Design and Construction of Steel Plate Shear Walls - Eatherton ...

Proceedings of the 8 th U.S. National Conference on Earthquake EngineeringApril 18-22, 2006, San Francisco, California, USAPaper No. 588DESIGN AND CONSTRUCTION OF STEEL PLATE SHEAR WALLSMatthew Eatherton 1ABSTRACTWith the first U.S. code for steel plate shear walls (SPSW) in the recently released2005 AISC Seismic Provisions, the system will have a new level of exposureamong design engineers in the U.S. There are several issues, however, that anengineer will face in deciding whether to use SPSW, and in the process of design.Aspect ratio limits in the provisions make SPSW impractical for low-rise, andshorter mid-rise structures unless between-floor stiffeners are used, but the use ofbetween-floor stiffeners is not well defined. Plate material and thickness is ofparamount importance in SPSW design, but the range of material or thicknessthat is appropriate is not clear. Three different methods for column design arepresented in the provisions, but each comes up with different forces.Also, in determining whether to use SPSW for a project, issues such as cost,constructability, column size, length of wall required, story drift and flooraccelerations should be considered. Using a 2 story sample building design, itwas found that SPSW yields a structure that uses 13% less steel than momentframes, considerably less field welding than moment frames or braced frames,and significantly less wall length than braced frames.IntroductionSteel plate shear walls (SPSW) consist of a plate bounded at the sides by columns, alsoreferred to as vertical boundary elements (VBE), and at the floor levels by beams, also referredto as horizontal boundary elements (HBE). The alternate nomenclature for beams and columnsemphasizes the boundary elements role of resisting the tension field developed in the plate.Figure 1 shows an example of a SPSW that was constructed in San Mateo County, CA.There has been a shift in the design methodology from the SPSW buildings built in the1970’s to the SPSW buildings built in the past couple decades. Early designs for SPSW panelsused stiffeners to preclude buckling in their relatively thick shear plate. As such, these walls arecommonly called “stiffened”. In the early 1980’s research was spearheaded in Canada by Kulak,Thorburn, Driver, Grondin, and others to develop a design methodology that utilized the postbucklingcapacity of web plates. It was found that, similar to shear in plate girders, theusefulness of a web plate is not limited to its buckling capacity. With boundary members1 Senior Design Engineer, GFDS Engineers, 543 Howard St, San Francisco, CA 94105

designed to resist the forces of the web plate, not onlydoes tension field action develop, but the tensiondiagonals can yield. Significant ductility and energyabsorption has been noted in this type of wall, that hasbeen referred to as “unstiffened” or “thin-walled”SPSW. It should be understood that the terms“stiffened” and “unstiffened” are a bit of a misnomer,however, as the essential difference in designmethodologies is the degree to which a plate is allowedto buckle, rather than whether stiffeners are used. Theweb plate of the SPSW shown in Fig 1 is designed todevelop tension field action at relatively low shear andwould therefore be considered unstiffened. The 2005AISC Seismic provisions and the rest of this paperonly address unstiffened SPSW.In the 1990’s considerable research on SPSWwas done in the United States by professors Bruneau,Berman, Elgaaly, Caccese, Astaneh, and others. U.S.design provisions were, for the first time, published inthe 2005 AISC Seismic provisions. Additionally,Bruneau and Sabelli are producing an AISC designguide on SPSW which is expected to includerecommendations for seismic and non-seismicapplications for SPSW. With these upcomingpublications, SPSW will gain a new level of exposurewith U.S. engineers. This paper is geared towardsdesign engineers who might be considering usingSPSW and contains:1. Discussion of design considerations whenusing the 2005 AISC Seismic Provisions.2. Comparison of SPSW to special concentrically braced frames and special momentframes.3. Summary of reasons why the author used SPSW for 3 large residences in NorthernCalifornia and experiences encountered in their design and construction.4. Suggestions for design of SPSW and future editions of SPSW code provisions.Design Considerations for SPSWFigure 1 – Steel plate shear wall usedin a high-end residence in San MateoCounty, CA.The 2005 AISC Seismic Provisions refer to SPSW as special plate shear walls. The termspecial indicates that, like special concentrically braced frames or special moment frames, thatspecial plate shear walls are expected to have increased ductility over their ordinarycounterparts. While the AISC Seismic Provisions do not include ordinary steel plate shear walls,if they are included in future editions it can be conjectured that one of the differences may besimple shear beam-to-column connections (as opposed to moment connections required forSPSW).In the process of SPSW design, the author has come across several issues that require

