13920

1. IS 13920 : 1993(Reaffirmed 1998)Edition 1.2(2002-03)Indian StandardDUCTILE DETAILING OF REINFORCEDCONCRETE STRUCTURES SUBJECTED TOSEISMIC FORCES — CODE OF PRACTICE(Incorporating Amendment Nos. 1 & 2)UDC 69.059.25 (026) : 624.042.7© BIS 2002B U R E A U O F I N D I A N S T A N D A R D SMANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARGNEW DELHI 110002Price Group 7 2. Earthquake Engineering Sectional Committee, CED 39FOREWORDThis Indian Standard was adopted by the Bureau of Indian Standards, after the draft finalized bythe Earthquake Engineering Sectional Committee had been approved by the Civil EngineeringDivision Council.IS 4326 : 1976 ‘Code of practice for earthquake resistant design and construction of buildings’while covering certain special features for the design and construction of earthquake resistantbuildings included some details for achieving ductility in reinforced concrete buildings. With aview to keep abreast of the rapid developments and extensive research that has been carried out inthe field of earthquake resistant design of reinforced concrete structures, the technical committeedecided to cover provisions for the earthquake resistant design and detailing of reinforced concretestructures separately.This code incorporates a number of important provisions hitherto not covered in IS 4326 : 1976.The major thrust in the formulation of this standard is one of the following lines:a) As a result of the experience gained from the performance, in recent earthquakes, ofreinforced concrete structures that were designed and detailed as per IS 4326 : 1976, manydeficiencies thus identified have been corrected in this code.b) Provisions on detailing of beams and columns have been revised with an aim of providingthem with adequate toughness and ductility so as to make them capable of undergoingextensive inelastic deformations and dissipating seismic energy in a stable manner.c) Specifications on a seismic design and detailing of reinforced concrete shear walls have beenincluded.The other significant changes incorporated in this code are as follows:a) Material specifications are indicated for lateral force resisting elements of frames.b) Geometric constraints are imposed on the cross section for flexural members. Provisions onminimum and maximum reinforcement have been revised. The requirements for detailing oflongitudinal reinforcement in beams at joint faces, splices, and anchorage requirements aremade more explicit. Provision are also included for calculation of design shear force and fordetailing of transverse reinforcement in beams.c) For members subjected to axial load and flexure, the dimensional constraints have beenimposed on the cross section. Provisions are included for detailing of lap splices and for thecalculation of design shear force. A comprehensive set of requirements is included on theprovision of special confining reinforcement in those regions of a column that are expected toundergo cyclic inelastic deformations during a severe earthquake.d) Provisions have been included for estimating the shear strength and flexural strength ofshear wall sections. Provisions are also given for detailing of reinforcement in the wall web,boundary elements, coupling beams, around openings, at construction joints, and for thedevelopment, splicing and anchorage of reinforcement.Whilst the common methods of design and construction have been covered in this code, specialsystems of design and construction of any plain or reinforced concrete structure not covered by thiscode may be permitted on production of satisfactory evidence regarding their adequacy for seismicperformance by analysis or tests or both.The Sectional Committee responsible for the preparation of this standard has taken intoconsideration the view of manufacturers, users, engineers, architects, builders and technologistsand has related the standard to the practices followed in the country in this field. Due weightagehas also been given to the need for international co-ordination among standards prevailing indifferent seismic regions of the world.In the formulation of this standard, assistance has been derived from the following publications:i) ACI 318-89/318R-89, Building code requirements for reinforced concrete and commentary,published by American Concrete Institute.ii) ATC-11. Seismic resistance of reinforced concrete shear walls and frame joints : Implicationsof recent research for design engineers, published by Applied Technology Council, USA.iii) CAN3-A23. 