in general to the different material properties that mayhave existed in both the steel and wood panel members. With respect to thePLY 8-8 US C- A, B, C walls, the higher ultimate strength and stiffnessobtained for the COLA-UCI tests can most likely be traced to the use ofsheathing structural 1 grade panels in the original tests, whereas regularsheathing grade PLY was used in the construction of the match tests.The addition of a single horizontal stiffener located at the mid-height of thewall did not increase the shear capacity and was not recommended since itincreased the construction difficulties and the cost of installation.

118 Chapter III3.2 FACTORS AFFECTING CFSSSW BEHAVIOR UNDERLATERAL LOADING: THEY INDIVIDUATION ANDANALYSISThe performance of house structures braced with cold-formed/light gaugesteel (CFS/LGS) framing under horizontal load is determined by thehorizontal (diaphragms) and vertical (stud walls) lateral force resistingsystems (LFRSs) behavior. If both horizontal diaphragms and vertical studwalls are frames braced with structural panels and/or with diagonal bracing,the same basic structural parameters influence their shear behavior. Forinvestigating this influence, the rather large number of experimental programsconducted on CFSSSW with different assemblies has been illustrated in theprevious Sections. From the examination of these experimental programs, it ispossible to individuate the following basic factors that influence the lateralbehavior of CFSSSW: sheathing (type, thickness, orientation); framing (stud size, thickness and spacing, presence of X-bracing); fastener (type, size, spacing); geometry (wall aspect ratio, openings); type of loading (monotonic or cyclic); construction techniques and anchorage details.Their effects on shear wall behavior are synthesized in the following. Amore complete summary of the conclusions obtained by several researchers isgiven in Appendix B.3.2.1 Sheathing (type, thickness, orientation)The basic behavior of different sheathing types and thicknesses has beenstudied by Tarpy (1980), Tarpy & Girard (1982), Serrette et al. (1996a, b,1997a, b), Salenikovich et al. (1999), Dubina & Fulop (2002).Those studies included walls constructed with PLY, OSB, GWB, GSB,FBW, CP, SSS, and SCS. For understanding the different structural capacityassociated to different sheathing types and thicknesses, a comparison betweenthe average values of shear strength derived from the existing experimental

Testing of cold-formed steel stud shear walls: review of existing literature 119results is reported in Table 3.2. These values are normalized with respect toaverage values of shear strength for walls braced with 11.1mm thick OSB.From these comparisons, it is possible to conclude that the PLY provided alittle (about 10%) higher shear strength in comparison with the OSB; whereasthe capacity of the GWB and GSB is much (about 60%) lower than that of theOSB. Moreover, the adding of GWB to the opposite side of the wall assemblyincreased the shear strength by about 40%. Finally, the SSS presented arelatively smaller (about 10%) shear strength than those of OSB.Sheathing type and thickness No of specimens Average Standard deviationOSB t=11.1mm 1.00PLY t=11.9mm 13 1.10 0.09GWB t=12.7mm + GWB t=12.7mm 2 0.83 0.01OSB t=11.1mm+GWB t=12.7mm 4 1.39 0.58SSS t=0.46mm 1 0.91SSS t=0.69mm 3 0.86 0.12GWB t=12.7mm+GSB t=12.7mm 2 0.78 0.36+:double sheathing (internal and external sheathings)t: thicknessTable 3.2: Normalized shear capacity for different sheathing type and thickness.Serrette & Ogunfunmi (1996) and Serrette et al. (1994, 1997a) examinedthe influence of sheathing orientation and the contribution of horizontal steelstraps installed at mid-height of the walls and fastened to the blocking. Acomparison between the shear strength for walls with sheathing orientedvertically and horizontally, with and without solid blocking, is reported inFigure 3.1. In particular, this comparison demonstrates that the panels orientedparallel to the studs provided the same shear strength than those appliedperpendicular to the studs with strap blocking. In addition, when in the case ofpanels perpendicular to studs blocking was omitted, the shear capacity of thewall, was reduced by more than 50%.

120 Chapter III3025Ultimate shearstrength[kN/m]VERTICALHORIZONTAL + SOLID BLOCKHORIZONTAL201510Serrette et al .(1996a)1A2,1A31A5,1A6Serrette et al .(1997a)OSB-T4OSB-T5Serrette et al .(1994)687Serrette et al .(1997a)PLY-T4PLY-T7PLY-T6Serrette et al .(1997a)GYP-T2GYP-T150OSB OSB PLY PLY GWB+GWBFigure 3.1: Influence of the sheathing orientation.3.2.2 Framing (stud size, thickness and spacing, presence of X-bracing)The effects of framing stud size, thickness and spacing have been studiedby Tarpy & Girard (1982), Tissel (1993) and Serrette et al. (1997b). Thosestudies indicated that the use of thicker (1.09mm thickness) and multiplechord studs (back-to-back coupled C-sections) allowed the development of thefull shear strength of the wall panels. In addition, the reduction of the studspacing did not increase significantly the shear performance.The contribution of steel flat strap tension X-bracing has been investigatedby Serrette & Ogunfunmi (1996), Serrette et al. (1997b) and Gad et al.(1999a). In particular, Serrette et al. concluded that, although the adding offlat strap improved the shear behavior, their employment is not practical.3.2.3 Fastener (type, size, spacing)An extensive experimental study on the effect of fastener type, size andspacing has been performed by Tarpy & Hauenstein (1978), Tarpy (1980),Tarpy & Girard (1982), Tissel (1993), Serrette et al. (1996a, b, 1997a, b), Gadet al. (1999a), COLA-UCI (2001). Those studies showed that the reduction ofthe fastener spacing at the panel edges improved significantly the shearperformance. Furthermore, they proved that for PLY (11.9mm thick) or OSB

Testing of cold-formed steel stud shear walls: review of existing literature 121(11.1mm thick) panels fastened to members with a thickness from 0.84mm to1.09mm, 4.2x25mm (diameter x length) flat-head or bugle-head self-drillingscrews should be used, while for gypsum panels (12.7mm thick) 3.5x25.4mmbugle-head self-drilling screws should be adopted.3.2.4 Geometry (wall aspect ratio, openings)McCreless & Tarpy (1978), Tarpy & Girard (1982) and Serrette et al.(1996a, 1997b) studied the effect of the wall aspect ratio (height/length)variation. The shear strength values obtained from the cited test results arereported as a function of aspect ratio (H/L) in Figure 3.2. The Figureillustrates, according to the McCreless & Tarpy (1978) and Serrette et al.(1996a) investigations, how the shear strength is practically insensitive to theaspect ratio, when this is in the range [0.3 , 2]. Moreover, according to resultsgiven in Serrette et al. (1997b), the shear strength appreciably decreases whenthe aspect ratio increases from 2 to 4.The NAHB Research Center (1997), Salenikovich et al. (1999) and Dubina& Fulop (2002) examined the influence of the opening size. The shearstrength values obtained from their tests are reported as a function of thesheathing area ratio (r) in Figure 3.3, where r is defined in following equation:1r (3.1)Ao1h Liwith Ao: the total area of openings; h: the height of the wall; and Li: the lengthof the full height wall segment.The Figure shows that a reduction of r increases the shear capacity. TheNAHB Research Center and Salenikovich et al. also investigated thesuitability of using the PSW design method, originally developed for woodstructures (Sugiyama & Matsumoto 1994), also in case of CFSSSW. Inparticular, they concluded that the PSW method reveals a conservativeprediction of shear strengths.

122 Chapter IIIM78: McCreless & Tarpy (1978); TG82: Tarpy & Girard (1982); S+96a:Serrette et al. (1996a); S+97a: Serrette et al. (1997a)H: height of the wall; L: length of the wallFigure 3.2: Influence of the aspect ratio.N97: NAHB Research Center (1997); S+99: et al. (1999); FD02: Dubina &Fulop (2002)-m: monotonic test; -c: cyclic test=1/(1+Ao/HLi): sheathing area ratioAo: total area of openings; H: height of the wall; Li: length of the full heightwall segmentFigure 3.3: Influence of the openings.

Testing of cold-formed steel stud shear walls: review of existing literature 1233.2.5 Type of loading (monotonic or cyclic)The effect of cyclic loading on the lateral strength, stiffness and ductility ofsteel stud shear walls systems has been investigated by Serrette et al. (1996a,b and 1997b), Salenikovich et al. (1999), COLA-UCI (2001), Dubina & Fulop(2002) and Branston et al. (2003). The results of those studies showed thatcyclic loadings reduce the shear performance of steel stud shear walls, incomparison with monotonic loads.The ultimate shear strengths obtained under both monotonic and cyclicloading tests, using nominally identical specimens are shown in Figure 3.4.The comparison between monotonic and cyclic test results reveals that theshear strength under cyclic loads is about 10% in average lower than thatunder monotonic load.Moreover, a typical cyclic response of CFSSSW is characterized bysignificant pinching of the hysteresis response, with reduced energydissipation capacity, as shown in Figure 3.5 for a test performed by Branstonet al. (2003).S+96a: Serrette et al. (1996a); S+96ab: Serrette et al. (1996a, b); S+97b:Serrette et al. (1997b); S+99: Salenikovich et al. (1999); FD02: Dubina &Fulop (2002); B03: Branston et al. (2003)Figure 3.4: Influence of cyclic loading.

124 Chapter IIIFigure 3.5: Cyclic response for OSB 4-8 US C-A test performed by Branston et al. (2003).3.2.6 Construction techniques and anchorage detailsThe study of the effect of construction techniques and anchorage detailshas been performed by Tarpy & Hauenstein (1978), Tarpy (1980), Tarpy &Girard (1982), NAHB Research Center (1997) and Gad et al. (1999a). Almostall the cited references highlight the important effect of the corner foundationanchorage details on the shear response of steel stud walls. In fact, if the upliftloads are not directly transmitted from the end studs to the foundation by rigidattachment as such as clip angles or hold-downs, then a significant bending ofthe bottom track occurs, up to failure with a reduced shear strength andstiffness.REFERENCESASTM E 564-76 (1976) Standard Practice for Static Load Test for Shear Resistanceof Framed Walls for Buildings. ASTM (American Society for Testing and Materials).West Conshohocken, PA, USA.

Testing of cold-formed steel stud shear walls: review of existing literature 125AISI (1996) Builder’s Steel-Stud Guide. Publication RG-9607, AISI (American Ironand Steel Institute). Washington DC.Brantson, A., Boudreault, F., Rogers, C.A. (2003) Testing on steel frame / woodpanels shear walls. Progress Report, Departement of Civil Engineering and AppliedMechanics, McGill University. Montreal.COLA-UCI (2001) Report of a testing program of light-framed walls with woodsheathedshear panels. Final report to the City of Los Angeles Department ofBuilding and Safety, Structural Engineers Association of Southern California. Irvine,CA, USA.Dubina, D. & Fulop, L.A. (2002) Seismic performance of wall-stud shear walls. InProceedings of the 16 th International Specialty Conference on Cold-formed SteelStructures. St. Louis, MO, USA: 483-500.Gad, E.F., Duffield, C.F., Hutchinson, G.L., Mansell, D.S., Stark, G. (1999a) Lateralperformance of cold-formed steel-framed domestic structures. EngineeringStructures, Elsevier, Vol.21, No.1: 83-95.Gad, E.F., Chandler, A.M., Duffield, C.F., Stark, G. (1999b) Lateral behaviour ofplasterboard-clad residential steel frames. Journal of Structural Engineering, ASCE,Vol.125, No.1: 32-39.McCreless, S. & Tarpy, T.S. (1978) Experimental investigation of steel stud shearwall diaphragms. In Proceedings of the 4 th International Specialty Conference onCold-formed Steel Structures. St. Louis, MO, USA: 647-672.NAHB Research Center (1997) Monotonic Tests of cold-formed steel shear wallswith openings. (NAHB) National Association of Home Builders. Upper Marlboro,MD, USA.Salenikovich, A.J., Dolan, J.D., Easterling, W.S. (2000) Racking performance of longsteel-frame shear walls. In Proceedings of the 15 th International Specialty Conferenceon Cold-formed Steel Structures. St. Louis, MO, USA: 471-480.Serrette, R. (1994) Light gauge steel shear wall test. Light Gauge Steel ResearchGroup, Department of Civil Engineering, Santa Clara University. Santa Clara, CA,USA.Serrette, R.L. & Ogunfunmi, K. (1996) Shear resistance of gypsum-sheathed lightgaugesteel stud walls. Journal of structural engineering, ASCE, Vol.122, No.4: 386-389.Serrette, R., Nguyen, H., Hall, G. (1996a) Shear wall values for light weight steelframing. Report No.LGSRG-3-96, Light Gauge Steel Research Group, Department ofCivil Engineering, Santa Clara University. Santa Clara, CA, USA.

126 Chapter IIISerrette, R., Hall, G., Nguyen, H. (1996b) Dynamic performance of light gauge steelframed shear walls. In Proceedings of the 13 th International Specialty Conference onCold-formed Steel Structures. St. Louis, MO, USA: 487-498.Serrette, R.L., Encalada, J., Juadines, M., Nguyen, H. (1997a) Static racking behaviorof plywood, OSB, gypsum, and fiberboard walls with metal framing. Journal ofStructural Engineering, ASCE, Vol.123, No.8: 1079-1086.Serrette, R., Encalada, J., Matchen, B., Nguyen, H., Williams, A. (1997b) Additionalshear wall values for light weight steel framing. Report No.LGSRG-1-97, LightGauge Steel Research Group, Department of Civil Engineering, Santa ClaraUniversity. Santa Clara, CA, USA.Sugiyama, H & Matsumoto, T. 1984. Empirical equations for the estimation ofracking strength of plywood-sheathed shear walls with openings. Summaries ofTechnical Papers of Annual Meeting, Transactions of the Architectural Institute ofJapan, No.338.Tarpy, T.S. (1980) Shear resistance of steel-stud wall panels. In Proceedings of the5 th International Specialty Conference on Cold-formed Steel Structures. St. Louis,MO, USA: 331-348.Tarpy, T.S. & Girard, J.D. (1982) Shear resistance of steel-stud wall panels. InProceedings of the 6 th International Specialty Conference on Cold-formed SteelStructures. St. Louis, MO, USA: 449-465.Tarpy, T.S. & Hauenstein, S.F. (1978) Effect of construction details on shearresistance of steel-stud wall panels. Vanderbilt University. Nashville, TN, USA. Aresearch project sponsored by American Iron and Steel Institute. Project No.1201-412.Tissell, J.R. (1993) Wood structural panel shear walls. Report No.154, APA (TheEngineering Wood Association). Tacoma, WA, USA.

127Chapter IVEvaluation of seismic capacity:the monotonic testThe number of experimental tests, which have been performed to study thelateral behavior of cold-formed steel stud shear walls (CFSSSWs) is ratherwide. The basic factors that influence the shear response of CFSSSWs havebeen objects of previous studies, as presented in Chapter 3. Although theexisting experimental database appears sufficient, there has been littleresearch on the lateral-load transfer from the horizontal diaphragms to studwalls. The same consideration applies for the influence of construction details,such as bearing stiffeners and joist track profiles, anchorage details,connections between joists, bearing stiffeners, joist track and top stud track.Moreover, there has not been specific study on the effect of gravity loads onthe shear walls behavior even if it may be anticipated to be small. For thisreason, an experimental phase based on two identical stud shear wall subassemblies,tested under both monotonic and cyclic loading has beendedicated to evaluate the seismic capacity.In this Chapter, the following Section (Section 4.1) is dedicated to definethe study case and the relevant assumptions. In the Section 4.2 the generaldesign principles are presented. The experimental program is illustrated inSection 4.3. In particular, for both monotonic and cyclic tests the descriptionof test specimens, the test set-up and instrumentation are presented in Sections4.3.1 through 4.3.3. While the Section 4.3.4 is devoted to illustrate the testprocedure for the only monotonic test. Finally, the test results for themonotonic test are presented in Section 4.4.

128 Chapter IV4.1 THE STUDY CASE: BASIC ASSUMPTIONSThe study case examined is a typical one-family one-story dwelling as thatshows in Figure 4.1. The plan dimensions of the house are about 7 x 11m,while its height is about 6m. The assumptions on the main dimensions of thestructure are presented in Table 4.1.The structure is a stick-built construction in which both horizontal (roofand floors) and vertical (walls) diaphragms are cold-formed frames sheathedwith structural panels.L=11.4mW=7.0m(a) first floorNW=6.4m(b) east elevationFigure 4.1: Typical analyzed stick-built house.

Evaluation of seismic capacity: the monotonic test 129Number of stories (n) 2Length (L)11.4 mWide (W)7.0 mHeight (H)6.4 mRoof slope 100%Area (A) 75 m 2Table 4.1: Main structural dimension.ElementUnit loadroof 0.75 kN/m 2floor 0.75 kN/m 2walls 0.35 kN/m 2Table 4.2: Unit dead loads.According to the units load reported in Table 4.2, the assumedcharacteristic gravity loads, to be considered for computing the lateral seismicforces, are: dead loads: g k = 2.2 kN/m 2 (including roof, floor and walls); snow loads: q ks = 0.5 kN/m 2 ; live loads: q kl = 2.0 kN/m 2 ;As it may be observed by comparison between dead, snow and live loadvalues, the great advantage of this structural typology is the lightness. In factthe dead loads represent only about 50% of the total load.Therefore, according to rules given in Eurocode 1 – Part 1 (ENV 19911996) for the loads that must be considered acting together with seismic loads,dead and live loads are combined in this way:wk gk EIqks qkl= 3.0 kN/m 2 (4.1)in which:w k :is the seismic weight; EI = 0.3 is the combination coefficient.For the choice of the seismic area, it is assumed that the house is located ina medium seismic zone in Central Italy (design value of the peak groundacceleration a g =0.25g). The soil conditions assumed are, according to

130 Chapter IVclassification of the Eurocode 8 (prEN 1998-1 2001): (A) rock; (B) stiff soil;(C) soft soil; (D) very soft soil; and (E) alluvium soil. Finally, the Type 1 (farfield) design elastic spectrum S aed (T) reported in Eurocode 8 is adopted: T Saed( T ) ag S1 2.5 1 if 0 T T B TBSaed ( T ) ag S 2.5if T B T T C (4.2) TCSaed ( T ) ag S 2. 5 T if T C T T D TCTDSaed ( T ) ag S 2.52 T if T T Dwhere:S aed (T):is the design elastic spectrum acceleration;T: is the first mode vibration period;S: is the soil factor;: is the damping factor (=1 for a damping ratio =0.05)a g :is the design peak ground acceleration;T B and T C : are the limits of constant spectral acceleration branch;T D :is the value that defines the beginning of the constantdisplacement response range.The factors S, T B , T C , and T D , for the horizontal direction are reported inTable 4.3.Soil type S T B T C T DA 1.00 0.15 0.4 2.0B 1.20 0.15 0.5 2.0C 1.15 0.20 0.6 2.0D 1.35 0.20 0.8 2.0E 1.40 0.15 0.5 2.0Table 4.3: Values of parameters describing the Eurocode 8 Type 1 elastic response spectrum.For the purpose of seismic analysis the following hypotheses are adopted: the ground motion acting in North-South direction (see Fig. 4.1); the floor and roof sheathings act as rigid diaphragms; the possible torsional effects are neglected;

Evaluation of seismic capacity: the monotonic test 131the dynamic lateral behavior of the structure is represented by thedynamic lateral behavior of the walls;the “Segment” method is used for describing the shear behavior of theCFSSSWs, assuming that the sum of the length of the full height wallsegments (w i ) in North-South direction is w i =18.0m;the dynamic lateral behavior of the CFSSSWs is described by a SDOFsystem;the acting lateral force corresponding to design seismic action shouldbe less than the force corresponding to the elastic limit state of theCFSSSWs.According to the listed assumptions, it is possible to define basicparameters of the SDOF system representing a piece of wall with unit length(1m). In fact, the seismic weight per unit length (w s ) results:wk Aws = 12.5 kN/m (4.3) wiand, considering the following lateral stiffness per unit length (k) (Gad et al.1999):k = 0.5 – 3.0 kN/mm/m (4.4)it is possible to compute the natural vibration period (T) of the SDOF:ws gT 2/ = 0.1 – 0.3 s (4.5)kFinally, a damping ratio =0.05 is adopted.4.2 GENERAL DESIGN PRINCIPLESThe structure has been designed in accordance with the PrescriptiveMethod For Residential Cold-Formed Steel Framing (NASFA 2000).The wall height of the example house is 2500mm. Studs are made of100x50x10x1.00mm (web depth x flange size x lip size x thickness) C(channel lipped)-section, while joists consist of 260x40x10x1.50mm C-section. The studs and the joists are spaced 600mm on center. The walls aresheathed with 9.0mm thick oriented strand board (OSB) external panels and12.5mm thick gypsum wallboard (GWB) internal panels. The floor sheathings

132 Chapter IVare made of 18.0mm thick OSB panels. The panel-to-wall framingconnections are 4.2x25mm self-drilling flat head screws for the OSB panelsand 3.5x25mm self-drilling bugle head screws for GWB panels.All CFSSSW components (steel members, panels and connections) aredesigned according to capacity design principles, in such a way to promote thedevelopment of the full shear strength of panel-to-wall framing connections.For determining the panel-to-wall framing connections spacing, the lateralforce (v S ) acting on a wall with unit length may by calculated by the followingformula:vS Saed( T ) ws(4.6)in which the weight per unit length is w s =12.5 kN/m (from Eq. 4.3), a g =0.25,=1, and the design elastic spectrum acceleration (S aed (T)) may be obtainedfrom Equation 4.2 for different soil types, as reported in Figure 4.2.Considering the natural vibration period T ranging from 0.1 to 0.3s (accordingto Eq. 4.5), the maximum values of the design elastic spectrum acceleration(S aed (T=0.1-0.3s) max ) and corresponding lateral force values may be obtained,as reported in Table 4.4.Finally, considering the maximum value of the acting lateral force(v S =11kN/m), panel-to-wall framing connections spaced at 150mm at theperimeter and at 300mm in the field may be adopted. In fact, for this fastenerspacing, the estimated lateral strength is about v R =18kN/m, while the forcecorresponding to the elastic limit state is about v E = v R / 1.5 = 12kN/m.All calculations are shown in detail in Appendix C.

Evaluation of seismic capacity: the monotonic test 1331.00.9Saed(T) / g0.8E0.70.60.5CD0.40.30.2AB0.1T [s]0.00.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0Figure 4.2: Eurocode 8 Type 1 elastic spectrum acceleration.Soil type Saed(T=0.1-0.3s) max / g v S (kN/m)A 0.63 7.9B 0.75 9.4C 0.72 9.0D 0.84 10.5E 0.88 11.0max 0.88 11.0Table 4.4: Maximum elastic spectrum acceleration and corresponding lateral force values.4.3 TEST PROGRAMAlthough the existing experimental database is rather wide, there has beenlittle research on the lateral-load transfer from the horizontal diaphragms tostud walls. The same consideration applies for the influence of constructiondetails, such as bearing stiffeners and joist track profiles, anchorage details,connections between joists, bearing stiffeners, joist track and top stud track.Moreover, there has not been specific study on the effect of gravity loads onthe shear walls behaviour even if it may be anticipated to be small.

134 Chapter IVFor this reason, the main part of the experimental program has been basedon two full-scale identical CFSSSW sub-assemblies, tested under bothmonotonic and cyclic loading.4.3.1 Description of test specimensThe generic specimen of the stud shear wall sub-assembly is shown inFigures 4.3 a and b. In particular, Figure 4.3a provides a drawing of thegeneric specimen, while Figure 4.3b shows a picture of its set-up.The sub-assembly is a satisfactory model of the typical lateral loadresisting systems of house structures braced with CFSSSWs and sheathed withstructural panels. Typical construction details are shown in Figures 4.4 and4.5. In particular, Figure 4.4a illustrates a drawing of the detail of thefoundation anchorage of the end studs; besides the installation of the holddownconnector is shown in Figure 4.4b. Figure 4.5 shows, instead, the detailof the connections between floor joists and wall studs.The specimen was designed in accordance with general design principlesgiven in the Section 4.3. In fact, the generic wall framing, which was 2400mmlong and 2500mm height, consisted of single top and bottom tracks made of100x40x1.00mm (web depth x flange size x thickness) U (unlipped)-sectionsand both single intermediate and double back-to-back end studs, made of100x50x10x1.00mm (web depth x flange size x lip size x thickness) C(lipped)-sections, spaced 600mm on center. The floor framing consisted of260x40x10x1.50mm C-section joists, which were spaced 600mm on center,with single span of 2000mm and of 260x40x1.00mm U-section tracks.

