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IS. 456 : 2000, ( R••fflrmed 2005 ), , Indian Standard, , PLAIN AND REINFORCED CONCRETE CODE OF PRACTICE, ( Fourth Revision), Tenth Reprint APRIL 2007, (IncludingAmendments No. I and 2), , ICS 91.100.30, , C BI52000, , BUREAU, , OF, , INDIAN, , STANDARDS, , MANAK BHAVAN. 9 BAHADUR SHAH ZAFAR MARG, NEW DELIiI 110002, July 2000, , Price Rs. 830.09 + Rs. 120.09

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IS 456: 2000, , CONTENTS, PAGE, , SECTION 1 GENERAL, J, , SCOPE, , )J, , 2, , REFERBNCES, , 11, , 3, , TERMINOLOGY, , 11, , 4, , SVMBOU, , 11, , SECTION 2 MATERIALS, WORKMANSHIP, INSPECTION AND TESTING, , 5, , 6, , 13, , MATERIALS, , 5.1, , Cement, , 13, , 5.2, , Mineral Admixtures, , 13, , 5.3 Aggregates, 5.4 Water, , 14, , 5.5 Admixtures, 5.6 Reinforcement, , IS, 15, , 5.7, , 15, , 14, , Storage of Materials, , CONCRETE, , 15, , 6.1, , Grades, , 15, , 6.2, , Properties of Concrete, , 15, , 7, , WORKABIUTY OF CONCRETE, , 17, , 8, , DURABILITY OF CONCRETE, , 17, , 8.1, 8.2, , 18, , 9, , 17, , General, Requirements for Durability, , CONCRETE MIX PROPORTIONING, , 22, , 9.1, 9.2, , Mix Proportion, Design Mix Concrete, , 22, 22, , 9.3, , Nominal Mix Concrete, , 23, , 23, , 10 PRODUlllON OF CONCRETE, , 11, , 23, , 10.2, , Quality AssuranceMeasures, Batching, , 24, , 10.3, , Mixing, , 24, , 10.1, , FORMWORK, , 25, , 1J.1, 11.2, , General, Cleaning and Treatment of Fonnwork, , 25, , Stripping Time, , 25, , 11.3, , 25, , 12, , ASSEMBLY OF REINFORCEMENT, , 25, , ·13, , TRANSPORTING, PLACING, COMPACTION AND CURING, , 26, , J3.1, , 26, , 13.2, 13.3, , Transportingand Handling, Placing, Compaction, , 26, 26, , 5

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IS 456: ZOOO, PAGE, , 27, 27, 27, , 13.4 ConstructionJoints and Cold Joints, , 13.5 Curing, 13.6 Supervision, , 27, , 14 CONCRETING UNDER SPECIAL Cosornoss, , 15, , 27, , 14.1 Work in Extreme Weather Conditions, 14.2 Under-Water Concreting, , 27, , SAMPLING AND STRENGTH OF DESIGNED CONCRETE MIX, , 29, , 15.1 General, 15.2 Frequency of Sampling, IS.3 Test Specimen, 15.4 Test Results of Sample, , 29, , 29, 29, 29, , 16 ACCEPTANCE CRITERIA, , 29, , 17, , 30, , INS"EcrlON AND TESTING OF STRUCTURE, , SECTION 3 GENERAL DESIGN CONSIDERATION, 18, , 19, , 20, , BASES RlR DESIGN, , 32, , 18.1 Aim of Design, 18.2 Methods of Design, , 32, , 32, , 18.3 Durability, Workmanship and Materials, 18.4 Design Process, , 32, , LOADS AND FORCES, , 32, , t 9.1, , 32, , 32, , General, , 19.2 Dead Loads, , 32, , 19.3 Imposed Loads, Wind Loads and Snow Loads, 19.4 Earthquake Forces, , 32, 32, , 19.5 Shrinkage, Creep and Temperature Effects, , 32, , 19.6, J9.7, 19.8, 19.9, , 33, , Other Forces and Effects, Combinationof Loads, Dead Load Counteracting Other Loads and Forces, Design Load, , 33, , 33, 33, , STABILITY OF THE STRUC1lJRE, , 33, , 20.1, , 33, , Overturning, , 20.2 Sliding, 20.3 Probable Variation in Dead Load, , 33, 33, , 20.4 MomentConnection, 20.5 Lateral Sway, , 33, 33, , 21 FIRE REsiSTANCE, , 33, , 22, , ANALYSIS, , 34, , 22.1 General, 22.2 Effective Span, , 34, 34, , 22.3 Stiffness, , 3.5, , 6

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IS 456: 2000, PAGE, , 23, , 24, , 25, , 26, , 27, , 22.4, , Structural Frames, , 35, , 22.5, , Moment and Shear Coefficients for Continuous Beams, , 35, , 22.6, , Critical Sections for Moment and Shear, , 36, , 22.7, , Redistribution of Moments, , 36, , 36, , BEAMS, , 23.0, , Effective Depth, , 36, , 23.1, , T-Beams and L-Beams, , 36, , 23.2, , Control of Deflection, , 37, , 23.3, , Slenderness Limits for Beams to Ensure Lateral Stability, , 39, , SOLID SLABS, , 39, , 24. 1, , General, , 39, , 24.2, , Slabs Continuous Over Supports, , 39, , 24.3, , Slabs Monolithic with Supports, , 39, , 24.4, , Slabs Spanning in Two Directions at Right Angles, , 41, , 24.5, , Loads on Supporting Beams, , 41, , COMPRESSION MEMBERS, , 41, , 25.1, , Definitions, , 41, , 25.2, , Effective Length of Compression Members, , 42, , 25.3, , Slenderness Limits for Columns, , 42, , 25.4, , Minimum Eccentricity, , 42, , REQUIREMENTS QOVERNING REINFORCEMENT AND DETAILING, , 42, , 26. I, , General, , 42, , 26.2, , Development of Stress in Reinforcement, , 42, , 26.3, , Spacing of Reinforcement, , 45, , 26.4, , Nominal Cover to Reinforcement, , 46, , 26.5, , Requirements of Reinforcement for Structural Members, , 46, 50, , EXPANSION JOINTS, , SECTION 4 SPECIAL DESIGN REQUIREMENTS FOR, STRUCTURAL MEMBERS AND SYSTEMS, , 28, , 51, , CONCRETE CORBELS, , 28.1, 28.2, , 51, , General, Design, , 51, , 51, , 29 DEEP BEAMS, 29.1, 29.2, , 29.3, 30, , 51, SI, 51, , General, Lever Arm, Reinforcement, , RIBBED, HOLU)W BLOCK OR VOlDEn SLAB, , 52, , 30.1, 30.2, , General, , 52, , Analysis of Structure, , 52, , 30.3, 30.4, , Shear, , 52, , Deflection, , 52, , 7

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IS 456: 2000, PAGB, , 31, , 30.5, 30.6, , Size and Position of Ribs, Hollow Blocks and Formers, , S2, 52, , 30.7, 30.8, , Arrangement of Reinforcement, PrecastJoists and HollowFiller Blocks, , 53, 53, , .53, 53, , FLAT SLABS, , 31.1, 31.2, 31.3, , 31.4, 31.5, 31.6, , 31.7, 31.8, , General, Proportioning, Detenninationof Bendin. Moment, , S3, S3, 54, , Direct Desip Method, , 5'6, , EquivalentFnme Method, Shear in Flat Slab, Slab Reinforcement, Openingsin Flat Slabs, , S1, .59, 61, , 32 WAUS, 32.1 General, 32.2 EmpiricalDesignMethodfor Wall~ Subjected to Inplane Vertical Loads, 32.3 WallsSubjectedto CombinedHorizontal and Vertical Forces, 32.4 Design for Horizontal Shear, 32.S Minimum Requirements for Reinforcement in Walls, , 61, 61, , 33, , 63, , 34, , STAIRS, , 33.1, , Effective Span of Stairs, , 33.2, 33.3, , Distribution of Loadingon Stairs, Depth of Section, , 61, , 62, 62, 62, , 63, 63, 63, , FOOT1NOS, , 63, , 34. J, 34.2, 34.3, , General, , 63, , Moments and Forces, Tensile Reinforcement, , 64, 65, , 34.4, , Transfer of Load at the Base of Column, , 6S, , 34.5, , Nominal Reinforcement, , 66, , SECTION 5 STRUCTURAL DESIGN (LIMIT STATE METHOD), 3S, , 3S.1, , 35.2, 35.3, , 3S.4, 36, , 67, , SAFETY AND SERVICEAlIUI'Y RsoUIREMBNTS, , General, Limit State of Collapse, Limit States of Serviceability, Other Limit States, , CHARACTBRISTIC AND DEsIGN, , 67, 67, 67, 67, , V ALtms AND PAR11AL SAFETY FACIORS, , 36.1 Ch8rIcteristic Strenath of Materials, 36.2 CharacteristicLoads, 36.3 Desip Values, 36.4 Partial Safety Factors, , 67, 67, 68, 68, 68, , 37 ANALYSIS, , 37.1, , 67, , 68, , Analysis of Structure, , 8, , .

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IS 456: 1000, PAGE, , 38, , LIMIT STATB OPCOLLAPSE: FLEXURE, , 69, , 38.1, , 69, , A.lumptions, , 39 LIMIT STATB OF COUAPSS: COMPRESSION, 39.1 Assumptions, 39.2, 39.3, 39.4, 39.5, 39.6, 39.7, , 70, , MinimumEccentricity, Short Axially Loaded Members in Compression, Compression Members with HelicalReinforcement, Memben Subjected to Combined Axial Load and U~iaxial Bendins, Memben Subjectedto Combined Axial Load and Biaxial Bending, SlenderCompression Members, , 72, , 40 LlMrr STATS OP COLLAPSE: SHEAR, 40.1, , 40.2, 40.3, 40.4, , 4O.S, 41, , 42, , 43, , 70, 71, 71, 71, 71, 71, 71, , Nominal Shear Stress, DesianShear Strensth of Concrete, , 72, 12, , Minimum ShearReinforcement, DesiSD of Shear Reinforcement, Bnhanced ShearStrength of Sections Close to Supports, , 72, 72, , 74, , LIMrr STATE OP COLLAPSB : TORSION, 41.1 General, 41.2 Critical Section, 41.3 Shear and Torsion, 41.4 Reinforcement in Members Subjected to Torsion, , 74, , LIMIT STATE OF SBRVlCEABD.nY: DEFLECTION, , 75, , 42.1, , 75, , 74, 7S, , 75, 75, , FlexuralMembers, , 43.1, , FlexuralMembers, , 16, 76, , 43.2, , Compre~ion, , 76, , LIMIT STATE OF SERVICEABILITY' CRACKING, , Members, , ANNEX A, , LIST OF REFERRED INDIAN STANDARDS, , 71, , ANNEXB, , STRUCTURAL DESIGN (WORKING STRESS METHOD), , 80, , B-1, , B-1.1, , General Design Requirements, , 80, , B-l.2, , Redistribution of Moments, Assumptions for Design of Members, , 80, 80, , B-l.3, , B-2, , 80, 80, 80, 80, , PBRMIsslBLB STRESSBS, , 8-2.1, 8-2.2, B-2.3, , B-3, , 80, , GENERAL, , Permissible Stresses in Concrete, Permissible Stresses in Steel Reinforcement, Increase in Permissible Stresses, , 81, , PBRMIssIBLE LoADS IN COMPRBSSION MEMBERS, , B-3.1, , 8-3.2, B-3.3, 8-3.4, , 211e 815/07-3, , 81, , Pedestals and Sbort Columns with Lateral Ties, Shon Columns with Helical Reinforcement, , Lon. Columns, Composite Columns, , 81, 81, "\r., , 81

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IS456:~, , PAGI, B-4, , MEMBBRS SUlJBCTID TO COMBINED AxIAL loAD AND BINDING, , 83, , 8-4.1, B-4.2, , 83, 83, 83, , B-4.3, , D-S, , 83, , SHEAR, , B-S,1, B-5,2, B-S.3, B-5.4, B·'.', B-6, , De,iID Baed on Uncracked Section, Delilft Baed on Cracked Section, Members Subjected to Combined Direct Load and Flexure, , Nominal ShearStress ., neaip ShearStrenlth of Concrete, Minimum Shear Reinforcement, Desiln of ShearReinforcement, Enhanced Shear Strength of Sections Close to Supports, , TORSION, , B-6.1, , General, , B-6.2, B-6.3, B-6.4, , Critical Section, Shear and Torsion, Reinforcement in Members Subjected to Torsion, , e-l, C-4, , DIFLECI10N DUE TO CREEP, , DBPLECI10N, , DuE TO SHRINKAGE, , ANNEX D SLABS SPANNING IN TWO DIRECTIONS, 0·1, D-2, , IUmtAINID, , 85, 8S, 86, 86, 86, 86, 86, , 88, 88, 88, 89, , TOTAL D8PLIIcnON, SHOIlT- TBIM DBPLICTION, , 84, 8S, , 88, , ANNEX C CALCULATION OF DEFLECTION, C-2, C-3, , 83, , 90, 90, 90, , SLAM, , SIM,ty SuppotnS SUBS, , ANNEX B SPPRCTIVI LaNOTH OF COLUMNS, , 92, , ANNEX F CALCULAnONOF CRACK WID1lI, ANNEX G MOM!NTS OP ltBSlSTANCB FORRECTANGULAR AND T-SECI10NS, , 95, , G-l, , RscrANOULAR SBC110NS, , 0-1.1, 0-1.2, , 0-2, , Sections without Comprealion Reinforcement, Sections with Compression Reinforcement, , 96, 96, 96, 96, , 96, , FLANOED SEC110N, , ANNEX H COMMITTEE COMPOSITION, , 98, , 10

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II .. •, , 2, , AMENDMENT NO., , TO, IS 456: 2000, , 2~Or, , SE'riMBER, ~., , tW\U'", , PLAI.N AND REINFO~D CONCRETE CODE OF 'PRACTICE, ( FIJUrth, , Revision) ,, , ( Page 13, clause 5.2.1.1, line 1 ) 'Grade rens 3812'., , Substitute 'IS 3812 (Part 1)' for, , ( Page 13, clause 5.2.1.2 and corresponding Note ) following for theexisting:, , Substitute the, , . Silica fume conforming to IS 15388 may be used as partreplacement of cement, provided uniform blending with the cement is ensured., NOTE - Silica fume is usually used in proportion of, content of a mix.', , ~, , to 10 percent of the cement, , t Page 13. Note under clause 5.2.1.3, line 5 ) - Substitute 'be' for, , 'range, , from being'! ., , ( Page 25.. clause 10.3.3, line 4 ) - Delete the word 'and'., ( Page 65. clause 34.2.4.2. line 1 ) -, , Substitute 'on' for 'or'., , [ Page 65. clause 34.3.1 (a).. line 2 I - Delete the words, direction' ., , ~extending, , in each, , ( Page 66, clause 34.4.3.. line 5 ) - Substitute 'not' for 'no'., , ( Page 78,..1nnex A ) - Substitute the following for the existing entries for, 153812: 1981:, ·/S 1\/0., , ,Title, , IS 3812 (Part 1) : 2003, , Specification for pulverized fuel ash : Part I For, usc as pozzolana in cement, cement mortar and, concrete (secondrevision)', , ('Page 79. Annex A ) ._-- Add the following at the end:, 41~')1, , No., , IS 15388 : 2001, , 2116 815/07-1, , Title, Specification for silica fume'

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18 456: 2000, , Indian Standard, PLAIN AND REINFORCED CONCRETE CODE OF PRACTICE, ( Fourth Revision ), FOREWORD, , ThisIndianStandard (Fourth Revision) wasadopted by the Bureau of Indian Standards, afterthedraftfinalized, . by theCementandConcrete Sectional Committee hadbeenapproved by theCivilEngineering Division Council., , This standardwas first published in 1953 underthe title 'Codeof practice for plainand reinforced concrete for, general building construction' and subsequently revised in 1957. The code was further revised in 1964 and, published under modified title 'Code of practice for plainand reinforced concrete', thusenlarging the scopeof, use of this code to structures otherthan general building construction also. Thethirdrevision was published in, 1978, and it includedlimit state approach to design. This is the fourth revision of the standard. This revision, was takenup witha viewto keeping abreast withthe rapiddevelopment in the fieldof concrete technology and, to bringin furthermodifications/improvements in the lightof experience gained whileusingtheearlierversion, of the standard., This revision incorporates a number of important changes. The majorthrustin the revision is on the following, lines:, a) In recent years. durability of concrete structures have become the cause of concern to all concrete, technologists. This has led to the needto codify the durability requirements worldover. In this revision, of the code. in order to introduce in-built protection from factors affecting a structure, earlierclause on, durability has been elaborated and a detailed clause covering different aspects of design of durable, structure has been incorporated., b) Sampling and acceptance criteriafor concrete havebeenrevised. With this revision acceptance criteria, has been simplified in line with the provisions given in BS 5328 (P8l1 4):1990 'Concrete: Part 4, Specification for the procedures to be used in sampling, testing and assessing compliance of concrete'., Some of the significant changes incorporated in Section 2 are as follows:, a) All the threegrades of ordinary Portland cement, namely 33 grade, 43 gradeand 53 gradeand sulphate, resisting Portland cement have been included in the list of types of cementused (in addition to other, types of cement)., b) The permissible limits for solids in waterhavebeen modified keeping in viewthe durability requirements., c) The clause on admixtures has been modified in view of the availability of new types of admixtures, including superplasticizers., d) In Table2 'Grades of Concrete', grades higherthan M 40 have been included., e) It has been recommended that minimum grade of concrete shall be not less than M 20 in reinforced, concrete work (see also 6.1.3)., f) The formula for estimation of modulus of elasticity of concrete has been revised., g) In the absence of proper correlation between compacting factor, vee-bee time and slump, workability, has now been specified only in termsof slump in line withthe provisions in BS 5328(Parts 1 to 4)., h) Durability clausehasbeenenlarged to include detailed guidance concerning thefactors affecting durability., The table on 'Environmental Exposure Conditions' has been modified to include 'very severe' and, 'extreme' exposure conditions. This clause also covers requirements for shape and size of member,, , depthof concrete cover, concrete quality, requirement against exposure to aggressive chemical andsulphate, attack,minimum cementrequirement andmaximum watercementratio,limitsof chloride content. alkali, silica reaction, and importance of compaction, finishing and curing., j) Aclause on -'Quality Assurance Measures' has been incorporated to givedue emphasis to goodpractices, of concreting., k) Properlimitshavebeenintroduced on theaccuracy of measuring equipments to ensureaccurate batching, of concrete., , 2116 BIS/07-:.!.