3-M84, 1984, Design of concrete structures for buildings, Canadian StandardsAssociation.iv) SEADC, 1980, Recommended lateral force requirements and commentary, published byStructural Engineers Association of California, USAThe composition of the technical committees responsible for formulating this standard is given inAnnex A.This edition 1.2 incorporates Amendment No. 1 (November 1995) and Amendment No. 2(March 2002). Side bar indicates modification of the text as the result of incorporation of theamendments. 3. IS 13920 : 19931Indian StandardDUCTILE DETAILING OF REINFORCEDCONCRETE STRUCTURES SUBJECTED TOSEISMIC FORCES — CODE OF PRACTICE1 SCOPE1.1 This standard covers the requirements fordesigning and detailing of monolithic reinforcedconcrete buildings so as to give them adequatetoughness and ductility to resist severeearthquake shocks without collapse.1.1.1 Provisions of this code shall be adopted inall reinforced concrete structures which arelocated in seismic zone III, IV or V.1.1.2 The provisions for reinforced concreteconstruction given herein apply specifically tomonolithic reinforced concrete construction.Precast and/or prestressed concrete membersmay be used only if they can provide the samelevel of ductility as that of a monolithicreinforced concrete construction during or afteran earthquake.2 REFERENCES2.1 The Indian Standards listed below arenecessary adjunct to this standard:3 TERMINOLOGY3.0 For the purpose of this standard, thefollowing definitions shall apply.3.1 Boundary ElementsPortions along the edges of a shear wall thatare strengthened by longitudinal andtransverse reinforcement. They may have thesame thickness as that of the wall web.3.2 CrosstieIs a continuous bar having a 135° hook with a10-diameter extension (but not < 75 mm) ateach end. The hooks shall engage peripherallongitudinal bars.3.3 Curvature DuctilityIs the ratio of curvature at the ultimatestrength of the section to the curvature at firstyield of tension steel in the section.3.4 HoopIs a closed stirrup having a 135° hook with a10-diameter extension (but not < 75 mm) ateach end, that is embedded in the confined coreof the section. It may also be made of two piecesof reinforcement; a U-stirrup with a 135° hookand a 10-diameter extension (but not < 75 mm)at each end, embedded in the confined core anda crosstie.3.5 Lateral Force Resisting SystemIs that part of the structural system whichresists the forces induced by earthquake.3.6 Shear WallA wall that is primarily designed to resistlateral forces in its own plane.3.7 Shell ConcreteConcrete that is not confined by transversereinforcement, is also called concrete cover.3.8 Space FrameA three dimensional structural systemcomposed of interconnected members, withoutshear or bearing walls, so as to function as acomplete self-contained unit with or withoutthe aid of horizontal diaphragms or floorbracing systems.3.8.1 Vertical Load Carrying Space FrameA space frame designed to carry all verticalloads.3.8.2 Moment Resisting Space FrameA vertical load carrying space frame in whichthe members and joints are capable of resistingforces primarily by flexure.IS No. Title456 : 1978 Code of practice for plain andreinforced concrete ( thirdrevision)1786 : 1985 Specification for high strengthdeformed steel bars and wiresfor concrete reinforcement( third revision )1893 : 1984 Criteria for earthquake designof structures ( fourth revision ) 4. IS 13920 : 199324 SYMBOLSFor the purpose of this standard, the followingletter symbols shall have the meaningindicated against each; where other symbolsare used, they are explained at the appropriateplace. All dimensions are in mm, loads inNewton and stresses in MPa (N/sq mm) unlessotherwise specified.5 GENERAL SPECIFICATION5.1 The design and construction of reinforcedconcrete buildings shall be governed by theprovisions of IS 456 : 1978, except as modifiedby the provisions of this code.5.2 For all buildings which are more than3 storeys