Evaluation of seismic capacity: the monotonic test 135(a) Drawing of specimens(b) Set-up of specimensFigure 4.3: Global 3D view of the generic sub-assembly.end studhold-downconnectorhold-downanchorintermediatestudshearanchorstud trackX-bracing(a) Drawing of detail of foundation anchorages(b) installation of a hold down connectorFigure 4.4: A close-up view of the connection between end studs and foundation.joist trackfloor OSBpanelbearingstiffenerstud trackend studjoistX-bracingwallOSB panelwallGWB panelFigure 4.5: A close-up view of the connection between the floor joists and the wall studs.

136 Chapter IVAll frame members were cold-formed and fabricated from FeE350G(S350GD+Z/ZF) hot dipped galvanized (zinc coated) (EN 10142 2002) Gradesteel (nominal yield strength f y =350MPa and nominal tensile strengthf t =420MPa). The used cold-formed steel (CFS) profiles were manufactured bythe Company GUERRASIO (Roccapiemonte, Salerno, Italy). They are shownin Figure 4.6.Wall and floor external sheathings were made of Type 3 oriented strandboard (OSB/3) (EN 300 1997), which were manufactured by the CompanyKRONO FRANCE. The thicknesses of the wall and floor OSB sheathingswere 9.0 and 18.0mm, respectively. The internal sheathings of the wall weremade of 12.5mm thickness gypsum wallboards (GWB) (ISO 6308 1980),which were manufactured by the Company BPB ITALIA. The sheathingorientation was always vertical. Both OSB and GWB sheathings are shown inFigure 4.7 a and b, respectively.The fasteners adopted for the frame (steel-to-steel) connections were4.2x13mm (diameter x length) self-drilling modified-truss head screws. Forthe stud-to-OSB and stud-to-GWB sheathing connections, 4.2x25mm selfdrillingflat head screws and 3.5x25mm self-drilling bugle head screws wereused, respectively. These screws were spaced at 150mm at the perimeter andat 300mm in the field. 4.2x38mm self-drilling flat head screws were adoptedfor joist-to-OSB sheathing connections. The screws, which were used toassemble the specimens, are shown in Figure 4.8. They were manufactured bythe Company TECFI s.r.l. (Villaricca, Naples, Italy).The foundation was simulated by two 280x380mm (depth x width)rectangular concrete beams. The walls were connected to the foundation byintermediate shear anchors and purposely-designed welded steel hold-downconnectors were used at the end studs (see Fig. 4.9). In particular, as shearanchors 8.0mm diameter mechanical anchors were employed (see Fig. 4.10a),while adhesive-bonded anchors were adopted to connect the hold-downconnectors with the foundation (see Fig. 4.10b). Both the used mechanical andadhesive-bonded anchors were manufactured by the Company HILTIITALIA.

Evaluation of seismic capacity: the monotonic test 137(1) (2) (3) (4) (5)(1) bearing stiffener; (2) stud; (3) stud track;(4) joist; (5) joist track.Figure 4.6: CFS profiles (manufactured by GUERRASIO).(2)(1)(a) (1) OSB wall sheathing; (2) OSB floor sheathingmanufactured by KRONO FRANCE(b) GWB sheathing manifactured by BPB ITALIAFigure 4.7: Sheathings.(1) (2) (3) (4)(1) 3.5x25mm bugle head; (2) 4.2x32mm flat head; (3)4.2x25mm flat head; (4) 4.2x13mm modified truss head.Figure 4.8: Self-drilling screws (manufactured by TECFI s.r.l.).

138 Chapter IVFigure 4.9: Hold-down connector.(1)(2)HST M8 mechanical anchorsAdhesive-bonded anchors(1) HIT-RE 500; (2) HIS-N(8.8) M20 3.5x25mm bugle head.Figure 4.10: (a) shear and (b) hold-down anchors (manufactured by HILTI ITALIA).All the components of the stud shear wall sub-assembly (members,sheathings and connections) have been designed according to capacity designprinciples, in such a way to promote the development of the full shear strengthof sheathing-to-wall framing connections. For this reason, the shear anchorsand the hold-down connectors have been designed to prevent either shearfailure at the base of the walls or failure due to overturning. Besides, doublelipped C-sections at the ends of the walls have been adopted to avoid failuredue to buckling in end studs.

Evaluation of seismic capacity: the monotonic test 139Global transverse stability of the sub-assembly was achieved by means ofpre-tensioned steel round bar X-bracing (see Figures 4.3a, 4.4a and 4.5).Main details of the specimen components are given in Table 4.5, whereasdrawings of the main construction details of the sub-assembly specimen arereported in Appendix D.Cold formed steel (CFS) membersFeE350G (S350GD+Z/ZF) hot dipped galvanized (zinc coated) steelSteel grade(Nominal yield strength f y =350MPa; nominal tensile strength f t =420MPa)StudsC 100x50x10x1.00mm (2400mm long) (by GUERRASIO)Wall membersTracksU 100x40x1.00mm (2700mm long) (by GUERRASIO)JoistC 260x40x10x1.50mm (2200mm long) (by GUERRASIO)FloortracksU 260x40x1.00mm (2700mm long) (by GUERRASIO)membersBearing stiffeners C 100x50x10x1.00mm (260mm long) (by GUERRASIO)Sheathings1200x2500x12.5mm (width x height x thickness) GWB vertically orientedInteriorWall(PLACOLAST PLACO by BPB ITALIA)sheathings1250x2500x9.0mm Type 3 OSB vertically oriented (KRONOPLY 3 byExteriorKRONO FRANCE)1250x2500x18.0mm Type 3 OSB vertically oriented (KRONOPLY 3 byFloor sheathingKRONO FRANCE)Concrete beams foundationConcrete type C20/25 (characteristic strength on a cube 150x150x150mm f ck,cube =25MPa)Dimensions 380x280mm rectangular section (3590mm long)Frame-to-foundation connectionsHold-downPurposely-designed welded steel hold-downconnectorHold-down anchors HIT-RE 500 with HIS-N(8.8) M20 adhesive-bonded anchors (by HILTI ITALIA)Shear anchors HST M8 mechanical anchors (by HILTI ITALIA) spaced at 100mmSteel-to-steel connections4.2x13mm (diameter x lenght) modified truss head self drilling screws (byCFS membersTECFI s.r.l.)CFS members-to-hold6mm diameter boltsdown connectorSteel-to-Sheathing connections3.5x25mm bugle head self drilling screws (by TECFI s.r.l.) spaced atInterior150mm at the perimeter and at 300mm in the fieldWalls4.2x25mm flat head self drilling screws (by TECFI s.r.l.) spaced at 150mmExteriorat the perimeter and at 300mm in the field4.2x32mm flat head self drilling screws (by TECFI s.r.l.) spaced at 150mmFloorfor sheathing-to-track connections and at 250mm for sheathing-to-joistconnectionsTable 4.5: Full-scale specimen materials and construction data.

140 Chapter IV4.3.2 Test set-upTwo types of load were applied: gravity and racking loads.The CFSSSW sub-assembly simulated a section of a rectangular house withplan dimension equal to a x b = 3.6x4.2m. The applied total gravity load wasequal to 45kN. This load was equivalent to dead (including roof, floor andwalls), snow and live loads applied to the plan area, it being: w k x a x b =3.0x3.6x4.2=45kN, where w k is the seismic weight (see Eq. 4.1).Racking loads were uniformly applied to the floor by means of twoprogrammable servo-hydraulic actuators (MTS System Corporation), each onecharacterised by a range of displacement of 500mm and a load capacity of500kN. The concentrated actuators’ loads were transformed into a distributedload applied to the floor panels by means of a purposely-designed loadtransfer system that is shown in Figure 4.11. It consisted of transversal andlongitudinal hot rolled members. In particular, four CPN100 transversalprofiles were positioned over the floor sheathings, while the transversalmembers placed lower down the floor sheathings were two CNP100 (externalprofiles) and two flat straps (internal profiles). The upper and bottomtransversal members were bolted back-to-back using two 8.0mm diameterbolts spaced at 250mm on center. In such a way the transversal profile and thefloor sheathings were closely connected together. As longitudinal membersfour HEA100 (two for each side) profiles were used. These profiles werebolted with the transversal profile using four 14mm diameter bolts for eachjoint, as illustrated in Figure 4.11.The load actuators were restrained to keep the horizontal position and asliding-hinge is placed between the load actuator and the ends part of thelongitudinal members, in order to act as a filter transferring to the structureexclusively horizontal racking loads. This testing apparatus allowed thecapacity of the floor to transmit forces to the walls to be checked, up to failureof the vertical stud-to-sheathing connections. The Figure 4.12 shows theglobal view of the test set-up.

Evaluation of seismic capacity: the monotonic test 141HEA100CNP100No. 2 - 8mmdiameter boltsspaced at 250mmon centerNo. 4 -14mmdiameterboltsHEA100CNP100Flat strap100x6mmFigure 4.11: Load transfer system.

142 Chapter IVFigure 4.12: Test set-up.4.3.3 InstrumentationFourteen linear variable differential transducers (LVDTs) were used tomeasure displacements of the specimens during the tests, as shown in Figures4.13 a and b. In particular, five LVDTs were installed for each wall (Fig.4.13a): LVDTs w1 was used to measure the horizontal displacements at thetop of the wall (lateral in-plane displacement); LVDTs w2 and w3 measuredthe horizontal displacements at the bottom of the wall (lateral in-planesliding); LVDTs w4 and w5 measured the vertical displacements at the bottomof the wall (uplift and compression). One LVDT (f1) was installed for eachfoundation beam (Fig. 4.13a) to measure the horizontal displacement. Finally,two LVDTs (d1 and d2) were installed on the floor (Fig. 4.13b) to measure thelateral longitudinal displacements.The horizontal displacements of the floor (d1 and d2) and walls (w1, w2and w3) were measured using LVDTs with a range of displacement of 250mmand an accuracy of 0.02mm. For measuring the horizontal displacements ofthe foundations (f1 and f2) LVDTs with a range of displacement of 100mm

Evaluation of seismic capacity: the monotonic test 143and an accuracy of 0.01mm were used. Finally, the vertical displacements ofthe walls (w4 and w5) were measured using LVDTs with a range ofdisplacement of 20mm and an accuracy of 0.01mm. All LVDTs used for thistesting program were Penny & Giles Controls.Only for a wall (wall 2), two clinometers with a range of measuring of 20°and an accuracy of 0.02° (i1 and i2) were used to measure the angle betweenthe end studs at the bottom of the wall and the horizontal plane.The load was measured through the actuator load cells.Data was acquired at 20Hz (one data point every 0.05 seconds).aw1a2Wall 2d2w4w5w2i1(a) Wallsactuator load (No. 2)LVDT (No. 14)inclinometer (No. 2)i2w3f1a1Wall 1(b) Floord1Figure 4.13: Instrument arrangement.4.3.4 Test procedure for the monotonic testIn the monotonic loading regime, the specimen was subjected to progressivehorizontal deflection. In particular, the loading procedure for the monotonictest was articulated in two phases.In the first phase, to evaluate the permanent set at 2, 4, 6 and 10mm, thespecimen were unloaded at these displacements. In the second phase, thespecimen was loaded up to a displacement of 150mm without unloaded. Thistest protocol involved displacements at rate of 0.10mm/s for displacementsless than 10mm and at rate of 0.20mm/s for displacement exceeded 10mm.

144 Chapter IV4.4 TEST RESULTSThe measured responses of all instruments are reported in Appendix E.The global behavior of the CFSSSW sub-assembly under monotonicracking loads may be represented through the relationship between themeasured unit shear resistance (v) and the mean displacement (d) of thespecimen. In particular, the value of v and d are defined as:V1 V2v (4.7)L td 1 dd 2(4.8)2where:V 1 and V 2 : are the forces measured by the actuators a1 and a2, respectively;d 1 and d 2 : are the displacements measured by the actuators a1 and a2,respectively;L t =4.800m: is the total length of the walls.The v-d response curve is showed in Figure 4.14.In the same Figure the values of the experimental lateral strength(v EXP =18.5kN/m), estimated lateral strength (v R =17.9kN/m) and acting seismicforce (v S =11.0kN/m) are also reported. From the comparison between theexperimental and the estimate lateral strength, it is possible to observe that thecalculation of the shear strength using the semi-empirical methodologiesillustrated in the Chapter 2 (developed in detail in Appendix C for the studycase) appears to be valid, it revealing a small conservative prediction of 3%.

Evaluation of seismic capacity: the monotonic test 1452Experimental lateral strength (v EXP = 18.5kN/m)Estimate lateral strength (v R = 17.9kN/m)1Acting seismic force (v S = 11.0kN/m)34Figure 4.14: Unit shear resistance (v) vs. mean displacement (d) curve.In Figure 4.14 the following significant load steps are represented: Step 1: lateral displacement equal to 10mm. At this step, in OSBsheathings-to-frame connections the tilting of the screws about theplane of the stud flange started, while for the GWB sheathings-toframeconnections the bearing of the GWB panels begun. At thisdisplacement level, the deformations of walls as well as the localdeformation of the sheathing-to-frame connections were not evident,as shown in Figure 4.15. Step 2: maximum shear resistance (lateral displacement equal to36mm). At this load step the tilting of the screws in the OSBconnections, as well as the bearing in the GWB panels were evident, asshown in Figures 4.16 b and c, respectively. Also the globaldeformation of walls was clearly observable, as shown in Figure 4.16a. Step 3: lateral displacement equal to 80mm. At this displacement level,in both the OSB and GWB-to-frame connections the screw headsinitiated to pull through the sheathings, as shown in Figures 4.17 c andd. At this point, due to the rotation of the sheathings, the upper sides of

146 Chapter IVthe GWB panels knocked against the joist, as shown in Figure 4.17b.Probably this phenomenon produced a residual shear resistance(constant shear force for displacement varying from 70 to 110mm).Step 4: lateral displacement equal to 130mm. At this step, the screwheads had completely pulled through the sheathings, as shown inFigures 4.18 c and d. As a consequence, the sheathings werecompletely unzipped along the panel edges, as shown in Figure 4.18b.(a) Deformation of the Wall(b) Deformation of the OSB connections(c) Deformation of the GWB connectionsFigure 4.15: Specimen condition at Step 1(d=10mm).For all displacement levels, the evolution of the deformation of thespecimen was coherent with the sheathing-to-wall framing connectionsfailure. In fact, wall framing deformed into a parallelogram and the sheathingshad rigid body rotation, as shown in Figures 4.15a, 4.16a, 4.17a and 4.18a.Moreover, any buckling phenomenon was not observed for the studs as wellas deformations of the OSB sheathing-to-floor framing connections were notobserved during the testing. On the contrary, for floor tracks, a local bucklingphenomenon occurred for lateral displacement larger than about 30mm.

Evaluation of seismic capacity: the monotonic test 147Finally, both the shear and the tension anchors did not suffer any type offailure.(a) Deformation of the wall(b) Deformation of the OSB connections(c) Deformation of the GWB connectionsFigure 4.16: Specimen condition at Step 2 (maximum shear resistance - d=36mm).

148 Chapter IV(a) Deformation of the wall(b) GWB panel-to-joist contact(c) Deformation of the OSB connections(d) Deformation of the GWB connectionsFigure 4.17: Specimen condition at Step 3 (d=80mm).

Evaluation of seismic capacity: the monotonic test 149(a) Deformation of the wall(b) Unzipping(c) Deformation of the OSB connections(d) Deformation of the GWB connectionsFigure 4.18: Specimen condition at Step 4 (d=130mm).

150 Chapter IVThe Figure 4.19 shows the force (V) vs. displacement (d) response curvesfor the two tested walls. In particular, force vs. displacement curves obtainedfrom measures of the actuators a1 and a2 have been reported for the walls 1and 2, respectively. From the comparison of lateral responses of two wallssome interesting observations are possible:the walls had the same behavior for displacements less than about30mm (displacement for which the applied load approached themaximum shear resistance), while they exhibited different response forlarger displacements; the maximum shear resistances were 47 and 44kN for wall 1 and 2,respectively; therefore, the wall 1 was more resistant than wall 2 ofabout 7%.The measure of all horizontal LVDTs placed on the specimen in terms offorce vs. horizontal displacement relationships are illustrated in Figures 4.20 aand b. In particular, the Figure 4.20a shows the force measured from theactuator a1 as a function of the displacements recorded by the LVDTs locatedon the side of the wall 1 (LVDTs a1; d1; w1,1; w1,2; w1,3 and f1), while theforce measured from the actuator a2 as a function of the displacementsrecorded by the LVDTs located on side of the wall 2 (LVDTs a2; d2; w2,1;w2,2; w2,3; f2) are shown in Figure 4.20b. From the examination of theseFigures, for both walls it is possible to observe that: the anchorage between the beam foundations of the specimen and thelaboratory floor was full effective; in fact the displacements measuredby LVDTs f1 and f2 were slight (displacements less than 0.2mm); the load transfer system between the load actuators and the floor of thespecimen was effective; in fact the difference between thedisplacements recorded by actuators (a1 and a2) and those measuredby the LVDTs placed on the floor (d1 and d2) were slight(displacements less than 0.9mm); the load transfer system between the floor and the walls was effective;in fact, the floor-to-walls sliding was small; in particular, thedifference between the displacements measured by the LVDTs placedon the floor (d1 and d2) and those recorded by the LVDTs located onthe top side of the walls (w1,1 and w2,1) were less than 4mm.

Evaluation of seismic capacity: the monotonic test 151Figures 4.21 a and b show the forces measured from the actuators (a1 anda2 for Figures 4.21a and b, respectively) as a function of the verticaldisplacements recorded by the LVDTs located at the bottom side of the walls(w1,4; w1,5 and w2,4; w2,5 for Figures 4.21a and b, respectively). From theexamination of these curves, for both walls it is possible to observe that thevertical displacements measured on the tension side were larger than thoserecorded on the compression side. In particular, this behavior was moreevident for displacements less than those corresponding to the maximum shearresistance.Figure 4.19: Shear (V) vs. displacement (d) curves for wall 1 and wall 2.(a) wall 1 (b) wall 2Figure 4.20: Shear (V) vs. displacement (d) measured by horizontal LVDTs.

152 Chapter IV(a) wall 1(b) wall 2Figure 4.21: Shear (V) vs. displacement (d) measured by vertical LVDTs.4.5 REFERENCESEN 300 (1997) Oriented Strand Boards (OSB) - Definitions, Classification andSpecifications. CEN (European Committee for Standardization). Bruxelles.ENV 1991-1 (1996) Eurocode 1: Basis of Design and Actions on Structures – Part 1:Basis of Design. CEN (European Committee for Standardization). Bruxelles.EN 10142 (2002) Continuously hot-dip zinc coated low carbon steel sheet and stripfor cold forming. Technical delivery conditions. CEN (European Committee forStandardization). Bruxelles.Gad, E.F., Duffield, C.F., Hutchinson, G.L., Mansell, D.S., Stark, G. (1999) Lateralperformance of cold-formed steel-framed domestic structures. EngineeringStructures, Elsevier, Vol.21, No.1: 83-95.ISO (1980) Gypsum plasterboard – Specification. ISO (International Organization forStandardization). Geneva.NASFA (2000) Prescriptive Method For Residential Cold-Formed Steel Framing(Year 2000 Edition). NASFA (North American Steel Framing Alliance). Lexington,KY, USA.prEN 1998-1 (2001) Eurocode 8: Design of structures for earthquake resistance –Part 1: General rules – Seismic actions and rules for buildings. CEN (EuropeanCommittee for Standardization). Bruxelles.

153Chapter VEvaluation of seismic demandsAn experiment can provide only information on capacities, but, because ofthe strong interrelation between capacity and demand, due consideration mustbe given to seismic demand issues. This requires some significant problems tobe preliminarily solved: the development of reliable mathematical models of the hysteresisbehaviour of panel shear walls typical of light-gauge cold-formedframed constructions; the assessment of deformation demands under a sufficiently largedatabase of earthquake ground motions is needed.The need to carry out this type of statistical-numerical analysis derivesfrom the peculiar hysteresis behaviour of cold-formed steel stud shear wall(CFSSSW) systems, which are characterized by strong pinching and reducedductility. In fact, commonly performed studies on the evaluation of seismicdemand have been derived on the basis of a bilinear hysteresis assumption. Inthis Chapter, the calibration of a mathematical model, able to well interpretingthe hysteretic behavior of CFSSSWs’s response, is illustrated in Section 5.1.The evaluation of the seismic demand using the calibrated mathematicalmodel and some accelerograms of Central Italian earthquakes is presented theSection 5.2. Finally, because the applicability of the standard load histories toCFSSSW systems need to be verified, Section 5.3 is dedicated to define adeformation history for a cyclic testing.

154 Chapter V5.1 MODEL OF THE HYSTERETIC BEHAVIOR OF CFSSSWSYSTEMSOn the basis of experimental evidence of existing tests on CFSSSWsystems, a mathematical model, able to well interpret several behavioralaspects of their response, has been used (Della Corte et al. 1999). Inparticular, the proposed model is able to account for the following aspects ofthe mechanical cyclic behavior: non linearity; pinching.In the following, the mathematical formulation of the used model is firstlydescribed. Then, model parameters are calibrated for the simulation of someavailable experimental tests. The comparison between numerical andexperimental results shows the reliability of the model in capturing the stablepart of the hysteretic behavior. A this stage of the research the model is unableto describe the unstable part of the cyclic response.For describing the shear behavior of CFSSSWs, the relationship betweenshear force (V) and lateral displacement () is used.It is appropriate to preliminarily state some fundamental concepts,extensively used in the following. The basic parameter for the description of ageneric loading history is the deformation excursion, which is constituted by aloading branch and by the subsequent unloading branch of the V- path. Thedeformation range of excursion ( p ) is the deformation range between thebeginning and the peak deformation of the excursion (ATC 1992). As it willbe explained herein after, the beginning of a loading branch and the end of anunloading branch, always stand on a straight line passing through the originwith a slope equal to the one concerned with the hardening of the system, asshown in Figure 5.1.The adopted mathematical function for describing the shear behavior ofCFSSSWs is introduced in two steps. In fact, the mathematical formulation isfirstly referred to systems without pinching effect. Then, pinching phenomenatypically present in the lateral behavior of these structures are introduced.

Evaluation of seismic demands 155Figure 5.1: Basic definitions (Della Corte et al. 1999).5.1.1 The loading branch without pinchingFor the description of the loading branch in absence of pinching, amathematical formulation proposed by Richard & Abbott (1975) has beenadopted. This formulation, expressed in terms of shear force (V) versus lateraldisplacement () relationship, can be written as follows:k0 khV kh(5.1)1n nk0kh1 V0 where:k 0 : is the initial stiffness of the system;k h : is the slope of the straight-line asymptote of the V- curve(hardening line);V 0 : is the intersection between V axis and hardening line;n: is a shape parameter, which regulates the sharpness of transitionfrom the elastic to the fully plastic behavior (increasing values of ncorrespond to an increasing sharpness).

156 Chapter VFigure 5.2 illustrates the graphical representation of the Richard-Abbottmathematical formulation, also reporting the meaning of adopted symbols.Besides to the parameters previously specified, the conventional yield andultimate limits need to be specified. In particular, the conventional yieldstrength is defined as the intersection between the straight-line with a slopeequal to k 0 going through the origin and the hardening line. The conventionalultimate strength is defined as the point corresponding to the maximum valueof the shear force (limit of the stable part of the hysteretic behavior).Consequently it is possible to define the shear force (V y ) and displacement ( y )corresponding to the conventional yield point and the ultimate force (V u ) anddisplacement ( u ) corresponding to the conventional ultimate point, as shownin Figure 5.2.Numerical upper bound curveExperimental responseFigure 5.2: The loading branch without pinching.5.1.2 The loading branch with pinchingFor describing pinching, two limit curves are introduced, representing anupper bound and a lower bound to possible V- values, respectively. Bothcurves have a Richard-Abbot type law, with the following parameters:k 0 , V 0 , k h , n for the upper bound curve;

Evaluation of seismic demands 157k 0p , V 0p , k hp , n pfor the lower bound curve.A point (V, ) of the real path is considered to belong also to a Richard-Abbott type curve, whose, parameters are defined as follows:k k k k t(5.2)Vkn0t 0 p 00 p0t V0p V0V0phtpt t(5.3) k k k t(5.4)hphhp n n n t(5.5)pwhere the parameter t, ranging in [0, 1], defines the transition law from thelower bound to the upper bound curve. Its mathematical formulation is to bedefined in such a way to reproduce the shape of the curve as experimentallyobserved. In the proposed model, in order to describe a pinching-typebehavior, parameter t is defined by the following relationship:2 / limt (5.6) / limin which, t 1 , t 2 and lim are three additional parameters to be defined on thebasis of experimental data. Figure 5.3 illustrates, qualitatively, the descriptionof pinching with reference to one single excursion from the origin.tt1pt1 1 Figure 5.3: The loading branch without pinching (Della Corte et al. 1999).