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IS 456: 2000, , m) The clause on 'Construction Joints' has been modified., n) The clause on 'Inspection' has been modified to give more emphasison quality assurance., , The significant changes incorporatedin Section 3 are as follows:, a) Requirements for 'Fire Resistance' have been furtherdetailed., h) 'The figure for estimation of modification factor for tension reinforcement used in calculation of basic, values of span to effective depth to control the deflection of flexural member has been modified., c) Recommendations regarding effective length of cantilever have been added., d) Recommendations regardingdeflection due to lateral loads have been added., e) Recommendations for adjustmentsof support moments in restrainedslabs have been included., f), , In t.he detemination of effective length of compression members.stability index has been introduced to, determine sway or no sway conditions., , g) Recommendations have been made for lap lengthof hooksfor bars in direct tensionand flexuraltension., h) Recommendations regarding strength of welds have been modified., j), , Recommendations regarding cover to reinforcement have been modified. Cover has been specified, based on durability requirements for differentexposureconditions. The term 'nominal covert has been, introduced. The cover has now been specified based on durability requirement as well as for fire, requirements., , The significantchange incorporated in Section4 is the modification of the clauseon Walls. The modifiedclause, includes design of walls against horizontal shear., In Section 5 on limit state method a new clause has been added for calculation of enhanced shear strength of, sections close to supports. Some modifications have also been made in the clause on Torsion. Formula for, calculation of crack width has been added (separatelygiven in Annex F)., , \Vnrking stress method has now been given in Annex B so as to give greater emphasis to limit state design. In, thisAnnex, modificanonsregarding torsion and enhanced shear strengthon the same lines as in Section 5 have, been made,, , Whilst the common methods of design and construction have been covered in this code, special systems of, design and construction of any plain or reinforcedconcrete structure notcovered by this code may be permitted, on production of satisfactory evidence regarding their adequacy and safety by analysis or test or both, (see, , 19)., , In this code it has been assumed that the design of plain and reinforcedcement concrete work is entrusted to a, qualifiedengineerand that theexecutionof cementconcretework iscarriedout underthe directionof a qualified, and experienced supervisor., In the formulation of this standard, assistance has been derived from the following publications:, BS 5328 : Part 1 : 1991 Concrete: Part 1 Guide to specifyingconcrete, British Standards Institution, , BS 5328 : Part 2 : 1991 Concrete : Part 2 Methods for specifying concrete mixes, British Standards, Institution, BS 5328 : Part 3 : 1990 Concrete: Part 3 Specificationfor tbe procedures to be used in producing and, transporting concrete. British Standards Institution, BS 532R : Part 4 : 1990Concrete; Part 4 Specification for the proced.ures to be used in sampling, testing, and assessing complianceof concrete, British Standards Institution, BS 8110 : Part 1 : 1985 Structural use of concrete: Part t Code of practice for design and construction,, British Standards Institution, BS RItO: Part 2 : 1985 Structural use of concrete: Part 2 Code of practice for special circumstances,, British Standards Institution, , ACT 319 ~ 1989 Building code requirements for reinforcedconcrete, AmericanConcrete Institute, AS 3600 : 1988Concrete structures. StandardsAssociationof Australia, , 2

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-...., IS 456: 2000, , DIN 1045July 1988Structural use of concrete, design and construction. Deutschcs lnsritut fur Normung E.V., CEB..FIP Model code 1990, Comite Euro .. International Du Bclon, The composition of the technical committee responsible for the formulation of this standard is given In, , Annex H., For the purpose of deciding whether a particular requirement of this standard is complied with, the final value,, observed or calculated, expressing the result of a test or analysis shall he rounded off in accordance with, IS 2: 1960 'Rules for rounding off numerical values (revised)'. The number of significant places retained in the, rounded off value should be the same as that of the specified value ill this standard., , 3

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IS 456: 2000, SECTION 1 GENERAL, , -, , 1 SCOPE, , EL, , 1.1 This standard deals with the general structuraluse, of plain and reinforced concrete., 1.1.1 For the purpose of this standard, plain concrete, structures are those where reinforcement, if provided, is ignoredfor determination of strengthof the structure., 1.2 Special requirements of structures, such as shells,, folded plates, arches.bridges,chimneys,blastresistant, structures, hydraulic structures, liquid retaining, structures and earthquakeresistant structures,covered, in respective standards have not been covered in this, standard; these standards shall be used in.conjunction, with this standard., , E., , -, , e, , -, , let., , -, , t; f t1 t, I, H. Hwe Ie(, 1, , -, , 2 REFERENCES, The Indian Standards listed in Annex A contain, provisions which through reference in this text,, , I,, , -, , 'f -, , constitute provisions of thil standard. At the time of, publication, the edition. indicated were valid. All, standards are subject to revision and parties to, agreements based on this standard are encouraged to, investigate the possibility of applying the most recent, editions of the standards indicated in Annex A. ., , K, k, , Ld, U, , -, , Lw -, , 3 TERMINOLOGY, , -, , For the purpose of this standard, the definitions Biven, in IS 4845 and IS 6461 (Parts 1 to 12) shall generally, apply., , 4 SYMBOLS, For the purpose of this standard, the following letter, , symbols shallhavethe mcanina indicated against each;, where other symbols are used. they are explained at, the appropriate place:, A - Area, b, - Breadth of beam, or shorter dimension, of a rectanguler column, bet" Effective width of slab, b,, Effective width of flanac, b., - Breadth of web or rib, D - Overall depth of beam or slab or, diameter of column; dimension of a, rectangular column in the direction, under consideration, Dr - Thickness of flange, DL - Dead load, d, - Effective depth of beam or slab, d' - Depth of compression reinforcement, from the highly compressed face, Ec - . Modulus of elasticity of concrete, , ler, , -, , lea, , -, , Iey, , -, , I., I'n, , -, , I", ly, 10, I., , -, , -, , 12, , -, , I', , -, , 2, , M, , m, , n, p, , q", 11, , -, , -, , -, , Earthquakeload, Modulus of elasticity of steel, Eccentricity, Characteristic cube compressive, stren.th of concrete, Modulus of rupture of concrete, (flexural tensile aU-oath), Splittin, tensile lU'eftltb of concrete, Desip Itren,th, Characteriatic ItrenJth of steel, Unsupportedhei,ht of wall, Effective hei,ht of wall, Effective moment of inertia, Momentof inertia of the gross section, excluding reinforcement, Moment of intertiaof cracked section, Stiffness of member, Constant or coefficient or factor, Developmentlength, Live load or imposed load, Horizontal distancebetweencentresof, lateral restraint, Length of a column or beam between, adequate lateral restraints or the, unsupportedlength of a column, Effective span of beam or slab or, effective length of column, Effective length about x-x axis, Effective leng~ about y-y axis, Clear span, face-to-face of supports, for shorter of the two spans at right, &lgles, Length of shorter lide of slab, Lin.th of loftier aide of slab, Distance between points of zero, , I:, , lnomen.. in a beam, Span in the direction in which, moments are determined, centre to, centre of supports, Span transv~se to I" centre to centre, of supports, 12 for the shorter of the; continuous, , spans, Bendin. moment, Modular ratio, , Number of samples, Axial load on a compression member, Calculatedmaximumbearingpressure

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IS 456: 2000, qn, , -, , Calculated maximum bearing pressure, of soil, , r, , -, , Radius, , s, , -, , Spacing of stirrups or standard, deviation, , T, , -, , Torsional moment, , Ym, 8m, e ec, , Partial safety factor for material, Percentage reduction in moment, Creep strainof concrete, G&:hI;, Permissible stress in concrete in, bending compression, a&;e Permissible.stress in concrete indirect, compression, oftK: - Permissible stress in metal in· direct, compression, GM: - Permissible stress in steel in, compression, (J", - Permissible stress in steel in tension, a"v - Permissible tensile stress in shear, reinforcement, t hd - Design bond stress, t&;, Shear stress in concrete, t e• mI&X- Maximum shear stress in concrete, with shear reinforcement, , - Wall thickness, V - Shear force, W - Total load, WL, Wind load, w - Distributed load per unit area, Wd, Distributed dead load per unit area, WI, Distributed imposed loadper unitarea, , x, Z, , - Depth of neutral axis, Modulus of section, , l, , -, , a. 8 Yr, , -, , Lever arm, Anile or ratio, Partial safety factorfor load, , .., , J:!, , -, , 'tv, , -, , Nominal shear stress, , ,, , -, , Diameter of bar

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IS 456: 2000, SECTION 2 MATERIALS, WORKMANSHIP,, , INSPECTION AND TESTING, have no relation whatsoever with the characteristics, guaranteed by the Quality Marking as relevant to that, cement. Consumers are, therefore, advised to go by, the characteristics as given in the corresponding, Indian Standard Specification or seek specialist, advise to avoid any problem in concrete making and, , 5 MATERIALS, , s.t Cement, The cement used shall he any of the following and the, type selected should be appropriate for the intended, , use:, a), , 33 Grade ordinary Portland cement, conforming to IS 269, , b), , 43 Grade ordinary Portland cement, conforming to IS 8112, , c), , S3 Grade ordinary Portland cement, conforming to IS 12269, , d), , Rapid hardening Portland cement conforming, to IS 8041, , e), , Portland slag cement conforming to IS 4;5, , 5.2.1.1 Fly ash (pulverized fuel ash), , f), , Portland pozzolana cement (fly ash based), conforming to IS 1489 (Part 1), , g), , Portland pozzolana cement (calcined clay, based) conforming to IS 1489 (Part 2), , Fly ash conforming to Grade 1 of IS 3812 may be, used as part replacement of ordinary Portland cement, provided uniform blending with cement is ensured., , h), , Hydrophobic cement conforming to IS 8043, , j), , Low heat Portland cement conforming to, IS 12600, , k) Sulphate, , resisting, , Portland, , construction., , 5.2 Mineral Admixtures, , 5.1.1 Pozzolanas, Pozzolanic materials conforming to relevant Indian, Standards may be used with the permission of the, engineer-in-charge, provided uniform blending with, cement is ensured., , 5.2.1.2 Silicafume, Silica fume conforming to a standard approved by the, deciding authority may be used as part replacement of, cement provided uniform blending with the cement is, ensured., , cement, , NOTE-The silica fume (very fine non-crystalline silicon, dioxide) isa by-product of the l1UU1ufacture of silicon, ferrosilicon, or the like. from quartz and carbon in electric arc furnace. It is, usually used inproportion of Sto 10percent of the cement content, of a mix,, , conforming to IS 12330, Other combinations of Portland cement with mineral, admixtures (see $.2) of quality conforming with, relevant Indian Standards laid down may also be used, in the manufacture of concrete provided that there are, satisfactory dati on their suitability, such as, performance test ~ concrete containing them., 5.1.1 Low heat Portland cement conforming to, IS 12600 shall be used with adequate precautionswith, regard to removal of formwork, etc., , 5.1.1.3 Rice husk ash, Rice husk ash giving required performance and, uniformity characteristics may be used with the, approval of the deciding authority., NOTE-Rice husk esh is produced by burning rice husk and, contain largeproportion of silica. To achieve amorphous state,, ricehusk ahay beburntat controlledtemperature, It is necessary, toevoluat8 the productfroma particularsourcefor performance, and unirofmity since it con ran,e from beinl as deleteriousas, silt when.~ncorporated in concrete. Waterdemand and dryinl, shrinkage ',should be studiedbefore using rice husk., , 5.1.Z Hiah alumina cement conforming to IS 6452 or, supersulphated cement conforming to IS 6909 may be, used only under special circumstances with the prior, approval of the engineer-in-charge. Specialistliterature, Inay be consu Ited for guidance regarding the use of, , 5.2.1.4 M'takaoline, , these types of cements., 5.1.3 The attention of the engineers-in-charge and, users of cement is drawn to the fact that quality of, various cements mentioned in 5.1 is to be determined, on the basis of its conformity to the performance, characteristics given in the respective Indian Standard, Specification for that cement. Any trade-mark or any, trade nameindicating any special features not covered, in. the standard or any qualification or other special, performance characteristics sometimes claimedl, indicatedon the bass or containersor in advertisements, alongside the 'Statutory QualityMarking' or otherwise, , Metakaollne having fineness between 700 to, 900 m 2/kg' may be used as pozzolanic material in, concrete., NOTE-MetokQoline is obtained by calcination of pure or, refined koollntic clay orD temperature between 6500C and 8~O°C,, followed by .rindin. to achieve a fineness of 700 to 900 m:llka., The resultiDI material hOI hilh.'pozzoianicity., , S.2.2 GroundGranulated Blast Furnace Slag, Ground granulated blast furnace slag obtained by, grinding granulated blast furnace slag conforming to, IS 12089 may be used as part replacement of ordinary, 13

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IS 456: 2000, , Portland cements provided uniform blending with, cement is ensured., 5.3 Allre.ates, , Aggregates shall comply with the requirements of, IS 383. As far as possiblepreferenceshall be givento, natural aggregates. ., 5.3.1 Other types of aggregates such as sial and, crushed overbumt brick or tile, which may be found, suitable with regard to strength. durability of concrete, andfreedom from harmful effects may be usedforplain, concrete members. but such aggregates should not, contain more than 0.5 percentof sulphates as SO]and, should not absorb more than 10 percent of theirown, mass of water,, 5.3.2 Heavy weight aggreiates Of light weight, aggregates such as bloatedclay aggregates and sintered, fly ash aggregates may also be used provided the, engineer-in-charge is satisfied with the data on the, properties of concretemade with them., NOTE-Some of the provisioDI of the code would require, modIfication whenthese alPlates areused: speclalilt literatuJe, may be consulted for auidance., , 5.3.3 Sizt, , ~f Aggregate, , Thenominal maximum sizeofcoarse aggregate should, be as large as possible within the limits specified but, in no case greater than one-fourth of the minimum, thickness of the member, provided that the concrete, can be placed without difficulty so as to surround all, reinforcement thoroughly and fill the comers of the, form, For most work, 20 nun alareaate is suitable., Where there is no restriction to the flow of concrete, into sections, 40 nun or laraor size may be permitted., Inconcrete elements withthinsections, closelyspaced, reinforcement or smallcover, consideration should be, liven to the use of 10 mm nominal maximum lize., Plums above 160 nun and up to any reuonable aize, may be used in plain concreteworkup to a maximum, limit of 20 percent by volume of concrete when, specifically permitted by the enaineer-in-charao. The, plums shallbedistributed evenly andIhall benotcloser, than 1'0 mm from the lurface., 5.3.3.1 For heav.iJy reinforced concrete memben u, in the else of ribs of main beams, the nominal, maximum aize of the a'lf'late Ihould usually be, re.trietedto ~ mm lei. thantheminimum clear eli.tanee, between themain bars or S mm lell than the minimum, cover to the reinforcement whichever i. Imaller., 5.3.4 Coarse and fine alsrelate Ihall be batched, separately. All.in-alar.,lte may be used only where, lpecifically permitted by tho enlineer-in-char,e., , free from injurious amounts of oils.acids, alkalis, salta,, sugar, organic materials or other substances that may, be deleterious to concrete or steel., Potable water is generally considered satisfactory, for mixina concrete. As a guide the following, concentrations represent the maximum pennissible, values:, a) To neutralize 100 ml sample of water, usir.1, phenolphthalein as an indicator, it should not, require more than' ml of 0.02 nonnal NaOH., The details of test are aiven in 8.1 of IS, 3025 (Part 22)., b) To neutralize 100 ml sample of water, uains, mixed indicator, it should not require more, than 2' ml of 0.02 nonnal H2SO•. The details, of test shall be as given in 8 of IS 3025, (Part 23)., c) Permissible limits for solids shall be as liven, in Table 1., 5.4.1 In case of doubt regardinl development of, strength. the suitability of water for makingconcrete, shall be ascertained by the compressive streolth and, initial setting timetestsspecified in 5.4.1.1and5.4.1.3., 5.4.1.1 The sample of water taken for teslin, Ihall, represent thewaterproposed to beusedfor concreting,, due account being paid to seasonal variation. The, sample shall not receive any treatment before te_un,, otherthanthatenvisaged in theregular supply of water, proposed foruseinconcrete. Thesample shallbeltored, in a clean container previo~lly rinsed out with limilar, water., 5.4.1.2 Averalo 28 days compressive Itten.th of at, leastthree l~O nun concrete cubesprepared with water, proposed to be used shall not be lell than 90 percent, of the average of strenlth of three similar concrete, cubes prepared with diltilled water, Th. cube••hall, be prepared. cured and tested in accordance with the, requirements of IS 516., 5.4.1.3 The initial •• ttinl timeof te.t blockmadewith, the appropriate cement and the water propolld to be, used .hall not be le•• than 30 min and .hall not dlff., by ± 30 min fromthe initial .etlina time of control, telt block prepared with the lame cement ,and diltiJled, water. The telt block. ,han be preparedand tilted In, accordance with the requirementa of IS 4031 (P.n 5)., 5.4.1 The pH valueof water ,hall be not lell than 6., , 5.4.3 Sea Water, , Mixinl or curin, of concrete with .ea waler il not, recommended because 'ofPf"Once of harmful.lltl in, ... water. Under unavoidable Circumltaneel 1M water, may be used formixin.orcuriolin plainconcrete with, noembedded steel after hayiJllliven due conllderation, toposlible.disadvantapa and precaution. includin, UII, , 1.4 Water, , of appropriate cement system., , . Waterused for mixin, and cunn'lhall be clean and, , 14

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IS 456 : 2000, Table 1 Permissible Limit for Solids, tCtaus« 5.4), , n, ii), iii), iv), , l'crDli~~ible, , 'Iesred as per, , 51, Nil,, , Limit,, , Mllx, , Organic, Inorganic, Sulphates (as SO), Chlorides (as CIl, , IS ~02~ (Part IS), IS ~025 (Purt Ill), IS ~02'i (Part 24), IS .1025 (Part ~2), , 2001ll!!!1, 11M10 mg!1, 400 mg/l, 2IM)() IIIg!1, for concrete 1101 coutaining, , embedded steel and, , ~(JO, , 1IIg/\, , I<Jr reinforced concrete work, , v), , Suspended mailer, , IS 3025 (Part 17), , 2 000 1lIg11, , 5.6.1 All reinforcement shall he free from loose mill, scales. loose rust and coats of paints. oil. mud or any, other substances which may destroy or reduce hondo, Sand blasting or other treatment is recommended to, dean reinforcement., , 5.4.4 Water found satisfactory for mixing is also, suitable for curing concrete. However, water used for, curing should not produce any objectionable stain or, unsightly deposit \10 the concrete surface. The presence, of tannic add or iron compounds is objectionable,, , 5.6.2 Special precautions like coating (If reinforcement, may be required for reinforced concrete clcmenIs in, exceptional cases and for rehabilitation of structures., Specialist literature may he referred to in such cases., , 5.5 Admixtures, 5.5.1 Admixture. if used shall comply with IS 9103., Previous experience with and data (IIi such materials, should he considered in relation to the likely standardsof, supervisionand workmanshipto the work being specified., , 5.6.3 The modulus of elasticity of steel shall be taken, as 200 kN/l1llJ1·~. The characteristic yield strength of, different steel shall be assumed as the minimum yield, stress/0.2 percent proof stress specified in the relevant, Indian Standard., , 5.5.2 Admixtures should not impair durability (If, concrete nor combine with the constituent to form, , harmful compounds nor increase the risk of corrosion, of reinforcement., , 13.7 Storage of'Materials, , 5.5.3 The workability, compressive strength and the, slump loss of concrete with and without the usc of, admixtures shall be established during the trial mixes, before lise of admixtures, , Storage of materials shall he as described in IS 40K2., 6 CONCRETE, , 6.1 Grades, , 5.5.4 The relative density of liquid admixtures shall, he checked for cadi drum containing admixtures and, compared with till' specified value before acceptance., , The concrete shall be in grades designated as per, Tanlc 2, , 5.5.5 The chloride content of admixtures shall, be independently tested fill e ach hutcl) before, acceptance., , 6.1.1 The characteristic strength is defined as the, strength of material below which not more than, 5 percent of the test results arc expected to fall., , 5.5,6 If two or more admi xture s art' used, simultaneously in the same concrete mix. Jala should, be obtained to assess their interaction and to ensure, their compatibility,, , 6.1.2 Tile minimum grade of concrete for plain and, reinforced concrete shall be as per Table 5., 6.1.3 Concrete of grades lower than those given in, Table 5 may he used for plain concrete constructions., lean concrete, SImple foundations, foundation for, masonry walls and other simple or tcmporury, reinforced concrete construction., , 5.6 Reinforcement, TIll' reinforcement shall be any of the following:, , a) Mild steel and medium tensile steel bars, conforming to IS 432 (Part I)., , 6.2 Properties of Concrete, 6.2.1, , h) High strength deformed steel bars conforming, to IS 1786., , IIIClI'(/.I'(,, , of Strength with Agi', , There is normally a gain of strength beyond 2S days., The quantum of increase depends upon the )!radc and, type of cement, curing and cnvuoruucnral conditions,, etc. The design should 1)(' h:1S,xl on 2x dav-, charactcristic strength "f com.r. " 'lIlkss there is a evidence II I, , c) Hard-drawn steel wire fabric conforming to, IS 1566., , d) Structural steel conforming to Grade A of, , IS 2062., 15