in height, the minimum grade ofconcrete shall be M20 ( fck = 20 MPa ).5.3 Steel reinforcements of grade Fe 415 ( seeIS 1786 : 1985 ) or less only shall be used.However, high strength deformed steel bars,produced by the thermo-mechanical treatmentprocess, of grades Fe 500 and Fe 550, havingelongation more than 14.5 percent andconforming to other requirements ofIS 1786 : 1985 may also be used for thereinforcement.Ag — gross cross sectional area ofcolumn, wallAh — horizontal reinforcement areawithin spacing SvAk — area of concrete core of columnAsd — reinforcement along each diagonalof coupling beamAsh — area of cross section of bar formingspiral or hoopAst — area of uniformly distributedvertical reinforcementAv — vertical reinforcement at a jointCw — centre to centre distance betweenboundary elementsD — overall depth of beamDk — diameter of column core measuredto the outside of spiral or hoopd — effective depth of memberdw — effective depth of wall sectionEs — elastic modulus of steelfck — characteristic compressive strengthof concrete cubefy — yield stress of steelh — longer dimension of rectangularconfining hoop measured to itsouter facehst — storey heightLAB — clear span of beamlo — length of member over whichspecial confining reinforcement isto be providedlw — horizontal length of wallls — clear span of coupling beamMu — factored design moment on entirewall section— hogging moment of resistance ofbeam at end A— sagging moment of resistance ofbeam at end A— hogging moment of resistance ofbeam at end B— sagging moment of resistance ofbeam at end B— moment of resistance of beamframing into column from the leftM u, limAhM u, limAsM u, limBhM u, limBsM u, limbL— moment of resistance of beamframing into column from the rightMuv — flexural strength of wall webPu — factored axial loadS — pitch of spiral or spacing hoopsSv — vertical spacing of horizontalreinforcement in webtw — thickness of wall web— shear at end A of beam due to deadand live loads with a partial factorof safety of 1.2 on loads— shear at end B of beam due to deadand live loads with a partial factorof safety of 1.2 on loadsVj — shear resistance at a jointVu — factored shear forceVus — shear force to be resisted byreinforcement— depth of neutral axis from extremecompression fibreα — inclination of diagonalreinforcement in coupling beamρ — vertical reinforcement ratioρc — compression reinforcement ratio ina beamρmax — maximum tension reinforcementratio for a beamρmin — minimum tension reinforcementratio for a beamτc — shear strength of concrete— maximum permissible shear stressin sectionτv — nominal shear stressM u, limbRVD L+aVD L+bxu, x *uτc,max 5. IS 13920 : 199336 FLEXURAL MEMBERS6.1 GeneralThese requirements apply to frame membersresisting earthquake induced forces anddesigned to resist flexure. These members shallsatisfy the following requirements.6.1.1 The factored axial stress on the memberunder earthquake loading shall not exceed0.1 fck.6.1.2 The member shall preferably have awidth-to-depth ratio of more than 0.3.6.1.3 The width of the member shall not be lessthan 200 mm.6.1.4 The depth D of the member shallpreferably be not more than 1/4 of the clearspan.6.2 Longitudinal Reinforcement6.2.2 The maximum steel ratio on any face atany section, shall not exceed ρmax = 0.025.6.2.3 The positive steel at a joint face must beat least equal to half the negative steel at thatface.6.2.4 The steel provided at each of the top andbottom face of the member at any section alongits length shall be at least equal to one-fourth ofthe maximum negative moment steel providedat the face of either joint. It may be clarifiedthat redistribution of moments permitted inIS 456 : 1978 (clause 36.1) will be used only forvertical load moments and not for lateral loadmoments.6.2.5 In an external joint, both the top and thebottom bars of the beam shall be provided withanchorage length, beyond the inner face of thecolumn, equal to the development length intension plus 10 times the bar diameter minusthe allowance for 90 degree bend(s) ( seeFig. 1 ). In an internal joint, both face bars ofthe beam shall be taken continuously throughthe column.6.2.6 The longitudinal bars shall be spliced,only if hoops are provided over the entire splicelength, at a spacing not exceeding 150 mm ( seeFig. 