158 Chapter VIn case of a generic deformation history, the parameter lim must be relatedto the maximum experienced deformation in the direction of the loadingbranch being described. Therefore, it could be evaluated through theparameter , defined by the following relationship: (5.7)limwhere:0: is the absolute value of the deformation corresponding to thestarting point of the current excursion; max : is the maximum absolute value of deformation experienced, in allprevious loading history, in the direction of loading branch to bedescribed (Figure 5.4).5.1.3 The unloading branchThe unloading-branch is assumed to be linear with a slope equal to theinitial stiffness k 0 up to the intersection with the straight line obtained drawingthe parallel to the hardening line going through the origin, as showed in Figure5.5. This allows the Bauschinger effect to be considered.0maxFigure 5.4: The loading branch without pinching (Della Corte et al. 1999).

Evaluation of seismic demands 159Figure 5.5: The unloading branch (Della Corte et al. 1999).5.1.4 Calibration of the modelIn order to investigate on the capability of the illustrated model forinterpreting the stable part of the hysteretic behavior of CFSSSWs, the valuesof upper bound curve (k 0 , V 0 , k h , n), lower bound curve (k 0p , V 0p , k hp , n p ) andtransition (t 1 , t 2 , ) parameters need to be evaluated. Besides to theexperimental results obtained with the monotonic tests carried out in thisresearch, other existing experimental cyclic tests have been considered. Inparticular, monotonic and cyclic test results have been used to evaluate upperbound curve and transition parameters, respectively. While, the results of bothmonotonic and cyclic tests have been used to estimate the lower bound curveparameters.All existing selected experimental cyclic tests were tests performed onCFSSSWs similar to those tested in the current research. In fact, theconsidered walls were sheathed with oriented strand board (OSB) panels andhad panel-to-wall framing connections spaced at about 150mm at theperimeter and at about 300mm in the field. In particular, the selected tests arelisted hereafter: S+96ab-1(OSB1): AISI OSB1 – Serrette et al. (1996a,b); S+96ab-1(OSB2): AISI OSB2 – Serrette et al. (1996a,b); S+97b-18(E1): AISI E1 – Serrette et al. (1997b); S+97b-18(E2): AISI E2 – Serrette et al. (1997b); C01-4(A): 17A - COLA–UCI (2001).

160 Chapter VA summary of the geometry and material data of specimens is given inTable 5.1.All tests have been performed with fully reversing cyclic displacementsfollowing the TCCMAR (Technical Coordinating Committee for MasonryResearch) sequentially phased displacement procedure, suggested by theStructural Engineers Association of South California (SEAOSC 1997).The TCCMAR procedure uses the concept of the first major event (FME),which is defined as the first significant limit state that occurs during the test.In case of CFSSSWs the FME is defined as the yield limit state (YLS). TheFME can be determined from preliminary load tests on an identical testspecimen.S+96ab-1S+97b-18(OSB1) and (OSB2)(E1) and (E2)C01-4 (A)Type of loading Cyclic Cyclic CyclicWall size (1) 2440 x 1220 2440 x 610 2440 x 2440Aspect ratio (2) 2.00 4.00 1.00Openings No openings No openings No openingsSteel grade (3) A653 Grade SQ 33 A653 Grade SQ 33 A446 Grade AStuds (4) C 89x41x10x0.84/610 C 89x43x13x0.84/610 C 89x41x10x0.84/610Tracks (5) U 89x32x0.84 U 89x32x0.84 U 89x38x0.84Frame screws (6) 4.2x13 wafer-head 4.2x13 mod. truss head 4.2x13 mod. truss headSheathings (7) 11.1mm tick OSB 11.1mm tick OSB 11.1mm tick OSBSheathing fasteners (6) 4.2x25 flat head 4.2x25 flat head 4.2x25 bugle headSpacing sheathingfasteners (8)152/305 152/305 152/305Type of anchorage Tie hold-down Hold-down Strip hold-down(1) height x length (mm)(2) height / length(3) A653 Grade SQ 33: Yield strength = 228 MPa, Ultimate tensile strength = 311 MPa(3) A446 Grade A: Yield strength = 228 MPa, Ultimate tensile strength = 311 MPa(4) C: lipped channel section web depth x flange size x lip size x thickness / spacing (mm)(4) Double back-to-back coupled studs were employed at ends of walls(5) U: unlipped channel section web depth x flange size x thickness (mm)(6) diameter x length (mm)(7) 610 x 2440 mm panel size(8) perimeter/field (mm)Table 5.1: Wall geometry and material data.The TCCMAR procedure consists of applying three cycles of fullyreversing, displacement-controlled load at each wall displacement incrementrepresenting 25%, 50%, and 75% of the FME displacement. Then, the walldisplacement is increased for one load cycle to 100% of the FMEdisplacement. Next, cycles of displacement for one cycle each at 75%, 50%,

Evaluation of seismic demands 161and 25% of the maximum displacement (100% of the FME displacement) areapplied. This is followed by three cycles of displacement at maximumdisplacement (100% of the FME displacement) to stabilize the loaddisplacementresponse of the wall. Then, the next increment of increaseddisplacement (125% of the FME displacement) is applied, followed by similarstabilization cycles of loading. This incremental cyclic load-displacementsequence is continued to 150%, 175%, 200%, 250%, 300% of the FMEdisplacement, or until the wall exhibits greatly diminished shear load capacity.The test protocols used for the selected tests are illustrated in Table 5.2 andFigure 5.6. Figure 5.7 shows the results of the selected tests in terms of shearforce (V) versus lateral displacement () curves.The results of the calibration of the model in terms of lower bound curveand transition parameters obtained on the basis of Serrette and COLA-UCItests are shown in Table 5.3 for a wall with a length of 1m (wall with unitlength). Figure 5.8 shows the comparison between the experimental responseand the numerical one for the C01-4(A) specimen. In particular, in Table 5.3are reported the values of transition parameters (t 1 , t 2 , ) together to values ofthe ratios between the lower and upper bound curve parameters ((k 0p /k 0 ) c ,(V 0p /V 0 ) c , (k hp /k h ) c , (n p /n) c ).The comparison between the experimental monotonic response and thenumerical one are illustrated in Figure 5.9.The results of the calibration of the model in terms of upper and lowerbound curve parameters obtained on the basis of the monotonic test are shownin Table 5.4. The values of the lower bound curve parameters have beencalculated starting from the ratios between the lower and upper bound curveparameters ((k 0p /k 0 ) c , (V 0p /V 0 ) c , (k hp /k h ) c , (n p /n) c ), which have been previouslyderived from existing cyclic tests and the values of upper bound curveparameters calibrated on monotonic test results (k 0 , V 0 , k h , n). In particular, thefollowing assumptions have been used:k0 p k0 p/ k0 k0(5.8)V0 pV0 c 0khpkh kc hnn ncV0 / V(5.9)knphpp / (5.10) / (5.11)pc

162 Chapter VS+96ab-1S+97b-18(OSB1) and (OSB2)(E1) and (E2)C01-4 (A)No. of cycles Displ. (mm) No. of cycles Displ. (mm) No. of cycles Displ. (mm)3 5.1 3 5.1 3 5.73 10.2 3 10.2 3 11.53 15.2 3 15.2 3 17.21 20.3 3 20.3 1 22.91 15.2 1 25.4 1 17.21 10.2 1 19.1 1 11.51 5.1 1 12.7 1 5.73 20.3 1 6.4 3 22.91 25.4 3 25.4 1 28.61 19.1 1 30.5 1 21.51 12.7 1 22.9 1 14.31 6.4 1 15.2 1 7.23 25.4 1 7.6 3 28.61 30.5 3 30.5 1 34.41 22.9 1 40.6 1 25.81 15.2 1 30.5 1 17.21 7.6 1 20.3 1 8.63 30.5 1 10.2 3 34.41 40.6 3 40.6 1 40.11 30.5 1 50.8 1 30.11 20.3 1 38.1 1 20.01 10.2 1 25.4 1 10.03 40.6 1 12.7 3 40.11 50.8 3 50.8 1 45.81 38.1 1 61.0 1 34.41 25.4 1 45.7 1 22.91 12.7 1 30.48 1 11.53 50.8 1 15.24 3 45.81 61.0 3 61.0 1 57.31 45.7 1 71.1 1 42.91 30.5 1 53.3 1 28.61 15.2 1 35.6 1 14.33 61.0 1 17.8 3 57.31 71.1 3 71.1 1 68.71 53.3 1 51.51 35.6 1 34.41 17.8 1 17.23 71.1 3 68.71 80.21 60.11 40.11 20.03 80.21 91.61 68.71 45.81 22.93 91.6Table 5.2: Cyclic test protocols.

Evaluation of seismic demands 16310080604020displacement(mm)Cyclic frequency = 0.67Hz00-205 10 15 20 25 30 35 40 45 50 55-40-60-80-10010080604020S+96ab-1(OSB1) and (OSB2)displacement(mm)Cyclic frequency = 1.00Hztime (s)00-205 10 15 20 25 30 35 40 45 50 55-40-60-80-10010080604020S+97b-18(E1) and (E2)displacement(mm)time (s)Cyclic frequency =0.25Hz for dispacements 40.6mm0.50Hz for dispacements > 40.6mm00-205 10 15 20 25 30 35 40 45 50 55-40-60-80-100C01-4 (A)time (s)Figure 5.6: Cyclic test protocols.

164 Chapter VS+96ab-1 (OSB1)S+96ab-1 (OSB2)S+97b-18 (E1)S+97b-18 (E2)C01-4 (A)TestAverage of maximum+/- loadDispl. at averageof maximum +/-loadS+96ab-1 (OSB1) 685 lb/ft. (10.0 kN/m) 1.8 in. (46 mm)S+96ab-1 (OSB2) 758 lb/ft. (11.1 kN/m) 1.8 in. (46 mm)S+97b-18 (E1) 700 lb/ft. (10.2 kN/m) 2.8 in. (71 mm)S+97b-18 (E2) 700 lb/ft. (10.2 kN/m) 2.8 in. (71 mm)C01-4 (A) 773 lb/ft. (11.3 kN/m) 1.5 in. (38 mm)Figure 5.7: Cyclic response.Experimental responseNumerical responseFigure 5.8: Numerical vs. experimental cyclic response for the C01-4(A) specimen.

Evaluation of seismic demands 165ParameterS+96ab-1 S+96ab-1 S+97b-18 S+97b-18Assumed Dev.C01-4(A) Mean(OSB1) (OSB2) (E1) (E2)values St.(k 0p / k 0 ) c 0.92 0.99 1.09 1.08 0.96 1.00 1.00 0.61(V 0p / V 0 ) c 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.05(k hp / k h ) c 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00(n p / n) c 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00t 1 [-] 8 10 10 10 12 10 10 1.4t 2 [-] 0.50 0.40 0.50 0.60 0.50 0.50 0.50 0.07 [-] 1.20 1.00 0.50 0.50 0.50 0.75 0.75 0.34Table 5.3: Results of calibration of lower bound curve and transition parameters obtained onthe basis of existing cyclic tests (values for a 1m long wall).Parameter Monotonic test Assumed valuesk 0 [kN/mm] 2.80 2.80V 0 [kN] 16 16k h [kN/mm] 0.11 0.11n [-] 1.2 1.2k 0p [kN/mm] 1.00 x 2.80 = 2.80V 0p [kN] 0.01 x 16 = 0.16k hp [kN/mm] 0.00 x 0.11 = 0.00n p [-] 1.00 x 1.2 = 1.2V y [kN] 17 17 y [mm] 6.0 6.0V u [kN] 19 19 u [mm] 36 36Table 5.4: Results of calibration of upper and lower bound curve parameters obtained on thebasis of monotonic tests carried-out in the current research (values for a 1m long wall).25V (KN/m)20Vu"Numerical upper bound curve""Experimental monotonic response"Serie315Vy105 (mm)0yu0 5 10 15 20 25 30 35 40Figure 5.9: Numerical vs. experimental monotonic response.

166 Chapter V5.2 ASSESSMENT OF DEFORMATION DEMANDOne single test of a seismic-resistant component or sub-assembly mustrepresent a compromise between the need to correctly characterize the specificstructural component subject to a specific deformation history and therequirement to obtain general conclusions applicable to the same componentwith different loading regimes. The only way to fully achieve this compromiseis to analytically study the probable deformation histories the componentwould be subjected to. This characterization requires at least the evaluation ofthe following demand parameters: maximum level of deformation experienced by the structure; number of repetition of several discrete values of ductility demands; cumulative plastic deformation engagement of the structure; distribution of plastic deformation ranges.It is well known that the loading histories produced by different groundmotions on a given structure are significantly scattered, consequently, theestimation of the deformation demand will be carried out under a sufficientlylarge data-base of earthquake ground motions.5.2.1 Data-base of considered earthquake ground motionsThe selected earthquakes include 26 far field records from Central Italy.The considered geographic region (zone in which are located the recordingstations) is identified as medium-high seismic zone by the Italian seismicdesign code (Ordinanza PCM 2003). In fact, the value of the design peakground acceleration of the seismic zone (PGA zone ), having a 10% probabilityof exceedance in 50 years, is 0.25g. Consequently, a value of the design peakground acceleration (PGA des ) equal to 0.25g it has been adopted.The considered earthquakes are the “Lazio-Abruzzo” earthquake, occurredon March, 7 th 1984 at 17h49m; the “Umbro-Marchigiano” earthquake,occurred on September 1997, 26 th at 00h33m; and the “Umbro-Marchigiano”earthquake, occurred on September 1997, 26 th at 09h40m. For theseearthquakes the Richter magnitude ranges from 5.6 to 5.8, the focal depthranges from 6 to 8km, and the source mechanism is of normal type.

Evaluation of seismic demands 167The earthquake records have been chosen to cover, whenever possible, allthe soil types classified by Eurocode 8 (prEN 1998-1 2001). In particular, foreach soil type, three accelerograms have been selected in such a way that theshape of the average elastic response spectrum of these records is close to theshape of the Eurocode 8 Type 1 elastic spectrum acceleration (with a dampingratio of 0.05). For the accelerograms selected according to these assumptionsthe recorded peak ground acceleration (PGA rec ) value range from 0.01 to0.76g, the distance between the epicentre and the recording station rangesfrom 11 to 100km, and the record length ranges from 14 to 60s.Earthquakes, recording stations and waveform parameters of consideredrecords are reported in Table 5.5. For each station, Table 5.5 also shows thedesign ground acceleration according to the Italian seismic design code(PGA zone ). In the same Table, a label has been defined for each earthquakerecord. As example, the label “UM-B-1” refers to a recording of the “Umbro-Marchigiano” (UM), which has been carried out on B soil type (B).The geographical localization of the epicenter of the selected strongmotions and of the recording stations is presented in Figure 5.10.In Figures 5.11 a, b, c, d, and e comparisons between the elastic responsespectra (S ae (T,=0.05)) of the selected records scaled to a design value of theground acceleration equal to its design peak ground value(PGA=PGA des =0.25g) and the design elastic spectral acceleration(S aed (T,=0.05)) defined by Eurocode 8 for soil type A, B, C, D, and E,respectively, are reported.

168 Chapter VEarthquake nameDate and timeRichter MagnitudeFocal depthFault mechanismRecordlabelStation name (orientation)PGA zone / g PGA rec / gRecordlength[s]Epicentraldistance[km]LA-A-01 Ponte Corvo(N-S) 0.25 0.064 32.441 31 -LA-A-02 Roccamonfina (N-S) 0.25 0.036 22.740 50 -LA-A-03 Bussi (E-W) 0.25 0.019 25.000 51 -Faultdistance Soil type[km]Rock(A)Lazio Abruzzo1984/05/07 - 17:49:435.78 kmNormalLA-B-01 Ripa-Fagnano (E-W) 0.25 0.017 14.910 64 -LA-B-02 Poggio-Picenze (E-W) 0.25 0.011 15.530 72 -LA-B-03 Poggio-Picenze (N-S) 0.25 0.017 15.530 72 -LA-C-01 Ortucchio (N-S) 0.35 0.061 21.220 26 -LA-C-02 Taranta Peligna (E-W) 0.35 0.077 32.131 39 -LA-C-03 Barisciano (E-W) 0.25 0.012 16.540 71 -Garigliano-Centrale Nucleare 1LA-D-01(N-S)0.25 0.060 26.211 53 -Garigliano-Centrale Nucleare 1LA-D-02(E-W)0.25 0.059 26.231 53 -Garigliano-Centrale Nucleare 2LA-D-03(N-S)0.25 0.060 26.101 53 -LA-E-01 Cassino-Sant' Elia (N-S) 0.25 0.147 27.261 23 17LA-E-02 Cassino-Sant' Elia (E-W) 0.25 0.114 27.271 23 17Umbro-Marchigiano UM-A-01 Cagli (N-S) 0.25 0.013 25.240 59 501997/09/26 - 09:40:305.8UM-A-02 Nocera Umbra (E-W) 0.25 0.760 41.129 11 46 kmNormal UM-A-03 Pennabilli (N-S) 0.25 0.015 28.731 100 92Umbro-Marchigiano1997/09/26 - 00:33:165.6UM-B-01 Bevagna (N-S) 0.25 0.034 46.108 25 257 kmNormalUM-B-02 Bevagna (E-W) 0.25 0.079 50.308 23 26Stiff soil(B)Soft soil(C)Very softsoil(D)Alluvium(E)Rock(A)Stiff soil(B)Umbro-Marchigiano1997/09/26 - 09:40:305.86 kmNormalUmbro-Marchigiano1997/09/26 - 00:33:165.67 kmNormalUM-B-03 Senigallia (E-W) 0.25 0.037 26.801 78 71UM-C-01 Castelnuovo-Assisi (N-S) 0.25 0.159 55.077 22 23UM-C-02 Rieti (N-S) 0.25 0.015 59.786 67 66UM-C-03 Rieti (E-W) 0.25 0.018 59.786 67 66UM-E-01 Norcia-Altavilla (E-W) 0.25 0.046 13.760 32 30UM-E-02 Norcia-Zona Industriale (N-S) 0.25 0.034 52.197 32 26UM-E-03 Norcia-Zona Industriale (E-W) 0.25 0.037 52.197 32 26Table 5.5: Data-base of selected earthquake records.Soft soil(C)Alluvium(E)

Evaluation of seismic demands 169Umbro - MarchigianoPGA (g) values with a10% probability ofexceedance in 50 yearsLazio - Abruzzo Epicenter StationFigure 5.10: Geographical distribution of the selected strong-motion records.1.41.21.00.80.6Sae(T;=0.05)/gLazio-Abruzzo 1984Soil type: AEC8LA-A-01LA-A-02LA-A-03meanPGA=PGA des =0.25g1.41.21.00.80.6Sae(T;=0.05)/gUmbria-Marche 1999Soil type: AEC8UM-A-01UM-A-02UM-A-03meanPGA=PGA des =0.25g0.40.40.20.20.0T (s)0.0T (s)0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Figure 5.11a: Elastic spectra of earthquake records for type A soil.

170 Chapter V1.41.21.00.80.6Sae(T;=0.05)/gLazio-Abruzzo 1984Soil type: BEC8LA-B-01LA-B-02LA-B-03meanPGA=PGA des =0.25g1.41.21.00.80.6Sae(T;=0.05)/gUmbria-Marche 1999Soil type: BEC8UM-B-01UM-B-02UM-B-03meanPGA=PGA des =0.25g0.40.40.20.20.0T (s) 0.0T (s)0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Figure 5.11b: Elastic spectra of earthquake records for type B soil.3.22.82.42.01.6Sae(T;=0.05)/gLazio-Abruzzo 1984Soil type: CEC8LA-C-01LA-C-02LA-C-03meanPGA=PGA des =0.25g3.22.82.42.01.6Sae(T;=0.05)/gUmbria-Marche 1999Soil type: CEC8UM-C-01UM-C-02UM-C-03meanPGA=PGA des =0.25g1.21.20.80.80.40.40.00.0T (s)T (s)0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Figure 5.11c: Elastic spectra of earthquake records for type C soil.1.41.21.00.80.60.4Sae(T;=0.05)/gLazio-Abruzzo 1984Soil type: DEC8LA-D-01LA-D-02LA-D-03meanPGA=PGA des =0.25g0.20.0T (s)0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Figure 5.11d: Elastic spectra of earthquake records for type D soil.

Evaluation of seismic demands 1711.41.21.00.80.6Sae(T;=0.05)/gLazio-Abruzzo 1984Soil type: EEC8LA-E-01LA-E-02meanPGA=PGA des =0.25g1.41.21.00.80.6Sae(T;=0.05)/gUmbria-Marche 1999Soil type: EEC8meanUM-E-01UM-E-02UM-E-03PGA=PGA des =0.25g0.40.40.20.20.00.0T (s)T (s)0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Figure 5.11e: Elastic spectra of earthquake records for type E soil.5.2.2 Displacement demand evaluationIn order to perform the analysis a purposely developed computer code hasbeen used (Ghersi & Noce 1999). This program allows non-linear dynamicanalysis of two-dimensional structures to be carried out.Figure 5.12 shows the representation of the numerical model adopted toschematize the CFSSSW with unit length as a SDOF system.MFRichard Abbott element v()vh = 2800 mmTrusselementEA Ground acceleration a(t)atFigure 5.12: Numeric model schematization.In the model, the hysteretic lateral behavior of the CFSSSW is described bya “Richard Abbott” element in which the assumed values of upper bound

172 Chapter Vcurve, lower bound curve and transition parameters are the results of thecalibration explained in Section 5.1.4 (see Tables 5.3 and 5.4). According tobasic assumptions illustrated in Chapter 4 (Section 4.2), the assumed value ofmass (M) is equal to M=1250kg. In order to take in to account the secondorder effects, a vertical load (F) corresponding to 100% of the mass value hasbeen considered. A damping ratio of 0.05 has been also used in the model.For performing the earthquake analyses, the incremental dynamic analysis(IDA) or dynamic pushover (DPO) procedure is utilised.The IDA procedure needs the definition of two parameters. The first isrelated to the structural performance and can be linked to the damage level ofthe structure after an earthquake. The second is a parameter associated to themagnitude of the earthquake records. In particular, the most used structuralperformance and record intensity parameters are the following (Fulop &Dubina 2003): Structural Performance Parameters (SPP): inter-story drift (/h); top story displacement; maximum plastic rotation; accumulated plastic rotation. Record Intensity Parameters (RIP): elastic spectral acceleration corresponding to the first mode period(T 0 ) of the structure (S ae (T 0 )); recorded peak ground acceleration.Fixed a structural system and the related SPP, an earthquake record and theassociated RIP, the IDA procedure consists in determining IRP valuecorresponding to each prefixed SPP value. As a result of the IDA, a curverelating the SPP to the RIP can be drawn.The IDA parameters used in the current research are the inter-story drift(/h) and the elastic spectral acceleration of the SDOF system (S ae ). Inparticular the accelerograms are scaled from 0.05 to 1.95g.An example of IDA is reported in Figure 5.13 where the significant steps ofthe procedure are shown. This analysis has been carried out on the SDOF

Evaluation of seismic demands 173system previously defined for which the inter-story drift (/h) has beenadopted as SPP. In the example, the UM-B-1 accelerogram has beenconsidered as agent earthquake and the elastic spectral acceleration (S ae ) hasbeen assumed as IRP.The UM-B-1 record has been scaled form 0.05 to 1.95g. In particular,Figure 5.13a shows the record scaled to design peck ground accelerationPGA des (PGA=0.25g) and Figure 5.13b illustrates the elastic responseacceleration spectra of the record for PGA values of 0.25, 0.95 and 1.45g.Assuming as natural vibration period T=0.13s (obtained for a mass M=1250kgand a stiffness k=k 0 =2.80kN/mm), for each prefixed PGA level it is possibleto identify the S ae value (S ae,0.05 =0.63g, S ae,0.25 =2.40g, S ae,0.45 =3.66g) fromFigure 5.13b.The non-linear dynamic response of the SDOF system, in terms of shearforce (V) versus inter-story drift (/h), is reported in Figures 5.13c, d, and e foreach assumed PGA level. The maximum absolute value of /h ((/h) max ) canbe extracted from the V-/h curves ((/h) max,0.25 =0.001, (/h) max,0.95 =0.024,(/h) max,0.45 =0.073). Reporting for each obtained value of the (/h) max thecorrespondent S ae value the IDA curve can be drawn, as shown in Figure5.13f.The IDA curves, obtained considering all selected earthquake records, arereported in Figures 5.14 a and b, grouped for “Lazio-Abruzzo” and “Umbro-Marchigiano” earthquakes, respectively. The same curves are shown inFigures 5.15 a through e, grouped for the different soil types.Reporting the inter-story drift corresponding to the yield limit( y /h=6/2800=0.0021) and ultimate limit state ( u /h=36/2800=0.013) on theIDA curves, the associated elastic spectral accelerations S aey and S aeu can bedetermined. The S aed , S aey and S aeu values and the S aeu /S aey , and S aeu /S aed ratioscomputed for each earthquake records are also reported in Table 5.6.Moreover, the mean and the standard deviation values have been calculatedfor both the Lazio-Abruzzo (LA) and Umbro-Marchigiano (UM) recordgroups, for all soil type groups and for all accelerograms.