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IS 456: 1000, 'Dable2 Gndes of Concnte, (Clause 6.1.9.2.2.15.1.1 and 36.1), Group, , Grade DeI.....IIOIl, , Spedfted Cba, , 1Ie, , eo.,...." S, til, ISO ami Cube at 210.,.", Nlmm2, , (I), , (2), , (3), , Ordinary, Concrete, , M 10, M IS, , 10, , IS, 20, , M20, Slalldllrd, Concrete, , M2S, M30, M3S, , 2S, 30, , M40, , 40, 45, , 3S, , M4S, MSO, MSS, Hi,h, Strength, Concrete, , SO, SS, , M60, , 60, 65, 70, , M6S, M70, M7S, M80, , 75, 80, , NOTES, I Inthedesipotion of concrete mixM refersto the mixlUld the, number to the specified compnlUive Itrenath of 150 mm size, cube lit 28 days.expressed in N/mmJ., 1 Forconcrete of com~ssive strenath areaterthan M55.desip, parameters givenin the llalldllrd maynot be applicable and the, values may be obtained from specialized literatures and, experimcntalresults., , justifya higherstrength fora particular structure due to, age., 6.2.1.1 For concrete of grade M 30 and above. the, rate of increase of compressive strength withageshall, be basedon actualinvestigations., 6.2.1.2 Where members are subjected to lowerdirect, load duringconstruction, they should be checkedfor, stresses resulting from combination of directloadand, bending duringconstruction., , where, Ec is the short tenn static modulus of elasticity in, N/mm2•, Actual measured values may differ by ± 20 percent, from the values obtained from the aboveexpression., , 6.2.4 Shrinlcage, The total shrinkage of concrete depeRds upon the, constituents of concrete, size of the member and, environmental conditions. For a givenhumidity and, temperature, the total shrinkage of concrete is most, influenced by the total amount of waterpresentin the, concrete at the time of mixing and, to a lesserextent,, by the cementcontent., 6.2.4.1 In the absence of test data, the approximate, value of the total shrinkage strain for deslan may be, takenas 0.000 3 (for moreinfonnation, see IS 1343)., 6.2.S Crtepof Concrete, Creep of concrete depends, in addition to the factors, listed in 6.2.4, on the stress in the concrete. age at, loading and the duration of leading. As long as the, stress in concrete does not exceed one-third of its, characteristic compressive strength, creep may be, assumed to be proportional to the stress., 6.1.5.1 Intheabsence ofexperimental data and detailed, information on theeffectof thevariables, the ultimate, creep strain may be estimated from the following, values ofcreep coefficient (that is.ultimate creep strain!, elastic strain at the age of loading); for long span, structure, it is advisable to determine actual creep, strain, likelyto take place:, , 6.2.2 Tensile Strength of Concrete, The flexural and splitting tensile strengths shall be, obtained as described in IS 516 and IS 5816, respectively. When the designer wishes to use an, estimateof the tensilestrength from the compressive, strength, the following formula may be used:, Flexural strength, fer, , Creep Coefficient, , I year, , 1.1, , 2.2, 1.6, , NOTE-The ultill1lle creep 1UIin. eatimlled as described above, does not include the elastic IItI'lIin., , 6.2.6 Thermal Expansion, The coefficient of thermal expansion depends on IllltUI'e, of cement, the aggregate,. the cement content, the, relative humidity and the size of sections. The value, of coefficient of thermal expansion for concrete with, different aggregates may be takenas below:, , = 0.7..[l; N/mm2, , where f", is thecharacteristic cubecompressive strength, of concretein N/mm 2•, , 6.2.3 Elastic Deformation, The modulus of elasticity is primarily influenced by, the elastic properties of the aggregate and to a lesser, extent by the conditions of curing avet age of the, concrete, the mix proportions and the type of cement., The modulus of elasticity is normally related to the, compressive strengthof concrete., 6.2.3.1 The modulus of elasticity of concrete can be, assumed as follows:, ", , Ageat Loading, 7 days, 28 days, , Type ofAggregate, Quartzite, Sandstone, Granite, Basalt, Limestone, , Coefficient ofThermal, .Expansionfor Concrrte/"C, 1.2 to 1.3 x 10'5, 0.9 to 1.2 x 10", . 0.7 to 0.95 x 10", 0.8 to 0.95 x 10", 0.6lQ,.o.9 x 10'5, ..1, , '.", , 16

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IS 456: 2000, 7 WORKABILITY OF CONCRETE, , be compacted with the means available. Suggested, ranges of workabihty of concrete measured in, accordance with IS J 199 are given below:, , 7.1 The concrete mix proportions chosen should be, such that the concrete is of adequate workability for, the placing conditions of the concrete and can properly, , Placing Conditions, (I), , Blindingconcrete;, Shallow sections;, Pavements using pavers, Mass concrete:, Lightly reinforced, sections in slabs,, beams, walls,columns:, , Degree oj·, Workllbi lity, , Slump, , (2), , (3), , Very low, , See 7.J.l, , Low, , 25-75, , Medium, , 50-100, , (mm), , Floors;, , Hand placed pavements;, Canal lining;, Strip footings, Heavily reinforced, sections in slabs., , beams, walls. columns;, Slipform work;, Pumped concrete, Trench fill;, In-situ piling ., Trernie concrete, , 75-100, , Iligh, , 100-150, , Very high, , See 7.1.2, , NOTE-For most of the placing conditions, mtcrnul vibrators (needle vihrators) are suitable. The diameter of the needle shall be, determined based on the density and spacing of reinforcement bars and thickness of sections. Fur tremie concrete, vibrators are not, , required to be used (s,e also l:t~~)., , a suitably low permeability is achieved by having an, adequate cement content sufficiently low free water/, cement ratio, by ensuring complete compaction of the, concrete. and by adequatecuring., , 7.1.1 In the 'very low' category ofworkability where, strict control is necessary, for example pavement, quality concrete, measurement of workability hy, determination of compacting factor will he more, appropriate than slump (see IS 1199) and a value of, compacting factor of 0.75 to 0.80 is suggested., , The factors influencing durability include:, , a) the environment;, , 7.1.2 In the 'very high' category of workability,, measurement of workability hy determinationof flow, will be appropriate (see IS 9103)., , h) the cover to embedded steel;, c) the type and quality of constituent materials;, , 8 DURABILITY OF CONCRETE, 8.1. General, , d) the cement content and water/cement ratio of, , A durable concrete is one that performs satisfactorily, in the working environment during its anticipated, exposure conditions during service. The materialsand, , e) workmanship, to obtain full compaction and, efficient curing; and, , the concrete;, , f), , mix proportions specified and used should be such as, to maintain its integrity and, if applicable, to protect, embedded metal from corrosion., 8.1.1 One of the main characteristics influencing the, durability of concrete is its permeability to the ingress, of water, oxygen, carbon dioxide. chloride, sulphate and, otherpotentially deleterious substances. Impermeability, is governed by the constituentsand workmanship used, in making theconcrete. With normal-weight aggregates, 2116 818/07-4.., , the shape and size of the member., , The degree of exposure anticipated for the concrete, during its service life together with other relevant, factors relating to mix composition. workmanship., design and detailing should be considered. The, concretemix to provideadequatedurability under these, conditions should be. chosen taking account of the, accuracy of current testing regimes for control and, compliance as described in this standard., 17

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IS 456: 2000, 8.2 Requirements for DurabUity, , 8.2.1 Shapeand Size ofMember, The shape or design details of exposed structures, should be such as to promote good drainage of water, and to avoid standing pools and rundown of water., Care should also betaken to minimize any cracks that, may collect or transmit water. Adequate curing is, essential to avoid the harmful effects of early loss of, rnoisture (see 13.5).Member profiles and their, intersections with othermembers shall be designed and, detailed in a way to ensure easy flow of concrete and, proper compaction during concreting., Concrete is more vulnerable to deterioration due to, chemical or climatic attack when it is in thin sections,, in sections under hydrostatic pressure from one side, only, in partially immersed sections and At comers and, edges of elements. The life of the structure can be, lengthened by providing extra cover to steel, by, chamfering the corners or by using circular crosssections or by using surface coatings which prevent or, reduce the ingress of water, carbon dioxide or, aggressive chemicals,, 8.2.2 Exposure Conditions, 8.2.2.1 General environment, general environment to which the concrete will, be exposed during its working life is classified into, five levels of severity, that is, mild, moderate, severe,, very severe and extreme as described in Table 3., , The, , ., , Table 3 Environmental Exposure Conditions, (Clauses 8.2.2.1 and 35.3.2), SI No., (1), , Environment, (2), , Exposure Conditions, (3), , i), , Mild, , Concrete surfaces protected against, weatheror aggressiveconditions, except, , ii), , Moderate, , Concrete surfaces sheltered from severe, rain or freezingwhilst wet, Concrete exposedto condensation al'd min, Concrete continuously under water, Concrete in contactor bt!ried undernonaggressive soil/ground \Yater, Concrete surfaces sheltered from, saturated salt air in coastal area, Concrete surfaces exposed to severe, rain, alternate wettinl and drying or, occasionalfreezing whilst wet or severe, condensation., Concrete ~letely immersed in seawater, Concl1'tc exposed to coosual environment, COncrelC surfaces exposed to sea water, spray. corrosive fumes orsevere freezin,, conditions whilst wet, Concrete in contact witb or buried, under aaressive lub-loiVaround water, Surface of members in tidal zone, Memben in direct contact with liquldl, solidaggressive chemicals, , those situated in ccestal area., , iii), , Severe, , iv), , Very severe, , v), , Extreme, , 8.2.2.2 Abrasive, Specialist literatures may be referred to for durability, requirements of concrete surfaces exposed to abrasive, action, forexample, in case ofmachinery andmetal t)'fes., 8.2.2.3 Freezing and thawing, Where freezing and thawing actions under wet, conditions exist. enhanced durability can be obtained, by the useof suitable airentraining admixtures. When, concrete lower than grade M 50 is used under these, conditions, the mean total air content by volume of, the fresh concrete at the time of delivery into the, construction should be:, Nominal Maximum Size, Aggregate, , Entrained Air, Percentage, , (mm), , 20, , 40, , S±l, 4±t, , Since air entrainment reduces the strength, suitable, adjustments may be made in the mix design for, achieving required strength., 8.1.1.4 Exposure to sulphate attack, Table 4 givesrecommendations for the type of cement,, maximum free water/cement ratio and minimum, cement content, which are required at different sulphate, concentrations in near-neutral ground water having, pH of6 to 9., For the very high sulphate concentrations in Class S, conditions, some form of liningsuch as polyethylene, or polychloroprene sheet; or surface coating based on, asphalt, chlorinated rubber, epoxy; or polyurethane, materials should also be used to prevent access by the, sulphate solution., , 8.2.3 Requirement of Concrete Cover, 8.1.3.1 The protection of the steel in concrete against, corrosion depends upon an adequate thickness of good, quality concrete., 8.2.3.2 The nominal coverto the reinforcement shall, be provided as per 26.4., 8.%.4 Concrete Mix Proportions, 8.1.4.1 General, The free water-cement ratio is an important factor in, governing the durability of concrete andshould always, be the lowestvalue. Appropriate valuesfor minimum, cementcontentand the maximum free weler-cemenl, ratio are given in Table S for different exposure, conditions. The minimum cement content and, maximum water-cement ratio apply to 20 mm nominal, maximum size aggresate. For othersizesof aggregate, they should be changed 81 given in Table6., 18

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IS 456: 2000, , 8.2.4.2 Maximum cementcontent, Cement content not including fly ash and ground, granulated blast furnace slag in excess of 450 kglml, should not be used unless special consideration has, , been given in design to the increased risk of cracking, due to drying shrinkage in.thin sections, or to early, thermal cracking and to the increased risk of damage, due to alkali silica reactions., , Table 4 Requirements for Concrete Exposed to Sulphate Attack, (Clauses 8.2.2.4 and 9.1.2), Concentration of SuJpbates,, Expressed u SOJ, , ClaVi, , SI, , No., , Type of Cement, , ...., , ..., 1..- ~oil ,, Total SOl, SOlin, 2:1 Water:, , Dense, ruDy Compacted Concrete., , Made wltb 20 mm Nominal, Maximum Size Allre.ate., ComplyIDl witb IS 383, , In Ground, Water, , #, , SoilExtract, , Minimum, Cement, Content, kllm J, , Percent, , gil, , gil, , (3.), , (4), , (5), , Traces, , Less than, , «, , 1.0, , Less than, n.3, , 1.0 to, , 0.3 to, , 1.9, , 1.2, , (2), , (I), 1), , 0.2), , (6), , (7), , ,, Maximum, Face WaterCement, Ratio, , (8), , 280, , 0.5S, , Ordinary Portland, cement or, Portlandslag, cementor, Portland, pozzolana cement, , 330, , 0.50, , Supersulphated, cement or, sulphateresisting, Portlandcement, , 310, , o.so, , Supersulphated, cement or, sulphateresisting, Portland cement, Portland pozzolana, cement or Portland, slag cement, , 330, , 0.50, , 350, , 0.45, , 370, , O,4S, , 4(X), , 0.40, , Ordinary Portland, cement or Portland, slag cement or, Portlandpozzolana, cement, , ii), , 2, , iii), , 0.2 to, 0.5, , 0.5 to, 1.0, , iv), , 4, , 10to, 2.0, , 1.91U, 3.1, , 11, , [0, , S,O, , 1.110, 2.5, , 2.5 to, 50, , Supersulphatcd, or sulphate, resisting, , Portland cement, 5, , v), , More thin, 2.0, , More chan, , Morethan, , 5.0, , 5.0, , Sulphateresisting,., Portland cement, supersulphated c;eanent, with protectivecoatings, , or, , NOTES, 1, 2, 3, 4, , 5, 6, 7, , Cement content given in this table is Irrespective of grades of cement., Use of supersulphated cement is generally restricted where the prevailingtemperatureis above 40 f'C., Supersutpbated cement gives an acceptable life providedthat the concrete is dense and prepared with a water-cementratio of 0.4 or, less, in mineral acids, down to pH 3.~., The cement contents given in col 6 of this table are the minimum recommended. For SO, contents near the upper limit of any class., cement contents above these minimum are advised., For severe conditions. such ~ thin sections under hydrostatic pressureon one side only and sections panty immersed.considerations, should be given to a further reduction of water-cement ratio., Portland slag cement conforming to IS 45.5 with slag content more than 50 percentexhibits better sulphate resisting properties., Where chl()ride is encountered along with sulphates in soil or ground water.ordinary Portlandcement with C 1A content from ~ to 8, percent shall be desirable to he used in concrete, insteadof sulphate resistingcement.Alternatively. Portland ~lllg erment conforming, to IS 4~~ having more than ~o percentslag Of a blendof ordinaryPortlandcementand slag may beused providedsutlicient information, is available on performance of.such blended cements in these conditions., , 19

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IS 456: 2000, , expansionand disruption of concrete. To prevent this,, the total water-soluble sulphatecontent of the concrete, mix.expressed as SOl' should notexceed 4 percent by, mass of the cement in the mix. The sulphate content, should be calculated as the total from the various, constituents of the mix., The 4 percentlimitdoes not apply to concrete made, , 8.2.5 Mix Constituents, 8.2.5.1 General, , For concrete to be durable, carefulselectionof the mix, and materials is necessary, so that deleterious, , constituents do not exceed the limits., , 8.2.5.1 Chlorides in concrete, , with supersulphated cement complying withIS 6909., , Whenever there is chloride in concrete there is an, increased risk of corrosion of embedded metal. The, higher the chloridecontent, or if subsequently exposed, to warm moist conditions. the greater the risk of, corrosion. All constituents may contain chlorides and, . concrete may be contaminated by chlorides from the, external environment. To minimize the chances of, deterioration of concrete from harmful chemical salts,, the levels of such harmful salts in concrete coming, from concrete materials, that is, cement, aggregates, water and admixtures. as well as by diffusion from the, environment should be limited. The total amount of, chloride content (as Cl) in the concrete at the time of, placing shall be as given in Table 7., , 8.2.5.4 Alkali-aggregate reaction, Some aggregates containing particular varieties of, silica may be susceptible to attack by alkalis (N~O, and ~O) originating from cement or other sources,, producing an expansive reaction which can cause, cracking and disruption of concrete. Damage to, concrete from this reaction will normally only occur, when all the following are present together:, a) A high moisture level, within the concrete;, b) A cement with high alkali content, or another, source of alkali;, , c) Aggregate containing an alkali reactive, constituent., , The total acid soluble chloride content should be, calculated from the mix proportions and the measured, chloridecontents of each of the constituents. Wherever, possible, the total chloride content of the concrete, should be determined,, , Where the service records of particular cementl, aggregatecombination are wellestablished,and do not, include any instances of cracking due to alkaliaggregate reaction, no further precautions should be, necessary. When the materials are unfamiliar,, precautions should take one or more of the following, forms:, a) Use of non-reactive aggregate from alternate, sources., , 8.2.5.3 Sulphates in concrete, Sulphates are present in most cements and in some, aggregates; excessive amounts of water-soluble, sulphatefrom theseor other mix constituentscan cause, , Table 5 Minimum Cement Content, Maximum Water-Cement Ratio and Minimum Grade of Concrete, for DifTerent Exposures with Normal Weight Aggregates of 20 mm Nominal Maximum Size, (Clause» 6.1.2, 8.2.4.1 and 9.1.2), SI, No., , t;xposure, , Reinforced Concrete, , Plain Concrete, ~, , Minimum, Cement, Content, , ...., , Maximum, FreeWater·, Cement Ratio, , "Minimum, Grade of, Concrete, , ..., , Minimum, Gradeof, Concrete, , (6), , (7), , (8), , 300, , O.5~, , M20, , M25, MJO, M3S, M40, , Content, , (3), , (4), , 0.60, , (~), , i), , Mild, , 220, , iii), , Moderate, Severe, , 240, , 0.60, , MIS, , 300, , O.SO, , iii), , 2S0, , O.SO, , M20, , 320, , O.4~, , iv), , Very severe, , 260, , 0.45, , M20, , 340, , 0.45, , Extreme, , ~80, , 0.40, , M2~, , 360, , 0.40, , v), , ..., , Maxirnum, FreeWaterCement Ratio, , kgln}l, , kglm', (2), , --, , Minimum, Cement, , NC)T&,, , I Celnentcontent prescribed in this table is irrapeetive of the grDdes of cementand it is inclusive of additions mentioned in 5.2. The, additions such DIfly ashor around granulated blastfurnace slag mayhe takeninto ICcount in the concrete composition with respecllO, the cementcontentand water-cement ratio if the suitability is established and as lonl as the maximum 81nounts cakcn into ac&.~unt do, not exceedthe limil or pozzolona and alae specified in IS 1489 (Part I) and IS 4S~ respectively., 2 Minimum grade·for plainconcrete undermild exposu~ condition it nolspecified., , 20