judgment outside of what is presented in the AISC Seismic Provisions. Questions such as howthin a plate is appropriate, how slender a wall is possible, what plate material can be used, andhow to interpret the code when it comes to column design are important in the design process,and are discussed below. First, a brief description of the design process is required to highlightsome of the issues.Design ProcessTo achieve the high level of ductility expected of SPSW, the boundary members have tobe designed to remain elastic as the plate yields. As a result, size of beams and columns aredesigned based on the plate thickness. Plate design, however, is based on angle of inclination ofthe tension field, which is dependent on the boundary members. The design process, therefore,becomes iterative, but with closed form equations is well suited for a spreadsheet.In order to begin the design process it is necessary to assume an angle of inclination, α,for the tension field relative to the vertical. AISC Seismic Provisions give an equation for α, thatwill need to be checked after boundary members are designed. The capacity of the wall andboundary member sizes will not be so sensitive to α, however, that multiple iterations are usuallynecessary, unless drift controls the design. In fact, the equation for α, is not entirely accurate.The equation is based on pinned beam to column connections with SPSW panels above andbelow. While α equations are available for other conditions, it was determined by the authors ofAISC Seismic that these variations in α are not significant. An initial estimate of 40º willusually suffice.After the plate is sized using the assumed angle, α, the expected yield force of web platethat will be applied to HBE’s and VBE’s should be calculated. The expected yield stress of theweb plate is R y F y . When reducing the expected yield stress into vertical and horizontalcomponents, the fact that the length of plate on the angle is longer than the vertical or horizontallength should be taken into account to avoid overly conservative design. For instance, thevertical component of the expected yield stress to be applied to the HBE is R y F y (cos α)(cos α)rather than just R y F y (cos α). The upcoming AISC Design Guide by Bruneau and Sabellidiscusses this further.SPSW Aspect Ratio and Intermediate HBE’sThe length of an SPSW panel is limited by an aspect ratio of 0.8

esisting elements.How to use intermediate HBE’s between floors is notwell defined in the AISC Seismic Provisions. The commentarymentions that additional horizontal intermediate boundaryelements can be used to adjust the aspect ratio of a SPSWpanel, but the main body of the code requires that all HBE toVBE connections be moment connections and that all HBE toVBE intersections be laterally braced. It is the author’sinterpretation that these provisions do not apply to intermediateHBE’s. This should be addressed, however, in future editionsof the code.With the use of intermediate HBE’s, the slendernessand capacity of a wall is perfectly adjustable. Walls as slenderas the one shown in Fig 2 have been designed and constructed.A nonlinear pushover analysis was done on this wall to ensurethat the boundary elements will remain elastic while the webplate yields.Web Plate Thickness and MaterialWhen sizing the web plate there a few things to keep inmind. It is ideal to size the plate at each level to just satisfy thedesign shear force. This will make it more likely that the platewill yield at multiple floors and it will make for a moreeconomical design of the columns.At upper floors of a mid-rise or all floors of a low-risebuilding it becomes clear that even 3/16” to 1/8” plate can havemore capacity than is needed. The question quickly becomes: Figure 2 – Steel plate shearhow thin of plate should be used? AISC Seismic Provisions wall used in a high-enddo not limit plate slenderness, instead, the commentary states residence in Atherton, CA.that story drift limitations will indirectly limit the plateslenderness. For designs such as the ones shown in Fig 1 and Fig 2 the material andconstructability may control instead.As the web plate gets thinner the connection to boundary members becomes moredifficult. The connection shown in Fig 3 is from a SPSW used for a high-end residence in SanMateo County, California. 14 gage plate was specified with continuous welds on both sides tothe boundary members. Inadvertently, the steel fabricator shipped some of the panels to sitewith only intermittent welds around the panel perimeter. It was discovered that, while thehorizontal welds were fairly easy to complete in the field, the welds along the VBE’s requiredspecial attention. Initial attempts at vertical welding presented some difficulty, when uphandwelding (starting at the bottom and going up) began burning through the light gage plate. Aspecial downhand (starting from the top and going down) procedure was developed by thefabricator and qualified by the special inspector. The resulting welds were found to be adequate,but this demonstrates some of the challenges when using light gage web plate.Another factor to consider when using thin web plate is the shear that causes the plate tobuckle. Plate buckling is expected to occur as the tension field develops, but it is not desirable