174 Chapter V0.58.0a (t)/gPGA=0.25gSae/g (IRP)PGA=01.45g0.47.0PGA=0.95g0.30.26.0PGA=0.25g5.00.10.04.0S ae,1.450 10 20 30 40 50 60-0.1-0.23.0S ae,0.952.0-0.31.0S ae,0.25-0.40.0t (s)T (s)-0.50.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0(a) Accelerogram of the UM-B-1 record (b) Elastic spectra of the UM-B-1 record30V [kN]30PGA=0.25gV [kN]PGA=0.95g20201010(/h) 0.25 /h (SPP)00(/h) 0.95 /h (SPP)-0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04-10-10-20-20-30-30(c) V - d/h response for PGA = 0.25g (d) V - d/h response for PGA = 0.95g30PGA=1.45g4.03.5203.0102.5(/h) 1.450/h (SPP)2.0-0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 1.5V [kN]-101.0Sae/g (IRP)-20-30(e) V - d/h response for PGA = 1.45g0.5/h (SPP)0.00.000 0.020 0.040 0.060 0.080 0.100 0.120 0.140(f) IDA curveFigure 5.13: IDA procedure example.The S aeu /S aey ratio can be considered as a measure of seismic toughness ofthe structures. For all earthquake records, this parameter ranges from 1.26 to3.89 with a mean value of 2.27 and a standard deviation of 0.62. Based onthese results a discrete ductility for the CFSSSW systems can be relied upon.The results are enough scattered, what highlights the dependence of theS aeu /S aey ratio from the considered earthquake record.

Evaluation of seismic demands 175From examination of the data reported in Table 5.6 it can also be observedthat the UM earthquake records are more severe than the LA group. In fact,the mean value of S aeu /S aey is slightly higher (about 12%) in the LA records.Moreover, the results indicate that the LA data are more scattered incomparison with UM data.The comparison between the results obtained for different soil types showsthat the accelerograms recorded on soil type D are the most severe. In fact, inthis case the lowest mean value of S aeu /S aey ((S aeu /S aey ) mean =1.52) has beenobtained. The least severe results have been found for soil types A and B, forwhich the mean values of S aeu /S aey are 2.17 and 2.13, respectively.Examining the scattering of data, it may be noted that the maximumdispersion has been obtained for the soil type C, while in the case of soil typeD the scattering of the results is the smallest one.765Sae/gLA-A-01 LA-A-02 LA-A-03LA-B-01 LA-B-02 LA-B-03LA-C-01 LA-C-02 LA-C-03LA-D-01 LA-D-02 LA-D-03LA-E-01 LA-E-0243210 / h0.000 y / h 0.005 0.010 u / h 0.015Figure 5.14a: IDA curves for “Lazio-Abruzzo” earthquake.

176 Chapter V765Sae/gUM-A-01 UM-A-02 UM-A-03UM-B-01 UM-B-02 UM-B-03UM-C-01 UM-C-02 UM-C-03UM-E-01 UM-E-02 UM-E-0343210 / h0.000 y / h 0.005 0.010 u / h 0.015Figure 5.14b: IDA curves for “Umbro-Marchigiano” earthquake.76543Sae/gLA-A-01LA-A-02LA-A-03UM-A-01UM-A-02UM-A-0321 / h00.000 y / h 0.005 0.010 u / h 0.015Figure 5.15a: IDA curves for soil type A.

Evaluation of seismic demands 17776543Sae/gLA-B-01LA-B-02LA-B-03UM-B-01UM-B-02UM-B-03210 / h0.000 y / h 0.005 0.010 u / h 0.015Figure 5.15b: IDA curves for soil type B.765LA-C-01LA-C-02LA-C-03UM-C-01UM-C-02UM-C-0343210 / h0.000 y / h 0.005 0.010 u / h 0.015Figure 5.15c: IDA curves for soil type C.

178 Chapter V765Sae/gLA-D-01LA-D-02LA-D-034321 / h00.000 y / h 0.005 0.010 u / h 0.015Figure 5.15d: IDA curves for soil type D.7654Sae/gLA-E-01LA-E-02UM-E-01UM-E-02UM-E-03321 / h00.000 y / h 0.005 0.010 u / h 0.015Figure 5.15e: IDA curves for soil type E.

Evaluation of seismic demands 179Earthquake record S aed / g S aey / g S aeu / g S aeu / S aey S aeu / S aedLA-A-01 0.63 1.03 2.06 2.00 3.30LA-A-02 0.63 0.88 2.08 2.35 3.33LA-A-03 0.63 1.01 2.46 2.44 3.93LA-B-01 0.68 0.87 1.68 1.94 2.46LA-B-02 0.68 1.38 2.53 1.83 3.70LA-B-03 0.68 1.13 3.11 2.75 4.55LA-C-01 0.72 1.79 6.17 3.44 8.62LA-C-02 0.72 2.09 5.09 2.43 7.11LA-C-03 0.72 4.36 16.99 3.89 23.73LA-D-01 0.68 1.02 1.56 1.53 2.28LA-D-02 0.68 1.08 1.53 1.42 2.24LA-D-03 0.68 1.04 1.69 1.62 2.47LA-E-01 0.87 1.02 3.10 3.05 3.56LA-E-02 0.87 1.36 3.63 2.68 4.18UM-A-01 0.63 1.15 3.29 2.86 5.22UM-A-02 0.63 1.78 3.76 2.11 5.96UM-A-03 0.63 0.87 1.10 1.26 1.75UM-B-01 0.58 1.10 1.99 1.81 3.43UM-B-02 0.58 1.27 2.29 1.81 3.95UM-B-03 0.58 0.79 2.10 2.66 3.62UM-C-01 0.62 1.81 4.20 2.33 6.78UM-C-02 0.62 1.47 2.24 1.52 3.61UM-C-03 0.62 1.02 2.20 2.16 3.54UM-E-01 0.74 2.14 5.37 2.51 7.26UM-E-02 0.74 1.46 3.44 2.35 4.64UM-E-03 0.74 1.59 3.51 2.20 4.74Mean (Type A soil records) 1.12 2.46 2.17 3.92St. Dev. (Type A soil records) 0.34 0.95 0.54 1.50Mean / St. Dev. (Type A soil records) 0.30 0.39 0.25 0.38Mean (Type B soil records) 1.09 2.28 2.13 3.62St. Dev. (Type B soil records) 0.23 0.49 0.45 0.69Mean / St. Dev. (Type B soil records) 0.21 0.22 0.21 0.19Mean (Type C soil records) 2.09 6.15 2.63 8.90St. Dev. (Type C soil records) 1.17 5.54 0.88 7.54Mean / St. Dev. (Type C soil records) 0.56 0.90 0.33 0.85Mean (Type D soil records) 1.05 1.59 1.52 2.33St. Dev. (Type D soil records) 0.03 0.08 0.10 0.12Mean / St. Dev. (Type D soil records) 0.03 0.05 0.07 0.05Mean (Type E soil records) 1.51 3.81 2.56 4.88St. Dev. (Type E soil records) 0.41 0.89 0.33 1.41Mean / St. Dev. (Type E soil records) 0.27 0.23 0.13 0.29Mean (LA records) 1.43 3.83 2.38 5.39St. Dev. (LA records) 0.91 4.03 0.73 5.59Mean / St. Dev. (LA records) 0.64 1.05 0.31 1.04Mean (UM records) 1.37 2.96 2.13 4.54St. Dev. (UM records) 0.41 1.18 0.47 1.57Mean / St. Dev. (UM records) 0.30 0.40 0.22 0.34Mean (all records) 1.40 3.43 2.27 5.00St. Dev. (all records) 0.71 3.04 0.62 4.18Mean / St. Dev. (all records) 0.51 0.89 0.28 0.84Table 5.6: IDA results.

180 Chapter V5.3 DEFINITION OF A LOAD HISTORY FOR A CYCLICTESTING5.3.1 Loading histories in quasi-static cyclic loading tests: basicprocedures for Multiple Step TestSeismic capacity measures for a structural component or sub-assembly arestrength, stiffness, inelastic deformation capacity and cumulative capacitysuch as energy dissipation capacity. All these parameters are expected todeteriorate as the number of damaging cycles and the amplitude of cyclingincreases. The type of deterioration depends on the failure mode of thestructural element and the adopted loading history. Figure 5.16a shows atypical example of deterioration for a CFSSSW subject to the loading historyreported in Figure 5.16b. The typical cyclic behavior of CFSSSWs denotesstrong pinching and reduced ductility.(a) Cyclic response of a CFSSSW(b) Time historyFigure 5.16: Deterioration of a CFSSSW system (Branston et al. 2003).The choice of a loading history for seismic testing of a structuralcomponent or sub-assembly should be based on the following cumulativedamage concepts, as reported in Krawinkler (1996). Every excursion in the inelastic range causes damage in a structure thatbrings it closer to failure. Moreover, the damage increases as theinelastic excursion amplifies. Thus, relative amount of damage caused

Evaluation of seismic demands 181by an inelastic excursion depends on the individual plastic deformationrange of the excursion ( p ) (see Fig. 5.17).For a given deformation amplitude the damage is largest for asymmetric excursion.The damage due to inelastic excursions is cumulative, thus it dependson the number of inelastic excursions (N p ) and the sum of normalizedplastic deformation ranges ( pi / y ).The damage depends on sequence effects, which means that it dependson the sequence in which large and small excursions are applied to thestructure. In particular, the importance of sequence effects has not yetbeen established.Figure 5.17: Basic parameters in a typical cyclic of loading (ATC 1992).Besides to the maximum level of deformation experienced by the structure,which can be defined by the maximum normalized deformation (=(/ y ) max ),the main capacity parameters for characterizing the loading histories are thenumber of inelastic excursions (N p ), their individual plastic deformation range( p ) and the sum of normalized plastic deformation ranges ( pi / y ), which

182 Chapter Vmay be used as the basic cumulative damage parameter. For improving theloading history description may be appropriate to add another parameter todescribe the distribution of individual plastic deformation range. The latter canbe represented by the ratio between the mean value (( p ) av ) and themaximum value (( p ) max ) of the plastic deformation range (( p ) av /( p ) max ).This parameter (( p ) av /( p ) max ) with the ones employed by Krawinklerwill be used in the current research to determine the loading history.The demands imposed by an earthquake on a structural component or subassemblydepend on its configuration in a structure, the strength and elastic aswell inelastic dynamic characteristics of the structure, and the seismic input towhich the structure may be subjected.For developing loading histories, Nassar and Krawinkler (1991) madegeneral considerations starting from studies on seismic demands on singledegree of freedom (SDOF) systems. These studies have been based on bilinear(with 10% strain hardening) and stiffness degrading SDOF systems withductilities () ranging from 2 to 8 subjected to a set of 15 Western U.S.earthquake ground motions. The magnitude of the earthquakes was variedfrom 5.7 to 7.7, their durations varied significantly, and they representedground motions at stiff soil sites.As a result of these studies, the Authors show the significant dependence ofsome demand parameters (N p and pi / y ) on the natural period (T) of thestructures and the ductility ratio (). In particular: The number of inelastic excursions (N p ) amplifies with an increase inthe natural period of the structure (T) for T 0.2s, but decreases withan increase of T for T 0.2s. Moreover, for each T value, N p increaseswhen the ductility ratio () amplifies (see Fig. 5.18). Similar to N p , the sum of normalized plastic deformation ranges( pi / y ) increases with an amplification of natural period (T) for T 0.2s but decreases with an increase of T for T 0.2s. Moreover, foreach T value, N p increases when the ductility ratio () amplifies (seeFig. 5.19). The magnitudes of individual plastic deformation ranges ( p ) of theinelastic excursions can be represented by a lognormal distribution.Large plastic deformation ranges are less frequent than small ones. Infact, Hadidi-Tamjed (1987) reports that the mean of the plastic

Evaluation of seismic demands 183deformation ranges (( p ) av ) in an earthquake is usually less than 15%of the maximum plastic deformation range (( p ) max ).On basis of these results, Krawinkler (1996) suggests the choice of testingprogram and associated loading history. In particular, if cumulative damagemodeling is not object of the research, the monotonic load-displacementresponse can be easily predictable, the deterioration is slow, then the “MultipleStep Test” is the recommended test program.Figure 5.18: Dependence of mean number of inelastic excursions on natural period andductility ratio (Krawinkler 1996).Figure 5.19: Dependence of mean number of the sum of normalized plastic deformationranges on natural period and ductility ratio (Krawinkler 1996).

184 Chapter VThe loading history for a “Multiple Step Test” consists of a series ofstepwise increasing deformation cycles, as shown in Figure 5.20. In Figure5.20, indicates the deformation control parameters, and representsincrement in peak deformation. In this history, the cycles should be symmetricand several cycles should be completed during each step. The firsts load stepsshould be performed in the elastic range to obtain stable and reliable values ofstiffness properties. The following steps should be performed at and beyondyielding.Figure 5.20: Loading history for Multiple Step Test (Krawinkler 1996).For satisfying these requirements, the Author reports a table (Table 5.7) inwhich shows, for three selected period (T=0.2s, T =0.5s, T =2.0s) and fourductility ratio levels (=2, =4,=6,=8), representative values of predictedand experimental SDOF seismic demands obtained from the loading historyreported in Figure 5.20 in which = y .

Evaluation of seismic demands 185T N p pi / ymean mead + st. dev. experim. mean mead + st. dev. experim.2 12 19 6 4 7 110.24 28 42 16 28 41 576 36 55 24 54 76 1278 39 59 32 78 109 2292 8 12 6 3 5 110.54 19 30 16 23 36 576 24 35 24 41 64 1278 26 38 32 64 97 2292 4 7 6 3 4 112.04 7 10 16 13 20 576 9 12 24 25 36 1278 10 14 32 38 52 229Table 5.7: Predicted and experimental demands for a bilinear SDOF (Krawinkler 1996).The values of the total number of inelastic excursions (N p ) and the sum ofnormalized plastic deformation ranges ( pi / y ) reported in Table 5.7, aswell as that frequently adopted in loading sequences for CFSSSWs (SEAOSC1997) testing, have been derived based on a bilinear hysteresis assumption. Asa consequence, a study aiming at characterizing the deformation history toCFSSSW structural systems is needed.5.3.2 Definition of the deformation history for the cyclic testingUsing a sufficiently large database of earthquake ground motion records,the choice of an appropriate loading history for a “multiple step test” needs (a)definition of the demand parameters and (b) definition of the magnitude of theearthquake records.Selection of the demand parameters has been based on cumulative damageconcepts, as explained in Section 5.3.1. As a result of these considerations theassumed parameters are the following:maximum level of deformation that, from the results of monotonictests carried-out in the current research, can be characterized by avalue of ductility ratio equal to =(/ y ) max = u / y =36/6=6; number of inelastic excursions (N p ); sum of normalized plastic deformation ranges ( pi / y );

186 Chapter V distribution of individual plastic deformation range (( p ) av /( p ) max ).These demand parameters strictly depends on the definition of theindividual plastic excursion. The typical cyclic behavior of CFSSSWs ischaracterized by strong pinching; consequently definition of the inelasticexcursion is strictly related to the adopted convention.In the current research the individual plastic deformation range of theexcursion i ( pi ) is defined by the difference between the deformationcorresponding to the null value of the shear force achieved on the unloadingbranchof the excursion i ( i,0 ) and the maximum value of deformationscorresponding to the null values of the shear force achieved on the unloadingbranchof the previous excursion ( max,0 =max{ 1,0 ; 2,0 ; … i-1,0 }), asshown in Figure 5.21.The evaluation of assumed deformation demand parameters under theselected earthquake ground motions has been carried out by scaling records.In particular, each accelerogram has been scaled in such way that the elasticspectral acceleration (S ae ) be equal to the spectral acceleration inducing theultimate lateral displacement (S aeu ) obtained through the IDA. In other words,each design accelerogram (PGA=PGA des =0.25g) has been scaled by S au /S ad .The S au /S ad values are reported in Table 5.6.V (kN) Excursion (i+1)+Excursion (i)+ p,(i)- p,(i)- (mm) p,(i)+ p,(i+1)+Excursion (i+1)-Excursion (i)-Figure 5.21: Assumed definitions of individual plastic deformation range.

Evaluation of seismic demands 187Results of the statistic characterization of the deformation demand aresynthesized in Figures 5.22 a through d and Table 5.8. In particular, themaximum normalized deformation ((/ y ) max ) (see Fig. 5.22a), the number ofinelastic excursion (N p ) (see Fig. 5.22b), the sum of normalized plasticdeformation ranges ( pi / y ) (see Fig. 5.22c), and the ratio between themean value and the maximum value of the plastic deformation range(( p ) av /( p ) max ) (see Fig. 5.22d) are reported for each accelerogram. Alsothe mean and the standard deviation values have been calculated for allearthquake records, for all soil types and for both the LA and UM recordgroups.For all accelerograms, the (/ y ) max values range from 5.1 to 7.5 with amean value of 6.1 and a standard deviation of 0.4; N p ranges from 9 to 45 witha mean and standard deviation values of 24 and 11, respectively; the range of pi / y is from 5.6 to 9.2 with a mean value of 7.5 and a standard deviationof 1.0; finally, (( p ) av /(( p ) max ranges from 0.09 to 1.21 and its mean andstandard deviation values are 0.28 and 0.22, respectively.From results reported in Figures 5.22 and Table 5.8, it can also be notedthat the mean values of the parameters associated to the damage level (N p and pi / y ) are similar for both the LA and UM record groups. In particular, themean values of N p and pi / y result moderately higher (about 18 and 10%,respectively) for UM records. Also the dispersion of data results moderatelyhigher for UM records in the case of N p and pi / y . For the parameterrelated to the distribution of individual plastic deformation range(( p ) av /( p ) max ), both the mean and standard deviation values in LAearthquake records are sensibly higher in comparison with UM records. Inparticular, the mean value results about 50% higher in LA earthquake.The comparison between the results obtained for different soil types showsthat the highest mean values for the parameters N p and pi / y have beenobtained for the soil type D, while the mean values of N p and pi / y resultthe lowest for soil types B and E, respectively. Also the scattering of data isthe highest for the soil type D in the case of N p , while for pi / y themaximum dispersion has been obtained for the soil type C. For the parameter(( p ) av /( p ) max ), the maximum and minimum mean values have been foundfor soil types E and D, respectively, while the scattering results larger in thecase of soil type C.

188 Chapter V876543210mean + st.devmeanmean – st.devmean: 6.1 - st.dev: 0.4LA-A-01LA-A-02LA-A-03LA-B-01LA-B-02LA-B-03LA-C-01LA-C-02LA-C-03LA-D-01LA-D-02LA-D-03LA-E-01LA-E-02UM-A-01UM-A-02UM-A-03UM-B-01UM-B-02UM-B-03UM-C-01UM-C-02UM-C-03UM-E-01UM-E-02UM-E-03Figure 5.22a: Results of the statistic characterization of the deformation demand in terms ofmaximum normalized deformation.50454035302520151050mean + st.devmeanmean – st.devmean: 24 - st.dev: 11LA-A-01LA-A-02LA-A-03LA-B-01LA-B-02LA-B-03LA-C-01LA-C-02LA-C-03LA-D-01LA-D-02LA-D-03LA-E-01LA-E-02UM-A-01UM-A-02UM-A-03UM-B-01UM-B-02UM-B-03UM-C-01UM-C-02UM-C-03UM-E-01UM-E-02UM-E-03Figure 5.22b: Results of the statistic characterization of the deformation demand in terms ofnumber of inelastic excursion.

Evaluation of seismic demands 1891098mean + st.devmeanmean: 7.5 - st.dev: 1.0mean – st.dev76543210LA-A-01LA-A-02LA-A-03LA-B-01LA-B-02LA-B-03LA-C-01LA-C-02LA-C-03LA-D-01LA-D-02LA-D-03LA-E-01LA-E-02UM-A-01UM-A-02UM-A-03UM-B-01UM-B-02UM-B-03UM-C-01UM-C-02UM-C-03UM-E-01UM-E-02UM-E-03Figure 5.22c: Results of the statistic characterization of the deformation demand in terms ofsum of normalized plastic deformation ranges.1.31.21.11.00.90.80.70.60.50.40.30.20.10.0mean + st.devmeanmean – st.devmean: 0.28- st.dev: 0.22LA-A-01LA-A-02LA-A-03LA-B-01LA-B-02LA-B-03LA-C-01LA-C-02LA-C-03LA-D-01LA-D-02LA-D-03LA-E-01LA-E-02UM-A-01UM-A-02UM-A-03UM-B-01UM-B-02UM-B-03UM-C-01UM-C-02UM-C-03UM-E-01UM-E-02UM-E-03Figure 5.22d: Results of the statistic characterization of the deformation demand in terms ofration between the mean value and the maximum value of the plastic deformation range.

190 Chapter VEarthquake record ( p / y ) max N p pi / y ( p ) av /(( p ) maxLA-A-01 6.1 28 7.6 0.15LA-A-02 6.1 34 7.1 0.13LA-A-03 5.9 13 6.9 0.39LA-B-01 5.9 16 7.2 0.32LA-B-02 6.2 13 6.0 0.28LA-B-03 6.0 13 7.8 0.38LA-C-01 6.3 12 6.6 0.27LA-C-02 6.4 10 7.2 0.40LA-C-03 6.4 14 6.7 0.31LA-D-01 6.1 28 8.5 0.17LA-D-02 7.5 32 8.7 0.21LA-D-03 6.0 32 7.2 0.19LA-E-01 5.6 33 6.7 1.21LA-E-02 6.0 35 6.6 0.17UM-A-01 6.3 9 7.4 0.24UM-A-02 5.1 25 5.6 0.19UM-A-03 6.7 30 9.2 0.33UM-B-01 6.3 32 8.1 0.31UM-B-02 5.8 37 9.2 0.16UM-B-03 6.2 11 7.7 0.36UM-C-01 6.3 29 7.8 0.09UM-C-02 5.8 42 8.6 0.10UM-C-03 6.4 45 9.0 0.10UM-E-01 6.0 11 7.1 0.46UM-E-02 6.0 18 7.3 0.17UM-E-03 6.5 24 7.9 0.18Mean (Type A soil records) 6.0 23 7.3 0.24St. Dev. (Type A soil records) 0.5 10 1.2 0.10Mean / St. Dev. (Type A soil records) 0.08 0.43 0.16 0.44Mean (Type B soil records) 6.1 20 7.7 0.30St. Dev. (Type B soil records) 0.2 11 1.1 0.08Mean / St. Dev. (Type B soil records) 0.04 0.55 0.14 0.27Mean (Type C soil records) 6.3 25 7.6 0.21St. Dev. (Type C soil records) 0.2 16 1.0 0.14Mean / St. Dev. (Type C soil records) 0.04 0.62 0.13 0.64Mean (Type D soil records) 6.5 31 8.1 0.19St. Dev. (Type D soil records) 0.9 2 0.8 0.02Mean / St. Dev. (Type D soil records) 0.13 0.08 0.10 0.11Mean (Type E soil records) 6.0 24 7.1 0.44St. Dev. (Type E soil records) 0.3 10 0.6 0.45Mean / St. Dev. (Type E soil records) 0.05 0.42 0.08 1.02Mean (LA records) 6.2 22 7.2 0.33St. Dev. (LA records) 0.4 10 0.8 0.27Mean / St. Dev. (LA records) 0.07 0.45 0.11 0.82Mean (UM records) 6.1 26 7.9 0.22St. Dev. (UM records) 0.4 12 1.0 0.12Mean / St. Dev. (UM records) 0.07 0.46 0.13 0.53Mean (all records) 6.1 24 7.5 0.28St. Dev. (all records) 0.4 11 1.0 0.22Mean / St. Dev. (all records) 0.07 0.45 0.13 0.77Table 5.8: Results of the statistic characterization of the deformation demand.