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1S4S6:2000, Table 6 Adjustments to Minimum Cement, Contents for Allregates Other Than 20 mm, Nominal Maximum Size, , evaporation may cause seriousconcentrations of salts, with subsequent deterioration, even where the original, .salt content of the soil or water is not high., , (Clause 8.2.4.1), SI, No., , Nominal Maximum Adjustments to Minimum CemeDt, Contents In 1able 5, Aarepte Size, k&lm:mm, , (I), , (2), , (3), , i), ii), iii), , 10, 20, , +40, , 40, , -30, , NOTE - Guidance feaarding requirements for conaete exposed, in 1~4., , 10 sulphnte anaek is liven, , 8.1.6.2 Drainage, At sites where alkali concentrations are high or may, become very high.the groundwatershould be lowered, by drainage so that it will not come into direct contact, with the concrete., Additional protection may be obtained by the use of, chemically resistant stone facing or a layer of plaster, of Paris covered with suitable fabric, such as jute, thoroughly impregnated with bituminous material., , o, , Table 7 Limits of Chloride Content or Concrete, (Clause 8.2.5.2), SI, , Type or Use 01Concrete, , Maximum Total, Acid Soluble, , No., , 8.2.7 Compaction; Finishing and Curing, , Chloride ConteDt, Exp~cd, , Adequate compaction without segregation should be, ensured by providing suitable workability and by, employing appropriate placing and compacting, equipment and procedures. Full compaction is, particularly important in the vicinity of construction, and movement joints and of embedded water bars and, reinforcement., , as klhnJor, , CODcrete, (I), i), , (2), , Concretecontaining metal and, , (3), , 0.4, , steam cured at elevated tempe-, , ii), iii), , ratureand pre-stressed concrete, Reinforced concrete or plain concrete, containingembedded metal, Concrete not containing embedded, metalor any material requiring, protection from chloride, , 0.6, , Good finishing practices are essential for durable, concrete., , J.O, , Overworking the surface and the addition of waterl, cement to aid in finishing should be avoided; the, resulting laitance will have impaired strength and, durability and will be particularly vulnerable to, freezing and thawing under wet conditions., , b) Usc of low alkali ordinary Portland cement, having total alkali content not more than 0.6, percent(as Na20 equivalent)., , Furtheradvantagecan be obtainedby useof fly, , It is essential to use proper and adequate curing, techniques to reduce the permeability of the concrete, and enhance its durability by extending the hydration, of the cement, particularly in its surface zone, , ash (Grade I) conforming to IS 3812 or, , granulated blastfurnace slag conforming to, IS 12089 as part replacement of ordinary, Portland cement (having total alkali content as, Na20 equivalent not more than 0.6 percent),, provided fly· ash content is at least 20 percent, or slag content is at least 50 percent., , isee 13.5)., 8.2.8 Concrete in Sea-water, , Concrete i~ sea-water or exposed directly along the, sea-coast shall be at least M 20 Grade in the case of, plain concrete and M 30 in case of reinforced concrete., The use of slag or pozzolana cement is advantageous, under such conditions., , c) Measures to reduce the degree of saturation of, the concrete during service such as use of, impermeable membranes,, d) Limiting the cement content in the concrete mix, , and thereby limiting total alkali content in the, concrete mix. For more guidance specialist, literatures may be referred., , 8.2.8.1 SPecial attention shall be given to the design, of themixto obtainthe densestpossibleconcrete; slag., broken brick. soft limestone, soft sandstone, or other, porous or weak aggregatesshall not be used., 8.2.8.2 As far as possible, preferenceshall be givento, precast members unreinforced, well-cured and, hardened. without sharp corners, and having trowelsmooth finished surfaces free from crazing. cracks or, other defects; plasteringshould be avoided., 8.2.8.3 No construction joints shall be allowed within, 600 mm below low water-level or within 600 mm of, the upper and lower planes of wave action. Where, , 8.2.6 Concretein Aggressive Soils and Water, 8.2.6.1 General, The destructive action of aggressive waters on concrete, is progressivee The rate of deterioration decreases as, the concrete is made stronger and more impermeable,, , and increasesas the salt contentof the waterincreases., Where structures are only partially immersed or are in, contactwithaggressive soilsor waters on onesideonly,, 21

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IS 456: 1000, , a) Type of aggregate,, , unusually severeconditionsor abrasionare anticipated,, suchparts of the workshall be protectedby bituminous, or silico-fluoridecoatings or stone facingbeddedwith, bitumen., 8.2.8.4 In reinforcedconcrete structures,care shall he, taken to protect the reinforcement from exposure to, saline atmosphereduring storage, fabricationand use., It may be achieved by treating the surface of, reinforcement with cement wash or by suitable, methods., 9 CONCRETE MIX PROPORTIONING, 9.1 Mix Proportion, , The mix proportions shall be selected to ensure the, workabilityof the freshconcrete and when concrete is, hardened, it shall have the requiredstrength,durability, and surface finish., 9.1.1 The determinationof the proportionsof cement,, aggregates and water to attain the required strengths, shall he made as follows:, a) By designing the concrete mix; such concrete, shall be called 'Design mix concrete', or, b) By adopting nominal concrete mix: such, concreteshall becalled 'Nominal mixconcrete'., , b) Maximum cement content. and, c) Whether an admixture shall or shall not be, used and the type of admixture and the, condition of use., 9.2 Design Mix Concrete, , 9.2.1 As the guarantor of quality of concrete used in, theconstruction, theconstructor shall carry outthemix, design and the mix so designed (not the method of, design) shall be approved by the employer within the, limitations of parameters and other stipulations laid, down by this standard., 9.2.2 The mix shall be designed to produce the grade, of concrete having the required workability and a, characteristic strengthnot less than appropriate values, given in Table2. The target mean strength of concrete, mix should be equal to the characteristicstrength plus, 1.65 times the standard deviation., 9.2.3 Mix design done earlier not prior to one year, may be considered adequate for later work provided, there is. no change in source and the quality of the, materials,, 9.2.4 Standard Deviation, , Design mix concrete is preferred to nominal mix. If, design mix concrete cannot be used for any reason on, the work for grades of M 20 or lower) nominal mixes, may be usedwiththe permission of engineer-in-charge., which, however. is likely to involve a higher cement, , The standard deviationfor each gradeof concrete shall, be calculated, separately., 9.2.4.1 Standard deviation blued on test strength of, sample, a) Number of test results of sample,s'-The total, number of test strength of samples required to, constitute an acceptable record far calculation, of standard deviation shall be not less than 30., Attempts should be made to obtain the 30, , samples, as early as possible, whena mix is used, for the first time., , content., , 9.1.2 Information Required, , In specifying a particular grade of concrete, the, following informationshall be included:, a) Type of mix, that is, design mix concrete Of, nominal mix concrete:, h) Grade designation;, c) Type of cement;, d) Maximum nominal size of aggregate;, , b) In case of significant changes in concrete-, , When significant changes are made in the, production of concrete batches (for example, changes in the materials used, mix design,, equipment or technical control). the standard, deviation value shan be separately calculated, for such batches of concrete., , e) Minimum cement cont.ent (for design mix, , concrete);, f), g), , h), j), k), , Maximum water-cement ratio;, Workability;, Mix proportion (for nominal mix concrete);, Exposure conditions as per Tables 4 and 5;, Maximum temperature of concrete at the time, of placing;, , c) Standard deviation to be brough: up to date-, , The calculation of the standard deviation shall, be broughtup to date after every change of mix, design., 9.2.4.2 Assumed standard deviation, , Where sufficient test results for a particular grade of, concrete are not available. the value of standard, deviation given inTable 8 may be assumed for design, of mix in the first instance. As soon as the results of, samples are available, actual calculated standard, deviationshall be used and the mix designed properly., , m) Method of placing; and, n) Degree of supervision., 9.1.2.1 In appropriate circumstances. the following, additional information may be specified:, , 22

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IS 456: 2000, However, when adequate past records for a similar grade, existandjustifyto the designer a valueof st,Uldard deviation, different from that showninTable 8, it shall bepermissible, to use that value., , 10 PRODUCTION OF CONCRETE, 10.1 Quality Assurance Measures, 10.1.1 In order that the properties of the completed, structure be consistent with the requirements and the, assumptions made during the planning and the design,, adequate quality assurance measures shall be taken., The construction should result in satisfactory strength,, serviceability and long term durability so as to lower, the overall life-cycle cost. Quality assurance in, construction activity relates to proper design, usc of, adequate materials and components to be supplied by, the producers, proper workmanship in the execution, of works by the contractor and ultimately proper care, during the use of structure including timely, maintenance and repair by the owner., , Table 8 Assumed Standard Jleviation, (Clau~'e 9.2.4.2, , and Tub/£' 11), , Grade of, Concrete, , StKndard, Deviation, N/narn z, , AS5Uftl,d, , MIO, MIS, , l5, , M20, M2S, , 4.0, , MJO, MJS, M40, M4S, M SO, , 5.0, , 10.J.2 Quality assurance measures are both technical, and organizational. Some common cases should be, specified in a general Quality Assurance Plan which, shall identify the key elements necessary to provide, fitness of the structure and the means by which they, are to be provided and measured with the overall, purpose to provide confidence that the realized project, will work satisfactorily in service fulfilling intended, needs. Thejob of quality control and quality assurance, would involve quality audit of both the inputs as well, as the outputs. Inputs are in the form of materials for, concrete: workmanship in all stages of hatching., mixing, transportation, placing, compaction and, curing: and the related plant, machinery and, equipments: resulting in the output in the form of, concrete in place. To ensure proper performance, it is, necessary that each step in concreting which wi11 be, , NOTE--The above values correspond to the site control having, properstorageof cement;weighhatchingof all material»; controlled, addition of water; regular checking of all ,nate.-juls. ag~rcgate, &J'adings and moisture content; and periodical checking of, work3hility and strength. W~rc there i~ deviation from th~ above, the values given in the abnve tnble shall he inc.:fea~cd hy I N/nun! ., , 9.3 Nominal Mix Concrete, Nominal mix concrete may be used for concrete of, M 20 or lower. The proportions of ruutcnals for, nominal mix concrete shall be in accordance with, 1:1ble 9., 9.3.1 The cement 'content of the mix specified in, Table 9 for any nominal mix shall be proportionately, increased if the quantity of water in a nux has to he, increasedto overcor..e the difficultiesof placementand, compaction, so that the water-cement ratio as specified, is not exceeded., , covered by the next step is inspected as the work, proceeds (see also 17)., , Table «) Proportions for Nominal Mix Concrete, (Clausrs 9.3 lind, Grade of, Concrete, , 9.~.l), , Total Quantity of Dry Aggre-, , Preportion of Fine, , gates by i\lass per SO kg of, Cement, to be Taken as the SUID, of the Individual M1I$..'ies of, Ftnt aod Coarse Al:gregH1es, kg,, , A~gregate to ~oarse, , Quantity of Wat~r per, SO kg of Cement, Max, , Axgre"ate (hyl\1a'tt), , I, , MtlX, , (I), , (2), , M5, , ROO, , M7.~, , 625, , M 10, , 480, , M 15, , 330, , 32, , M20, , 2~O, , 30, , (4), , Generally 1:2 but subject to, an upper limit of I: 11 and a, lowerlimit of 1:21/1., , '1, , 60, , 45, 34, , NOTE-11le proportion of the fineto coarse aggregates should be adjustedfromupperlimit 10 lowerlimit progressively as the ~rading, of fine agl~gates becomes finer and the maximum size of coarse a~gregate becomes larger, Graded coarse aggregate shall be used., , Examplt, For M Avera,,, ,radina of fine aggregate (that is. Zone II of Table 4 of IS ~83). the proportions shall be L 1'1" 1:1 and l:2'/:! for, maximum sizeof ngg~gntes 10 mm, 20 mm and40 mm respectively,, , 23

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IS 456: 2000, 10.1.3 Each party involved in the realization of a, project should establish and implement a Quality, Assurance Plan. for its participation in the project., Supplier's and subcontractor's activities shall be, covered in the plan. The individual QualityAssurance, Plans shall tit into the general QualityAssurancePlan., A Quality Assurance Plan shall define the tasks and, responsibilities of all persons involved. adequate, control and checking procedures,and the organization, and maintaining adequate documentation of the, building process and its results. Such documentation, should generally include:, a) test reports and manufacturer's certificate for, materials. concrete mix design details;, b) pour cards for site organization and clearance, for concrete placement;, c) record of site inspectionof workmanship, field, tests;, d) non-conformance reports. change orders;, e) quality control charts; and, 1) statistical analysis., NOTE-Quahty controt charts are recommended whereverthe, concrete is in continuousproductionover considerable period., , 10.2 Batching, Toavoidconfusionand error in batching,consideration, should be given to using the smallest practicalnumber, of different concrete mixes on any site or in anyone, plant. In hatching concrete.thequantityof bothcement, and aggregateshall be determinedby mass;admixture., if solid. by mass; liquid admixture may however be, measured in volume or mass; water shall be weighed, OJ' measured by volume in a calibrated tank (set' also, IS 4925)., Ready-mixed concrete supplied by ready-mixed, concreteplantshall be preferred. Forlargeand medium, project sites the concrete shall be sourced from readymixed concrete plants or from on site or off site, hatching and mixing plants (see IS 4926)., 10.2.1 Except where itcan he shown to the satisfaction, of the engineer-in-charge that supply of properly, gradedaggregateof uniformqualitycan be maintained, over a period of work. the grading of aggregateshould, be controlled by obtaining the coarse aggregate in, different sizes and blending them in the right, proportions when required. the different sizes being, stocked in separate stock-piles. The material should, be stock-piledfor severalhours preferablya day before, use. The grading of coarse and fine aggregate should, be checked as frequently a.s possible. the frequency, for a given job being determined by the engineer-incharge to ensure that the specified grading is, maintained., 10.2.2 The accuracy of the measuringequipmentshall, be within ± 2 percent of the quantity of cement being, , mea.sured and within ± 3 pereent of the quantity of, aggregate. admixturesand water being measured., 10.2.3 ProportionflYpe andgradingof aggregates shall, be made by trial in such a way so as to obtain densest, possible concrete. All ingredients of the concrete, should be used by mass only., 10.2.4 Volume batching may be allowed only where, weigh-batching is not practical and provided accurate, bulk densities of materials to be actually used in, concrete haveearlier been established. Allowancefor, bulking shall be made in accordance with IS 2386, (Part 3). The mass volume relationship should be, checked a.s frequently as necessary. the frequency for, the givenjob being determined by engineer-in-charge, 10 ensure that the specified grading is maintained,, 10.2.S It is important to maintain the water-cement, ratioconstant at its correct value.To this end. determination of moisture contents in both fine and coarse, aggregatesshall bemade as frequentlyas possible. the, frequency for a given job being determined by the, engineer-in-charge according to weather conditions., The amount of the added water shall be adjusted to, compensate for any observed variations in the moisture, contents. For the determination of moisture content, in the aggregates.IS 2386 (Part 3) may be referred to., To allow for the variation in mass of aggregate due to, variation in theirmoisture content,suitableadjustments, in the massesof aggregatesshall also be made. In the, absence of exact data. only in the case of nominal, mixes. the amount of surface water may be estimated, from the values given in Table 10., , . 24, , Table 10 Surface Water Carried by Aggregate, (Clause 10.2.5), Approximate Quantity of Surface, Water, .., (3), , (4), , 120, , Modernlel)' wet sand, , 7.5, 5.0, , iii), , Moistsand, , 2.5, , 40, , IV), , "Moist gravelor crushed rock 1.25-2,5, , (I), , (2), , i), , Very wet sand, , ii), , II, , 80, , 20-40, , Courserthe oggregllte. less the wllterit will corry., , 10.2.6 No substitutionsin materials used on the work, or alterations in the established proportions.except as, permitted in 10.2.4 and 10.2.S shall be made without, additional tests to show that the quality and strength, of concrete are satisfactory., 10.3 Mixing, Concrete shan be mixed in a mechanical mixer. The, mixer should comply with IS 179" and IS 12119. The, mixersshall befitted with watermeasuring(metering), devices. The mixingshall be continueduntil there is a, uniform distribution of the materials and the mass is