for service loads, e.g. a stout wind.Researchers who have run tests onSPSW’s report extremely loudbanging as the loading reverses.Even though there haven’t beenany documented cases of SPSWbuildings making loud bangingsounds in wind storms, SPSW arerelatively new and it may yetbecome an issue. Theory ofelasticity texts give formulas forcalculating plate buckling and it isworthwhile to understand the loadat which an SPSW will buckle.Introducing intermediate HBE’swith shorter panel lengths willincrease the buckling load.The third consideration when choosing plate thickness is the material specification.Section 6.1 of the AISC Seismic Provisions limits the materials that can be used in the seismicload resisting system. Acceptable plate material includes A36 or A1011 Grade 55 (in either SSor HSLAS). A1011 is hot rolled sheet steel and as such should have more pronounced yieldingand more ductility than cold rolled sheet metal. It would be much more preferable, however, touse A1011 grade 30 or 33 sheet steel as it has a lower yield and more elongation. While thecommentary discusses low yield point plate material, it is suggested that future editions of theAISC Seismic Provisions explicitly allow these materials.Whenever light gage plate is used for the web plate it is the author’s opinion that it isworthwhile to require coupon tests to measure actual yield strength and percent elongation.Since the performance of the building is so directly tied to the plate material, the greaterunderstanding of the primary energy dissipating element will easily justify the slight additionalcost.Column DesignFigure 3 – Field welding of gage plate that requiredspecial procedure.The main body of the 2005 AISC Seismic Provisions states that the required strength ofVBE’s shall be based upon the forces corresponding to the expected yield strength, in tension, ofthe web calculated at an angle, α. To reach this level of force the beams are required to developplastic hinges. The commentary describes three methods that can be used to design the VBE.The first, nonlinear pushover analysis, will give the most accurate understanding of the SPSWresponse. Axial loads and moments in the columns caused by web plate yielding and plastichinging of the HBE can be used to design the columns to remain elastic. It is important to notethat elastic modeling of SPSW will not capture the intent of the design process: to size VBE’s toremain elastic while the web plate yields. To design the VBE for yielded plate and plastichinging of HBE’s requires consideration of the nonlinear response of the elements. Nonlinearpushover analyses, however, are not that common in most design offices.The second method called combined linear elastic computer programs and capacitydesign concept (LE+CD) uses an elastic model of the wall, considering moment connections and

web plate to determine the loads in VBE. The VBE axial force determined using the model isthen amplified by Ω o and combined with the effect of the web plate yielding for the story forwhich the VBE is being designed. This method seems inconsistent with the wording of theprovisions, in that the axial force is multiplied by Ω o , but the VBE moments from plastichinging of the HBE and from web plate yielding in panels above are not included. Sincemoments created by the web plate at only the floor in question are considered, this method couldresult in a VBE that becomes inelastic before the web plate has fully yielded.The third method comes from the Canadian steel code (CAN/CSA S16-01). Overturningmoments from the design lateral forces are calculated and then factored up to a levelcorresponding to the expected yield strength of the web plate. A distribution of overturningmoment is then specified for which axial loads in VBE’s can be obtained. The local bendingmoments from web plate yielding are required to be factored up to the level of expected yieldstrength of the plate also. Affects of moments caused by plastic hinging in the HBE is notaddressed, but since it is not specifically left out it should be included.These three methods produce three different results. The disparity between thesemethods should be addressed in future editions of the code provisions if not in future research.The AISC Seismic Provisions also require that HBE’s and VBE’s satisfy the weak beam/strong column requirements for moment frames without consideration of the webs. Themoments in VBE’s caused by the web plate tension field are fairly severe. Similarly, the axialloads caused by the overturning moments from web plates yielding are quite high. If these loadsare not considered in the weak beam / strong column check, then hinging in the HBE’s ratherthan the VBE’s is not ensured, and the usefulness of the provision is not clear.Comparison of SPSW to Other Lateral SystemsWith this added tool in our toolbox of lateral resisting systems, it is worthwhile to make acomparison between SPSW and some of the other choices available. A sample building wasdesigned using special plate shear walls, special concentrically braced frames and specialmoment frames. A two story office building was selected that has 4-30’ bays in one directionand 3-30’ bays in the other direction. The two floor heights are each 15’. RAM software wasused to optimize the gravity structure. Lateral bracing members for SMF and SPSW wereincluded, but gusset plates, continuity plates, shear tabs, base plates and stiffeners were notconsidered in the summation of frame weight. Fig 4 shows an isometric view of each building.Cost ComparisonAn elevation of the SPSW design is shown in Figure 4. The design was carried out perthe 2005 AISC Seismic Provisions with the some liberties taken, such as the addition ofintermediate HBE’s and the use of ASTM A1011 grade 33 plate. Four SPSW panels wererequired in each direction. Some additional floor members were required to brace the SPSW atboth columns and at both floors. The VBE design considered the moments and axial forces dueto all web plates fully yielding and HBE’s developing plastic hinges.The special concentrically braced frame was accomplished with HSS6x6x3/8 columns,HSS5x5x1/4 braces at the first floor and HSS4x4x1/4 braces at the second floor. Four bracedframes were used in each direction, and each braced frame extended the entire length of one bay,30’.