Evaluation of seismic demands 191REFERENCESATC (1992) Guidelines for cyclic seismic testing of components of steel structures(ATC-24). ATC (Applied Technology Council). Redwood City, CA, USA.Branston, A., Boudreault, F., Rogers, C.A. (2003) Testing on steel frame / woodpanels shear walls. Progress Report, Departement of Civil Engineering and AppliedMechanics, McGill University. Montreal.COLA-UCI (2001) Report of a testing program of light-framed walls with woodsheathedshear panels. Final report to the City of Los Angeles Department ofBuilding and Safety, Structural Engineers Association of Southern California, Irvine,CA,USA.Della Corte, G., De Matteis, G., Landolfo, R. (1999) A mathematical modelinterpretino the cyclic behaviour of steel beam-to-column joint. In Proceedings of theXVII Congresso CTA (CTA 1999). Napoli.Fulop, L.A. & Dubina, D. (2003). Are the cold-formed wall stud shear wallsdissipative systems in seismic resistant buildings? How much?. In Proceedings of the4 th International Conference on Behavior of Steel Structures in Seismic Areas(STESSA 2003). Mazzolani F.M. (ed.). A.A. Balchema Publishers.Ghersi, A. & Noce, (1999) Modalità di utilizzazione del programma DIANA. Istitutodi Scienza delle costruzioni, Università di Catania. Catania.Hadidi-Tamjed, H. (1987) Statistical response of inelastic SDOF systems subjected toearthquake. Ph.D. Dissertation. Department of Civil Engineering, StanfordUniversity.Krawinkler, H. (1996) Cycling loading histories for seismic experimentation onstructural components. Earthquake Spectra. Vol. 12, No.1:1-12.Nassar, A.A. & Krawinkler, H. (1991) Seismic demands for SDOF and MDOFsystems. John A. Blume Earthquake Engineering Center Report No.95, Departmentof Civil Engineering, Stanford University.Ordinanza PCM (2003) Primi elementi in materia di criteri generali per laclassificazione sismica del territorio nazionale e di normative tecniche per lecostruzioni in zona sismica. Ordinanza della Presidenza del Consiglio dei MinistriNo.3274/2003.prEN 1998-1 (2001) Eurocode 8: Design of structures for earthquake resistance –Part 1: General rules – Seismic actions and rules for buildings. CEN (EuropeanCommittee for Standardization). Bruxelles.Richard, R.M. & Abbott, B.J. (1975) Versatile elastic-plastic stress-strain formula.Journal of mechanical division. ASCE, Vol.101, No.4:511-515.

192 Chapter VSEAOSC (1997) Standard method of cyclic (reversed) load tests for shear resistanceof framed walls for buildings. Structural Engineers Association of SouthernCalifornia (SEAOSC). Whittier, CA, USA.Serrette, R., Nguyen, H., Hall, G. (1996a) Shear wall values for light weight steelframing. Report No. LGSRG-3-96, Light Gauge Steel Research Group, Departmentof Civil Engineering, Santa Clara University. Santa Clara, CA, USA.Serrette, R., Hall, G., Nguyen, H. (1996b) Dynamic performance of light gauge steelframed shear walls. In Proceedings of the 13 th International Specialty Conference onCold-formed Steel Structures. St. Louis, MO, USA: 487-498.Serrette, R., Encalada, J., Matchen, B., Nguyen, H., Williams, A. (1997b) Additionalshear wall values for light weight steel framing. Report No. LGSRG-1-97, LightGauge Steel Research Group, Department of Civil Engineering, Santa ClaraUniversity. Santa Clara, CA, USA.

193Chapter VIThe cyclic testThe second step of the experimental program, which consists in the cyclictesting of cold-formed steel stud shear wall (CFSSSW) sub-assemblies, isillustrated in this Chapter.The specimen tested under cyclic loading was nominally identical to thattested under monotonic loading. Moreover, also the test set-up and theinstrumentation adopted in the cyclic testing were the same as in themonotonic one. Consequently, because the description of the test specimen,test set-up and instrumentation have been previously illustrated in Chapter 4,only the test procedure and test results are presented in the current Chapter. Inparticular, the Section 6.1 is devoted to present the test procedure, while thetest results are presented in Section 6.2.

194 Chapter VI6.1 TEST PROCEDUREIn the cyclic test, the specimen was subjected to fully reversing cyclichorizontal displacements according to the definition of the deformation historyparameters, which have been illustrated in the Chapter 5 (Section 5.3.2). Inparticular, the test specimen was subjected to fully reversing cyclicdisplacements consisting of a series of stepwise increasing deformationcycles, by following a procedure similar to the one described in ATC (1992)for a multiple step test (see Chapter 5 Section 5.3.1).The load history consisted on applying three cycles of fully reversing,displacement-controlled load at each wall displacement incrementrepresenting 25% (= 1.5mm), 50% (= 3.0mm) and 75% (= 4.5mm) of theconventional yield limit state (YLS) displacement ( y = 6.0mm). Then, thewall displacement was increased for three load cycles to 100% of the YLSdisplacement. Next, cycles of displacement for three cycles each at 150%(= 9.0mm), 200% (= 12.0mm), 300% (= 12.05mm), 400%(= 24.0mm) and 600% (= 36.0mm) of the YLS displacement were applied.At this point the load history based on the statistic characterization ofdeformation demand, which has been illustrated in Section 5.3.2, wascompleted. However, to capture the behavior of the specimen under largerdisplacement amplitudes, other cycles of displacement for three cycles each at700% (= 42.0mm), 800% (= 48.0mm), 900% (= 54.0mm), 1000% (=60.0mm), 1100% (= 66.0mm), 1200% (= 72.0mm), and 1300% (=78.0mm) of the YLS displacement were applied.This test protocol involved displacements at rate of 2.00mm/s.The adopted test protocols are illustrated in Table 6.1 and Figure 6.1. TheFigure 6.2 shows the numerical cyclic response in terms of unit shear force (v)versus lateral displacement () curves obtained for the assumed load historyby using the model of the hysteretic behavior of CFSSSW systems, whichhave been already illustrated and calibrated in the Section 5.1. As a result, therepresentative values of predicted seismic demands, which have been obtainedfrom the assumed loading history, are:

The cyclic test 195 maximum level of deformation: (/ y ) max =6.0; number of inelastic excursion: N p =25; sum of normalized plastic deformation ranges: pi / y =6.2; ration between the mean value and the maximum value of the plasticdeformation range (( p ) av /( p ) max )=0.28.From the examination of the value of these parameters it can be deducedthat the adopted load history is reasonable. In fact, the mean deformationdemand parameters obtained from the statistic characterization are close tothose characterizing the adopted loading history, as illustrated in Table 6.2.Moreover, from comparison between the results obtained in this research,which takes in-to account the cyclic behavior of CFSSSW systems, and thosereported for a bilinear SDOF by Krawinkler (1996) ((N p =30 and pi / y =36in average, see Figs. 5.18 and 5.19) a reduction of the parameters associated tothe damage level may be noted in the case of CFSSSW systems. In particular,the decreasing is of 24% for N p and 79% for pi / y .No. ofcyclesDisplacement(mm)3 1.5 253 3.0 503 4.5 753 6.0 1003 9.0 1503 12.0 2003 18.0 3003 24.0 4003 36.0 6003 42.0 7003 48.0 8003 54.0 9003 60.0 10003 66.0 11003 72.0 12003 78.0 1300Table 6.1: Cyclic test protocol.Displacement / YLSdisplacement (%)

196 Chapter VIload history based on thestatistic characterizationof deformation demandFigure 6.1: Cyclic test protocol.Figure 6.2: Numerical cyclic response.

The cyclic test 197( p / y ) max N p pi / y ( p ) av /(( p ) maxStatistic characterization (mean value) 6.1 24 7.5 0.28Statistic characterization (st. dev. value) 0.4 11 1.0 0.22Adopted load history 6.0 25 6.2 0.28Table 6.2: Comparison between the deformation demand parameters obtained from thestatistic characterization (see Table 5.8) and the adopted loading history.6.2 TEST RESULTSThe measured responses of all instruments are reported in Appendix F.The global cyclic response may be represented by the unit shear resistance(v) vs. mean displacement (d) curve, where v and d have been defined inChapter 4 (see Equations 4.7 and 4.8). The v-d response curve is showed inFigure 6.3.In this Figure the values of the maximum (positive) experimental loadsobtained at the first (v EXP+1 ) and last (the third one) (v EXP+3 ) hysteretic loop arereported together with the minimum (negative) experimental loadscorresponding to the first (v EXP-1 ) and third (v EXP-3 ) hysteretic loop. Inparticular, the experimental maximum loads were obtained for a lateraldisplacement of +36mm. They resulted v EXP+1 =+16.4kN/m andv EXP+3 =+10.2kN/m for the first and third cycle, respectively. For the negativeloads the minimum values were found for a lateral displacement of -24mm.Their values were v EXP-1 =-14.8kN/m and v EXP-3 =-12.5kN/m for the first andthird cycle, respectively.From the comparison between the experimental loads obtained at the first(v EXP+1 and v EXP-1 ) and third (v EXP+3 and v EXP-3 ) hysteretic loops, a reduction of38% and 16% for positive (v EXP+1 vs. v EXP+3 ) and negative (v EXP-1 vs. v EXP-3 )shear strengths, respectively was noted. These results highlight a clear shearstrength degradation. From the comparison between the positive (v EXP+1 andv EXP+3 ) and negative (v EXP-1 and v EXP-3 ) experimental loads, for the firsthysteretic loop (v EXP+1 vs. v EXP-1 ) it was observed a higher shear capacity of11% for positive loads, while for the third hysteretic loop (v EXP+3 vs. v EXP-3 ) ahigher shear strength of 23% was found for negative loads.

198 Chapter VIIn Figure 6.3 the estimated lateral strength (v R ) is also reported. From thecomparison between the mean value of the experimental lateral strengthobtained at first hysteretic loop (v EXP1 = v EXP+1 - v EXP-1 / 2 = 15.6kN/m) and theestimated lateral strength (v R =17.9kN/m) it is possible to observe that, in thecase of loads applied cyclically, the semi-analytical calculation illustrated inthe Chapter 2 gives a 15% overestimation of shear strength. Moreover, if themean experimental value of experimental lateral strength obtained at thirdhysteretic loop (v EXP3 = v EXP+3 - v EXP-3 / 2 = 11.4kN/m) is considered, the semianalyticalprediction gives a 57% overestimation of the lateral strength.Experimental lateral strength(v EXP+1 = 16.4kN/m)Estimate lateral strength (v R = 17.9kN/m)Experimental lateral strength(v EXP+3 = 10.2kN/m)Experimental lateral strength(v EXP-3 = -12.5kN/m)Experimental lateral strength(v EXP-1 = -14.8kN/m)Estimate lateral strength (v R = 17.9kN/m)Figure 6.3: Unit shear resistance (v) vs. mean displacement (d) curve.During the test two different behaviors could be identified. For lateral displacement less than the one corresponding to maximumshear resistance the behavior of OSB sheathings-to-frame connectionsresulted from a combination of the tilting of the screws about the planeof the stud flange and the screw heads pulling through the OSBsheathings, as shown in Figure 6.4 a and b, respectively. The responseof GWB sheathings-to-frame connections was characterized by acombination of the bearing of the GWB panels and the screws heads

The cyclic test 199pulling through the GWB panels, as shown in Figure 6.5 a and b,respectively.For these displacement levels the skeleton-to-panels deformation wascongruent. In fact, the wall framing deformed into a parallelogram andthe sheathings had rigid body rotation.For lateral displacement larger than the one corresponding to themaximum shear resistance, the heads of the end screws completelypulled through the sheathings in the bottom half of the walls (seeFigures 6.6 a and b for OSB and GWB sheathings, respectively) or, insome cases, the screws caused the rupture of the sheathing edges (seeFigs. 6.7 a and b for OSB and GWB sheathings, respectively). As aresult, both the OSB and GWB sheathings became unzipped along thepanel edges in the bottom half of the specimen (see Fig. 6.8).Moreover, for displacement levels more than 42mm also thedistortional buckling in the end studs of the wall 1 was observed, asshown in Figure 6.9.For these displacement levels the deformation of the wall framing stillhad the shape of a parallelogram, while due to the rupture sheathingto-frameconnections, the rotation of the sheathings was limited. Asshown in Figure 6.10.As in the case of monotonic test, in the cyclic test any deformation of theOSB sheathing-to-floor framing connections was not observed and the shearand the tension anchors did not suffer any type of failure.

200 Chapter VI(a) Tilting of the screws(b) Screw heads pull throughFigure 6.4: Behavior of OSB sheathing-to-frame connections.(a) Bearing of the panels(b) Screw heads pull throughFigure 6.5: Behavior of GWB sheathing-to-frame connections.

The cyclic test 201(a) OSB sheathing-to frame connections(b) GWB sheathing-to frame connectionsFigure 6.6: Failure of sheathing-to-frame connections due to screw heads pull through.(a) OSB sheathing-to frame connections(b) GWB sheathing-to frame connectionsFigure 6.7: Failure of sheathing-to-frame connections due to rupture of sheathing edges.

202 Chapter VIFigure 6.8: Unzipping of sheathings.Figure 6.9: Buckling of end studs.Figure 6.10: Deformation of walls for lateral displacement amplitudes more than 36mm.

The cyclic test 203The comparison between the cyclic and monotonic behavior is shown inFigure 6.11. In this Figure both cyclic and monotonic responses arerepresented through the unit shear resistance (v) vs. mean displacement (d)curves. From the comparison of these curves it may be observed as the cyclicloading produced a 11% reduction of the shear strength (by considering thecomparison between the lateral strength found in the monotonic test and theone obtained from the cyclic test at first hysteretic loop of positivedisplacements). On the contrary, by comparing the lateral strength obtainedfrom the monotonic test with the lateral strength corresponding to the cyclictest at third hysteretic loop of positive displacements the reduction of shearcapacity increased up to 45%; whereas, considering the shear strengthobtained for negative displacements a 20% and 32% degradation appeared inthe cyclic test at first and third hysteretic loops, respectively.Moreover, the difference between the cyclic and monotonic responsebecame significant for the unstable part of the behavior (for displacementamplitudes more than 36mm).The force (V) vs. displacement (d) response curves for the two walls isshown in Figure 6.12. In particular, in this Figure the force vs. displacementcurves obtained from measures of the actuators a1 and a2 have been reportedfor the walls 1 and 2, respectively. From the comparison of lateral responsesof two walls observations similar to those deduced for the monotonic test arepossible: the walls had a similar behavior for positive displacements less than+36mm (displacement corresponding to the maximum shear load),while they exhibited different responses for larger displacements; considering the first hysteretic loops, the maximum shear loads (forpositive displacements) were +40 and +39kN for wall 1 and 2,respectively; therefore, the two walls revealed the same shear capacity;whereas considering the third hysteretic loops, the maximum shearloads were +26 and +23kN for wall 1 and 2, respectively; therefore,the wall 1 appeared to be lightly more resistant than wall 2 of about13%;

204 Chapter VIthe walls sowed similar response for smaller negative displacementswith significant variation of the behavior for displacements less than-36mm;considering the first hysteretic loops, the minimum shear loads (fornegative displacements) were -37 and -34kN for wall 1 and 2,respectively; consequently, the wall 1 was lightly more resistant thanwall 2 of about 9%; whereas considering the third hysteretic loops, theminimum shear loads were -26 and -23kN for wall 1 and 2,respectively; therefore, the difference between walls in terms of shearresistance was of 13%.Figure 6.11: Cyclic vs. monotonic behavior.

The cyclic test 205Figure 6.12: Shear (V) vs. displacement (d) curves for wall 1 and wall 2.REFERENCESATC (1992) Guidelines for cyclic seismic testing of components of steel structures(ATC-24). ATC (Applied Technology Council). Redwood City, CA, USA.Krawinkler, H. (1996) Cycling loading histories for seismic experimentation onstructural components. Earthquake Spectra. Vol. 12, No.1:1-12.

207ConclusionsSeismic performance analysis of low-rise residential buildings built withcold-formed steel members has been the objective of this research.The attention has been focused on the seismic behavior of sheathed coldformedsteel stud shear walls through the evaluation of the seismic capacity(experimental phase), seismic demand (theoretical phase) and theircomparison.On the base of observations and results of the experimental and theoreticalinvestigation, the following conclusions may be drawn:Global experimental behavior: monotonic response vs. cyclic responseIn case of monotonic loading, for all displacement levels, wall framingsdeformed into a parallelogram and the sheathings had rigid body rotation, insuch a way that the evolution of the deformation was coherent with thesheathing-to-wall framing connections failure.In case of cyclic loading, the global behavior of the specimen was similar tothat observed in the monotonic testing for displacements less than the onecorresponding to the maximum shear capacity, while the skeleton-to-panelsdeformation was not congruent for higher displacement levels. Moreover, onlyin the case of cyclic testing, the distortional buckling in the end studs of thewall 1 was observed for displacement amplitudes more than 42mm.In both the monotonic and cyclic testing any deformation of the orientedstrand board (OSB) sheathing-to-floor framing connections was not observed,and the shear and the tension anchors did not suffer any type of failure.

208Local (sheathing-to-wall framing connections) experimental behavior:monotonic response vs. cyclic responseSheathing-to-wall framing connections in the case of monotonic testexhibited similar behavior, but they degraded more gradually than during thecyclic test.In particular, for lower displacement levels the behavior of OSB sheathingsto-frameconnections resulted from a combination of the tilting of the screwsabout the plane of the stud flange and the screw heads pulling through theOSB sheathings, while the response of gypsum wallboard (GWB) sheathingsto-frameconnections was characterized by combination of the bearing of theGWB panels and the screws heads pulling through the GWB panels.For higher lateral displacements, the heads of the end screws completelypulled through the sheathings or, in some cases, the screws caused the ruptureof the sheathing edges. As a result, both the OSB and GWB sheathingsbecame unzipped along the panel edges.Comparison of shear responses of two walls: monotonic response vs. cyclicresponseFor both the monotonic and cyclic loading, the walls had similar behaviorfor small displacements, while they exhibited different response for largedisplacement levels.In particular, the wall 1 was more resistant than wall 2 of about 7% in thecase of the monotonic test. In the case of cyclic test, considering the firsthysteretic loops, the two walls revealed the same shear capacity for positivedisplacements, while the wall 1 was lightly more resistant than wall 2 of 9%for the negative ones; whereas, considering the third hysteretic loops the wall1 was lightly more resistant than wall 2 of 13% for both positive and negativedisplacements.Monotonic response vs. cyclic response in terms of shear strengthBy comparing the unit shear strength found in the monotonic test and theone obtained from cyclic test at the first hysteretic loops of positive

Conclusions 209displacements, the cyclic loading produced a 11% reduction. This reductionbecame of 20% for negative displacements; whereas, considering the shearstrength obtained in the cyclic test at third hysteretic loops the degradationincreased up to 45% and 32% for positive and negative displacements,respectively.Moreover, the difference between the cyclic and monotonic responsebecame significant for the unstable part of the behavior.Shear strength degradation under cyclic loadingFrom comparison between the experimental loads obtained at the first andthird hysteretic loops a clear shear strength degradation was observed. In factthe 38% and 16% reduction of shear capacity resulted for positive andnegative shear strengths, respectively.Effectiveness of lateral-load transfer from horizontal diaphragms to stud wallsThe lateral-load transfer from horizontal diaphragms to stud walls waseffective. In fact the floor-to-walls sliding was small in both the monotonicand cyclic tests.Reliability of semi-empirical calculation of the shear strengthThe calculation of shear strength by using the semi-empiricalmethodologies appears valid, it revealing a small conservative 3% predictionin the case of monotonic loading. On contrary, in the case of cyclic loading,the results give 15% and 57% overestimation of the shear capacity, if thehighest (first hysteretic loops) and lowest (third hysteretic loops) strengthcurves, respectively are used.Incremental Dynamic Analysis (IDA) resultsFrom the examination of the IDA results, a discrete ductility for theCFSSSW systems has been found. In fact, considering the S aeu /S aey ratio (inwhich S aey and S aeu are the elastic spectral accelerations corresponding to yield

210limit ( y ) and ultimate limit displacements ( u ), respectively) as a measure ofseismic toughness, for all the examined earthquake records, this parameterranges from 1.26 to 3.89 with a mean value of 2.27 and a standard deviationof 0.62.The comparison between the results obtained for different soil types hasshown that the accelerograms recorded on soil type D are the most severe andthe least scattered; whereas, the least severe results have been found for soiltypes A and B, while the maximum dispersion of data has been obtained forthe soil type C.Definition of the load historyOnce fixed the maximum level of the normalized deformation(=(/ y ) max = u / y =36/6=6), as result of the statistic characterization ofdeformation history, the following parameters have been obtained: number ofinelastic excursions (N p =24 in average); sum of the normalized plasticdeformation ranges ( pi / y =7.5 in average); ratio between the mean valueand the maximum value of the plastic deformation range(( p ) av /( p ) max =0.28 in average).From comparison between the results obtained in this research (that takein-to account the cyclic behavior of CFSSSW systems) and those reported fora bilinear SDOF system by Krawinkler (N p =30 and pi / y =36 in average,see Figs. 5.18 and 5.19) a reduction of the parameters associated to thedamage level has been observed in the case of CFSSSW systems. Inparticular, a decrease of 24% for N p and 79% for pi / y has been found.The test procedure, made of fully reversing cyclic displacements itconsisting of a series of stepwise increasing deformation cycles, which hasbeen derived in this research, results to be reasonable. In fact, the value ofparameters associated to the damage level corresponding to this deformationhistory (N p =25, pi / y =6.2 and ( p ) av /( p ) max =0.28) are close to thoseobtained from statistic characterization.

