F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

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Design and detailing-illustrative examples 439M = 40% of 307 kNm (Fig. 11.5-5: Case 2)= 123 kNmM (123)(10 6 )fcubd 2 = (40)(350)(500Z) = 0.03SFrom Table 4.7-2,zd = 0.94Xd = 0.13< K' of Table 4.7-1From eqn (4.7-9),M (123)(10 6 )As = 0.87/yz = (0.87)(460)(0.94)(500)= 654 mm 2 2T25 U-bars (982 mm 2 )From Table 4.10-2ultimate anchorage bond length = 32(j) = 800 mmUsing eqns (6.6-3(a) (b)),required anchorage length = ~~i (800) = 533 mm 2The curtailment diagram for the longitudinal reinforcement is shown inFig. 11.5-10, which should be read in conjunction with the reinforcementdetails in Fig. 11.5-12 (seep. 444).Step 6 Shear reinforcementFor further explanations of the calculations, see Comments on Step 6 atthe end.(a)From Fig. 11.5-12, the minimum tension reinforcement along thebeam may reasonably be taken as 2T25, i.e. As= 982 mm 2 •100As _ (100)(982) = O 56bvd - (350)(500) ·From Table 6.4-1,Vc = 0.61 N/mm 2(b) Minimum links (see Section 6.4: 'Shear resistance in designcalculations: Step 4') will be provided where v :s: (vc + 0.4), i.e.where V :S: (vc + 0.4)bvd.V :s: (0.61 + 0.4)(350)(500) N= 177 kN
440 Practical design and detailingMu440kNm~----- 2 ------~~645kNmNotes:1. d = Effectve depth of beam2. l u= Ultimate anchorage length ( Eqn 6.6-3(b))Fig.ll.S-10 Curtailment diagramIn Fig. 11.5-11, the 177 kN limits for minimum links aresuperimposed on the shear force envelope.(c) From eqn (6.4-2),Asv ( . 1. k ) 0.4bv- mm. m s = 0 87 '[,Sv • yvR12Linkspacing 150 300(min.links)280kNR16R12150 200 300 200(min. links)189kNFig.ll.S-11 Link diagram
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Reinforced and Prestressed Concrete
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First edition 1975Reprinted three t
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viContents3 Axially loaded reinforc
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viii Contents9.5 The ultimate limit
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Preface to the Third EditionThe thi
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NotationThe symbols are essentially
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Notationxvhmax (hmin)IMMadd=larger
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Notation xvnVtminVtuVuwkwkXXtYtzZt
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Chapter 1Limit state design concept
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Statistical concepts 3occur in prac
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Statistical concepts 5results in th
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Statistical concepts 7an important
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Statistical concepts 9Example 1.3-1
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Statistical concepts 11these limits
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Partial safety factors 13proof stre
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Limit state design and the classica
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ReferencesReferences 171 Harris, Si
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Cement 19composition of Portland ce
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Aggregates 21Mortar cubes3-day comp
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Aggregates 23of concrete mainly ind
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2.5(a)Strength of concreteStrength
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Strength of concrete 21- Ordinary P
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Creep and its prediction 29..EE....
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Creep and its prediction 31humidity
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Shrinkage and its prediction 33read
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Shrinkage and its prediction 35The
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2.5(d) Elasticity and Poisson's rat
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Durability of concrete 39(a) an upp
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Failure criteria for concrete 41e.g
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Failure criteria for concrete 43v,0
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Non-destructive testing of concrete
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Assessment of workability 47fSlump
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Principles of concrete mix design 4
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Traditional mix design method 51req
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w/c ratio by weight: 0.40 3.7 3.3 2
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DoE mix design method 55(a) The mix
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DoE mix design method 57always happ
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DoE mix design method 59For a given
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Step2Statistics and target mean str
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Statistics and target mean strength
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References 65(where 1.64a is the cu
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References 6732 Shacklock, B. W. Co
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Stress/strain characteristics of st
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Real behaviour of columns 71with a
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Real behaviour of columns 73settles
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Real behaviour of columns 75ultimat
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Design details 77horizontally cast
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Design and detailing-illustrative e
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References 83(a) Bar mark[ffJ IbJBa
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Chapter4Reinforced concrete beamsth
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A general theory for ultimate flexu
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Beams with reinforcement having a d
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Beams with reinforcement having a d
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Characteristics of some proposed st
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Characteristics of some proposed st
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BS 8110 design charts-their constru
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Derivation of design formulae 105co
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Derivation of design formulae 1010
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Step(b)Find lever arm z. From Fig.