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18456: 1000, , ubifortn in colour and consistenc.y. If there is, .e,re,ation alter unloading from the mixer, the, COhcrete should be remixed., 10.3.1 Por guidance, the mixing timeshall be at least, 2 min. Por other types of more efficient mixers,, manufacturers recommendations shalJ be followed;, for hydrophobic cement it may be decided by the, engineer-in-charge., , 10.3.2 Workability should be checked at frequent, intervals (Itt IS 1199)., 10.3.3 Dosages of retarders, plasticisers and, superplasticisers shall be restricted to O.S, 1.0and2.0, percent respectively by weight of cementitious, materials and unless a higher value is agreed upon, between the! Itllftufacturer and the constructor based, on performance test., , 11.3 Strlpplnl11me, Fonns shall not be released until the concrete has, achieved a strength of at leasttwice the stressto which, the concrete may be subjected at the time of removal, of fonnwork. The strength referred to shall be that of, concrete using the same cement and aggregates and, admixture, if any, withthesameproportions andcured, under conditions of temperature and moisture similar, to those existing on the work., 11.3.1 Whilethe above criteriaof strength shall be the, guiding factor for removal of formwork, in normal, circumstances where ambient temperature doesnotfall, below ISOC and where ordinaryPortland cement is used, andadequate curingis done,following striWng period, maydeemto satisfy the guideline given in 11.3:, Type of Formwor/c, , 11 FORMWORK, 11.1 General, The formwork shall be designed and constructed so, as to remain sufficiently rigid during placing and, compaction of concrete, andshall be suchas to prevent, loss of slurry from the concrete. For further details, regarding design, detailing, etc,reference may be made, to IS 14687. The tolerances on the shapes, lines and, dimensions shown in the drawing shall be within the, limitsgiven below:, , a) Deviation from specified, + 12, dimensions of cross-section _ 6 mm, of columns aad beams, b) Deviation from dimensions, offootinss, 1) Dimensio. in plan, +50 mm, , a), , b), , c), , d), , e), , -12, , 2) Eccentricity, , 3) Thickness, , 0.02 times the, widthofthefooting in the direction of deviation, butnotmore than, SOmm, ± o.os times the, specified thickness, , Thesetolerances applyto concrete dimensions only, and, notto positioniolof vertical reinforcing steel ordowels., 11.2 aeanm._ TnatmeDt 01Formwork, All rubbish, particularly, chippinss, shavings and, sawduat sball beremoved from the interior ofthefonns, before the concrete is placed. The face of formwork, incontactwith the concrete shallbe cleaned andtreated, with form release agent. Release agents should be, applied soas to providea thin unifonn coating to the, fonns withoutcoatingthe reinforcement., 2118 818/07-5, , Minimum Period, Before Striking, Formwork, Vertical fonnwork to columns,, 16-24 h, walls, beams, Soffitformwork to slabs, 3 days, (Props to be refixed, immediately afterremoval, of formwork), 7 days, Soffit fonnwork to beams, (Props to be refixed, immediately afterremoval, of formwork), Props to slabs:, 7 days, 1) Spanning up to 4.5 m, 14days, 2) Spanning over4.S m, Props to beams and arches:, 14 days, 1) Spanning up to 6 m, 21 days, 2) Spanning over 6 m, , For other cements and lower temperature, the, stripping time recommended above may be suitably, modified., 11.3.2 The'number of propsleft under, theirsizesand, disposition shall be such as to be able to safely carry, the full dead load of the slab, beam or arch as the case, may be tOlether with any live load likely to occur, during curingor further construction., 11.3.3 Where theshapeof theelementis suchthat the, formwork has re-entrant angles, theformwork shall be, removed as soonas possible afterthe concretehas set,, to avoid shrinkage cracking occurring due to the, restraint imposed., , 11 ASSEMBLY OF REINFORCEMENT, 12.1 Reinforcement shall be bent and fixed in, , accordance with procedure specified in IS 2502. The, highstrength defonnedsteelbarsshould notbere-bent, , 2S

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IS 456: 2000, , or straightcned without the approval of engineer-incharge., Bar bending schedules shall be prepared for all, reinforcement work., J2.2 All reinforcement shall be placed and maintained, in the position shown in the drawings by providing, proper cover blocks, spacers, supporting bars, etc., , 12.2.1 Crossing bars should not be lack-welded for, assembly of reinforcement unless permitted by, engineer-in-charge., 12.~~, , Placing of Relnforcement, , Rough handling, shock loading (prior to embedment), and the droppingof reinforcementfroma heightshould, be avoided. Reinforcement should he secured against, displacement outside the specified limits., 12.3.1 Tolerances on Placing, , (~f Reinforcement, , Unless otherwise specified by engineer-in-charge, the, reinforcement shall he placed within the following, tolerances:, a) for effective depth 200 nun, or less, , ± 10 nun, , b) for effective depth more than, 200 mm, , ± 15 mm, , t2.3~2, , Tolerancefor Cover, , Unless specified otherwise, actual concrete cover, should not deviate from the required nominal cover, by, , +10, 0 mrn,, , Nominal cover as given in 26.4.1 should be specified, to all steel reinforcement including links. Spacers, between the links (or the bars where no links exist), and the formwork should be of the same nominal size, as the nominal cover., Spacers, chairs and other supports detailed on, drawings, together with such other supports as, may he necessary, should be used to maintain the, specitied nominal cover to the steel reinforcement., Spacers or chairs should be placed at a maximum, spacing of I m and closer spacing may sometimes be, necessary., , steel bars are bent. aside at construction joints ana, afterwards bent back into their original positions. care, should be taken to ensure that at no time is the radius, of the bend Jess than 4 bar diameters for plain mild, steel or 6 bar diameters for deformed bars, Care shall, also be taken when bending hack bars, to ensure that, the concrete around the bar is not damaged beyond, the band., 12.6 Reinforcement should be placed and tied in such, a way that concrete placement be possible without, segregation of the mix. Reinforcement placingshould, allow compaction by immersion vibrator. Within the, concrete mass, different types of metal in cont.act, should be avoided to ensure that bimetal corrosiondoes, not t.ake place,, 13 TRANSPORTING, PLACING,, COMPACTI'()N AND CURING, 1.3.1 Transporting and Handling, , After mixing, concrete shall be transported to the, formwork as rapidly as possibleby methods which will, prevent the segregation Of Jossof any of the ingredients, or ingress of foreign matter or water and maintaining, (he required workability, , 13.1.1 During hoi Of cold weather. concrete shall be, transportedin deep containers. Other suitable methods, to reduce the loss of water hy evaporation in hot, weather and heat loss in cold weather may also be, adopted., 13.2 Placing, TIle concrete shall he deposited as nearly as practicable, in its final position to avoid rehandling. The concrete, shall he placed and compacted hefore initial setting of, concrete commences and should not be subsequently, disturbed. Methods of placing should be such as, to preclude scgreg.rtion. Care should be taken to, avoid displacement of reinforcement or movement, of Iorrnwork . As a general guidance, the maxi . ., mum permissible free fall of concrete may be taken, as 1.5 Ill., 13.3 COInpaction, Concrete should he thoroughly compacted and fully, worked around the reinforcement, around embedded, , Spacers, cover blocks should he of concrete of same, strength or PVC., , fixtures and into corners of the fonnwork., 1.2.4 Welded Joints or Mechanical Connections, , 13.3.1 Concrete shall be compacted using mechanical, vibrators complying with IS 2505, IS 2506. IS 2514, and IS 4656. Over vibration and under vibration of, concreteare harmful and should beavoided. Vibration, of very wet mixes should also he avoided., , Welded joints or mechanical connections in, reinforcement may be usedbut in allcasesof important, connections, tests shall he made to prove that thejoints, are of the full strength of bars connected. Welding of, reinforcements shall be done in accordance with the, recommendations of IS 2751 and IS 94 J7., 12.5 Where reinforcement bars upto 12 mm for high, strength deformed steel bars and up to 16mm for mild, , Whenever vibration has to be applied externally, the, design of formwork and the disposition of vibrators, should receive specialconsideration to ensure efficient, compaction and to avoid surface blemishes., 26

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IS 456: 2000, 13.4 ConstMlttion Joints and Cold Joints, , of ordinary Portland Cementand at least 10 days where, , Joints are a common source of weaknessand, therefore,, it is desirable to avoid them. If this is not possible., their number shall be minimized. Concreting shall be, carried out continuously up to construction joints,, the position and arrangement of which shall be, indicated by the designer. Construction joints should, compJywithlS 11817., Construction joints shall be placed at accessible, locations to permit cleaning out of laitance, cement, slurry and unsound concrete, in order to create rough/, unevensurface. It is recommendedto clean out laitance, and cement slurry hy using wire brush on the surface, of joint immediately after initial setting of concrete, and to clean out the same immediately thereafter. The, prepared surface should be in a clean saturated surface, dry condition when fresh concrete is placed. against it., , mineral admixturesor blendedcements are used. The, period of curing shall not be less than J0 days for, , In the case of construction joints at locations where, the previous pour has been cast against shuttering the, recommended method of obtaininga rough surface for, the previously poured concrete is to expose the, aggregate with ,1 high pressure water Jet or any other, appropriate means., Fresh concrete should be thoroughly vibrated near, construction joints so that mortarfrom the new concrete, flows between large aggregates and develop proper, , bond with old concrete., Where high shear resistance IS required at the, construct ion joints. shear keys "lay he provided., Sprayed curing membranes and release agents should, be thoroughly removed from joint surfaces., , 13.5, , (:urin~, , concrete exposed to dry and hot weather conditions., , In the case of concrete where mineral admixtures or, blended cements are used, it is recommended that, above minimum periods may be extended to 14 days., , 13.5.2 Membrane (.'. uring, Approved curing compounds may be used in lieu of, moist curing with the permission of the engineer..incharge. Such compounds shall beappliedtoall exposed, surfaces of the concrete as soon as possible after the, concrete has set. Impermeable membranes such as, polyethylene sheeting covering closely the concrete, surface may also be used to provide effective barrier, against evaporation., 13.5.3 For the concrete containing Portland pozzolana, cement, Portland slag cement or mineral admixture,, period of curing may be increased., 13.6 Supervision, , It is exceedingly difficult and costly to alter concrete, once placed. Hence, constant and strict supervision of, all the items of the construction is necessary during, the progress of the work, including the proportioning, and mixing of the concrete. Supervision is also of, extreme importance to check the reinforcement and, its placing before being covered., 13.6.1 Before any important operation. such as, concreting or stripping of the fonnwork is started,, adequate notice shall be gi yen to the construction, supervisor., , Curing is the process of preventing the Joss of moisture, 14 CONCRETING UNDER SPECIAL, from the concrete whilst maintaining a satisfactory . (~ONDITIONS, temperature regime. The prevention of moisture loss, from the concrete is panicularly important if the water- 14.1 Work in Extreme Weather Conditions, cement ratio IS low, if the cement has a high rate of During hot or cold weather, the concreting should be, strength development, if the concrete contains, done as per the procedure set out in IS 7861, granulated blast furnace slag or pulverised fuel ash., (Part 1) or IS 7861 (Part 2)., TIlecuringregime should also prevent the. development, 14.2 Under-Water Con~retinl, of high temperature gradients within the concrete., The rate of strength development at early ages of, , 14.ZL 1 When it is necessary to deposit concrete under, , concrete made with supersulphated cement is, significantly reduced at" lower temperatures., Supersulphated cement concrete is seriously affected, by inadequate curing and the surface has to be kept, moist for at least seven days., , water, the methods. equipment, materials and, proportions of the mix to be used shall be submitted to, and approved by the engineer-in-charge before the, work is started., , 13.5.1 Moist Curing, Exposed surfaces of concrete shall be kept, , continuously in a damp Of wet condition by pending, or by covering with a layer of sacking, canvas, hessian, or similar materials and kept constantly wet for at least, seven days from the date of placing concrete in case, , 14.2.2 Under-water concrete should have a slump, recommended in 7.1. The water-cement ratio shall not, exceed 0 6 and may need to be smaller, depending on, the grade of concrete or the type of chemical attack., For aggregates of 40 rom maximum particle size, the, cement content shall be at least 350 kg/m' of concrete., 14.1.3 Coffer-dams or forms shall be sufficiently tight, 27

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IS 456: 2000, , to ensure still water if practicable. and in any cue to, reducethe flowof waterto less than 3 m1min throup, the space into which concrete is to be deposited., Coffer-dams or fonns instillwatershallbesufficiently, tight to prevent loss of mortar through the walls., De-watering by pumping shall not be done while, concreteis being placedor until 24 h thereafter., 14.2.4 Concrete cast underwatershouldnotfallfreely, through the water. Otherwise it may be leached and, become segregated. Concrete shall be deposited, continuously until it is broughtto the required height., While depositing. the top surface shallbe kept asnearly, level as possibleand the fonnation of seams avoided., The methods to be used fordepositing concrete under, water shall be one of the following:, a) Tremie-Theconcrete isplacedthroup vertical, pipes the lowerend of whichis always inserted, sufficiently deep into the concrete which has, been placed previously but has not set. The, concrete emerging from the pipe pushes the, material that has already beenplacedto theside, and upwards and thusdoes not come intodirect, contact with water., When concrete is to be deposited under water, by means oftremie, the top sectionof the tremie, shall be a hopperlarge enoughto holdoneentire, batch of the mix or the entire contents the, transporting bucket, if any. Thetremie pipeshall, be not less than 200 mm in diameterand shall, be largeenoughto allowa freeflowof concrete, and strong enough to withstand the external, pressureof the water in which it is suspended,, evenif a panial vacuum develops inside the pipe., Preferably, flanged steel pipe of adequate, strength for the job should be used. A separate, lifting device shall be provided for each tremie, pipe with its hopper at the upper end. Unless, the lower end of the pipe is equipped with an, approved automatic check valve, the upperend, of, pipe shall be plugged with a wadding of, the gunny sackingor other approved material, beforedelivering the concreteto the tromie pipe, throughthe hopper, so that whenthe concrete is, forceddownfromthe hopperto the pipe, it will, force the plug (and along with it any water in, the pipe) down the pipe and out of the bottom, end. thus establishing a continuous stream of, concrete. It will be necessary to raiseslowly the, tremie in order to cause a uniform flow of the, concrete, but the tremieshall not beemptied10, that water entersthe pipe. At all timesafter the, placing of concrete is started and until all the, concrete is placed, the lowerend of the ttemie, pipeshall be below the topsurface of the plastic, concrete. This.will cause the concrete to build, up from below insteadof flowing out over the, , the, , 28, , .urface, and thus avoid formetion of laitance, layors. If tho cluqo in tho tremie is 10lt while, depositin,. tho tromio shall bo naised Ilxlve d1e, concrete surface, and unloss _04 by I c~k, valvo, it shall be rc-plulled at tho topend, as••, the beginninl. before refl11inl for dcpositin,, concrete., b) Direct plactment with pumps-As in the case, , of the tremie method, tho vertical end pieceof, the pipe lineisalways inserted sufficiently deep, into the previoosly castconcreteand shouldnot, move to tlte side during pumping., c) Dmpbouom bucket -The topof thebucketshall, bo covered with acanvas flap. The bottom doors, shall open freely downwvd and outward when, tripped. Thebucket shall bo (diedcompletely and, lowered slowly to avoid backwaah. The bottom, doors shall not be opened until tho bucketrests, on the surface upon which the concreto is to be, deposited and when dtscharged, shall be, withdrawn slowly until well above the concrete,, d) Bags - Bags of at least 0.028 m] capacity of, jute or other coarse cloth shall be filled about, two-thirds fullof concrete, the spareend turned, underso that baa is square ended and securely, tied. They shall be placed carefully in header, and stretcher courses so that the whole mass is, interlocked. Bagsusedfor thispurpose shall be, free from deleterious materials., e) Grouting-A series of round cages made from, SO mm mesh of 6 mm steel and extending over, the full heisht to be concreted shall be prepared, andlaid vortically over thearea to be concreted, so that tho distance between centres of thecases, and also to the faces of the concrete shall not, exceedone metre. Stone aggregate of not less, than SO mmnormorethan200mm size shall be, deposited outside the stool cages over the full, areaandheightto be concreted with due care to, preventdisplacement of the cages., A stable 1:2 cement-sand grout with a watercementratio of not loss than 0.6 and not marc, than 0.8shall be prepared ina mechanical mixer, andsentdownunderpressure (about0.2N/inm2), throulh 38 to 50nundiameter pipes tenninating, intosteelcages,about SO mmabovethe bottom, of the concrete. As the &rautio, proceeds, the, pipe shall be raised aradually up to a heiaht of, notmorethan6000 nun above its starlin, level, after which it may be withdrawn and pl,acod into, the noxt cale for further groutiol by the same, , procedure., After IfOUtinl the whole area for a heisht of, about 600 mm, the same operation shall be, repeated, if necessary. for the next layer of

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L~, , 600 mm and so on., The amount of grout to be sent down shall be, , sufficient to fillallthevoidswhich may be either, asc~rtained, , or assumed as 55 percent of the, , volume to be concreted., 14.2.5 To minimizethe formulation of laitance, great, care shall be exercised not to disturb the concrete as, far as possible while it is being deposited., , 15 SAMPLING AND STRENGTH OF, DESIGNED CONCRETE MIX, 15.1 General, , Samples from fresh concrete shall be taken as per, IS 1199and cubes shall be made, cured and tested at, 28 days in accordancewith IS S16., 15.1.1 In order to get a relatively quicker idea of the, quality of concrete, optional tests on beams for, modulus of rupture at 72 ± 2 h or at 7 days, or, compressive strength tests at 7 days may be carried, out in addition to 28 days compressive strength test., For this purpose the valuesshould be arrived at based, on actualtesting. In all cases,the 28 dayscompressive, strengthspecifiedinTable2 shallalone be thecriterion, for acceptanceor rejection of the concrete., , 456: 1000, , for testing at 28 days. Additional samples may be, required for variouspurposessuch as to determine the, , strengthof concreteat 7 days or at the time of striking, the formwork, or to determine the duration of curing., or to check the testing error. Additional samples may, also be required for testing samples cured by, accelerated methods as described in IS 9103. The, specimen shall be tested as described in IS S16., 15.4 Test Results of Sample, , The test results of the sample shall be the average of, the strength of three specimens. The individual, variation should not be more than ±lS percent of the, average. If more, the test result.~ of the sample are invalid., , 16 ACCEPTANCE CRITERIA, 16.1 Compressive Streoath, The concrete shall be deemed to comply with the, strength requirements when both the following, , condition are met:, a) The mean strength determined from any group, of four consecutive test results compiles with, the appropriate limits in col 2 of Table 11., b) Any individual test result complies with the, appropriate limits in col 3 of Table I)., , 15.1 Frequency of Sampling, 16.2 Flexural Strength, , 15.2.1 Sampling Procedure, A random sampling procedure shall be adopted to, , ensurethateach concretebatchshallhavea reasonable, chance of being tested that is, the sampling should be, spread over the entire period of concreting and cover, all mixing units., ., , When both the following conditions are met" the, concrete complies with the specified flexural strength., , a) The mean strengthdetermined from any group, of four consecutive test results exceeds the, specified characteristic strength by at least 0.3, N/mn12•, , 15.2.2 Frequency, , b) The strengthdetermined from any test result is, not less than thespecified characteristicstrength, , The minimum frequency of sampling of concrete of, each grade shall be iD accordance with the following:, Quantity of Concrete in the, , Number ofSamples, , Work, m', , I· 5, 6 - IS, 16 - 30, 31 - 50, 51 and above, , 1, 2, 3, 4, , 4 plus one, additional sample, for each additional, 50 m' or part thereof, , NOm-At leost one sample shall be taken from each shift., Whereconcrete is produced at continuous production unit, such, as ready-mixed concrete plant,frequency of'sampling lnay be, agreeduponmutually by suppliers and purchasers., , 15.3 Test Specimen, , Three test specimens shall be made for each sample, , less 0.3 N/mm1•, 16.3 Quantity of Concrete Represented by, Strength Teat Results, , The quantity of concrete represented by a group of, four consecutive test results shall include the batches, from which .the first and last samples were taken, together with all intervening batches., For the individual test result requirements given in, col 2 of Table II or in item (b) of 16.2, only the, particular batchfromwhichthe samplewastakenshall, be at risk., Where the mean rate of sampling is not specified the, maximum quantity of concrete that four consecutive, test results represent shall be limited to 60 m'., 16.4 If the concreteis deemednot to complypersuant, to 16.3. the structural adequacy of the parts affected, shall be investigated (see 17) and any consequential, action as needed shall be taken., 29