The special moment frame option was designed with two 2-bay frames in each direction.Laying out the frames so they don’t meet at the corners eliminated the need to considercombined orthogonal seismic forces. The columns are W14x159 and the beams at the first floorand roof are W24x62 and W18x40 respectively. The frames were drift controlled.The weight of the structural steel was summed up for each design and is tabulated inTable 1. Weights were then normalized to the weight of the moment frame structure. TheSPSW structure was 87% of the weight of the moment frame, while the SCBF structure was79% of the moment frame. As would be expected both SPSW and SCBF result in less steel thanthe moment frame, but SPSW may mean slightly more steel than SCBF. Even though SPSW issimilar to a braced frame with tension-only braces, the forces of the tension field on theboundary members causes some increase in their size over braced frames.Stopping with just a steel weight comparison would not give the full picture ofconstruction costs, however. One of the reasons that SPSW was used for the residence inAtherton, California (see later discussion) was that the panels came out of the shop fullyconstructed. The SPSW panels shown in Fig 4. could be shop constructed and erected withoutthe need for field welding. Table 1 shows the number of field pieces and field welds required foreach design. With 8% less pieces in the field and 256 less field welds, the SPSW option will beeasier and faster to erect than the SCBF.Other ConsiderationsThe three SPSW projects that the author was involved with were all highly architecturalbuildings. Thickness of walls, length of solid walls and locations of solid walls were the drivingforce behind the choice to use SPSW. As shown in Table 1, SPSW columns can be smaller thanmoment frame columns and take up less wall length than SCBF.Table 1 also includes inelastic drift, ∆m. The relative stiffness of the systems puts SPSWbetween a braced frame and a moment frame. When considering the relative performance ofdifferent systems it is important to examine not only drift, but also accelerations (Mayes et al2005). A well known example of acceleration related damage is the Olive View Hospital whichhappened to be constructed with steel plate shear walls (Celebi, 1997). During the NorthridgeEarthquake, peak acceleration at the roof was recorded to be 2.31g while peak groundacceleration was 0.82g. The amount of damage to secondary structures and equipmentincluding water damage from broken pipes greatly outweighed any structural damage.The Olive View Hospital is different from typical SPSW designed per the AISC SeismicProvisions in two very important ways. As discussed in the introduction there has been a shiftin the design methodology for SPSW. The Olive View Hospital used “stiffened” steel plateshear walls. That is, the 5/8” and ¾” thick web plate (Anon, 1978) was designed not to buckle.Additionally, in reaction to the failure of the previous Olive View Hospital in the WhittierEarthquake, high loads were used in an effort to reduce the amount of structural damage. It isobvious from the amount of acceleration amplification that the lateral resisting system remainedvirtually elastic during the Northridge Earthquake. If an SPSW plate thickness andconfiguration are designed to meet the seismic loads without significant design overstrength,then nonlinearities in the seismic response will reduce expected accelerations. It has been shownthat moment frames, being drift controlled, usually exhibit less inelasticity than other systems(Mayes et al, 2005). As such, it can be expected that SPSW would likely have less accelerationamplification than the SMF option.

(a)(b)(d)Figure 4 – Comparison buildings designedwith special plate shear walls (a), specialconcentrically braced frames (b) and specialmoment frames (c). Elevation view of theSPSW design (d).(c)Table 1.Factors for comparing SPSW, SCBF and SMF lateral resisting systems.Cost / Construction Design Architectural PerformanceSteel % of # of Number Resp. Cntllng Column Length Roof RepairWeight SMF Field of Field Mod. D/C Width Wall Defl. afterSystem (kips) Wt Pieces Welds R Ratio in Wall Used ∆m EQSPSW 173.8 87% 150 0 7.0 0.96 12" 120’ 3.1” Replace PlateSCBF 158.1 79% 162256fillet 6.4 0.97 6" 480’ 0.25” Replace BracesSMF 200.2100% 182 96 CJP 8.5 0.88 16" 0’ 9.0” Not as Easy