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Design procedure for rectangular be
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Design formulae and procedure-BS 81
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so thatDesign formulae and procedur
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Flanged beantS 127d' 60x = (0.45)(7
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Flanged beams 129(4.8-2)When using
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Flanged beams 131(b) If Kr of eqn (
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Moment redistribution-the fundament
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Design details (BS 81 10) 143(d) Tr
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Design details (BS 81 10) 145(a) Wh
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Problems 151effects of torsion have
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Problems 153where z values are give
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References 155theory of structures.
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Elastic theory: cracked, uncracked
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-(I)Elastic theory: cracked, uncrac
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Deflection control in design (BS 81
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Deflection control in design (BS 81
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The actual span/depth ratio = (11 m
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Calculation of short-term and long-
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StepSCalculation of short-term and
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Calculation of crack widths (BS 811
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Calculation of crack widths (BS 81
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Problems 195moment-area method, whi
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References 19719 ACI Committee 224.
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Shear failure of beams without shea
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(c)Shear failure of beams without s
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VI-iShear failure of beams without
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Effects of shear reinforcement 205F
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Effects of shear reinforcement 207A
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Shear resistance in design calculat
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Shear resistance in design ca/cu/at
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Table 6.4-2 Values of A.vl Sv (mm)f
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Shear resistance in design calculat
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From Table 6.4-2, useSize 12 links
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Shear strength of deep beams 219ver
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Bond and anchorage (BS 8110) 221lat
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Bond and anchorage (BS 8110) 223Tab
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Torsion in plain concrete beams 225
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Torsioll ill plaill cOllcrete beal1
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Effects of tors ion reinforcement 2
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Design practice (BS 8110) 231of bea
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Structural behaviour 233CUrve II(Un
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Table 6.11-1 Torsional shear stress
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Torsional resistance in design calc
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(b) From Table 6.11-1,Viu = 5 N/mm
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References 2452TVt = 2hmin[hmax - (
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References 247beams with web openin
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Principles of column interaction di
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rr-b--j_ld'• A~ •• TPrinciple
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ThereforeN = afcubh = 0.219 X 40 X
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(c)e = 200 mm. Thereforee/h = 200/5
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BS 81IO design procedure 265Table 7
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BS 8110 design procedure 267(b) In
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BS 8110 design procedure 269yIT ·l
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Biaxial bending-the technical backg
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Additional moment due to slender co
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Slender columns (BS 8110) 279height
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Slender columns (BS 81 10) 281K = 1
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M 1 = Nemin where emin = (0.05)(400
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Slender columns (BS 8110) 285Asc =
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Problems 2877.8 Computer programs(i
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Problems 289refers to a particular
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References 29111 Beeby, A. W. The D
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Yield-line analysis 2938.2 Yield-li
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Johansen's stepped yield criterion
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8.4 Energy dissipation in a yield l
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ThereforeEnergy dissipation in a yi
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Energy dissipation in a yield line
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Energy dissipation in a yield line
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Energy dissipation for a rigid regi
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m 1 [projection of eh on m1 moment
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Hil/erborg's strip method 319can be
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Hillerborg's strip method 321indica
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Hillerborg's strip method 323respec
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Design of slabs (BS 8110) 325( . .