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IS 456: 2000, 16.5 Concrete of each grade shall be assessed, separately., 16.6 Concrete is liable to be rejected if it is porous, or honey-combed. its placing has been interrupted, without providing a proper construction joint. the, reinforcement has been displaced beyond the, tolerances specified. or construction tolerances have, not been met. However. the hardened concrete, may be accepted after carrying out suitable, remedial measures to the satisfactionof the engineerin-charge., , e) there is a system to verify that the quality is, satisfactory in individual parts of the structure,, especiallythe critical ones., 17.2 Immediately after stripping the forrnwork, all, concreteshallbecarefully inspectedandanydefective, work or small defects either removed or made good, before concrete has thoroughly hardened., , 17.3 Testing, , 17 INSPECTION AND TESTING OF, STRU<"'""TURES, , In case of doubt regardingthe grade of concrete used,, either due to poor workmanship or basedon results of, cube strength tests, compressive strength tests of, concreteon the basisof 17.4 and/orloadtest (see 17.6), may be carried out., , 17.1 Inspection, , 17.4 Core Test, , To ensure that the construction complies with the, design an inspection procedure should be set up, covering materials, records. workmanship and, construction., 17.1.1 Tests should be made on reinforcement and, theconstituent materials ofconcretein accordance with, the relevant standards. Where applicable, use should, be made of suitable quality assuranceschemes., , 17.4.1 The points from which cores are to be taken, and the number of cores required shall be at the, discretion of the engineer-in-charge and shall be, representative of the whole of concrete concerned., In no case. however. shall fewer than three cores be, tested., 17.4.2 Cores shallbe preparedand tested asdescribed, in IS 516., , 17.1.2 Care should be taken to see that:, , 17.4.3 Concrete in the member represented by a core, , test shall be considered acceptable if the average, equivalent cube strengthof the cores isequal to at least, 85percentof thecubestrengthof the gradeof concrete, specifiedfor the correspondingage and no individual, core has a strengthless than 7S percent., , a) design and detail are capable of beingexecuted, to a suitable standard, with due allowance for, dimensional tolerances;, b) there are clear instructions on inspection, standards;, c) there are clear instructions on permissible, deviations;, d) clements critical to workmanship, structural, performance. durability and appearance are, identified; and, , 17.5 In case the core test results do not satisfy the, requirement.s of 17.4.3 or where such tests have not, been done, load test (17.6) may be resorted to., 17.6 Load Tests for Flexural Member, , 17.6.1 Load tests should be carried out as soon as, , Table 11 Characteristic Compressive Strength Compliance Requirement, (Claus~s, , Sp«lfted, , (;rade, , II), , M I~, , 16.1 and 16.3), , Mean of the Group of, , 4 Non-Onrlapplnl, , Individual Test, Results In N1mmJ, , Consecutive, nsf Results In NfmmJ, (2), , (3), , 4! 1... + 0.825 x established, , standarddeviation (rounded, off to neaJal 0.5 Nlmm1), , or, f.. +3NlmmJ., whicheveris greater, M 20, , or, above, , ~, , .f.., + 0.82S )( established, , ~, , f",~ N/mm1, , standarddeviation (rounded, off to nealat O.~ N/mmJ ), , or, L.. + 4 N/..mr. whichever, is~ter, , NOTE-In the absence of established valueof standard deviation. the valuesJiven in Table8 l114y be assumed.and llttempt shouldbe, l1llIde 10 obtain resultsof 30 samples lIS early lIS poasible to ambUsh die valueof standarddeviation., , 30

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IS 45(i : 200(), possible after expiry of 28 days from the lillie of placing, of concrete., , not, , apply., , 17.7 Members (1thcr Than Flexural Members, , 17.6.2 The structure should he subjected to a load equal, to full dead load of the structure plus 1.25 tillll'S the, imposed load tor a period of 24 h and then the unposed, load shall he removed,, , Memher-, other than flexural members should he, preferably investigated hy analysis., , NOTE--·-Dc:ad load includes self weight of the structural, members pili" weight of finishes and walls or partition». If any, ~l'\ considered in the design, ., , Non-destructive tests arc used to obtain estimation of, the properties of concrete in the structure. TIle methods, , 17.H Non-destructive Tests, , adopted include ultrasonic pulse velocity (sec IS J 33) I, (Pari I) J and rebound hammer [IS 13311 (Pari 2) L, pr n be pc net rat i()n, pull 0 utand mat lJ r i t y. Nondcstructi vc tests provide alternatives to core tests for, cstirnatiug the strength of concrete in a structure. or, , 17.6.3 The deflection due to iTJIPOSl~d load only shall, he recorded. If within 24 h of removal of the imposed, load. the structure docs not recover at least 75 percent, of the deflection under superimposed load, the test may, be repealed after a lapse of 72 h. If the rl~CO\'CI"y is Ics~, than XO percent . the structure shall be dc.eln~d 1o he, unacceptable., .7.()...l l Ir the maximum deflection in, during. 24 h under load, , i~, , less than, , 111111., , 4()/'~/1.)., , can xupplcmcut the data obtained 1'1"0111 a limited, n UIII her of cores. These methods art' based on, mcusur ing a concrete properly thaI bears sonic, rl~latic .nship to strength, The accuracy of these methods,, in part. is determined by the degree of correlation, h('l\\.'t'l'tl ~fn.. nc~th Hnd Ihe physical quality 1I1CtlSUrl,d, h) th~' nun destruct i vc texts., , shown, , where I is, , the effective span in m; and 1.), the overall depth of tlk', ~cclj()n in 111111, it i\ not ncccxs.n y fOI the teL·O\CI V 10, he measured and the recovery provi ,ion", of t 7.tl.~' ...,-hall, , Anv of th\..~"i~ mcthodx tna~' he .uloptcd. in which cusc the, cnll'ria ~h~lll he agreed upon prior to h'sling ., , ~H'n. 'I'I~IIH.'l", , 11

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IS 456: 1000, , SECTION 3 GENERAL DESIGN CONSIDERATION, be taken from Table 18 for the limit state of, collapse., , 18 BASES FOR DESIGN, 18.1 Aim of DesigD, , The aim of design is the achievementof an acceptable, probabilitythat structuresbeingdesignedwillperform, satisfactorily during their intended life. With an, appropriate degree of safety, they should sustain all, the loads and deformationsof normal construction and, use and have adequate durability and adequate, resistance to the effects of misuse and fire., 18.2 Methods of Design, , 18.2.1Structureand structuralelementsshall nonnally, be designed by Limit State Method. Account should, be taken of accepted theories, experiment and, experience and the need to design for durability., Calculations alonedo not producesafe,serviceable and, durable structures. Suitablematerials,qualitycontrol., adequate detailing and good supervision are equally, important., 18.2.2 Where the Limit State Method can not be, conveniently adopted, Working Stress Method (see, Annex B) may be used., , 18.3 DurabWty, Workmanship aDd ~terlall, It is assumed that the quality of concrete, steel and, other materials and of the workmanship, as verified, by inspections, is adequate fot safety. serviceability, and durability., , 18.4 DesllDProcess, Design. including design for durability, construction, and use in service should be considered as a whole., The realization of design objectives requires, compliance with clearly defined standards for, materials, production, workmanship and also, maintenance and use of structure in service., 19 LOADSAND'ORCES, 19.1 General, , In structural design, account shallbe taken of the dead., imposed and wind loads and forces such as those, caused by earthquake. and effects due to shrinkage,, creep, temperature, etc, where applicable., , 18.2.3Design Basedon Experimental Basis, Designs based on experimental investigations on, models or full size structure or element may be, accepted if they satisfy the primary requirements, of 18.1 and subject to experimental details and the, analysis connected therewith being approved by the, engineer-in-charge., , 18.2.3.1 Where .the design is based on experimental, investigation on full sizestructureor element,loadtests, shall be carried out to ensure the following:, a) The structure shall satisfy the requirements for, deflection (see 23.2) and cracking (see 35.3.2), when subjected to a load for 24 h equal to the, characteristic load multiplied by ) .33 Yr' where, "(rshall be taken fromTable 18,for thelimitstate, of serviceability. If within 24 h of the removal, of the load, the structure does not show a, recovery of at least 7S percent of the maximum, deflection shown during the24h under. the load,, the test loading should be repeated after a lapse, of 72 h.The recovery afterthe secondtestshould, beat least 7S percentof the maximumdeflection, shown during the second test., , 19.2 Dead Loads, Dead loads shall be calculated on the basis of unit, weights which shall be established takina into, considerationthe materialsspecifiedfor construction., 19.2.1Alternatively, the dead loads may becalculated, on the basis of unit weights of materials liven in, IS 875 (Part 1). Unless more accurate calculations are, warranted, the unit weights of plain concrete and, reinforced concrete made with sand and gravel or, crushed natural stone aggregate may be taken as, 24 kN/m:\ and 25 kN/m3 respectively., 19.3 Imposed Loads, WIndLoadsandSnow LoIds, , Imposed loads. wind loads and snow loads shall be, assumed in accordance with IS 87S (Part 2), IS 87S, (Part 3) and IS 875 (Part 4) respectively., 19.4 Earthquake Forces, The earthquake forces shall be calculated, accordance with IS 1893., , In, , 19.5 Shrlnkap, enep and Temperature Elfeets, If the effects of shrinkagc, creep and temperature are, liableto affectmaterially the safety andserviceability, of the structure. these shall be taken into account in, the calculations (see 6.2.4, 6.Z.5 and 6.2.6) and, IS 875(Part 5)., 19.5.1 In ordinarybuildinp, such• lowrisedwellinp, whose lateral dimension do Dot exceed 45 m, the, , NOTE-If the maximum deflection in mm, shown duriftl, 24 h under load is lessthan40 12/D where I is theeffectivespan, in m; and D is the overall depth of the section in rom, it i. not, necessary for the ~ to be measured., , b) The structure shall have adequate strenath to, sustainfor 24 h, a total load equal to the characteristic load multiplied by 1.331, where Y, shall, , 32

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IS 456: 2000, , effects due to temperature fluctuations and shrinkage, and creep can be ignored in design calculations., , 20.2 Sliding, , The structure shall have a factor against sliding of not, less than 1.4underthe most adverse combination of the, appliedcharacteristic forces. In thiscase only0.9 times, the characteristic dead load shall be taken into account., , 19.6 Other Forces and Effects, In addition, account shall be taken of the following, forces and effects if they are liable to affect materially, the safety and serviceability of the structure:, , 20.3 Probable Variation in Dead Load, , To ensure stability at all times, account shall be taken, of probable variations in dead loadduringconstruction,, repairor other temporarymeasures. Wind and seismic, loading shall be treated as imposed loading., , a) Foundation movement (see IS 1904),, b) Elastic axial shortening,, c) Soil and fluid pressures [see IS 875 (Part 5)],, , 20.4 Moment Connection, In designing the framework of a building provisions, shall be made by adequate moment connections or by, it system of bracings to effectively transmit all the, horizontal forces to the foundations., , d) Vibration,, , e) Fatigue., , o, , Impact [see IS 875 (Part 5)],, , g) Erection loads (see IS 875 (Part 2)], and, , h) Stressconcentrationeffect due to point loadand, the like., , 20.5 Lateral Sway, , LInder transient wind load the lateral sway at the top, should not exceed HI500, where 11 is the total height, of the building, For seismic loading, reference should, he made to IS J 893., , 19.7 Combination of Loads, , The combination of loads shall be as given in IS 875, (Part S)., , 21 FIRE RESISTANCE, , 19.8 Dead Load Counteracting Other Loads and, Fon:es, , 21.1 Astructure Of structural element required to have, fire resistance should be designed to possess an, appropriate degreeof resistanceto flame penetration;, heat transmission and failure. The fire resistance of a, structural clement is expressed in terms of time in hours, in accordance with IS 1641. Fire resistance of concrete, elements depends upon details of member size. cover, to steel reinforcement detailing and type of aggregate, (normal weight or light weight) used in concrete., General requirements for fire protection are given in, IS 1642., , When dead load counteracts the effects due to other, loads and forces in structural member or joint, special, care shall be exercised by the designer to ensure, adequate safety for possible stress reversal., 19.9 Deslgn Load, , Design load is the load to be taken for use in the, appropriate method of design; it is the characteristic, loadin case of workingstressmethodandcharacteristic, load with appropriate partial safety factors for limit, state design., , 21.2 Minimum requirements of concrete cover and, member dimensions for normal-weight aggregate, concrete members so its to have the required fire, resistance shall be in accordance with 26.4.3 and, Fig.l respectively., , 20 STABILITY OF THE STRlJCTlJRE, , ZO.1 Overturnina, The stability of a structure as a whole against, overturning shall be ensured so that the restoring, moment shan be not less than the sum of 1.2times the, maximumoverturning momentdue to thecharacteristic, dead load and 1.4 times the maximum overturning, moment due to the characteristic imposed loads. In, cases where dead load providesthe restoring moment,, only 0.9 times the characteristic dead load shall be, considered. Restoring moment due to imposed loads, shall be ignored., 20.1.1 The anchorages or counterweights provided, for overhanging members (during construction and, service) should be such that static equilibrium, should remain, even when overturning moment is, , 21.3 The reinforcement detailing should reflect the, changing pattern of the structural section and ensure, that both .individual clements and the structure as a, whole contain adequate support. tics, bonds and, anchoragesfor the required tire resistance.., , 21.3.1 Additionalmeasuressuch as application of fire, resistant finishes. provision of fire resistant false, ceilings and sacrificial steel in tensile zone, should he, adopted in case the nominal cover required exceeds, 40 mm for beams and 35 mm for slabs, to give, protection against spelling., 21.4 Specialist literature may be referred to for, determining fireresistance of the structureswhichhave, not been covered in Fig. 1 or Table 16A., , doubled., 2116 el5/07---6, , 33

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IS 456: 2000, , BEAMS, , -Pw~·, , SOLID SLAB, , RIB I WAFFEL SLAB, , SLABS, , ~, :, " ..:, ".. b, .t':, , ~ f, , ONE FACE EXPOSE, , -IbJ..., FULL V EXPOSED, COLUMNS, , --_....._. __......., , ------_._--, , -, , Column Dimension tb fir DJ, , Fire, Resis-, , MilJimum, , tllme, , ", 0.5, I, , 1.5, 2, 3, , 4, , Rib, Width, , Minimum, Thickness, , Width, b, , /11 Slabs, , bw, , ofFloors, D, , mm, , mill, , mID, , 200, 200, 200, , 125, 125, 12S, 125, , 75, , /team, , ZOO, 240, 280, , ISO, , 175, , 95, , 110, , 125, 150, 170, , ..., , ..., , ..., , Fully, Exposed, , 50%, , One, , EXPOliCd, , Face, Bxposed, , IIIID, , 111m, , mm, , 150, 200, 250, , m, 160, 2(X), , 140, , 175, , ~on, , 200, , 160, , 400, 450, , .100, , 200, 240, , 350, , -, , Minimum Wall Thicknt.u, , 1'<0.4%, , ...., , 04%sp.sl%, , 1'>1%, , mm, , mm, , tOO, , 150, , 120, , ISO, , 100, 120, 140, 160, 200, 240, , mm, 100, 100, 100, 100, 150, 180, , NOTES, 1 These minimum dimensions relatespecifically to the covers givenin Teble 16A., , :z p is the percentage of steel reinforcement., FlO. 1 MINIMUM DIMENSIONS OF REINFURCED CONCRE'1ll MEMBERS FOR FIRE RESiSTANCE, , 22 ANALYSIS, , 22.2 Effective Span, , 22.1 General, , Unless otherwise specified, the effective span of a, member shall be as follows:, a} Simply Supported Beam or Slab-The effective, spanof a member thatis notbuiltintegrally with, its supports shall be takenas clearspan plus the, effective depth ofslaborbeam or centre to centre, of supports. whichever is less., , All structures may be analyzed by the linear, clastic theory to calculate internal actions, produced by design loads. In lieu of rigorous elastic, analysis, a simplified analysis as given in 22.4 for, frames and as givenin 22.5forcontinuous beams may, be adopted., 34

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IS 456: 2000, , b) Continuous Beam or Slab - In the case of, continuous beam or slab. jf the width of the, support is less than 1/12 of the clear span, the, effective span shall be as in 22.2 (a). If the, supports are wider than 1/12 of the clear span, or 600 mm whichever is less, the effective span, shall be taken as under:, , 22.4.1 Arrangement oflmposed Load, a) Consideration may be limited to combinations, of:, , 1) Design dead load on all spans with full, design imposed load on two adjacent spans;, , and, 2) Design dead load on all spans with full, design imposed load on alternate spans., , 1) For end span with one end fixed and the, other continuous or for intermediate spans., the effective span shall be the clear span, between supports;, , b) When design imposed load does not exceed, three-fourths of the design dead toad, the load, arrangement may be designdead load and design, imposed load on all the spans., , 2) For end span with one end free and the other, continuous, the effective span shall be equal, to the clear span plus half the effectivedepth, of the beam or slab or the clear span plus, half the width of the discontinuous support,, whichever is less;, , NOTE ----. For beams and slabs continuous over support, 22.4.1Ca) rna)' be assumed,, , 22.4.2 Substitute Frame, , For determining the moments and shears at any floor, or roof level due to gravity loads, the beams at that, level together with columns above and below with their, far ends Ii xed may be considered to constitute the, frame., , 3) In the case of spans with roller or rocket, bearings. the effective span shall always he, the distance between the centres ofbearings., c) Cantilever- The effectivelengthof a cantilever, shall he taken as its length to the face of the, support plus half the effective depth except, where it forms the end of a continuous beam, where the length to the centre of support shall, be taken., , 22.4.2.1 Where side sway consideration becomes, , critical due to unsymmctry in geometry or loading,, rigorous analysis ITIay be required., , 22.4.3 For lateral loads, simplified methods may be, used to obtain the moments and shears for structures, that arc svmmetrical. For unsymmetrical or very tall, structures. more rigorous methods should be used., , d) Frames - In the analysis of a continuous Irarne,, centre to centre distance shall he used., 22.3 Stiffness, , 22.5 Moment and Shear Coefficientfi for, Continuous Beams, , 22.3.1 Relative Stiffness, , 22.5.1 Unless more exact estimates are made. for, beams of uni form cross-section which support, substantially uniformly distributed loads over three or, IlH ire :'\1 ',UlS which do notdiffer by more-than 15percent, of the longest, the bending moments and shear forces, used in design may be obtained using the coefficients, given in Table 1.2 and Table 13 respectively., , The relative stiffness of the members may be based on, the moment of inertia of the section determined on, the basis of anyone of the following definitions:, a) Gross section -, , The cross-section of the, , memberignoringreinforcement:, b) Transformed section - 'The concrete crosssection plus the area of rc intor ccmcrn, transformed on the basis of modular ratio (St'l', B-I.3); or, , For moments at supports where two unequal spans, meet or j n case where the spans are not equally loaded,, the average of ttlc two values for the negative moment, at the Stlppt ut may he taken for design., , c) Cracked section _.- The area of concrete in, compression plus the area of reinforcement, transformed on the basis of modular rutin., , Where coeflicients given in Table 12 are used for, calculationof bending moments,redistributionreferred, to in 22.7 shall not be permitted., , The assumptions made shall be consistent for (111 the, members of the structure throughout any analysis., , 22.5.2 Beamsand Slabs Over Free End Supports, Where a member is built into a masonry wall which, develops nnly partial restraint. the member shall be, designed to resist a negative moment at t.he face of the, support of W1/24 where W is the total design load, and l is the effective span, or such other restraining, moment as may be shown to he applicable, For such a, condition shear coefficient given in Table 13 at the, end support may be increased hy 0.05., , 22.3.2 For deflection calculations, appropriate values, of moment of inertia as specified in Annex C shGUIU, be used., 22.4 Structural Frames, , The simplifying assumptions as given in 22.4.1, to 22..4.3 may be used in the analysis of frames., 35