A-1Appendix ASummary of existing experimental results

A-2 Appendix AMc Creless & Tarpy (1978)Label TestType ofloading(1)wall size(2)aspectratio(2)opening(3)frame(4)frame fasteners(5)sheathing(6)sheathing fasteners(5)horizontal straps (HS)solid blocking (SB)(7)X-bracing(7)X-bracing fasteners(5)Type ofanchorage(8)Type offailure(9)ultimateshearh x L h / Lsheathingarea ratiosteel gradestud sizetrack sizestud spacing typetype;thickness;orientationtype; exterior spacing;interior spacingHB sizeSB size size type; number kN/mM78-1 AM78-2 A*3660x3660 1.00- 6.03HB ?SB ?F 5.11M78-3 B 3660x4880 0.75 5.75M78-4 C 3660x7320 0.50 C (FT) 5.30M78-5 D 3050x3660 0.83 F 5.47M78-6 E M 3050x4880 0.63 1.00?C89x?x?x0.84*U92x38x0.84610LPHSC4.8x13GWB;12.7;?+GWB;12.7;?BHSC3.5x25; 305; 305BHSC3.5x25; 305; 305- - BCA 5.20M78-7 F 3050x7320 0.42 - C (FT) 5.66M78-8 G 2440x2440 1.00 5.84M78-9 H 2440x3660 0.67 F 5.84M78-10 I 2440x4880 0.50 6.84M78-11 J 2440x7320 0.33 C (FT) 5.66length in mm; ?: not known; -: not present(1) M: monotonic; C: cyclic(2) h: heigth of the wall; L: length of the wall(3) r =1 / [1 + Ao / (h Li)] with Ao: area of openings and Li the length of the full height wall segment(4) C__x__x__x__ (lipped channel section) web depth x flange size x lip size x thickness; U__x__x__ (unlipped channel section) web depth x flange size x thickness; *: double back-to-back coupled end studs(5) BHSC: bugle-head screws FHSC: flat head screws; LPHSC: low profile head screws; MTHSC: modified truss head screws; WHSC: wafer head screws; __x__: nominal diameter x length; NA: Nails diameter; PI: Pins diameter(6) GSB: Gypsum sheathing board; GWB: Gypsum wallboard; FB: Fiber board; OSB: Oriented strand board; PLY: Plywood; SCS: Steel corrugated seet; SSS: Steel sheet sheathing;V: parallel to the frame (vertical); O: orthogonal to the frame (horizontal)(7) I__x__ flat strap wide x thickness(8) BCA: bolted clip angles; PCA: clip angles fixed wit powder actuated fasteners; HD: hold-down; SHD: strip-hold down(9) F: foundation uplift failure; S: stud buckling failure; X: X bracing yielding;C (FPO): connections failure (fasteners pull out failure); C (FPT): connections failure (fasteners pull throgh failure); C (FS): connections failure (fasteners shear failure); C (FT): connections failure (fasteners tilting failure); C (NS): connections faiO): c(net section failure);r

Summary of existing experimental results A-3Tarpy & Girard (1982)Label TestType ofloading(1)wall size(2)aspectratio(2)opening(3)frame(4)frame fasteners(5)sheathing(6)sheathing fasteners(5)horizontal straps (HS)solid blocking (SB)(7)X-bracing(7)X-bracing fasteners(5)Type ofanchorage(8)Type offailure(9)ultimateshearh x L h / Lsheathingarea ratiosteel gradestud sizetrack sizestud spacing typetype;thickness;orientationtype; exterior spacing;interior spacingHB sizeSB size size type; number kN/mTG82-1 A 2440x2440 1.00BCA6.03TG82-2 B 2440x3660 0.67 5.47TG82-3 E - 4.57TG82-4 GTG82-5 KA 36C89x25x13x0.84*U92x38x0.84610TG82-6 L M 1.00 ?TG82-7 M 2440x2440 1.00TG82-8 NGWB;12.7;H+GWB;12.7;HGSB;12.7;H+GWB;12.7;HGWB;12.7;H+PLY;12.7;HBHSC3.5x25; 305; 305BHSC3.5x25; 305; 305- 5.66PCA 3.82- - - F 6.20BCA 3.937.85TG82-9 P 5.28TG82-10 QGSB;12.7;H+GWB;12.7;HA 36C89x25x13x0.84*TG82-11 RBCA 6.93U92x38x0.84406length in mm; ?: not known; -: not present(1) M: monotonic; C: cyclic(2) h: heigth of the wall; L: length of the wall(3) r =1 / [1 + Ao / (h Li)] with Ao: area of openings and Li the length of the full height wall segment(4) C__x__x__x__ (lipped channel section) web depth x flange size x lip size x thickness; U__x__x__ (unlipped channel section) web depth x flange size x thickness; *: double back-to-back coupled end studs(5) BHSC: bugle-head screws FHSC: flat head screws; LPHSC: low profile head screws; MTHSC: modified truss head screws; WHSC: wafer head screws; __x__: nominal diameter x length; NA: Nails diameter; PI: Pins diameter(6) GSB: Gypsum sheathing board; GWB: Gypsum wallboard; FB: Fiber board; OSB: Oriented strand board; PLY: Plywood; SCS: Steel corrugated seet; SSS: Steel sheet sheathing;V: parallel to the frame (vertical); O: orthogonal to the frame (horizontal)(7) I__x__ flat strap wide x thickness(8) BCA: bolted clip angles; PCA: clip angles fixed wit powder actuated fasteners; HD: hold-down; SHD: strip-hold down(9) F: foundation uplift failure; S: stud buckling failure; X: X bracing yielding;C (FPO): connections failure (fasteners pull out failure); C (FPT): connections failure (fasteners pull throgh failure); C (FS): connections failure (fasteners shear failure); C (FT): connections failure (fasteners tilting failure); C (NS): connections faiO): c(net section failure);4.38r

A-4 Appendix ATissel (1993)Label TestType ofloading(1)wall size(2)aspectratio(2)opening(3)frame(4)frame fasteners(5)sheathing(6)sheathing fasteners(5)horizontal straps (HS)solid blocking (SB)(7)X-bracing(7)X-bracing fasteners(5)Type ofanchorage(8)Type offailure(9)ultimateshearT93-1 1h x L h / Lsheathingarea ratiosteel gradestud sizetrack sizestud spacing type?C64x41x?x1.88U64x88x1.88type;thickness;orientation610 PLY;9.5;Vtype; exterior spacing;interior spacingHB sizeSB size size type; number kN/m24.31T93-2 2T93-3 3?C89x41x?x150U89x41x1.50610SC4.8x?; 102; 305 15.95OSB;11.1;V 18.21T93-4 4 M 2440x2440 1.00 1.00 ?SC4.2x?; 152; 305 - - - ? ? 10.92T93-5 5?C89x41x?x1.19U89x41x1.19610PLY;9.5;VSC4.2x?; 102; 305 14.01T93-6 6 OSB;11.1;V SC4.2x?; 76; 305 15.98T93-7 7T93-8 8?C64x41x?x1,88U64x88x1.88610OSB;15.1;V PI3.7; 152; 305 15.88PLY;15.9;V PI3.7; 102; 305 27.22length in mm; ?: not known; -: not present(1) M: monotonic; C: cyclic(2) h: heigth of the wall; L: length of the wall(3) r =1 / [1 + Ao / (h Li)] with Ao: area of openings and Li the length of the full height wall segment(4) C__x__x__x__ (lipped channel section) web depth x flange size x lip size x thickness; U__x__x__ (unlipped channel section) web depth x flange size x thickness; *: double back-to-back coupled end studs(5) BHSC: bugle-head screws FHSC: flat head screws; LPHSC: low profile head screws; MTHSC: modified truss head screws; WHSC: wafer head screws; __x__: nominal diameter x length; NA: Nails diameter; PI: Pins diameter(6) GSB: Gypsum sheathing board; GWB: Gypsum wallboard; FB: Fiber board; OSB: Oriented strand board; PLY: Plywood; SCS: Steel corrugated seet; SSS: Steel sheet sheathing;V: parallel to the frame (vertical); O: orthogonal to the frame (horizontal)(7) I__x__ flat strap wide x thickness(8) BCA: bolted clip angles; PCA: clip angles fixed wit powder actuated fasteners; HD: hold-down; SHD: strip-hold down(9) F: foundation uplift failure; S: stud buckling failure; X: X bracing yielding;C (FPO): connections failure (fasteners pull out failure); C (FPT): connections failure (fasteners pull throgh failure); C (FS): connections failure (fasteners shear failure); C (FT): connections failure (fasteners tilting failure); C (NS): connections faiO): c(net section failure);r

Summary of existing experimental results A-5Serrette (1994)Label TestType ofloading(1)wall size(2)aspectratio(2)opening(3)frame(4)frame fasteners(5)sheathing(6)sheathing fasteners(5)horizontal straps (HS)solid blocking (SB)(7)X-bracing(7)X-bracing fasteners(5)Type ofanchorage(8)Type offailure(9)ultimateshearh x L h / Lsheathingarea ratiosteel gradestud sizetrack sizestud spacing typetype;thickness;orientationtype; exterior spacing;interior spacingHB sizeSB size size type; number kN/mS94-1 1 - - I51x0.84 ? 4.42S94-2 2 GWB;12.7;V SC3.5x?; 152; 305 - - 10.92+GWB;12.7;V SC3.5x?; 152; 305S94-3 3- I51x0.84 ? 13.56S94-4 4 A653 Grade SQ 33 SC3.5x?; 152; 305 15.31C152x41x?x0.84*S94-5 5 M 2440x2440 1.00 1.00? PLY;11.9;V PI2.9: 152; 305 ? ? 9.06U152x32x0.84S94-6 6 610 14.24S94-7 7 PLY;11.9;O SC4.2x?; 152; 305 6.14S94-8 8HB ?SB ?- - 14.30S94-9 9 PI2.9: 152; 305 - 8.76S94-10 10 11.50SC4.2x?; 152; 305 OSB;11.1;V HB ?S94-11 11 12.08SB ?S94-12 12 SC3.5x?; 152; 305 - 4.63length in mm; ?: not known; -: not present(1) M: monotonic; C: cyclic(2) h: heigth of the wall; L: length of the wall(3) r =1 / [1 + Ao / (h Li)] with Ao: area of openings and Li the length of the full height wall segment(4) C__x__x__x__ (lipped channel section) web depth x flange size x lip size x thickness; U__x__x__ (unlipped channel section) web depth x flange size x thickness; *: double back-to-back coupled end studs(5) BHSC: bugle-head screws FHSC: flat head screws; LPHSC: low profile head screws; MTHSC: modified truss head screws; WHSC: wafer head screws; __x__: nominal diameter x length; NA: Nails diameter; PI: Pins diameter(6) GSB: Gypsum sheathing board; GWB: Gypsum wallboard; FB: Fiber board; OSB: Oriented strand board; PLY: Plywood; SCS: Steel corrugated seet; SSS: Steel sheet sheathing;V: parallel to the frame (vertical); O: orthogonal to the frame (horizontal)(7) I__x__ flat strap wide x thickness(8) BCA: bolted clip angles; PCA: clip angles fixed wit powder actuated fasteners; HD: hold-down; SHD: strip-hold down(9) F: foundation uplift failure; S: stud buckling failure; X: X bracing yielding;C (FPO): connections failure (fasteners pull out failure); C (FPT): connections failure (fasteners pull throgh failure); C (FS): connections failure (fasteners shear failure); C (FT): connections failure (fasteners tilting failure); C (NS): connections faiO): c(net section failure);r

A-6 Appendix ASerrette & Ogunfunmi (1996)Label TestType ofloading(1)wall size(2)aspectratio(2)opening(3)frame(4)frame fasteners(5)sheathing(6)sheathing fasteners(5)horizontal straps (HS)solid blocking (SB)(7)X-bracing(7)X-bracing fasteners(5)Type ofanchorage(8)Type offailure(9)ultimateshearh x L h / Lsheathingarea ratiosteel gradestud sizetrack sizestud spacing typetype;thickness;orientationtype; exterior spacing;interior spacingHB sizeSB size size type; number kN/mSO96-1A-P;A-2;A-3- - I51x0.84 WHSC4.2x13; 14 X 4.95SO96-2SO96-3B-P;B-2;B-3;B-4;B-5C-1;C-2;C-3;C-4M 2440x2440 1.00 1.00A446 Grade AC152x32x?x0.84*U152x?x0.84610WHSC4.2x13 - - - BCA 10.47GSB;12.7;VGWB;12.7;VBHSC3.5x25; 152; 305BHSC3.5x25; 152; 305I51x0.84 WHSC4.2x13; 14 C (FT) 14.06I51x0.84SO96-4 C-5+I51x0.84WHSC4.2x13; 1419.02WHSC4.2x13; 14length in mm; ?: not known; -: not present(1) M: monotonic; C: cyclic(2) h: heigth of the wall; L: length of the wall(3) r =1 / [1 + Ao / (h Li)] with Ao: area of openings and Li the length of the full height wall segment(4) C__x__x__x__ (lipped channel section) web depth x flange size x lip size x thickness; U__x__x__ (unlipped channel section) web depth x flange size x thickness; *: double back-to-back coupled end studs(5) BHSC: bugle-head screws FHSC: flat head screws; LPHSC: low profile head screws; MTHSC: modified truss head screws; WHSC: wafer head screws; __x__: nominal diameter x length; NA: Nails diameter; PI: Pins diameter(6) GSB: Gypsum sheathing board; GWB: Gypsum wallboard; FB: Fiber board; OSB: Oriented strand board; PLY: Plywood; SCS: Steel corrugated seet; SSS: Steel sheet sheathing;V: parallel to the frame (vertical); O: orthogonal to the frame (horizontal)(7) I__x__ flat strap wide x thickness(8) BCA: bolted clip angles; PCA: clip angles fixed wit powder actuated fasteners; HD: hold-down; SHD: strip-hold down(9) F: foundation uplift failure; S: stud buckling failure; X: X bracing yielding;C (FPO): connections failure (fasteners pull out failure); C (FPT): connections failure (fasteners pull throgh failure); C (FS): connections failure (fasteners shear failure); C (FT): connections failure (fasteners tilting failure); C (NS): connections faiO): c(net section failure);r

Summary of existing experimental results A-7Serrette et al. (1996a)Label TestType ofloading(1)wall size(2)aspectratio(2)opening(3)frame(4)frame fasteners(5)sheathing(6)sheathing fasteners(5)horizontal straps (HS)solid blocking (SB)(7)X-bracing(7)X-bracing fasteners(5)Type ofanchorage(8)Type offailure(9)ultimateshearS+96a-1S+96a-2S+96a-3S+96a-4S+96a-5S+96a-6S+96a-7S+96a-81A6,1A71A2;1A3h x L h / Lsheathingarea ratiosteel gradestud sizetrack sizestud spacing typetype;thickness;orientationPLY;11.9;Vtype; exterior spacing;interior spacingHB sizeSB size size type; number kN/m2440x2440 1.00 OSB;11.1;V FHSC4.2x25; 152; 30513.291A5;1A6 OSB;11.1;O1E1;1E21D3;1D41D5;1D61D7;1D8 A653 Grade SQ 331F1;1F2M 2440x1220 2.00 1.00C89x41x10x0.84*C89x32x0.84610WHSC4.2x13HB I38x0.84SB ?FHSC4.2x25; 102; 305 20.61OSB;11.1;V FHSC4.2x25; 76; 305 25.33FHSC4.2x25; 51; 305 27.90BHSC3.5x32; 178; 178FHSC4.2x25; 152; 30515.5014.9114.96- - - HD C (FT) 17.75S+96a-91F3;1F4GWB;12.7;V+OSB;11.1;VBHSC3.5x32; 178; 178FHSC4.2x25; 102; 30522.77S+96a-101F5;1F6BHSC3.5x32; 178; 178FHSC4.2x25; 51; 30527.49S+96a-11S+96a-122A1;1A32A2;2A42440x2440 1.00GWB;12.7;O+GWB;12.7;OBHSC3.5x32; 178; 178BHSC3.5x32; 178; 178BHSC3.5x32; 102; 102BHSC3.5x32; 102; 102HB I38x0.84SB ?length in mm; ?: not known; -: not present(1) M: monotonic; C: cyclic(2) h: heigth of the wall; L: length of the wall(3) r =1 / [1 + Ao / (h Li)] with Ao: area of openings and Li the length of the full height wall segment(4) C__x__x__x__ (lipped channel section) web depth x flange size x lip size x thickness; U__x__x__ (unlipped channel section) web depth x flange size x thickness; *: double back-to-back coupled end studs(5) BHSC: bugle-head screws FHSC: flat head screws; LPHSC: low profile head screws; MTHSC: modified truss head screws; WHSC: wafer head screws; __x__: nominal diameter x length; NA: Nails diameter; PI: Pins diameter(6) GSB: Gypsum sheathing board; GWB: Gypsum wallboard; FB: Fiber board; OSB: Oriented strand board; PLY: Plywood; SCS: Steel corrugated seet; SSS: Steel sheet sheathing;V: parallel to the frame (vertical); O: orthogonal to the frame (horizontal)(7) I__x__ flat strap wide x thickness(8) BCA: bolted clip angles; PCA: clip angles fixed wit powder actuated fasteners; HD: hold-down; SHD: strip-hold down(9) F: foundation uplift failure; S: stud buckling failure; X: X bracing yielding;C (FPO): connections failure (fasteners pull out failure); C (FPT): connections failure (fasteners pull throgh failure); C (FS): connections failure (fasteners shear failure); C (FT): connections failure (fasteners tilting failure); C (NS): connections faiO): c(net section failure);8.5112.39r-

A-8 Appendix ASerrette et al. (1996a,b)Label TestType ofloading(1)wall size(2)aspectratio(2)opening(3)frame(4)frame fasteners(5)sheathing(6)sheathing fasteners(5)horizontal straps (HS)solid blocking (SB)(7)X-bracing(7)X-bracing fasteners(5)Type ofanchorage(8)Type offailure(9)ultimateshearS+96ab-1S+96ab-2S+96ab-3S+96ab-4S+96ab-5S+96ab-6S+96ab-7S+96ab-8OSB1;OSB2h x L h / Lsheathingarea ratiosteel gradestud sizetrack sizestud spacing typetype;thickness;orientationOSB3;OSB4 OSB;11.1;VOSB5;OSB6OSB7;OSB8PLY1;PLY2C 2440x1220 2.00 1.00A653 Grade SQ 33C89x41x10x0.84*C89x32x0.84610PLY3;PLY4 PLY;11.9;VPLY5;PLY6PLY7;PLY8type; exterior spacing;interior spacingHB sizeSB size size type; number kN/mFHSC4.2x25; 152; 305 10.22FHSC4.2x25; 102; 305 13.32FHSC4.2x25; 76; 305 18.61WHSC4.2x13 FHSC4.2x25; 51; 305 - - - HD C (FT) 24.81FHSC4.2x25; 152; 305 11.38FHSC4.2x25; 102; 305 14.41FHSC4.2x25; 76; 305 21.34FHSC4.2x25; 51; 305 23.71length in mm; ?: not known; -: not present(1) M: monotonic; C: cyclic(2) h: heigth of the wall; L: length of the wall(3) r =1 / [1 + Ao / (h Li)] with Ao: area of openings and Li the length of the full height wall segment(4) C__x__x__x__ (lipped channel section) web depth x flange size x lip size x thickness; U__x__x__ (unlipped channel section) web depth x flange size x thickness; *: double back-to-back coupled end studs(5) BHSC: bugle-head screws FHSC: flat head screws; LPHSC: low profile head screws; MTHSC: modified truss head screws; WHSC: wafer head screws; __x__: nominal diameter x length; NA: Nails diameter; PI: Pins diameter(6) GSB: Gypsum sheathing board; GWB: Gypsum wallboard; FB: Fiber board; OSB: Oriented strand board; PLY: Plywood; SCS: Steel corrugated seet; SSS: Steel sheet sheathing;V: parallel to the frame (vertical); O: orthogonal to the frame (horizontal)(7) I__x__ flat strap wide x thickness(8) BCA: bolted clip angles; PCA: clip angles fixed wit powder actuated fasteners; HD: hold-down; SHD: strip-hold down(9) F: foundation uplift failure; S: stud buckling failure; X: X bracing yielding;C (FPO): connections failure (fasteners pull out failure); C (FPT): connections failure (fasteners pull throgh failure); C (FS): connections failure (fasteners shear failure); C (FT): connections failure (fasteners tilting failure); C (NS): connections faiO): c(net section failure);r

Summary of existing experimental results A-9Serrette et al. (1997a)Label TestType ofloading(1)wall size(2)aspectratio(2)opening(3)frame(4)frame fasteners(5)sheathing(6)sheathing fasteners(5)horizontal straps (HS)solid blocking (SB)(7)X-bracing(7)X-bracing fasteners(5)Type ofanchorage(8)Type offailure(9)ultimateshearh x L h / Lsheathingarea ratiosteel gradestud sizetrack sizestud spacing typetype;thickness;orientationtype; exterior spacing;interior spacingHB sizeSB size size type; number kN/mS+97a-1 PLY-T1 BHSC3.5x25; 152; 305 C (FS) 15.02S+97a-2 PLY-T2-N PLY;11.9;V NA3.7; 152; 305 - 9.06S+97a-3 PLY-T4 15.62S+97a-4 PLY-T6 BHSC4.2x32; 152 ;305 C (FPO) 6.74S+97a-5 PLY-T7S+97a-6 PLYGYPPLY;11.9;O HB I31x0.84SB ?PLY;11.9;V+GWB;12.7;VNA3.7; 152; 305BHSC3.5X25; 178; 178 -15.62C (FS) 18.43S+97a-7 OSB-T1-N OSB;11.1;V NA3.7; 152; 305 8.86S+97a-8 OSB-T4 BHSC4.2x32; 152 ;305 C (FT) 13.81S+97a-9 OSB-T5 OSB;11.1;OS+97a-10 GYP-T1 M 2440x2440 1.00 1.00 A446 Grade AC152x41x10x0.84*S+97a-11 GYP-T2U152x25x0.84610WHSC4.2x13GWB;12.7;O+GWB;12.7;OBHSC3.5x25; 152 ;305BHSC3.5x25; 152 ;305HB I31x0.84SB ?14.30- - HD 9.8711.79S+97a-12 GYP-T3S+97a-13 GYP-T4GWB;12.7;V+GWB;12.7;VBHSC3.5x25; 178 ;178BHSC3.5x25; 178 ;178BHSC3.5x25; 102 ;102BHSC3.5x25; 102 ;10210.68C (FS) 14.71S+97a-14 FB-T4 FB;12.7;V BHSC3.5x25; 152 ;305 - 5.63S+97a-15 FB-T5 BHSC3.5x25; 102 ;305 6.04BHSC3.5x32; 152 ;305S+97a-16 FB-T6 FB;12.7;V10.83+ BHSC3.5x32; 152 ;305FB;12.7;V BHSC3.5x32; 102 ;305S+97a-17 FB-T715.21BHSC3.5x32; 102 ;305S+97a-18 FB-T8 FB;12.7;V BHSC3.5x32; 102 ;305 7.15length in mm; ?: not known; -: not present(1) M: monotonic; C: cyclic(2) h: heigth of the wall; L: length of the wall(3) r =1 / [1 + Ao / (h Li)] with Ao: area of openings and Li the length of the full height wall segment(4) C__x__x__x__ (lipped channel section) web depth x flange size x lip size x thickness; U__x__x__ (unlipped channel section) web depth x flange size x thickness; *: double back-to-back coupled end studs(5) BHSC: bugle-head screws FHSC: flat head screws; LPHSC: low profile head screws; MTHSC: modified truss head screws; WHSC: wafer head screws; __x__: nominal diameter x length; NA: Nails diameter; PI: Pins diameter(6) GSB: Gypsum sheathing board; GWB: Gypsum wallboard; FB: Fiber board; OSB: Oriented strand board; PLY: Plywood; SCS: Steel corrugated seet; SSS: Steel sheet sheathing;V: parallel to the frame (vertical); O: orthogonal to the frame (horizontal)(7) I__x__ flat strap wide x thickness(8) BCA: bolted clip angles; PCA: clip angles fixed wit powder actuated fasteners; HD: hold-down; SHD: strip-hold down(9) F: foundation uplift failure; S: stud buckling failure; X: X bracing yielding;C (FPO): connections failure (fasteners pull out failure); C (FPT): connections failure (fasteners pull throgh failure); C (FS): connections failure (fasteners shear failure); C (FT): connections failure (fasteners tilting failure); C (NS): connections faiO): c(net section failure);r

A-10 Appendix ASerrette et al. (1997b) - Monotonic testsLabel TestType ofloading(1)wall size(2)aspectratio(2)opening(3)frame(4)frame fasteners(5)sheathing(6)sheathing fasteners(5)horizontal straps (HS)solid blocking (SB)(7)X-bracing(7)X-bracing fasteners(5)Type ofanchorage(8)Type offailure(9)ultimateshearS+97b-1S+97b-2S+97b-3S+97b-4S+97b-5S+97b-6S+97b-7S+97b-81;23;45;67;89;1011;1213;1415;16h x L h / L2440x1220 2.00sheathingarea ratiosteel gradestud sizetrack sizestud spacing typeA653 Grade SQ 33C89x43x13x0.84*U89x32x0.84type;thickness;orientationtype; exterior spacing;interior spacing610 - -A653 Grade SQ 33C89x43x13x1.09*U89x32x1.09610HB sizeSB size size type; number kN/mI114x0.84 MTHSC4.2x13; 20 9.82I191x0.84 MTHSC4.2x13; 30FHSC4.2x25; 152; 305 7.84M 1.00 MTHSC4.2x13 OSB;11.1;V FHSC4.2x25; 102; 305 - HD 14.972440x610 4.00A653 Grade SQ 33C89x43x13x0.84*U89x32x0.84610FHSC4.2x25; 51; 305- -SSS;0.46;? MTHSC4.2x13; 152; 305 7.17SSS;0.69;? MTHSC4.2x13; 102; 305 C (NS) 14.452440x1220 2.00 SSS;0.46;? MTHSC4.2x13; 152; 305 7.05length in mm; ?: not known; -: not present(1) M: monotonic; C: cyclic(2) h: heigth of the wall; L: length of the wall(3) r =1 / [1 + Ao / (h Li)] with Ao: area of openings and Li the length of the full height wall segment(4) C__x__x__x__ (lipped channel section) web depth x flange size x lip size x thickness; U__x__x__ (unlipped channel section) web depth x flange size x thickness; *: double back-to-back coupled end studs(5) BHSC: bugle-head screws FHSC: flat head screws; LPHSC: low profile head screws; MTHSC: modified truss head screws; WHSC: wafer head screws; __x__: nominal diameter x length; NA: Nails diameter; PI: Pins diameter(6) GSB: Gypsum sheathing board; GWB: Gypsum wallboard; FB: Fiber board; OSB: Oriented strand board; PLY: Plywood; SCS: Steel corrugated seet; SSS: Steel sheet sheathing;V: parallel to the frame (vertical); O: orthogonal to the frame (horizontal)(7) I__x__ flat strap wide x thickness(8) BCA: bolted clip angles; PCA: clip angles fixed wit powder actuated fasteners; HD: hold-down; SHD: strip-hold down(9) F: foundation uplift failure; S: stud buckling failure; X: X bracing yielding;C (FPO): connections failure (fasteners pull out failure); C (FPT): connections failure (fasteners pull throgh failure); C (FS): connections failure (fasteners shear failure); C (FT): connections failure (fasteners tilting failure); C (NS): connections faiO): c(net section failure);S12.8026.63r