2 ). The lap length shall not be less thanthe bar development length in tension. Lapsplices shall not be provided (a) within a joint,(b) within a distance of 2d from joint face, and(c) within a quarter lengh of the member whereflexural yielding may generally occur under theeffect of earthquake forces. Not more than50 percent of the bars shall be spliced at onesection.6.2.7 Use of welded splices and mechanicalconnections may also be made, as per 25.2.5.2of IS 456 : 1978. However, not more than halfthe reinforcement shall be spliced at a sectionwhere flexural yielding may take place. Thelocation of splices shall be governed by 6.2.6.6.3 Web Reinforcement6.3.1 Web reinforcement shall consist ofvertical hoops. A vertical hoop is a closedstirrup having a 135° hook with a 10 diameterextension (but not < 75 mm) at each end that is6.2.1 a) The top as well as bottomreinforcement shall consist of at leasttwo bars throughout the memberlength.b) The tension steel ratio on any face, atany section, shall not be less thanρmin = 0.24 ; where fck and fyare in MPa.fck fy⁄FIG. 1 ANCHORAGE OF BEAM BARS IN ANEXTERNAL JOINTFIG. 2 LAP, SPLICE IN BEAM 6. IS 13920 : 19934embedded in the confined core ( see Fig. 3a ). Incompelling circumstances, it may also be madeup of two pieces of reinforcement; a U-stirrupwith a 135° hook and a 10 diameter extension(but not < 75 mm) at each end, embedded in theconfined core and a crosstie ( see Fig. 3b ). Acrosstie is a bar having a 135° hook with a 10diameter extension (but not < 75 mm) at eachend. The hooks shall engage peripherallongitudinal bars.6.3.2 The minimum diameter of the barforming a hoop shall be 6 mm. However, inbeams with clear span exceeding 5 m, theminimum bar diameter shall be 8 mm.6.3.3 The shear force to be resisted by thevertical hoops shall be the maximum of :a) calculated factored shear force as peranalysis, andb) shear force due to formation of plastichinges at both ends of the beam plus thefactored gravity load on the span. This isgiven by ( see Fig. 4 ):where , and , are the sagging and hogging moments of resistance ofthe beam section at ends A and B, respectively. These are to be calculated as per IS 456 : 1978.LAB is clear span of beam. and are the shears at ends A and B, respectively, due tovertical loads with a partial safety factor of 1.2 on loads. The design shear at end A shall be thelarger of the two values of Vu,a computed above. Similarly, the design shear at end B shall be thelarger of the two values of Vu,b computed above.i) for sway to right:and andii) for sway to left:andFIG. 3 BEAM WEB REINFORCEMENTMu, limAsM u, limAhMu, limBsMu, limBhVD L+a VD L+b 7. IS 13920 : 199356.3.4 The contribution of bent up bars andinclined hoops to shear resistance of the sectionshall not be considered.6.3.5 The spacing of hoops over a length of 2d ateither end of a beam shall not exceed (a) d/4,and (b) 8 times the diameter of the smallestlongitudinal bar; however, it need not be lessthan 100 mm ( see Fig. 5 ). The first hoop shallbe at a distance not exceeding 50 mm from thejoint face. Vertical hoops at the same spacing asabove, shall also be provided over a lengthequal to 2d on either side of a section whereflexural yielding may occur under the effect ofearthquake forces. Elsewhere, the beam shallhave vertical hoops at a spacing not exceedingd/2.7 COLUMNS AND FRAME MEMBERSSUBJECTED TO BENDING AND AXIALLOAD7.1 General7.1.1 These requirements apply to framemembers which have a factored axial stress inexcess of 0.1 fck under the effect of earthquakeforces.7.1.2 The minimum dimension of the membershall not be less than 200 mm. However, inframes which have beams with centre to centrespan exceeding 5 m or columns of unsupportedlength exceeding 4 m, the shortest dimension ofthe column shall not be less than 300 mm.7.1.3 The ratio of the shortest cross sectionaldimension to the perpendicular dimension shallpreferably not be less than 0.4.7.2 Longitudinal Reinforcement7.2.1 Lap splices shall be provided only in thecentral half of the member length. It should beproportioned as a tension splice. Hoops shall beprovided over the entire splice length atspacing not exceeding 150 mm centre to