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IS 456 : 2000, , Table 11 Bending Moment Coefficients, (Clause 22.5.1), , .., , Type of Load, , Span Moments, ".", , Near Middle, of End Span, (1), , Dead load nodimposed, load (fixed), Imposed load (not, , ,, , t"t, , At Middle, of Interior, Span, , At Support, Next to the, End Support, , Supports, , (2), , (:l), , (4), , (5), , 1, +12, , I, +16, , 1, 10, , +-, , I, 12, , +-, , fixed), , Support Moments, , ,, , ;, , At Other, , Interior, , I, 10, , I, 12, , 1, 9, , 1, 9, , NOTE- For obtainingthe bendingmoment, the coefficient shall be multiplied by the total design load and effectivespan., , Table 13 Shear for Coefficients, iClauses 22.5.1 and 22.5.2), Type 01Load, , At End, Support, , At Support Next to the, End Support, , At AllOther, Interior Supports, , t"t, , &;ter Side, , InnerSide, , (2), , (3), , (4), , (~), , Dead loud and imposed, load (fixed), , 0.4, , 0.6, , 0.55, , 0.5, , Imposed load (not, , 0.45, , 0.6, , 0.6, , 0.6, , (I), , fixed), , NOTE- For obtainingthe shear force. the coefficientshall be multiplied by the total designload., , 22.6 Critical Sections for Moment and Shear, , 23 BEAMS, , 22.6.1 For monolithic construction, the moments, computed at the face of the supports shall be used in, the design of the members at those sections. For non.., monolithic construction thedesignof the membershall, be done keeping in view 22.2., , 23.0 Effective Depth, Effectivedepth of a beam is the distance between the, centroid of the area of tension reinforcement and the, maximum compression fibre, excluding the thickness, of finishing material not placed monolithically with, themember andthethickness of any concrete provided, to allow for wear. This will not apply to deep beams., , 22.6.2 Critical Section/or Shear, , The shears computed at the face of the support shall, be used in the design of the member at that section, except as in 22.6.2.1., , 23.1 T-Beams and L·Beams, 23.1.1 General, , 22.6.Z.1 When the reaction in the direction of the, applied shear introduces compression into the end, region of the member, sections located at a distance, Jess than d from the face of the support may be, designed for the same shear as that computed at, distance d (see Fig. 2)., , A slab which is assumed to act as a compression, flange of a T-beam or L-beam shall satisfy the, following:, a) The slab shall be cast integrally with the web,, or the web and the slab shall be effectively, bonded together in any other manner; and, b) If the main reinforcement of the slab is parallel, to the beam, transverse reinforcement shall be, provided as in Fig. 3; such reinforcement shall, not be less than 60 percent of the main, reinforcementat mid span of the slab., , N()TE-The above clauses are applicablefor beamsgenerally, carryinguniformly distributedloudor wherethe principal load, is located furtherthan "2d (ruin the face of the support., , 22.7 Redistribution of Moments, , Redistribution ofmoments may be done in accordance, with 37.1.1 for limit state method and in accordance, with8-1.2 forworking stressmethod. However, where, simplified analysis using coefficients is adopted,, redistribution of moments shall not be done., , 23.1.2 Effective Width of Flang,, , In the absence of more accurate determination. the, effective widthof flange may be takenas thefollowing, , 36

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IS 456: 2000, , d, , (0), , (b), , t, , FIG., , 2, , TYPICAL SUPPORT CONOmONS FOR LOCATING FACI'ORED SHEAR FORCE, , but in no case greater than the breadthof the webplus, halfthesumof thecleardistances to theadjacent beams, on either side., a) ForT-beams,h,, , =~ +b", + 6D,, , b) For L-beams, b,, , I, =~, + bw + 3 D,, 12, , structureor finishes or partitions. Thedeflectionshall, generally be limitedto the following:, a) The final deflection due to all loads including, the effects of temperature, creep and shrinkage, and measured from the as-cast level of the, supports of floors, roofs and all other horizontal, members, shouldnotnormally exceedspanl2S0., b) The deflection including the effects of, temperature, creepandshrinkage occurring after, erection of partitions and the application of, finishes should not normally exceed span/3S0, or 20 mm whichever is less., , c) For isolated beams, the effective flange width, , shallbe obtainedas belowbut in nocasegreater, than the actual width:, , T - beam,b, .~I)o + b.., .:JL, , b, , +4, , 23.2.1 The verticaldeflectionlimits may. generallybe, assumed to be satisfiedprovidedthat the spanto depth, ratiosare notgreater thanthe valuesobtainedas below:, a) Basic values of span to effective depth ratios, for spans up to 10m:, , · O.S In b, L - beam, b '=~+ w, ...!l. +4, b, , Cantilever, 7, Simplysupported, 20, Continuous, 26, b) For spans above 10 m, the values in (a) may be, multiplied by 10/span in metres, except for, cantileverin whichcase deflection calculations, should be made., c) Depending on the area and the stress of, steelfor tensionreinforcement, the valuesin (a), or (b) shall be modifiedby multiplying withthe, modification factor obtainedas per Fig. 4., d) Depending on the area of compression, reinforcement, the value of span to depth ratio, be further modified by multiplying with the, modification factor obtainedas per Fig. S., , where, , b,, , In, , =effective width of flange,, =distance betweenpoints of zero moments, , in the beam,, b", = breadth of the web,, , Dr, , =thickness of flange, and, , b = actual width of the flange., NOTE - Por continuous beams and frame., ",,' may be, assumed lUI 0.7 time.the effective span., , 23.2 Control of Defledlon, The deflection of • structure or part thereof shall not, adversely affect the appearance or efficiency of the, 37

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IS 456 : 2000, , BEAM, , I, , I, , I, , I, , I, , I, , T-+----+-+----+--I I, , Xl, , t--~-, , SECTION XX, FIG., , 3 TRANSVERSE REINFORCEMENT IN FLANGB OFT-BEAM WHEN MAIN REINFORCEMENT Of, SLABIS PARAIJ.EL TOTHE BEAM, , e) For flanged beams, the values of (a) or (b) be, modified as per Fig. 6 and the reinforcement, percentage foruseinFig.4 and 5 shouldbebased, , 2·0, \, , ',6, , \\ \ \, , \', , \, , ~, , NOTE-When deflections are required to be calculated, the, method given in Annex C may be used., , r-,, , ", , r-,, \ \ -, <, r-, I<,, ........, , \, , on area of sectionequal to b,d., , I'-..., , r-, <,, <,, , 10.",., , r---, , r----, , r-.... I"'--, , -.., ~, , ~, f•• '45, , r--r-- I-- f--..., , ~ I-..., f""90, fu240, h·290, , -, , ,, I, , Note: f. IS STEEL STRESS OF SERVICE, ,LOADS IN N/mm2, I, , o, , 0'4, , 0,', , ", , ',2, , 1'6, , 2·0, , 2", , PERCENTAGE TENSION REINFORCEMENT, , I. .0.58 f., •, , ArMof CI'OII' _tion ohteel required, ., AreaofCmll • aection of steel provided, , Flo. 4 MODIACATJON FAcroR FOR TENSION REINFORCEMENT, , 38, , 2'8 )0

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18456: 2000, , .-.-. ~, ~, , ~, , ~, , 100""", , ~, , L/ V, , V, , /, , ,/, 0-50, , '-00, , 1-50, , 2-00, , 2-50, , PERCENTAGE COMPRESSION REINFORCEMENT, FIG.5, , MOOIHCATION FACTOR FOR COMPRESSION REtNPoRCBMENT, , 1'100, , a:, , 1/, , 0095, , /, , e~ e-sc, , /", , &L, , z 0.85, , Q, , /, , t, , ~ 0·80, , a:, , 0·75, 0.70, , FIG., , 6, , /, , o, , 0'2 0'4 0·8 0'8 1·0, RATIO OF WEB WIDTH, TO FLANGE WIDTH, , REDUCTION FACTORS FOR RA'110S OF' SPAN TO EJ-rEcnVE DEPTH FOR FLANGED BEAMS, , NOTBS, 1 For slabsspanninl in two directions,the shorterof the two, spans should be used for calculating the span to etTective, depth ratios., 2 For two-wavslabsof shorter spans(up to 3.~ m) with mild, stoel reinforcement, the span to overall depth ratios given, below may generally be assumed 10 satisfy vertical, deflectionlimits for loading class up to 3 kN/mJ•, Simplysupportedslabs, 3S, Continuous slabs, 40, , 23.3 Slenderness Limit'! for Beams to Ensure, Lateral Stability, A simply supported or continuous beam shall be so, proportioned that the clear distance between the lateral, ., , restraints does not exceed 60 b Of, , 250b z, --, , d, , whichever, , is less, where d is the effective depth of the beam and, b the breadth of the compression face midway betwecn, the lateral restraints., , For highstn:ngthdefonned barsof smde Fe41~. the values, givenaboveshould be multiplied by 0.8., , For a cantilever, the clear distance from the free end, of the cantilever to the lateral restraint shall not, , 100b z, , exceed 25 b or _.d, , 24.2 Slabs Continuous Over Supports, Slabs spanning in one direction and continuous over, supports shall bedesigned according to the provisions, applicable to continuous beams., , whichever is less., , 24 SOLID SLABS, , 24.3, , 24.1 General, , S~~bs, , Monolithic with Supports, , Bendingmomentsin slabs (except flat slabs)constructed, monolithically with the supports shall becalculated by, takingsuch slabs either as continuous over supports and, , The provisions of 13.2 for beams apply to slabs, also., , 39

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IS 456: 2000, , capable of free rotation.or as membersof a continuous, framework with the supports, taking into account the, stiffness of such supports. If suchsupports are formed, due to beamswhichjustify fixityat the supportof slabs,, then the effects on the supporting beam, such as, the, bending of the web in the transverse direction of the, hewn and the torsionin the longitudinal direction of the, beam. whereverapplicable, shall also be consideredin, the design of the beam., , c) For two or more loads not in a line in the, direction of thespan. if theeffective width of, slabfor one load does notoverlapthe effective, width of slab for anotherload, both calculated, as in (a) above,thenthe slab for each loadcan, be designedseparately. If the effectivewidth, ofslabforoneload overlaps theeffective width, of slab for an adjacent load, the overlapping, portion of the slab shall be designed for the, combined effectof the twoloads., , 24.3.1 For the purpose of calculation of moments in, slabs in a monolithic structure, it will generally be, sufficiently accurateto assumethatmembersconnected, to the ends of such slabs are fixed in position and, direction at the ends remote from their connections, with the slabs., , Table14Values 01 k for Sbnply Supported and, Continuous Slabs, (Clause 24.3.2.1), , 24.3.1 Slabs Carrying ConcentratedLoad, , O.S, , 0.6, 0.7, 0.8, 0.9, 1.0 and above, , ber, , where, ber, , lef, , where, effective width of slab,, , =, , distance of the centroid of the, concentrated load from nearer support,, , Ir f, , =, , effective span, and, , a, , = width of the contact area of the, , 2.16, 2.24, , = 1.2a, , l, , +a, , ill, , = effective width,, =distance of the concentrated load from the, , a, , = widt.h of contact area of the concentrated, , face of the cantilever support, and, , = constant havingthe valuesgiven inTable, 14depending upon the ratio of the width, of the slab (/~ to the effective span Ie{ ,, , x, , 0.4, 0.8, 1.16, 1.48, 1.72, 1.96, 2.12, 2.24, 2.36, 2.48, , d) For cantilever solid slabs, the effective width, shall he calculated in accordance with the, following equation:, , ber = kx (1- ..!..)+ a, k, , 51••, 0.4, 0.8, 1.16, 1.44, 1.68, 1.84., 1.96, 2.08, , 0.1, , a) For a single concentrated load. the effective, width shall be calculated in accordance with the, following equation provided that it shall not, exceed the actual width of the slab:, , =, , i lor CoatlDUQUI, , 0.2, 0.3, 0.4, , 24.3.2.1 If a solidslab supportedon twooppositeedges,, carries concentrated loads the maximum bending, moment caused by the concentrated loads shall be, assumed to be resisted by an effective width of slab, (measured parallel to the supportingedges) as follows:, , bd, , i lorSlmpl,, Supported S...., , load measured parallel to the supporting, edge., , Provided that the effective widthof the cantilever, slab shall not exceed one-third the length of the, cantilever slabmeasured parallel to thefixededge., Andprovidedfurtherthat when theconcentrated, loadisplaced neartheextreme endsof the length, of cantilever slab in the direction parallel to the, fixed edge. the effective width shall not exceed, the above value, nor shall it exceed half the, above valueplus thedistanceof the concentrated, load from the extreme end measured in the, direction parallel to the fixed edge., ., , concentrated load from nearer support, measured parallel to the supportededge., And provided further that in case of a load near, the unsupported edge of a slab. the effective, width shall not exceed the above value nor half, the above valueplusthedistance oftheload from, the unsupported edge., , 24.3.2.2 For slabs other than solid slabs, the effective, width shall depend on the ratio of the transverse and, longitudinal flexural rigidities of the slab. Where this, ratio is one, that is, where the transverse and, longitudinal flexural rigidities arc approximately, equal, the value of effective width as found for solid, slabs may be -used. But as the ratio decreases,, proportionately smaller value shall he taken., , b) For two or more concentrated loads placed in a, line in the direction of the span, the bending, moment per metre width of slab shall be, calculated separately for each load according to, its appropriate effective width of slab calculated, as in (a) above and added together for design, calculations., , 40

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IS 456: 2000, signs),the total should be equal to that from (a)., If the resulting support moments are significantly greaterthan the value from Table 26, the, tension steel over the supports will need to be, extended further. The procedure should be as, follows:, 1) Takethe spanmomentas parabolic between, supports: its maximum value is as found, from (d)., 2) Determine the points of contraflexure of the, new support moments [from (c)] with the, span moment [from (1)]., 3) Extendhalfthesupporttensionsteelat each, end to at least an effective depth or 12 bar, diameters beyond the nearest point of, contraflexure., 4) Extend the full area of the support tension, steel at each end to half the distance from, , 24.3.2.3 Any other recognizedmethodof analysisfor, Casel of Ilaba covered by 24.3.%.1 and 24.3.2.2 and, fot all othet ~ase8 of slabs may be used with the, approvai Of aM engineer*in-charge., 24.3.2.4 The critidil Medon for checking shear shall, be as Jiven in 34.2.4.1., 24.4 Slabs SpaDllinllD two Directions at Rllbt, , ADII_, , The slabs spanning in two directions at right angles, and carryinS uniformly distributed load may be, desilned by any acceptable theory or by usina, coefficients liven in Annex D. For determining, bending moments in slabs spanningin two directions, at right anales and carrying coaeentrered load, any, accepted method approved by the engineer-In-charge, may be adopted., NOTS-The IDOII commonly UJed elastic methods are based, on Apaud', or Wester-pard', theoryandthe most commonly, uled limitItaJe of coUapse methodis basedonJohansen's yieldline theory., , (3)., , 24.5 Loads on SuPportiDI Beams, , 14.4.1 Restrained Slab with Unequal Conditions at, Adjacent Pan,I,, , The loads on beams supporting solid slabs spanning, in two directions at right angles and supporting, uniformly distributed loads, may be assumed to be in, accordance with Fig. 7., , In some cases the support moments calculated from, , Table 26 for adjacent panels may differ significantly., The following procedure may be adopted to adjust, them:, a) Calculate the sum of moments at midspan and, IUpports (nea1ecting signs)., b) treat the values from Table 26 as fixed end, m<mieDts., c) According tCJ the relative stiffness of adjacent, spans, distribute the fixed end moments across, the supports, living new support moments., d) Adjult midspanmomentsuch that, whenadded, to the support moments from (c) (neglecting, , 25 COMPRESSION MEMBERS, , 25.1 Definitions, 25.1.1Columnor strut is a compressionmember, the, effective lengthof whichexceeds three times the least, lateral dimension., , 25.1.2 Shortand SlenderCompression Members, A compression member may be considered as short, , Dand hb, , · I, when both the slenderncb; ~o., , than 12:, , A, , LOAD IN THIS SHADED, , AREA TO BE CARRIED, , 8V BEAM 'e', LOAD IN THIS SHADED AREA, TO BE CARRIED BY BEAN '//, FlO., , 2116 818/07-1, , 7, , LOAD, , C ARRJIID BY SUPPORTING BEAMS, , 41, , B, , are less

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IS 456 : 2000, where, , 1 =, M, , effective length in respect of the major, , where, b, , axis,, D ==, Iry -, , b, , =, , D, , depth in respect of the major axis,, , effective length in respect of the minor, axis, and, width of the member,, , =, =, , width-of that cross-section, and, depthof the cross-section measuredin the, plane under consideration., , 25.4 Minimum Eccentricity, , All columns shall be designed for mmrmum, eccentricity, equalto theunsupported length of column!, compression member,, 500 plus lateral dimensions/30, subject to a minimum, of 20 rom. Where bi-axialbending is considered,it is, 25.1.3 Unsupported Length, sufficient to ensure that eccentricity exceeds the, The unsupported length, I, of a compression member ., minimum about one axis at a time., shall he taken as the clear distance between end, It shall otherwise be considered as a slender, , restraints except that:, a) in flat slab construction, it shall be clear distance, between the floor and the lower extremity of, the capital, the drop panel or slab whichever is, the least., , h) in beam and slab construction, it shall be the, clear distance between the floor and the, , underside of the shallower beam framing into, the columns in each direction at the next higher, floor level., c) in columns restrained laterally by struts, it shall, be the clear distance between consecutive, struts in each vertical plane, provided that to be, an adequate support, two such struts shall, meet the columns at approximately the same, level and the angle between vertical planes, through the struts shall not vary more than 3Qt', from a right angle. Such struts shall be of, adequate dimensions and shall have sufficient, anchorage to restrain the member against lateral, deflection., , 26 REQUIREMENTS GOVERNING, , REINFORCEMENT AND DETAILING, 26.1 General, Reinforcing steelof same type and grade shall be used, as main reinforcement in a structural member., However. simultaneous use of two different types or, grades of steel for main and secondary reinforcement, respectively is permissible., 26.1.1 Bars may be arranged singly. or in pairs in, contact, or in groups of three or four bars bundled in, contact. Bundledbars shall be enclosedwithin stirrups, or ties. Bundled bars shall be tied together to ensure, the bars remaining together. Bars larger than 32 mm, diameter shall not be bundled. except in columns., 26.1.2 The recommendations for detailing for, earthquake-resistant construction given in IS 13920, should be taken into consideration, where applicable, (see also IS 4326)., , 26.2 Development of Stress in Reinforcement, , The calculated tension or compression in any bar at, any section shall be developed on each side of the, section by an appropriate development length or end, anchorage or by a combination thereof., , d) in columns restrained laterally by struts or, , beams, with brackets used at the junction, it shall, be the clear distance between the floor and the, lower edge of the bracket, provided that the, bracket width equals that of the beam strut and, is at least half that of the colurnn., , 26.2.1 Development Length ofBars, The development length Ld is given by, , ,a., , 25.2 Effective Length of Compression Members, , _, L( 1 - - -, , In the absence of more exact analysis, the effective, length ler' of columns may be obtained as described in, Annex E., , 4fbd, , where, , , = nominaldiameter of the bar,, , 25.3 Slenderness Limits for Columns, , a ~ =stressin bar at the sectionconsideredat design, , 25.3.1 The unsupported length between end restraints, shall not exceed 60 times the least lateral dimension, of a column., , load, and, , t hd, , = design bond stress given in 26.Z.1.1., , NOTES, 1 The development IcnJlhincludca anchomae vDlues of hooks, in tension reinforcement., 2 For bars of sections other than cireular. the development, lenathshould be sufficient to develop the stras in the bar, by bone", , 25.3.2 If, in any given plane, one end of a column is, unrestrained, its unsupported length, it shall not exceed, JOOb 2, , ---', [), , 0°', , ...",,:, , ..... 'lI, , I,, :i, , 42, , .c., .;.