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Design of slabs (BS 8110) 327(a) 0.
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Problems 329Problems8.1 In yield-li
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References 331(a)(b)Problem8.5reinf
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Chapter9Prestressed concrete simple
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Stresses in service: elastic theory
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Stresses at transfer 347(9.3-6)wher
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Loss of prestress 349therefore wher
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Loss of prestress 351The equilibriu
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Loss of prestress 353p. 113 of Refe
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The ultimate limit state: flexure (
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TT~b1--400-l''Th ~ -illj -r-· Aps.
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The ultimate limit state: shear (BS
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The ultimate limit state: shear (BS
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= 400 - 1893 sin 3° = 301 kNCase 2
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Short-term and long-term deflection
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Problems 375Step3Determine the perm
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Problem 377Example 9.8-2 and compar
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References 37914 Guyon, Y. Limit-st
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Primary and secondary moments 381A~
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Analysis of prestressed continuous
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Analysis of prestressed continuous
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Linear transformation and tendon co
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Page 408 and 409: Applying the concept of the line of
Page 410 and 411: Summary of design procedure 393dePT
Page 412 and 413: (k:,~:J100100kN 100kN 100kN~ ~ ~ ~S
Page 414 and 415: Summary of design procedure 397(b)(
Page 416 and 417: Problems 399modulus is 78 x 10 6 mm
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Page 420 and 421: 7000f = 460 N/mm 2yLoads-including
Page 422 and 423: Materials and practical considerati
Page 424 and 425: Analysis of framed structure (BS 81
Page 430 and 431: Braced frame analysis 41336 kN/m an
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Page 434 and 435: Table 11.4-4 Moment distributionBra
Page 436 and 437: 11.4(c) Unbraced frame analysisUnbr
Page 438 and 439: Unbraced frame analysis 421IOkN J 5
Page 440 and 441: Unbraced frame analysis 423loading
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Page 448 and 449: 0iDesign and detailing-illustrative
Page 450 and 451: Design load F = 1.4gk + 1.6qkStep 3
Page 452 and 453: CASE IDesign and detailing-illustra
Page 454 and 455: Design and· detailing-illustrative
Page 466 and 467: leyfb = 4000/380 = 10.5 < 15Design
Page 468 and 469: Job No.: 1959/65/67Trinity and Newn
Page 470 and 471: Typical reinforcement details 453Co
Page 472 and 473: References 45512 Mayfield, B., Kong
Page 474 and 475: Program layout 457the efforts to ma
Page 476 and 477: Program layout 4596566676869707l727
Page 478 and 479: Program layout 46119819920020120220
Page 480 and 481: Program layout 46333133233333633533
Page 482 and 483: Program layout 465&65&66&67&68&69no
Page 484 and 485: 599600601'602603 1000 FORMAT6046056
Page 486 and 487: How to run the programs 469numbers
Page 488 and 489: Worked example 471(2) External docu
Page 490 and 491: Program NMDDOE 473The rectanqular s
Page 492 and 493: 12.3 Computer program for Chapter 3
Page 494 and 495: Program BDFLCK 477materials and the
Page 496 and 497: Program BSHEAR 479characteristic st
Page 498 and 499: Program RCIDSR 481The input data fo
Page 500 and 501: Program CTDMUB 483CommentThe comple
Page 502 and 503: 12. 7(e)Program SRCRPR 485Program S
Page 504 and 505: Program SSH EAR 487123' 56789101112
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Program PBSUSH 489123'5678910111213
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References 491The input data for th
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Appendix 1 How to order program lis
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Appendix 2 Design tables and charts
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Appendix 2 Design tables and charts
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:: rn.:r'''' ',I~ '~~r I ' .., I ',
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502 IndexBending moment envelope 13
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504 IndexFactor of safety 13, 14, 1
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506 Indexbends 222, 495bond,anchora
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508 IndexJohansen's stepped yield c
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F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

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