centre.Not more than 50 percent of the bars shall bespliced at one section.7.2.2 Any area of a column that extends morethan 100 mm beyond the confined core due toarchitectural requirements, shall be detailed inthe following manner. In case the contributionof this area to strength has been considered,then it will have the minimum longitudinal andtransverse reinforcement as per this code.FIG. 4 CALCULATION OF DESIGN SHEAR FORCE FOR BEAM 8. IS 13920 : 19936However, if this area has been treated asnon-structural, the minimum reinforcementrequirements shall be governed byIS 456 : 1978 provisions minimum longitudinaland transverse reinforcement, as perIS 456 : 1978 ( see Fig. 6 ).7.3 Transverse Reinforcement7.3.1 Transverse reinforcement for circularcolumns shall consist of spiral or circular hoops.In rectangular columns, rectangular hoops maybe used. A rectangular hoop is a closed stirrup,having a 135° hook with a 10 diameterextension (but not < 75 mm) at each end, that isembedded in the confined core ( see Fig 7A ).7.3.2 The parallel legs of rectangular hoop shallbe spaced not more than 300 mm centre tocentre. If the length of any side of the hoopexceeds 300 mm, a crosstie shall be provided(Fig. 7B). Alternatively, a pair of overlappinghoops may be provided within the columm ( seeFig. 7C). The hooks shall engage peripherallongitudinal bars.7.3.3 The spacing of hoops shall not exceed halfthe least lateral dimension of the column,except where special confining reinforcement isprovided, as per 7.4.7.3.4 The design shear force for columns shallbe the maximum of:a) calculated factored shear force as peranalysis, andb) a factored shear force given byVu = 1.4where and are moment ofresistance, of opposite sign, of beams framinginto the column from opposite faces ( seeFig. 8 ); and hst is the storey height. The beammoment capacity is to be calculated as perIS 456 : 1978.7.4 Special Confining ReinforcementThis requirement shall be met with, unless alarger amount of transverse reinforcement isrequired from shear strength considerations.FIG. 5 BEAM REINFORCEMENTFIG. 6 REINFORCEMENT REQUIREMENT FORCOLUMN WITH MORE THAN 100 mmPROJECTION BEYOND COREMbLu, lim MbRu, lim+hst----------------------------------------------MbLu, lim MbRu, lim 9. IS 13920 : 19937FIG. 7 TRANSVERSE REINFORCEMENT IN COLUMN 10. IS 13920 : 199387.4.1 Special confining reinforcement shall beprovided over a length lo from each joint face,towards midspan, and on either side of anysection, where flexural yielding may occurunder the effect of earthquake forces ( seeFig. 9. ). The length ‘lo’ shall not be less than(a) larger lateral dimension of the member atthe section where yielding occurs, (b) 1/6 ofclear span of the member, and (c) 450 mm.7.4.2 When a column terminates into a footingor mat, special confining reinforcement shallextend at least 300 mm into the footing or mat( see Fig. 10 ).7.4.3 When the calculated point ofcontra-flexure, under the effect of gravity andearthquake loads, is not within the middle halfof the member clear height, special confiningreinforcement shall be provided over the fullheight of the column.7.4.4 Columns supporting reactions fromdiscontinued stiff members, such as walls, shallbe provided with special confiningreinforcement over their full height ( seeFig. 11 ). This reinforcement shall also beplaced above the discontinuity for at least thedevelopment length of the largest longitudinalbar in the column. Where the column issupported on a wall, this reinforcement shall beprovided over the full height of the column; itshall also be provided below the discontinuityfor the same development length.7.4.5 Special confining reinforcement shall beprovided over the full height of a column whichhas significant variation in stiffness alongits height. This variation in stiffness may resultFIG. 8 CALCULATION OF DESIGN SHEARFORCE FOR COLUMN 11. IS 13920 : 19939FIG. 9 COLUMN AND JOINT DETAILINGFIG. 