Summary of existing experimental results A-11Serrette et al. (1997b) - Cyclic testsLabel TestType ofloading(1)wall size(2)aspectratio(2)opening(3)frame(4)frame fasteners(5)sheathing(6)sheathing fasteners(5)horizontal straps (HS)solid blocking (SB)(7)X-bracing(7)X-bracing fasteners(5)Type ofanchorage(8)Type offailure(9)ultimateshearS+97b-9S+97b-10S+97b-11S+97b-12S+97b-13S+97b-14S+97b-15S+97b-16S+97b-17S+97b-18S+97b-19S+97b-20S+97b-21S+97b-22sheathingarea ratiosteel gradestud sizetrack sizestud spacing typetype;thickness;orientationtype; exterior spacing;interior spacingHB sizeSB size size type; number kN/mh x L h / LA1;A2 A653 Grade SQ 33 PLY;11.9;V FHSC4.2x25; 76; 305 C25.90A3;C89x43x13x0,84 int.FHSC4.2x25; 51; 305 31.96A4C89x43x13x1.09* endsA5;U89x32x0.84A6610 OSB;11.1;V FHSC4.2x25; 76; 305 C (FT)22.23A7;A8B1;B2B3;B42440x1220 2.00C 1.00A653 Grade SQ 33C89x43x13x1.09*U89x32x1.09610 PLY;11.9;V FHSC4.2x25; 152; 305A653 Grade SQ 33C89x43x13x1.37*U89x32x1.37610C1;C2 - -C3;C4D1;D2E1;E2E3;E4E5;E6A653 Grade SQ 33C89x43x13x0.84*U89x32x0.84610FHSC4.2x25; 51; 305 30.03- -C (FT) 13.02MTHSC4.2x13 - HD C (FS) 13.19I114x0.84 MTHSC4.2x13; 20S11.98I191x0.84 MTHSC4.2x13; 30 12.24SSS;0.46;? MTHSC4.2x13; 152; 305 C (NS) 5.72FHSC4.2x25; 152; 305 S 10.52OSB;11.1;V FHSC4.2x25; 102; 305- -2440x610 4.00 FHSC4.2x25; 51; 305 23.70F1;F2 SSS;0.69;? MTHSC4.2x13; 102; 305 S+CF3;(FPO+NS)MTHSC4.2x13; 51; 305F4length in mm; ?: not known; -: not present(1) M: monotonic; C: cyclic(2) h: heigth of the wall; L: length of the wall(3) r =1 / [1 + Ao / (h Li)] with Ao: area of openings and Li the length of the full height wall segment(4) C__x__x__x__ (lipped channel section) web depth x flange size x lip size x thickness; U__x__x__ (unlipped channel section) web depth x flange size x thickness; *: double back-to-back coupled end studs(5) BHSC: bugle-head screws FHSC: flat head screws; LPHSC: low profile head screws; MTHSC: modified truss head screws; WHSC: wafer head screws; __x__: nominal diameter x length; NA: Nails diameter; PI: Pins diameter(6) GSB: Gypsum sheathing board; GWB: Gypsum wallboard; FB: Fiber board; OSB: Oriented strand board; PLY: Plywood; SCS: Steel corrugated seet; SSS: Steel sheet sheathing;V: parallel to the frame (vertical); O: orthogonal to the frame (horizontal)(7) I__x__ flat strap wide x thickness(8) BCA: bolted clip angles; PCA: clip angles fixed wit powder actuated fasteners; HD: hold-down; SHD: strip-hold down(9) F: foundation uplift failure; S: stud buckling failure; X: X bracing yielding;C (FPO): connections failure (fasteners pull out failure); C (FPT): connections failure (fasteners pull throgh failure); C (FS): connections failure (fasteners shear failure); C (FT): connections failure (fasteners tilting failure); C (NS): connections faiO): c(net section failure);16.4314.6417.09r

A-12 Appendix ANAHB (1997)Label TestType ofloading(1)wall size(2)aspectratio(2)opening(3)frame(4)frame fasteners(5)sheathing(6)sheathing fasteners(5)horizontal straps (HS)solid blocking (SB)(7)X-bracing(7)X-bracing fasteners(5)Type ofanchorage(8)Type offailure(9)ultimateshearh x L h / Lsheathingarea ratiosteel gradestud sizetrack sizestud spacing typetype;thickness;orientationtype; exterior spacing;interior spacingHB sizeSB size size type; number kN/mN97-1 1 1.00N97-2 2A0.76M 2440x12190 0.20N97-3 2B 0.76?C89x38x?x0.84 SC4.2x?U?x?x?610GWB;12.7;V+SC3.5x?; 178; 254OSB;11.1;V SC4.2x?; 152; 305- - -HD C (FPT)15.409.56- F 4.56N97-4 4 0.48 HD C (FPT) 4.78length in mm; ?: not known; -: not present(1) M: monotonic; C: cyclic(2) h: heigth of the wall; L: length of the wall(3) r =1 / [1 + Ao / (h Li)] with Ao: area of openings and Li the length of the full height wall segment(4) C__x__x__x__ (lipped channel section) web depth x flange size x lip size x thickness; U__x__x__ (unlipped channel section) web depth x flange size x thickness; *: double back-to-back coupled end studs(5) BHSC: bugle-head screws FHSC: flat head screws; LPHSC: low profile head screws; MTHSC: modified truss head screws; WHSC: wafer head screws; __x__: nominal diameter x length; NA: Nails diameter; PI: Pins diameter(6) GSB: Gypsum sheathing board; GWB: Gypsum wallboard; FB: Fiber board; OSB: Oriented strand board; PLY: Plywood; SCS: Steel corrugated seet; SSS: Steel sheet sheathing;V: parallel to the frame (vertical); O: orthogonal to the frame (horizontal)(7) I__x__ flat strap wide x thickness(8) BCA: bolted clip angles; PCA: clip angles fixed wit powder actuated fasteners; HD: hold-down; SHD: strip-hold down(9) F: foundation uplift failure; S: stud buckling failure; X: X bracing yielding;C (FPO): connections failure (fasteners pull out failure); C (FPT): connections failure (fasteners pull throgh failure); C (FS): connections failure (fasteners shear failure); C (FT): connections failure (fasteners tilting failure); C (NS): connections faiO): c(net section failure);r

Summary of existing experimental results A-13Selenikovich et al. (1999)Label TestType ofloading(1)wall size(2)aspectratio(2)opening(3)frame(4)frame fasteners(5)sheathing(6)sheathing fasteners(5)horizontal straps (HS)solid blocking (SB)(7)X-bracing(7)X-bracing fasteners(5)Type ofanchorage(8)Type offailure(9)ultimateshearS+99-1S+99-2A monotonicwithoutGWBA cyclicstabilizedwithoutGWBh x L h / Lsheathingarea ratiosteel gradestud sizetrack sizestud spacing typetype;thickness;orientationtype; exterior spacing;interior spacingHB sizeSB size size type; number kN/mM 11.85C 1.00OSB;11.1;V BHSC4.2x?; 152 ;305GWB;12.7;V BHSC4.2x?; 178; 254M+14.69S+99-3 A monotonicwith GWBOSB;11.1;V BHSC4.2x?; 152; 305S+99-4 B monotonic M 7.55B cyclic0.76 350S150-33S+99-5C 2440x12200 0.20C89x38x?x0.84* LPHSC4.2x? - - - HD C (FPT) 6.38stabilizedU89x38x0.84S+99-6 C monotonic M 5.07C cyclic0.56S+99-7C4.27stabilizedS+99-8 D monotonic M OSB;11.1;V BHSC4.2x?; 152 ;305 4.67D cyclic0.48S+99-9C3.68stabilizedS+99-10 E monotonic M 2.81E cyclic0.30S+99-11C2.04stabilizedlength in mm; ?: not known; -: not present(1) M: monotonic; C: cyclic(2) h: heigth of the wall; L: length of the wall(3) r =1 / [1 + Ao / (h Li)] with Ao: area of openings and Li the length of the full height wall segment(4) C__x__x__x__ (lipped channel section) web depth x flange size x lip size x thickness; U__x__x__ (unlipped channel section) web depth x flange size x thickness; *: double back-to-back coupled end studs(5) BHSC: bugle-head screws FHSC: flat head screws; LPHSC: low profile head screws; MTHSC: modified truss head screws; WHSC: wafer head screws; __x__: nominal diameter x length; NA: Nails diameter; PI: Pins diameter(6) GSB: Gypsum sheathing board; GWB: Gypsum wallboard; FB: Fiber board; OSB: Oriented strand board; PLY: Plywood; SCS: Steel corrugated seet; SSS: Steel sheet sheathing;V: parallel to the frame (vertical); O: orthogonal to the frame (horizontal)(7) I__x__ flat strap wide x thickness(8) BCA: bolted clip angles; PCA: clip angles fixed wit powder actuated fasteners; HD: hold-down; SHD: strip-hold down(9) F: foundation uplift failure; S: stud buckling failure; X: X bracing yielding;C (FPO): connections failure (fasteners pull out failure); C (FPT): connections failure (fasteners pull throgh failure); C (FS): connections failure (fasteners shear failure); C (FT): connections failure (fasteners tilting failure); C (NS): connections faiO): c(net section failure);7.91r

A-14 Appendix AFulop & Dubina (2002)Label TestType ofloading(1)wall size(2)aspectratio(2)opening(3)frame(4)frame fasteners(5)sheathing(6)sheathing fasteners(5)horizontal straps (HS)solid blocking (SB)(7)X-bracing(7)X-bracing fasteners(5)Type ofanchorage(8)Type offailure(9)ultimateshearh x L h / Lsheathingarea ratiosteel gradestud sizetrack sizestud spacing typetype;thickness;orientationtype; exterior spacing;interior spacingHB sizeSB size size type; number kN/mFD02-1 O M - - - 0.28FD02-2 I MSCS;0.5;O SC4.8x22; 114; 22914.69FD02-3 I C 12.68FD02-4 II MSCS;0.5;OGWB;12,T;VSC4.8x22; 114; 229 - - 16.59FD02-5 II C 1.00SCS;0,5;OGWB;12.5;VSC4.8x22; 250; 25015.95FD02-6 III M 2440x3600 0.68FD02-7 III C?C150x?x?x1.5*u154x?x1.5600?- -I110x1,5+ ?I110x1,5? 15.32F 14.87FD02-8 IV M 0.70SCS;0.5;O SC4.8x22; 114; 22911.17FD02-9 IV C 0.70 10.49FD02-10 OSB I M 1.00- -21.88FD02-11 OSB I C 1.00OSB;10;V BHSC4.8x22; 105; 25019.40FD02-12 OSB II M 0.70 12.33FD02-13 OSB II C 0.70 12.76length in mm; ?: not known; -: not present(1) M: monotonic; C: cyclic(2) h: heigth of the wall; L: length of the wall(3) r =1 / [1 + Ao / (h Li)] with Ao: area of openings and Li the length of the full height wall segment(4) C__x__x__x__ (lipped channel section) web depth x flange size x lip size x thickness; U__x__x__ (unlipped channel section) web depth x flange size x thickness; *: double back-to-back coupled end studs(5) BHSC: bugle-head screws FHSC: flat head screws; LPHSC: low profile head screws; MTHSC: modified truss head screws; WHSC: wafer head screws; __x__: nominal diameter x length; NA: Nails diameter; PI: Pins diameter(6) GSB: Gypsum sheathing board; GWB: Gypsum wallboard; FB: Fiber board; OSB: Oriented strand board; PLY: Plywood; SCS: Steel corrugated seet; SSS: Steel sheet sheathing;V: parallel to the frame (vertical); O: orthogonal to the frame (horizontal)(7) I__x__ flat strap wide x thickness(8) BCA: bolted clip angles; PCA: clip angles fixed wit powder actuated fasteners; HD: hold-down; SHD: strip-hold down(9) F: foundation uplift failure; S: stud buckling failure; X: X bracing yielding;C (FPO): connections failure (fasteners pull out failure); C (FPT): connections failure (fasteners pull throgh failure); C (FS): connections failure (fasteners shear failure); C (FT): connections failure (fasteners tilting failure); C (NS): connections faiO): c(net section failure);r-

Summary of existing experimental results A-15Branston et al. (2003)Label TestType ofloading(1)wall size(2)aspectratio(2)opening(3)frame(4)frame fasteners(5)sheathing(6)sheathing fasteners(5)horizontal straps (HS)solid blocking (SB)(7)X-bracing(7)X-bracing fasteners(5)Type ofanchorage(8)Type offailure(9)ultimateshearh x L h / Lsheathingarea ratiosteel gradestud sizetrack sizestud spacing typetype;thickness;orientationtype; exterior spacing;interior spacingHB sizeSB size size type; number kN/mB+03-1B+03-2OSB 4-8 USM- A, B, COSB 4-8 USC- A, B, CMC2440x1220 2.001.00A653 Grade SQ 33C89x41x10x0.84* OSB;11.1;V FHSC4.2x25; 102; 305U89x38x0.84610WHSC4.2x13 - - - HD C16.8016.00B+03-3B+03-4PLY 8-8 USM- A, B, CPLY 8-8 USC- A, B, CMC2440x2440 1.00A653 Grade SQ 33C89x41x10x0.84* PLY;11.9;V FHSC4.2x25; 152; 305U89x38x0.84610 11.80length in mm; ?: not known; -: not present(1) M: monotonic; C: cyclic(2) h: heigth of the wall; L: length of the wall(3) r =1 / [1 + Ao / (h Li)] with Ao: area of openings and Li the length of the full height wall segment(4) C__x__x__x__ (lipped channel section) web depth x flange size x lip size x thickness; U__x__x__ (unlipped channel section) web depth x flange size x thickness; *: double back-to-back coupled end studs(5) BHSC: bugle-head screws FHSC: flat head screws; LPHSC: low profile head screws; MTHSC: modified truss head screws; WHSC: wafer head screws; __x__: nominal diameter x length; NA: Nails diameter; PI: Pins diameter(6) GSB: Gypsum sheathing board; GWB: Gypsum wallboard; FB: Fiber board; OSB: Oriented strand board; PLY: Plywood; SCS: Steel corrugated seet; SSS: Steel sheet sheathing;V: parallel to the frame (vertical); O: orthogonal to the frame (horizontal)(7) I__x__ flat strap wide x thickness(8) BCA: bolted clip angles; PCA: clip angles fixed wit powder actuated fasteners; HD: hold-down; SHD: strip-hold down(9) F: foundation uplift failure; S: stud buckling failure; X: X bracing yielding;C (FPO): connections failure (fasteners pull out failure); C (FPT): connections failure (fasteners pull throgh failure); C (FS): connections failure (fasteners shear failure); C (FT): connections failure (fasteners tilting failure); C (NS): connections faiO): c(net section failure);16.40r

B-1Appendix BSummary of objectives and results ofexisting experimental studies

B-2 Appendix BObjectives Authors ConclusionsTarpy (1980)- the use of cement plaster increases the shear strength and thestiffness- the use of two layer of GWB increases the shear capacity, whiledecreasing the shear stiffness, in comparison with single layerTarpy & Girard (1982)- the use of PLY panels increases the shear strength in comparisonwith GWB panels- the use of GWB panels increases the shear strength in comparisonwith GSB panelsSerrette et al. (1996a,b)- the PLY panels carry slightly higher loads in comparison with OSBpanels- walls with OSB panels on one side and GWS panels on the otherside exhibit similar failure behavior, but degrade more gradually thanwalls with OSB panels on one side alone- walls with GWB panels on both sides have much lower shearstrength than walls with OSB panels- PLY and OSB panels show a small difference in the cyclic shearstrengthbehaviour of differentsheathing typeeffect of sheathingorientation andcontribution of blockingSerrette et al. (1997a)Serrette et al. (1997b)Selenikovich et al. (1999)Fulop & Dubina (2002)Serrette & Ogunfunmi (1996)Serrette et al. (1997b)Gad et al. (1999a)Serrette & Ogunfunmi (1996)Serrette et al. (1997a)Sheathing- the behavior of the PLY and OSB panels is comparable- the strength of GWB and FBW is relatively low in comparison withPLY and OSB panels- the use of GWB panels on the interior of the wall and PLY panels onthe exterior produce a higher shear capacity, by approximately 18%,in comparison with the PLY panels only- the walls sheathed with SSS have a ductile behavior without suddendecreases in shear load capacity- the use of thick sheathings increases the shear resistance, but thefailure mode move from rupture at the edges of the sheathing to screwpull-out from the framing- adding GWB panels increases the shear strength and stiffness offully sheathed walls under monotonic load- the behavior of GWB is satisfactory. In fact it could follow evenextreme deformation of the wall without significant damage- the use of X-B plus GWB reduces the permanent deflection andincreases the shear strength without decreasing the stiffness- the use of X-B plus GWB is not practical due to the need topretension the straps and the need for additional screws to connectthe straps- in the design of walls with X-B the designer must consider that theforce in the strap may be larger than that corresponding to the nominalyield strength- if X-B are installed on one side of the wall only, the effect ofeccentricity should be consideredFor walls laterally braced with X-B only:- the initial tension in the X-B increases the frame stiffness and whenthe X-B yield then the true stiffness of the X-B system defines thestiffness of the frame- the type of strap bracing-to-plate connections governs the failureload and mechanismFor walls laterally braced with X-B and plasterboard:- when X-B and plasterboard are combined, the overall stiffness andstrength of the system is simple addition of individual contributionsfrom X-B and plasterboard- sheathings oriented horizontally exhibit slightly higher shear strengththan panels oriented vertically- the walls with blocked panels oriented horizontally provideessentially the same shear capacity but higher stiffness than acomparable wall with panels oriented vertically- when blocking is omitted from the walls with horizontal panels, theshear capacity of the wall is reduced by more than 50%

Summary of objectives and results of existing experimental studies B-3Objectives Authors ConclusionsTarpy & Girard (1982)effect of framing studsize, thickness andspacingSerrette et al. (1997b)Framing- the reduction of the stud spacing does not increase significantly theshear strength and stiffness- the use of thicker and back-to-back coupled end studs for the wallswith PLY and OSB panels allows to fully develop the shear strength ofthe panels-to-frame connections also in the cases in which densefasteners schedules are usedObjectives Authors Conclusionseffect of fastener type,size and spacingTarpy & Hauenstein (1978)Tarpy (1980)Tarpy & Girard (1982)Serrette et al. (1996a,b)Serrette et al. (1997a)Serrette et al. (1997b)Gad et al. (1999a)COLA-UCI (2001)Fastener- reduction of the fastener spacing around the wall perimeterincreases the shear strength- reduction of the fastener spacing increases the shear strength andstiffness- the use of welded stud to track connections provides the same shearstrength as screw connections- reduction of the fastener spacing increases significantly the shearstrength- the use of 3.7mm diameter nails decreases the maximum shearstrength in comparison with No.6 and No.8 screws- the maximum shear strength is not influenced by the size of thefastener- the failure mode for the specimens with No.6 screws is fracture offasteners and thus walls with No.6 screws may fail at lower loads thanwalls with No.8 screws- for GWB and FB panels the reduction of the fastener spacingincreases significantly the shear strength- decreasing the screws spacing results in the increased maximumshear load- No.8 screws should be limited to 1,09mm thick framing; in fact, thisscrew behave well in the 0.84 and 1.09mm thick frames (screws pulloutor pull-trhough failure) but fractures in shear when 1.37mm thickframes are used- for walls laterally braced with X-B only the type of connectionsbetween the framing members dos not seem to have an influence onthe structural response of the braced frames- a reduction of the fastener spacing nonlinearly increases the shearstrength and stiffness for both the light-gauge steel framed and woodframed stud walls

B-4 Appendix BObjectives Authors ConclusionsNAHB (1997)- the calculation of the shear capacity using the “Perforated ShearWall Design Method” appears valid, but reveals a conservativeprediction of ultimate shear strength- long, fully sheathed walls are significantly stiffer and stronger butinfluence of the openingless ductile than walls with openingssize- the predictions of the “Perforated Shear Wall Design Method” areSelenikovich et al. (1999)conservative at all levels of monotonic and cyclic loading- the strength of fully sheathed walls is affected more significantly bycyclic loading than walls with openings- for the aspect ratio varying between 0.33 and 1 shear strength isMc Creless & Tarpy (1978) independent of H/L ratio but shear stiffness increases for smaller H/Leffect of height/length(H/L) variationSerrette et al. (1996a,b)Serrette et al. (1997b)Geometryratio- the shear strength is practically the same for the H/L ratio varyingbetween 1 and 2- the shear strength appreciably decreases when the aspect ratioincreases from 2 to 4Objectives Authors ConclusionsTarpy (1980)- cyclic loading decreases shear strength and damage threshold leveleffect of cyclic loadingSerrette et al. (1996a,b)Gad et al. (1999a)Selenikovich et al. (1999)Fulop & Dubina (2002)Type of loading- PLY and OSB panels show a small difference in the cyclic shearstrength- the shear behavior of walls observed in cyclic tests is somewhat notas good as the shear behavior exhibited in monotonic tests for walls ofsimilar constructions- as in the monotonic tests, in the cyclic tests the wall shear strengthincreases significantly with the reduction of the fastener spacing- for walls laterally braced with X-B only the dynamic characteristics ofthe frame are governed by the initial tension in the straps- cyclic loading does not influence the elastic behavior of the walls butreduces their deformation capacity- the strength of fully sheathed walls is affected more significantly bycyclic loading than walls with openings- very significant pinching and reduced energy dissipation characterizethe hysteretic behavior

Summary of objectives and results of existing experimental studies B-5Construction techniques and anchorage detailsObjectives Authors ConclusionsTarpy & Hauenstein (1978)- to avoid uplift failure it is recommended that a positive attachmentshould be furnished between the track and floor framing systemsTarpy (1980)- the corner anchorage influences the shear behavior dramatically- hold-down exhibits higher shear strength than bolt and washeranchors- densely spaced powder actuated fasteners (connected to asupporting concrete beam) provide similar restraint to the hold-down- the shear resistance dos not vary extensively when using differenttypes of interior shear anchorage- the use of a 45° stud placed at bottom corner between the chordmembers and the adjacent stud has little effect on the shear capacityeffect of constructiontechniques andanchorage detailsTarpy & Girard (1982)- when the bolt and washer anchorage details are used without clipangles the shear capacity decreases- the use of closely spaced powder actuated fasteners negligiblyincreases the shear behavior in comparison to using corner clips- it is recommended the use of clip angles- it is suggested a rigid attachment to connect the wall panel to thefloor or roof framing systemsNAHB (1997)Gad et al. (1999a)- hold-down reduces uplift and increases the ultimate shear capacityby allowing more sheathing-to-frame screws to resist shear- in-plane brick veneer walls attached to the frame via clip-on ties dosnot contribute to the stiffness of the system- different displacements between the frame and the out-of-plane brickveneer walls are mainly accommodated by deformation of the studflanges rather than deformation of brick ties- the plasterboard combined with ceiling cornices, skirting board andset corner joints, resists about 60-70% of the applied racking loadwhereas the X-B resists 30-40%