The last column shown in Table 1 is meant to point out the repair options that might beavailable after an earthquake. In the braced frame and SPSW it would be possible to replacedamaged components, while repair methods for moment frames would require additional work.Successful SPSW Projects in Northern CaliforniaThe author has been involved with three large residences where SPSW was determined tobe the best option. All three are in the final phases of construction at the end of 2005. Thereasons for using SPSW are described in the following list:1. Speed of construction. One of the residences had a very short construction schedule.It was determined that fully shop fabricated SPSW would allow faster erection.2. All three of the projects are highly architectural in that there are very few lengths ofsolid walls. It was necessary to fit lateral resisting elements into short lengths ofwalls or use moment frames. SPSW allowed the used of very slender elements (seefig 2).3. Braced frames in tall slender configurations require large gusset plates.Configurations as slender as shown in Fig 2 would not be practical as a braced frame.4. Thickness of walls was also important to the architects. Moment frames that wouldrequire thick walls or bump-outs to hide large columns was not an option.5. As is shown in the preceeding section, SPSW yields less structural steel weight andshould therefore be cheaper than moment frames.All three projects were designed before the AISC Seismic Provisions were available. Thedesigns were carried out using the Canadian Steel Code (CAN/CSA 2001). 2d pushover modelswere used to verify the designs. 12 gage and 14 gage web plates were used and small angleswere attached to the columns to provide a surface to which the plate was welded. Some type offish plate or angle was needed to allow for tolerances in the plate and column. Care was takennot to attach anything to the web plates or to drill holes through the web plate for plumbing orconduit. A gap of approximately 1” was left between infill studs and the web plate in an effortto reduce damage from minor earthquakes that might buckle the plate.ConclusionsSteel plate shear walls were an excellent choice of lateral systems for three largeresidences in Northern California. The high capacity possible in a SPSW panel that is relativelytall and slender helped satisfy the restrictive architectural requirements. A cost comparisonshows that the design of a sample 2 story building required 13% less steel than a comparablemoment frame and if detailed properly would not require field welding.The 2005 AISC Seismic Provisions and the upcoming AISC Design Guide for steel plateshear walls will give SPSW a new level of exposure among practicing engineers. The followingare suggestions for further research and future editions of the SPSW design provisions:1. It should be defined whether intermediate HBE’s (between floors) require momentconnections to the VBE’s. Also it should be stated that intermediate HBE’s do notrequire lateral bracing if the VBE is designed accordingly.2. Further research should be conducted to determine what level of plate slenderness causes

uckling of the plate under service loads and if this results in audible banging or othernegative effects.3. The materials allowed for the web plate should explicitly include ASTM A1011 SSGrades 30 and 33. These materials have greater ductility than ASTM A1011 HSLASGrade 55 which is already allowed.4. There are three methods presented for designing VBE’s that give significantly differentresults. These variations should be reconciled.5. The method for designing VBE’s called linear elastic computer programs and capacitydesign concept, considers axial forces amplified by Ω o , but moments due to web plateyielding in panels above or plastic hinging of the HBE’s is ignored. This appearsinconsistent with the intent of the provisions, which is that VBE’s remain elastic whilethe web plate yields.6. Strong column / weak beam design checks are specified to be carried out withoutconsidering web plate tension. Since a large portion of the axial forces and bendingmoments in the columns will be caused by web plate tension, this design check does notlimit the plastic hinging to HBE’s.ReferencesAmerican Institute of Steel Construction 2005. Seismic Provisions for Structural Steel BuildingsANSI/AISC 341-05 released online in December 2005Bruneau, Michel, Sabelli, Rafael and Pottebaum, Warren. 2006 AISC Design Guide for Steel Plate ShearWalls American Institute of Steel Construction (yet to be released).Canadian Standards Association 2001. Limit States Design of Steel Structures CAN/CSA S16-01published by Canadian Standards Association.Mayes, Ronald B, Goings, Craig B, Naguib, Wassim I, and Harris, Stephen K 2005. Comparative SeismicPerformance of Four Strucutral Systems 74 th Annual Convention of the Structural EngineersAssociation of California September 28-October 1, 2005.Celebi, Mehmat. 1997. Response of Olive View Hospital to Northridge and Whittier Earthquakes Journalof Structural Engineering, ASCE, 123, 389-396.Anonymous 1978. Quake-proof hospital has battleship-like walls Engineering News Record Sept. 21,1978 62-63.