10 PROVISION OF SPECIAL CONFINING REINFORCEMENT IN FOOTINGS 12. IS 13920 : 199310due to the presence of bracing, a mezzaninefloor or a R.C.C. wall on either side of thecolumn that extends only over a part of thecolumn height ( see Fig. 12 ).7.4.6 The spacing of hoops used as specialconfining reinforcement shall not exceed 1/4 ofminimum member dimension but need not beless than 75 mm nor more than 100 mm.7.4.7 The area of cross section, Ash, of the barforming circular hoops or spiral, to be used asspecial confining reinforcement, shall not beless thanwhereExample : Consider a column of diameter 300mm. Let the grade of concrete be M20, and thatof steel Fe 415, for longitudinal and confiningreinforcement. The spacing of circular hoops, S,shall not exceed the smaller of (a) 1/4 ofminimum member dimension = 1/4 × 300 =75 mm, and (b) 100 mm. Therefore, S = 75 mm.Assuming 40 mm clear cover to thelongitudinal reinforcement and circular hoopsof diameter 8 mm, Dk = 300 – 2 × 40 + 2 × 8 =236 mm. Thus, the area of cross section of thebar forming circular hoop works out to be47.28 mm2. This is less than the cross sectionalarea of 8 mm bar (50.27 mm2). Thus, circularhoops of diameter 8 mm at a spacing of 75 mmcentre to centre will be adequate.7.4.8 The area of cross section, Ash, of the barforming rectangular hoop, to be used as specialconfining reinforcement shall not be less thanwhereFIG. 11 SPECIAL CONFINING REINFORCEMENT REQUIREMENT FOR COLUMNS UNDERDISCONTINUED WALLSAsh = area of the bar cross section,S = pitch of spiral or spacing of hoops,Dk = diameter of core measured to theoutside of the spiral or hoop,fck = characteristic compressive strength ofconcrete cube,fy = yield stress of steel (of circular hoop orspiral),Ag = gross area of the column cross section,andAsh 0.09 SDkfckfy-------AgAk------- 1.0–=Ak = area of the concrete core =h = longer dimension of the rectangularconfining hoop measured to its outerπ4---D2kAsh 0.18 Shfckfy-------AgAk------- 1.0–= 13. IS 13920 : 199311NOTE : The dimension ‘h’ of the hoop could be reducedby introducing crossties, as shown in Fig. 7B. In thiscase, Ak shall be measured as the overall core area,regardless of the hoop arrangement. The hooks ofcrossties shall engage peripheral longitudinal bars.Example : Consider a column of 650 mm ×500 mm. Let the grade of concrete be M20 andthat of steel Fe 415, for the longitudinal andconfining reinforcement. Assuming clear coverof 40 mm to the longitudinal reinforcement andrectangular hoops of diameter 10 mm, the sizeof the core is 590 mm × 440 mm. As both thesedimensions are greater than 300 mm, either apair of overlapping hoops or a single hoop withcrossties, in both directions, will have to beprovided. Thus, the dimension ‘h’ will be thelarger of (i) 590/2 = 295 mm, and (ii) 440/2 =220 mm. The spacing of hoops, S, shall notexceed the smaller of (a) 1/4 of minimummember dimensions = 1/4 × 500 = 125 mm, and(b) 100 mm. Thus, S = 100 mm. The area ofcross section of the bar forming rectangularhoop works out to be 64.47 mm2. This is lessthan the area of cross section of 10 mm bar(78.54 mm2). Thus, 10 mm diameterrectangular hoops at 100 mm c/c will beadequate. Similar calculations indicate that, asan alternative, one could also provide 8 mmdiameter rectangular hoops at 70 mm c/c.8 JOINTS OF FRAMES8.1 The special confining reinforcement asrequired at the end of column shall be providedFIG. 12 COLUMNS WITH VARYING STIFFNESSface. It shall not exceed 300 mm ( seeFig. 7 ), andAk = area of confined concrete core in therectangular hoop measured to itsoutside dimensions. 14. IS 13920 : 199312through the joint as well, unless the joint isconfined as specified by 8.2.8.2 A joint which has beams framing into allvertical faces of it and where each beam widthis at least 3/4 of the column width, may beprovided with half the special confiningreinforcement required at the end of thecolumn. The spacing of hoops shall not exceed150 mm.9 SHEAR WALLS9.1 General Requirements9.1.1 The requirements of this section apply tothe shear walls, which are part of the lateralforce resisting system of the structure.9.1.2 The thickness of any part of the wall shallpreferably, not be less than 150 mm.9.1.3 The effective flange width, to be used inthe design of flanged wall sections, shall beassumed to extend beyond the face of the webfor a distance which shall be the smaller of (a)half the distance to an adjacent shear wall web,and (b) 1/10 th of the total wall height.9.1.4 Shear walls shall be provided withreinforcement in the longitudinal