B-6 Appendix BObjectives Authors Conclusionsdetermination of thedamage threshold levelMc Creless & Tarpy (1978)Tarpy & Hauenstein (1978)Tarpy (1980)Tarpy & Girard (1982)damage threshold level- the first noticeable wallboard damage occurrs:- at about 6 to 13mm total displacement (for the shorter walls)- at about 6mm (for the longer walls)- the real damage occurrs:- at about 13 to 19mm total displacement (for the shorter walls)- at about 6 to 13mm (for the longer walls).- a safety factor of 2.0 is recommended- cyclic loading decreases the damage threshold level- a safety factor of 2.0 is recommended to determine the design shearstrength from the ultimate shear strength for the type of stud shearwalls examinedsteel-frame versus wood-frameObjectives Authors Conclusions- the lateral load resisting mechanism for both W-F and S-F shearNAHB (1997)comparison betweenwalls appears to be similarsteel-frame (S-F) andwood-frame (W-F) COLA-UCI (2001)- with the same sheathing types and fastener spacing, S-F wallsexhibit somewhat higher shear strength and ductility but lesshysteretic damping than W-F wallsfull-scale tests versus small-scale testObjectives Authors Conclusionscomparison between fullscaleand small-scale Serrette et al. (1997a)test results- the normalized shear strength for small-scale tests is similar as thosefor full-scale tests, thus the small-scale tests are considered to beuseful in a evaluation of the relative resistance of different wallassemblies

C-1Appendix CEvaluation of seismic action and wall shearstrength for the study case

C-2 Appendix CEvaluation of seismic actionGeometry of the houseNumber of stories n= 2Length L= 11.4 mWide W= 7.0 mHeight H= 6.4 mRoof slope Tan()= 100 %Area A= 75 m 2Length of full height wall segments w i = 18.0 mUnit loadsDead loadsRoof g kR = 0.75 kN/m 2Floor g kF = 0.75 kN/m 2Walls g kW = 0.35 kN/m 2Snow loads q ks = 0.50 kN/m 2Live loads q kl = 2.00 kN/m 2Seismic weightTotal seismic weightW k,tot = G k + k Q kElement g k (kN/m 2 ) q k (kN/m 2 ) Area (m 2 ) G k (kN) Q k (kN) EI W k (kN)Roof 0.75 0.50 106 80 38 0.30 91Floor 0.75 2.00 75 56 150 0.30 101Walls 0.35 0.00 90 32 0 32W k,tot = 224Seismic weight per unit surfacew k = W k,tot / A = 3.0 kN/m 2Seismic weight per unit lenght of full height wall segmentsw s = W k,tot / w i =12.5 kN/m

Evaluation of seismic action and wall shear strength for the study case C-3Type 1 (far field) Eurocode 8 Design elastic spectrum = 1 damping factor (=1 for a damping ratio =0.05)a g = 0.25g design peak ground accelerationS: soil factorT B and T C : limits of constant spectral acceleration branchT D : value that defines the beginning of the constant displacement response rangeSoil type S T B T C T DA 1 0.15 0.4 2B 1.2 0.15 0.5 2C 1.15 0.2 0.6 2D 1.35 0.2 0.8 2E 1.4 0.15 0.5 2ws/ gT 2k= 0.1 - 0.3 s first mode vibration periodk = 0.5 - 3.0 kN/mm/m stiffness per unit lenght of full height wall segmentsMaximum design elastic spectrum for first mode vibration period ranging from 0.1 to 0.3sSoil type Saed / gA 0.63B 0.75C 0.72D 0.84E 0.88max 0.88

C-4 Appendix CSeismic force per unit lenght of full height wall segmentsv SSaed wsSoil type v S (kN/m)A 7.9B 9.4C 9.0D 10.5E 11.0max 11.0

Evaluation of seismic action and wall shear strength for the study case C-5Evaluation of strength of wallsGeometry of the wallLength L= 2400 mmHeight H= 2500 mmStuds spacing st s = 600 mmMaterialsSteel grade: FeE350G (S350GD+Z/ZF) hot dipped galvanized (zinc coated) steel (EN10147)(Nominal yield strength f y =350MPa; nominal tensile strength f t =420MPa)Wood-based panels: Type 3 OSB (KRONOPLY 3 by KRONO FRANCE)Gypsum-based panels: GWB (PLACOLAST PLACO by BPB ITALIA)

C-6 Appendix CFailure modesFrameSheathing-to-frameconnectionsFrame-to-foundationconnections

Evaluation of seismic action and wall shear strength for the study case C-7Sheathing-to-frame connection failure [see Section 2.2.1 in Chapter 2 ]F SF, bstfdfu,sFSFFF SF,ss30.5 tfd fus2.1, ts3 .2,SF, bp3.5tsdufCDKDb,wminFSFv S-Ft s = 9.0 mm thickness of OSB sheathingst f = 1.0 mm thickness of the framed= 4.2 mm nominal diameter of screwsd u = 2.8 mm unthreaded diameter of screwsf b,w = 38 MPa dowel bearing strength of OSB sheathingsf u,s = 420 Mpa ultimate tensile strength of members of the frameF S-F,ss = 4.0 kN shear design resistance of screwsBearing strength of steel frameF S-F,bs = 3.70 kN (=2.1) [see Eq. 2.5 in Chapter 2 ]Tilting strength of steel studsF S-F,ts = 2.75 kN [see Eq. 2.6 in Chapter 2 ]Shear resistance of fastenerF S-F,ss =4.00 kNBearing strength of wood panelsF S-F,bp = 2.44 kN (K D =2.20; C D =1.6) [see Eq. 2.8 in Chapter 2 ]Sheathing-to-frame connection strengthF S-F = 2.44 kN [see Eq. 2.4 in Chapter 2 ]

C-8 Appendix CShear strenght of the wall associated to sheathing-to-frame connection strengthEasley et al.'s methoda= 1250 mm length of the panelH= 2500 mm heigth of the wallst s = 600 mm studs spacingm= 1.0 number of interior studef s = 150 mm edge fasteners spacingff s = 300 mm field fasteners spacingn s =15 number of side fasteners, excluding those at the endn e =9 number of end fastenersn si =7 number of fasteners in each interior stud, excluding those at the endIe = S x 2 ei = 1350000 Is = S x 2 si = 0 = n s + 4I e + 2 n si I s / L = 18.46Force in the side fasteners s = F s / v a = H / = 135.46 [see Eq. 2.9 in Chapter 2 ]Force in the end fasteners ei = F ei / v a = ((a/n e ) 2 + (2x eimax H/(a)) 2 ) 1/2 = 190.26 [see Eq. 2.10 in Chapter 2 ] max = max { s ; ei } = 190.26Shear strenght of the wall associated to sheathing-to-frame connection strengthv S-F =1.40 (*) 1 / max F S-F = 17.94 KN/m [see Eq. 2.11 in Chapter 2 ]Shear strenght of the wall associated to sheathing-to-frame connection strengthSimplified methodef s = 150 mm edge fasteners spacingn' e = 6.67 number of end screws per unit lengthv S-F = 1.40 (*) n' e F S-F = 22.75 KN/m [see Eq. 2.12 in Chapter 2 ]* Assuming that the adding of GWB to the opposite side of the wall assembly increases theshear strength by about 40%

Evaluation of seismic action and wall shear strength for the study case C-9Frame (stud buckling) failure [see Section 2.2.2 in Chapter 2 ]Stud back-to-back coupled C100x50x10x1.00H = 2500 mm heigth of studsf ys = 350 Mpa yield strength of the studsf us = 420 Mpa ultimate tensile strength of the studsL x = 2500 mm unbraced length (out of plane - x-z plane)L y = 300 mm unbraced length (in plane - x-y plane)N b,out = 66.96 kN out of plane axial strength [see Eq. 2.17 in Chapter 2 ]N b,in = 74.03 kN in plane axial strength [see Eq. 2.17 in Chapter 2 ]Frame strengthF F = min(N b,out ; N b,in )=66.96 kNShear strenght of the wall associated to frame strengthv F = F S-F / H = 26.78 KN/m [see Eq. 2.40 in Chapter 2 ]The valuation of axial strength of studs has been carried out using“ColdForm” computer program (Included in: A., Ghersi, R., Landolfo, F.M.,Mazzolani (2002) Design of metallic cold-formed thin-walled members. SponPress). The results provided by Details window of this program are reported inthe following.EVALUATION OF THE EFFECTIVE CROSS-SECTION:Element 1 single edge fold stiffener, connected at end 2geometrical data: bP = 8.91 mm t = 1.00 mm bP/t = 8.91end 2 - fr = 1.41 mmaxial stresses: end 1 - sigma = 350.00 MPaend 2 - sigma = 350.00 MPacoefficients: k sigma = 0.5000lambdaP = 0.5414rho = 1.0000the element is fully effectiveElement 2doubly supported elementgeometrical data: bP = 47.83 mm t = 1.00 mm bP/t = 47.83end 1 - fr = 1.41 mmend 2 - fr = 1.41 mmaxial stresses: end 1 - sigma = 350.00 MPaend 2 - sigma = 350.00 MPa

C-10 Appendix Ccoefficients: k sigma = 4.0000lambdaP = 1.0271rho = 0.7651beff = 36.59 mm be1 = 18.30 mm be2 = 18.30 mmElement 3doubly supported elementgeometrical data: bP = 97.83 mm t = 1.00 mm bP/t = 97.83end 1 - fr = 1.41 mmend 2 - fr = 1.41 mmaxial stresses: end 1 - sigma = 350.00 MPaend 2 - sigma = 350.00 MPacoefficients: k sigma = 4.0000lambdaP = 2.1008rho = 0.4262beff = 41.69 mm be1 = 20.85 mm be2 = 20.85 mmElement 4doubly supported elementgeometrical data: bP = 47.83 mm t = 1.00 mm bP/t = 47.83end 1 - fr = 1.41 mmend 2 - fr = 1.41 mmaxial stresses: end 1 - sigma = 350.00 MPaend 2 - sigma = 350.00 MPacoefficients: k sigma = 4.0000lambdaP = 1.0271rho = 0.7651beff = 36.59 mm be1 = 18.30 mm be2 = 18.30 mmElement 5 single edge fold stiffener, connected at end 1geometrical data: bP = 8.91 mm t = 1.00 mm bP/t = 8.91end 1 - fr = 1.41 mmaxial stresses: end 1 - sigma = 350.00 MPaend 2 - sigma = 350.00 MPacoefficients: k sigma = 0.5000lambdaP = 0.5414rho = 1.0000the element is fully effectiveElement 6 single edge fold stiffener, connected at end 2geometrical data: bP = 8.91 mm t = 1.00 mm bP/t = 8.91end 2 - fr = 1.41 mmaxial stresses: end 1 - sigma = 350.00 MPaend 2 - sigma = 350.00 MPacoefficients: k sigma = 0.5000lambdaP = 0.5414rho = 1.0000the element is fully effectiveElement 7doubly supported elementgeometrical data: bP = 47.83 mm t = 1.00 mm bP/t = 47.83end 1 - fr = 1.41 mmend 2 - fr = 1.41 mmaxial stresses: end 1 - sigma = 350.00 MPaend 2 - sigma = 350.00 MPacoefficients: k sigma = 4.0000lambdaP = 1.0271rho = 0.7651beff = 36.59 mm be1 = 18.30 mm be2 = 18.30 mmElement 8doubly supported element

Evaluation of seismic action and wall shear strength for the study case C-11geometrical data: bP = 97.83 mm t = 1.00 mm bP/t = 97.83end 1 - fr = 1.41 mmend 2 - fr = 1.41 mmaxial stresses: end 1 - sigma = 350.00 MPaend 2 - sigma = 350.00 MPacoefficients: k sigma = 4.0000lambdaP = 2.1008rho = 0.4262beff = 41.69 mm be1 = 20.85 mm be2 = 20.85 mmElement 9doubly supported elementgeometrical data: bP = 47.83 mm t = 1.00 mm bP/t = 47.83end 1 - fr = 1.41 mmend 2 - fr = 1.41 mmaxial stresses: end 1 - sigma = 350.00 MPaend 2 - sigma = 350.00 MPacoefficients: k sigma = 4.0000lambdaP = 1.0271rho = 0.7651beff = 36.59 mm be1 = 18.30 mm be2 = 18.30 mmElement 10 single edge fold stiffener, connected at end 1geometrical data: bP = 8.91 mm t = 1.00 mm bP/t = 8.91end 1 - fr = 1.41 mmaxial stresses: end 1 - sigma = 350.00 MPaend 2 - sigma = 350.00 MPacoefficients: k sigma = 0.5000lambdaP = 0.5414rho = 1.0000the element is fully effectiveEFFECTIVENESS OF EDGE STIFFENERSEdge stiffener for element 2spring stiffness: k = 0.1296 MPageometrical data: Ar = 27.3 mm2 Ir = 212 mm4yGr = 92.97 mm zGr = 97.84 mmbuckling stress: sig cr,s = 176.24 MPareduction: lambda = 1.4092 chi = 0.4411 chiR = 0.4411Edge stiffener for element 4spring stiffness: k = 0.1296 MPageometrical data: Ar = 27.3 mm2 Ir = 212 mm4yGr = 92.97 mm zGr = 2.16 mmbuckling stress: sig cr,s = 176.24 MPareduction: lambda = 1.4092 chi = 0.4411 chiR = 0.4411Edge stiffener for element 7spring stiffness: k = 0.1296 MPageometrical data: Ar = 27.3 mm2 Ir = 212 mm4yGr = 7.03 mm zGr = 97.84 mmbuckling stress: sig cr,s = 176.24 MPareduction: lambda = 1.4092 chi = 0.4411 chiR = 0.4411Edge stiffener for element 9spring stiffness: k = 0.1296 MPageometrical data: Ar = 27.3 mm2 Ir = 212 mm4yGr = 7.03 mm zGr = 2.16 mm

C-12 Appendix Cbuckling stress: sig cr,s = 176.24 MPareduction: lambda = 1.4092 chi = 0.4411 chiR = 0.4411gross cross-sectioneffective cross-sectionEVALUATION OF DESIGN BUCKLING RESISTANCEarea of the gross section: Ag = 423 mm2area of the effective section: Aeff = 212 mm2reduction factor: betaA = 0.4998x-z plan:buckling length: l = 2.50 mradius of gyration of gross cross-section: i = 40.58 mmslenderness: lambda = 61.61relative slenderness: lambda bar = 0.5660imperfection factor: alfa = 0.21reduction factor: chi = 0.9024Design buckling resistance: Nb,Rd = 66.96 kNx-y plan:buckling length: l = 0.30 mradius of gyration of gross cross-section: i = 24.02 mmslenderness: lambda = 12.49relative slenderness: lambda bar = 0.1147imperfection factor: alfa = 0.34reduction factor: chi = 1.0000Design buckling resistance: Nb,Rd = 74.03 kN

Evaluation of seismic action and wall shear strength for the study case C-13Frame-to-foundation failure [see Section 2.2.3 in Chapter 2 ]Tension frame-to-foundation failurehold-down(F (F-F)N,hd )hold-down – to - frameminF (FF)N(F (F-F)N,hd-fr )hold-down – to – foundation(F (F-F)N,hd-fo ) v (F-F)NF (F-F)N,hd-fr) = 184.05 kN [see Eq. 2.45 in Chapter 2 ]F (F-F)N,hd-fo) = 258.40 kN [see Eq. 2.51 in Chapter 2 ]Tension frame-to-foundation connection strengthF (F-F)N = 184.05 kN [see Eq. 2.41 in Chapter 2 ]Shear strenght of the wall associated to the tension frame-to-foundation connection strengthv (F-F)N = F (F-F)N / H = 73.62 KN/m [see Eq. 2.59 in Chapter 2 ]Shear frame-to-foundation failureShear anchor – to – frame connection(F (F-F)V,a-fr )Shear anchor – to – foundation connection(F (F-F)V,a-fo )minF (FF)Vv (F-F)VF (F-F)V,a-fr) = 9.00 kN [see Eq. 2.47 in Chapter 2 ]F (F-F)V,a-fo) = 8.70 kN [see Eq. 2.57 in Chapter 2 ]Shear frame-to-foundation connection strengthF (F-F)V = 8.70 kN [see Eq. 2.54 in Chapter 2 ]Shear strenght of the wall associated to the tension frame-to-foundation connection strengthv (F-F)V = n' F (F-F)V = 87.00 KN/m (n'=10) [see Eq. 2.60 in Chapter 2 ]Shear strenght of the wall associated to the of the frame-to-foundation connection strengthv F-F = 73.62 KN/m [see Eq. 2.58 in Chapter 2 ]

C-14 Appendix CUnit shear strength [see Section 2.2 in Chapter 2 ]v min v ; v ; vS FFF F[see Eq. 2.3 in Chapter 2 ]Soil type v S (kN/m)v S-F17.9v F26.8v F-F73.6min 17.9Sheathing-to-frame connection failureframeconnectionsheathing

D-1Appendix DConstruction details of the sub-assemblyspecimen

D-2 Appendix Djoist track(U 260X40X1.00mm)bearing stiffener(C 100x50x10x1.00mm)Joist(C 260x40x10x1.50mmstud track(U 100X40X1.00mm)end stud(back-to-back coupledC 100x50x10x1.00mm)intermediate stud(C 100x50x10x1.00mm)stud track(U 100X40X1.00mm)X-bracingGlobal 3D view of specimen (without sheathings).

Construction details of the sub-assembly specimen D-3A close-up view of the tension connection between the wall and the foundation.A close-up view of the shear connection between the wall and the foundation.

D-4 Appendix DA close-up view of the back-to-back connection of coupled end studs.A close-up view of the connection between the intermediate stud and the bottom stud track.

Construction details of the sub-assembly specimen D-5joist track (U 260X40X1.00mm)bearing stiffener(C 100x50x10x1.00mm)No. 2 4.2x13mm modified truss head self drilling screwsstud track (U 100X40X1.00mm)joist (C 260x40x10x1.50mm)stud (C 100x50x10x1.00mm)A close-up view of the connection between the joist and the joist track.joist track (U 260X40X1.00mm)bearing stiffener(C 100x50x10x1.00mm)stud track (U 100X40X1.00mm)joist (C 260x40x10x1.50mm)4.2x13mm modified truss head self drilling screwsspaced at 75mm on centerA close-up view of the connection between the joist track and the top stud track.

D-6 Appendix DClose-up views of the connection between the joist, the joist track and the bearing stiffener.A close-up view of the connection between the joist and the X-bracing.

Construction details of the sub-assembly specimen D-71250x1450x18.0mm Type 3 OSB(KRONOPLY by KRONOFRANCE)floor sheathing1200x2500x12.5mm GWB(PLACOLAST by BPB ITALIA)interior wall sheathing1250x2500x9.0mm Type 3 OSB(KRONOPLY by KRONOFRANCE)exterior wall sheathingGlobal 3D view of specimen (with sheathings)

D-8 Appendix DGlobal 3D view of connections between the external sheathing and the wall framing

Construction details of the sub-assembly specimen D-93.5x25mm bugle head self drilling screwsspaced at 150mm (at the perimeter)with edge distance equal to 10mmstud track (U 100X40X1.00mm)stud (C 100x50x10x1.00mm)3.5x25mm bugle head self drilling screwsspaced at 300mm (in the field)1200x2500x12.5mm GWB(PLACOLAST by BPB ITALIA)interior wall sheathingstud track (U 100X40X1.00mm)Global 3D view of connections between the internal sheathing and the wall framing

D-10 Appendix D4.2x32mm flat head self drilling screwsspaced at 150mm(for sheathing-to-joist track connections)1250x1450x18.0mm Type 3 OSB(KRONOPLY by KRONOFRANCE)floor sheathing4.2x32mm flat head self drilling screwsspaced at 250mm(for sheathing-to-joist connections)joist track(U 260X40X1.00mm)Global 3D view of connections between the floor sheathing and the floor framing

E-1Appendix EMonotonic test results

E-2 Appendix Ea2Wall 2d2a1Wall 1actuator load (a1; a2)LVDT (d1; d2)Instrument arrangement for the floor.d1aw1w4w5w2i1Wall 1actuator load (a1)LVDT (w1,1; w1,2; w1,3; w1,4;w1,5)i2w3f1Wall 2actuator load (a2)LVDT (w2,1; w2,2; w2,3; w2,4;w2,5)clinometer (i2,1; i2,2)Instrument arrangement for the walls.

Monotonic test results E-35045kN40353025201510500 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150mmForce vs. displacement measured by the actuator a1.5045kN40353025201510500 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150mmForce measured by the actuator a1 vs. displacement measured by the LVDT w1,1.

E-4 Appendix E5045kN40353025201510500 1 2 3 4 5 6 7mmForce measured by the actuator a1 vs. displacement measured by the LVDT w1,2.5045kN40353025201510500 1 2 3 4 5 6 7mmForce measured by the actuator a1 vs. displacement measured by the LVDT w1,3

Monotonic test results E-5kN504540353025201510mm-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 050Force measured by the actuator a1 vs. displacement measured by the LVDT w1,4.5045kN40353025201510500 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15mmForce measured by the actuator a1 vs. displacement measured by the LVDT w1,5.

E-6 Appendix E5045kN40353025201510500 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150mmForce measured by the actuator a1 vs. displacement measured by the LVDT d1.5045kN40353025201510500 1 2 3 4 5 6 7mmForce measured by the actuator a1 vs. displacement measured by the LVDT f1.

Monotonic test results E-75045kN40353025201510500 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150mmForce vs. displacement measured by the actuator a2.5045kN40353025201510500 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150mmForce measured by the actuator a2 vs. displacement measured by the LVDT w2,1.

E-8 Appendix E5045kN40353025201510500 1 2 3 4 5 6 7mmForce measured by the actuator a2 vs. displacement measured by the LVDT w2,2.5045kN40353025201510500 1 2 3 4 5 6 7mmForce measured by the actuator a2 vs. displacement measured by the LVDT w2,3.

Monotonic test results E-9kN504540353025201510mm-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 050Force measured by the actuator a2 vs. displacement measured by the LVDT w2,4.5045kN40353025201510500 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15mmForce measured by the actuator a2 vs. displacement measured by the LVDT w2,5.

E-10 Appendix E5045kN40353025201510500 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150mmForce measured by the actuator a2 vs. displacement measured by the LVDT d2.5045kN40353025201510500 1 2 3 4 5 6 7mmForce measured by the actuator a2 vs. displacement measured by the LVDT f2.

Monotonic test results E-11deg504540353025201510mm-5 -4 -3 -2 -1 050Force measured by the actuator a2 vs. rotation measured by the clinometer i2,1.deg504540353025201510mm-5 -4 -3 -2 -1 050Force measured by the actuator a2 vs. rotation measured by the clinometer i2,2.

F-1Appendix FCyclic test results

F-2 Appendix Factuator load (a1; a2)LVDT (d1; d2)Instrument arrangement for the floor.Wall 1actuator load (a1)LVDT (w1,1; w1,2; w1,3; w1,4;w1,5)Wall 2actuator load (a2)LVDT (w2,1; w2,2; w2,3; w2,4;w2,5)clinometer (i2,1; i2,2)Instrument arrangement for the walls.

Cyclic test results F-3Force vs. displacement measured by the actuator a1.Force measured by the actuator a1 vs. displacement measured by the LVDT w1,1.

F-4 Appendix FForce measured by the actuator a1 vs. displacement measured by the LVDT w1,2.Force measured by the actuator a1 vs. displacement measured by the LVDT w1,3

Cyclic test results F-5Force measured by the actuator a1 vs. displacement measured by the LVDT w1,4.Force measured by the actuator a1 vs. displacement measured by the LVDT w1,5.

F-6 Appendix FForce measured by the actuator a1 vs. displacement measured by the LVDT d1.Force measured by the actuator a1 vs. displacement measured by the LVDT f1.

Cyclic test results F-7Force vs. displacement measured by the actuator a2.Force measured by the actuator a2 vs. displacement measured by the LVDT w2,1.

F-8 Appendix FForce measured by the actuator a2 vs. displacement measured by the LVDT w2,2.Force measured by the actuator a2 vs. displacement measured by the LVDT w2,3.

Cyclic test results F-9Force measured by the actuator a2 vs. displacement measured by the LVDT w2,4.Force measured by the actuator a2 vs. displacement measured by the LVDT w2,5.

F-10 Appendix FForce measured by the actuator a2 vs. displacement measured by the LVDT d2.Force measured by the actuator a2 vs. displacement measured by the LVDT f2.

Cyclic test results F-11Force measured by the actuator a2 vs. rotation measured by the clinometer i2,1.Force measured by the actuator a2 vs. rotation measured by the clinometer i2,2.