andtransverse directions in the plane of the wall.The minimum reinforcement ratio shall be0.002 5 of the gross area in each direction. Thisreinforcement shall be distributed uniformlyacross the cross section of the wall.9.1.5 If the factored shear stress in the wallexceeds 0.25 or if the wall thicknessexceeds 200 mm, reinforcement shall beprovided in two curtains, each having barsrunning in the longitudinal and transversedirections in the plane of the wall.9.1.6 The diameter of the bars to be used in anypart of the wall shall not exceed 1/10th of thethickness of that part.9.1.7 The maximum spacing of reinforcementin either direction shall not exceed the smallerof lw/5, 3 tw, and 450 mm; where lw is thehorizontal length of the wall, and tw is thethickness of the wall web.9.2 Shear Strength9.2.1 The nominal shear stress, τv, shall becalculated as:where9.2.2 The design shear strength of concrete, τc,shall be calculated as per Table 13 of IS 456 :1978.9.2.3 The nominal shear stress in the wall, τv,shall not exceed τc, max, as per Table 14 ofIS 456 : 1978.9.2.4 When τv is less than τc shearreinforcement shall be provided in accordancewith 9.1.4, 9.1.5 and 9.1.7.9.2.5 When τv is greater than τc, the area ofhorizontal shear reinforcement, Ah, to beprovided within a vertical spacing, Sv, is givenbywhere Vus = ( Vu – τc tw dw ), is the shear forceto be resisted by the horizontal reinforcement.However, the amount of horizontalreinforcement provided shall not be less thanthe minimum, as per 9.1.4.9.2.6 The vertical reinforcement, that isuniformly distributed in the wall, shall not beless than the horizontal reinforcementcalculated as per 9.2.5.9.3 Flexural Strength9.3.1 The moment of resistance, Muv, of thewall section may be calculated as for columnssubjected to combined bending and axial loadas per IS 456 : 1978. The moment of resistanceof slender rectangular shear wall section withuniformly distributed vertical reinforcement isgiven in Annex A.9.3.2 The cracked flexural strength of the wallsection should be greater than its uncrackedflexural strength.9.3.3 In walls that do not have boundaryelements, vertical reieforcement shall beconcentrated at the ends of the wall. Eachconcentration shall consist of a minimum of4 bars of 12 mm diameter arranged in at least2 layers.9.4 Boundary ElementsBoundary elements are portions along the walledges that are strengthened by longitudinaland transverse reinforcement. Though theymay have the same thickness as that of thewall web it is advantageous to provide themwith greater thickness.9.4.1 Where the extreme fibre compressivestress in the wall due to factored gravity loadsplus factored earthquake force exceeds 0.2fck,boundaty elements shall be provided along thevertical boundaries of walls. The boundaryVu = factored shear force,tw = thickness of the web, anddw = effective depth of wall section. Thismay by taken as 0.8 lw for rectangularsections.fckVus0.87 fy Ah dwSv------------------------------------= 15. IS 13920 : 199313elements may be discontinued where thecalculated compressive stress becomes lessthan 0.15fck. The compressive stress shall becalculated using a linearly elastic model andgross section properties.9.4.2 A boundary element shall have adequateaxial load carrying capacity, assuming shortcolumn action, so as to enable it to carry anaxial compression equal to the sum of factoredgravity load on it and the additionalcompressive load induced by the seismic force.The latter may be calculated as:where9.4.3 If the gravity load adds to the strength ofthe wall, its load factor shall be taken as 0.8.9.4.4 The percentage of vertical reinforcementin the boundary elements shall not be less than0.8 percent, nor greater than 6 percent. Inorder to avoid congestion, the practical upperlimit would be 4 percent.9.4.5 Boundary elements, where required, asper 9.4.1, shall be provided throughout theirheight, with special confining reinforcement, asper 7.4.9.4.6 Boundary elements need not be provided,if the entire wall section is provided withspecial confining reinforcement, as per 7.4.9.5 Coupled Shear Walls9.5.1 Coupled shear walls shall be connected byductile coupling beams. If the earthquakeinduced shear stress in the coupling beamexceedswhere ls is the clear span of the coupling beamand D is its overall depth, the entireearthquake induced shear and flexure shall,preferably, be resisted by diagonalreinforcement.9.5.2 The area of reinforcement to be providedalong each diagonal in a diagonally reinforcedcoupling beam shall be:where Vu is the factored shear force, and α isthe angle made by the diagonal reinforcementwith the horizontal. At least 4 bars of 8 mmdiameter shall be provided along each diagonal.The reinforcement along each diagonal shall beenclosed by special confining reinforcement, asper 7.4. The pitch of spiral or spacing of tiesshall not exceed 100 mm.9.5.3 The diagonal or horizontal bars of acoupling beam shall be anchored in theadjacent walls with an anchorage length of 1.5times the development length in tension.9.6 Openings in Walls9.6.1 The shear strength of a wall withopenings should be checked along criticalplanes that pass through openings.9.6.2 Reinforcement shall be provided along theedges of openings in walls. The area of thevertical and horizontal bars should be such asto equal that of the respective interrupted bars.The vertical bars should extend for the fullstorey height. The horizontal bars should beprovided with development length in tensionbeyond the sides of the opening.9.7 Discontinuous WallsColumns supporting discontinuous walls shallbe provided with special confiningreinforcement, as per 7.4.4.9.8 Construction JointsThe vertical reinforcement ratio across ahorizontal construction joint shall not be lessthan:where τv is the factored shear stress at thejoint, Pu is the factored axial force (positive forcompression), and Ag is the gross crosssectional area of the joint.9.9 Development, Splice and AnchorageRequirement9.9.1 Horizontal reinforcement shall beanchored near the edges of the wall or in theconfined core of the boundary elements.9.9.2 Splicing of vertical flexural reinforcementshould be avoided, as far as possible, in regionswhere yielding may take place. This zone offlexural yielding may be considered to extendfor a distance of lw above the base of the wall orone sixth of the wall height, whichever is more.However, this distance need not be greaterthan 2 lw. Not more than one third of thisvertical reinforcement shall be spliced at such asection. Splices in adjacent bars should bestaggered by a minimum of 600 mm.Mu = factored design moment on the entirewall section,Muv = moment of resistance provided bydistributed vertical reinforcementacross the wall section, andCw = center to center distance between theboundary elements along the twovertical edges of the wall.Mu Muv–Cw-------------------------- 16. IS 13920 : 1993149.9.3 Lateral ties shall be provided aroundlapped spliced bars that are larger than 16 mmin diameter. The diameter of the tie shall not beless than one fourth that of the spliced bar norless than 6 mm. The spacing of ties shall notexceed 150 mm center to center.9.9.4 Welded splices and mechanicalconnections shall confirm to 25.2.5.2 ofIS 456 : 1978. However, not more than half thereinforcement shall be spliced at a section,where flexural yielding may take place.ANNEX A( Clause 9.3.1 )MOMENT OF RESISTANCE OF RECTANGULAR SHEAR WALL SECTIONA-1 The moment of resistance of a slender rectangular shear wall section with uniformlydistributed vertical reinforcement may be estimated as follows:These equations were derived, assuming a rectangular wall section of depth lw and thickness twthat is subjected to combined uni-axial bending and axial compression. The vertical reinforcementis represented by an equivalent steel plate along the length of the section. The stress-strain curveassumed for concrete is as per IS 456 : 1978 whereas that for steel is assumed to be bi-linear. Twoequations are given for calculating the flexural strength of the section. Their use depends onwhether the section fails in flexural tension or in flexural compression.(a) Forwhereρ = vertical reinforcement ratio = Ast/( tw lw ),Ast = area of uniformly distributed vertical reinforcement,β = 0.87 fy/(0.003 5 Es),Es = elastic modulus of steel, andPu = axial compression on wall.(b) ForwhereThe value of xu/lw to be used in this equation, should be calculated from the quadratic equationwherexu/lw