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IS 456: 2000, 16.2.1.1 Design bond stress in limit state method for plain bars in tension shall be as below:, , Grade ofconcrete, , M20, , M25, , M30, , M35, , Design bondstreSJ,, f hd, N/mm2, , 1.2, , 1.4, , 1.5, , 1.7, , M 40 and above, , 1.9, , For deformed bars conforming to IS 1786these values, shall be increased by 60 percent., , 2) In the compression zone, front the mid depth, , For bars in compression. the values of bond stress for, bars in tension shall be increased by 25 percent., , b) Stirrups-Notwithstanding any of the, provisions of this standard, in case of secondary, reintorcement, such as stirrups and transverse, ties, complete development lengths and, anchorage shall be deemed to have been, provided when the bar is bent through an angle, , The values of bond stress in working stress design,, are given in B-2.1., , 26.2.1.2 Bars bundled ;11 contact, , of the beam., , of at least 90" round a bar of at least its own, diameter and is continued beyond the end of the, curve for a length of at least eight diameters, or, when the bar is bent through an angle of 135, and is continued beyond the end of the curve, for a length of at least six bar diameters or when, the bar is bent through an angle of 1HO° and is, , The development length of each bar of bundled bars, shall be that for the individual bar, increased by )0, percent for two bars in contact, 20 percent for three, bars·in contact and 33 percent for four bars in contact., , 0, , 26.2.2 Anchoring ReinforcingBars, 26.2.2.1 Anchoring bars in tension, a) Deformed bars may be used without end, anchorages provided development length, requirement is satisfied. Hooks should normally, he provided for plain bars in tension., b) Bends and hooks conform to IS 2502, , Bends and hooks shall, , J) Bends-The anchorage value of bend shall, , be taken as 4 times the diameter of the bar, for each 45 bend subject to a maximum of, 16 times the diameter of the bar., 2) Hooks-The anchorage value of a standard, U-type hook shall be equal to J6 times the, diamet.er of the bar., , continued beyond the end of the curve for a, length of at least four bar diameters., , 26.2.2.5 Bearing stresses at bends, The hearing stress in concrete for bends and hooks, describedin IS 2502 need not be checked. The bearing, stress inside a bend in any other bend shall be calculated, as given below:, , t, , ', , Bearing stress, , =, , Fht, rei>, , where, }/'ol, , =:, , tensile force due to design loads in a bar, or group of hal's,, , 26.2.2.2 Anchoring bars in compression, , ,. = internal radius of the bend, and, , The anchorage length of straight bar in compression, shall be equal to the development length of bars in, compression as specified in 26.2..1. The projected, length of hooks, bends and straight lengths beyond, bends if provided for a bar in compression, shall only, be considered for development length., , ¢ = size of the bar or, in bundle. the size of har, of equivalent area., , 16.2.2.3 Mechanical devices [or anchorage, , Any mechanical or other device capable of developing, the strengthof the bar without damage to concrete may, be used as anchorage with the approvalof the engineerin-charge., 26.2.2.4 Anchoring shear reinforcement, , a) Inclined bars - The development length shan, be as for bars in tension; this length shall be, measured as under:, 1) In tension zone, from the end of the sloping, Of inclined portion of the bar, and, , For limit stale method of design, this stress shall not, , exceed, , I .5f~k, 1+2~/a, , W, , tiere r.+', h h, .., k IS t e. c aractensuc cube, C·, , strength of concrete and a, for a particular bur or group, of hars in contact shall he taken as the centre to centre, distance between bars or groups of bars perpendicular, to the plane of the bend; for a bar Of group of, bars adjacent to the face of the member a shall he, taken as the cover plus size of bar ( q». For working, 'stress method of design. the bearing stress shall, , not exceed, , --~., J+2c/J/a, , 26.2.2.6 If a change in direction of tension or, compression reinforcement induces a resultant force, acting outward tending to split the concrete, such force

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IS456:~, , suchas increasing the lengthof lapand/oruSlnS spirals, or closely-spaced stirrups around the length of the, splice., , -.u.l Lap ,plie", a) Lapsplicesshall not beusedforbars larger than', 36 rom; for larger diameters, bars may be, welded (see 12.4); in cases where welding is, not practicable, lapping of bars larger than, 36 mm may be permitted, in which case, additional spiralsshouldbe provided around the, lapped bars., b) Lap splices shall be considered as staggered if, the centre to centre distance of the splices is, not Jess than 1.3timesthe laplength calculated, as described in (e)., c) Lap lengthincluding anchorage valueof hooks, for bars in flexural tension shall be Ld tse«, 26.2.1) or 30(/) whichever is greater, and for direct tension shall be 2Ld or 30~, whicheveris greater. The straightlengthof the, lap shall not be Jess than IS, or 200 mm. The, following provisions shall also apply:, Wherelap occurs for a tension bar located at:, I) top of a section 8S cast and the minimum cover, is less than twice the diameter of the lapped, bar,the lap length shall be increased by a factor, of 1.4., 2) comer of a section and the minimum cover to, either face is less than twice the diameter of, the lapped bar or where the clear distance, between adjacent laps is less than 7S mm or 6, times the diameter of lappedbar. whichever is, greater, the lap lengthshould be increased by a, factor of ).4.', Where both condition (1) and (2) apply. the lap, length should be increased by a factor of 2.0., ., , NOTE-Splices ia tension members shall be enclosed in, spirals madeof bon DOl lessthan6 mmdiameter withpitch, not lnofe than 100mm., , d) The lap lengthin compression shan be equal to, the development length in compression,, calculated as described in ~.1.1. but not less, than 24~., e) When bars of two differentdiameters are to be, spliced, the lap le"gth shall be calculated on, the basis of diameter of the smallerbar., t) When splicing of welded wire fabric is to be, carried out, lap splices of wires shall be made, so that overlap measured between the extreme, cross wires shall be not less than thespacingof, pross wires plus 100 mm,, _> In case of b"ndlod bars, lapped splices of, l1""dtcd ban shall bemade by splicingone bar, , at a time; suchindividual spliceswithina bundle, shall be staggered., , 16.1.5.2 Strength o/welds, The following values may be used where the strength, of the we1d has been proYed by tests to be at least as, , great 1$ d1~ of tho parent bar. .', a) Splices' in compression - For welded splices, and mechanical connection, 100 percent of the, desis" strength of joined bars., b) Splices in tension, I) 80 percent of the design strength of welded, , bars (100 percent if welding is Itrictly, supervised and if at any cross...aectionof the, member not more than 20 percent of the, tensile reinf(lr~tnent is welded)., , 2) \00, , pcf~nt, , of design strength of mecha-, , nical connection., 16.2.5.3 End-bearing splices, End-hearing splices shall be used only for bars in, compression. The ends of the bars shall be square cut, and concentric bearing ensured by suitable devices., 16.3 Spacinl of Relnloreenaent, 26.3.1 For the purposeof this ~I.-"se. the diametor of, round bar shall be its, diamoto" and in the, case of bars w~ich ~ro no, round or in tho case of, deformed bars or crimpod ~It tho diamoter shall be, taken as the <l,,,~etef of a oifcle .ivinJ an equivalent, effecti ve arcs". Whero Ipacin. limitations and, minimum CO"QfOtc cover (I" Z6A) are bued on bar, diameter. a group of ban bundled in contact shall be, treated as a linslo bar of diameter derived from the, , a, , n011\"'", , total ~quiY_'enl aroa., J6.3.1 Minimum Distance Between IndividUfJI Bars, The followi"g shall apply for .pacinl of ban:, a) The _orizontal distance between two parallel, main'reinforcinl bars shall usually be not less, thantho lreato., of tho foUowina:, , I), , ll-" di..meter of tho bar if the diameteR are, e4l~alt, , 2) Th~ diameter of the larler bar if the, diamolCrs are unoqual. and, 3) S 111m moro than tho nominal maximum size, , of ~p~ _IPlalO., ~OTB-This does not, , preclude the use orllllpr size of, D.I",.itel beyond the conceated reinfon:ement in the, lAme member; lhe aize of ,"relates ,nay be naduoocl, Ground con,clted reinforcement tQ comply with thil, provision., , b) Qreater horizontal distance than tho minimum, specified in (a) should be prov~dod wherevor, possible. However when needle vibrators aro, , 45

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IS 456 : 2000, used the horizontal distance between bars of a, group may be reduced to two-thirds the, nominal maximum size of the coarse aggregate,, provided that sufficient space is left between, groups of bars to enable the vibrator to be, immersed., , c) Where there arc two or more rows of bars, the, bursshall he vertically in line and the minimum, vertical distance between the bars shall be, 15 mrn, two-thirds the nominal maximum size, of aggregate or the maximum size of bars,, whichever is greater., , 26.3.3 Maxi/nun, Distance Between Bars in Tension, Unless the calculation of crack widths shows that a, greater spacing is acceptable, the followingrules shall, he applied to flexural members in normal internal or, external conditions of exposure., a) Beams - The horizontal distance between, parallel reinforcement bars, or groups, ncar the, tension face of a beam shall not be greater, than the value given in Table 15 depending on, the amount of redistribution carried out in, analysis and the characteristic strength of the, reinIorcement., b) Slabs, , 1) The horizontal distance between parallel main, reinforcement barsshallnotbemore thanthree, times the effective depth of solid slab or, 300 IntTI whichever is smaller., 2) The horizontal distance between parallel, reinforcement bars provided against, shrinkage and temperatureshall not be more, than five times the effective depth of a solid, slab or 450 mm whichever is smaIJer., , 26.4 Nominal Cover to Reinforcement, , 26.4.1 Nominal Cover, Nominal cover is the design depth of concrete cover, to all steel reinforcements, including links. It is the, dimension usedindesignand indicatedin the drawings., It shall be not less than the diameter of the bar., , 26.4.2 Nominal Coverto MeetDurability Requirement, Minimum values for the nominal cover of normalweight aggregate concrete which should be provided, to all reinforcement, including links depending on the, condition of exposure described in 8.2.3 shall be as, given in Table 16., 26.4.2.1 However for a longitudinal reinforcing, bar in a column nominal cover shall in any case not, be less than 40 mm, or less than the diameter of, such bar. In the case of columns of minimum, dimension of 200 mm or under,whose reinforcing bars, do not exceed 12mm, a nominal cover of 25 mm may, be used., 26.4.2.2 For footings minimumcover shall be 50 mm., , 26.4.3 Nominal Cover to Meet Specified Period of, Fire Re..sistance, Minimum values of nominal cover of normal-weight, aggregateconcrete to be provided to all reinforcement, including links to meet specified period of fire, resistance shall be given in Table 16A., 26.5 Requirements of Reinforcement for, Structural Members, , 26.5.1 Beams, 26.5.1.1 Tension reinforcement, , a) Minimum reinforcement-The minimum areaof, tensionreinforcementshall be not less than that, ...., , Table 15 Clear Distance Between Bars, tCtause 26.3.3), , f)., , Percentage Redistribution to or from Section Considered, -10, , 0, , - 15, , +I~, , +30, , Clear Distance Between Ban, NIJnln2, , nun, , mm, , mm, , mm, , mm, , 2~(), , 215, , 260, , 300, , 300, , 300, , 415, , 12~, , 15~, , 180, , 210, , 235, , 500, , 105, , 130, , 150, , 17S, , 195, , N()TE - The spacingsgiven in the tableare not applicable to members subjectedto particularly agressive environmentsunlessin the, calculation of'themoment of resistance, I., hasbeenlimited to300N/mm2 inlimitstartdesian ond alii limited to 16' N/mm2 in workin,, stress design., , 46

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IS 456: 2000, Table 16 Nominal Cover to Meet Durability Requirements, iClause26.4.2), Exposure, , Nominal Cencrete Cover In mm not Leu Than, , Mild, , 20, , Moderate, , 30, , Severe, , 45, , Very severe, , 50, , Extreme, , 75, , NOTES, 1 For main reinforcementup to 121nnldiameter bar for nliJd exposure the nominalcover may be reduced by 5 mm., 2 Unless specifiedotherwise. actual concretecover should not deviate from the requirednominalcover by + I 0 mm, , o, , 3 For exposurecondition'severe' and 'very severe'. reduction of 5 mm Inf:lY he made.whereconcretegrade is M35 and above., , Table 16A, , Nominal Cover to Meet Specified Period of Fire Resistance, iClauses 21.4 and 26.4.3 and Fig. I), , ..., , Fire, , Resis-, , Nominal Cover, , Beams, , tance, , Ribs, , Slabs, , Columns, , Simply, supported, , Continuous, , Simply, supported, , Continuous, , Simply, supported, , Continuous, , mm, , mm, , nun, , rnrn, , mm, , mm, , o.s, , 20, , 20, , 20, , 20, , 20, , min, 20, , I, , 20, , 20, , 20, , 20, , 20, , 20, , 40, , h, , 40, , 1.5, , 20, , 20, , 25, , 20, , ~, , 20, , 40, , 2, , ~, , 30, , .:u, , 25, , 4S, , J.1, , 40, , 3, , 60, 70, , ~, , .ll, , 5S, 65, , 45, 55, , 40, 40, , 4, , 50, , 45, 55, , 45, , NOTES, 1 The nominal covers liven relate specificallyto the minimummemberdimensionsgiven in Fig. I., 2 Casesthatlie below tbe boldlinerequireattention to the additional measures necessary to reducetherisksof spallingisee 21.3.1)., , given by the following:, ~ = 0.85, , fy, , bd, , A., , = minimum area of tension reinforcement,, = breadthof beamor the breadthof the web, of 'f-beam., , d, , f,, , Wherethedepthof the web in a beamexceeds750 mm,, sidefacereinforcement shall be providedalongthe two, faces. The total area of such reinforcement shall be not, less than 0.1 percent of the web area and shall be, , where, , b, , 26.5.1.3 Side face reinforcement, , = effective depth, and, = characteristic strengthof reinforcement in, N/mm2•, , b) Maximum, , reinfo~eme",- The maximum, , area of, tension reinforcement shall not exceed 0.04 bD., , distributed equally on two faces at a spacing, not exceeding 300 111m or web thickness whichever is, less., , 26.5.1.4 Transverse reinforcement in beamsfor shear, and torsion, The transverse reinforcement in beams shall be taken, around the outer-most tension and compression bars., , "In T-beams and f-beams, such reinforcement shall pass, aroundlongitudinal barslocatedclose to the outer face, of the flange., , 26.5.1.2 Compression reinforcement, , 26.5.1.5 Maximum spacing ofshear reinforcement, , The maximum area of compression reinforcement, shall not exceed 0.04 bD. Compression reinforcement, in beams shall be enclosed by stirrups for effective, lateral restraint. The arrangementof stirrups shall be, , The maximum spacing of shear reinforcement, measured alongtheaxisof the membershallnotexceed, 0.75 d for vertical stirrups and d for inclined stirrups, at 45'\ where d is the effective depth of the section, , as specified in 26.5.3.2., , 47

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IS 456: 2000, NOTE - Pedestal is a compreuion member. the effective, lenlthof which does notexceed three time.theleast lateral, , reinforcement need not. however, exceed, 20 mm (see Fig. 11)., , dimension., , c) Pitch anddiameter of laura;tits, , 26.5.3.2 Transverse reinforcement, a) General-A reinforced concrete compression, , J) Pitch-The pitch of transverse reinforce-, , mentshall be not more than the least of the, following distances:, , member shall have transverse or helical, reinforcement so disposed that every longitudinal bar nearest to the compression face, has effective lateral support against buckling, subjectto provisions in (b). Theeffective lateral, support is given by transverse reinforcement, either in the fonn of circular rings capable of, taking up circumferential tension or by, polygonal links(lateral ties)withinternal angles, not exceeding 13.50 • The ends of the transverse, reinforcement shall be properly anchored, [see 26.2.2.4 (b)]., b), , The least lateral dimension of the, compression members;, ii) Sixteen times the smallest diameterof, thelongitudinal reinforcement bar to be, tied: and, iii) 300 mm., i), , 2) Diameter-The diameter of the polygonal, links or lateral tiesshall be notlessthanonefourth of the diameter of the largest, longitudinal bar. and in no case less than, , Arrangement of transverse reinforcement, , 16mm., , 1) If the longitudinal bars are not spaced more, , than 75 mm on either side. transverse, reinforcement needonlyto go roundcorner, and alternate bars for the purpose of, providing effective lateral supports, (set Fig. 8)., 2) If the longitudinal bars spaced at a distance, of not exceeding 48 times the diameter of, the tie are effectively tiedin twodirections., additional longitudinal barsinbetween these, barsneedto be tiedin onedirection by open, ', ties (see Fig. 9)., 3) Where the longitudinal reinforcing bars in, a compression member are placedin more, thanonerow, effective lateral support to the, longitudinal bars in the inner rows may be, assumed to have been provided if:, i) transverse reinforcement is provided for, the outer-most row in accordance with, 26.5.3.2, and, , 1) Pitch-Helical reinforcement shall be of, regular formation with the turnsof the helix, spaced evenly and its endsshall be anchored, properly by providing one and a half extra, turns of the spiral bar. Where an increased, load on the column on the strength of the, helical reinforcement isallowed for, thepitch, of helical turnsshall benotmore than75mm,, normorethanone-sixth of thecorediameter, of thecolumn. norless than2.5 mm, norless, thanthreetimesthediameter of the steelbar, forming the helix. .In other cases, the, requirements of 26.5.3.2 shall be complied, with., 2) The diameter of the helical reinforcement, shall be in accordance with 26.5.3.2(c) (2)., 26.5.3.3 Incolumns where longitudinal barsareoffset, at a splice, the slopeof the inclined portion of the bar, with the axis of the column shall not exceed 1 in 6., and the portionsof the bar aboveand belowthe offset, shall be parallel to the axis of the column. Adequate, horizontal support at the offset bends shall be treated, as a matterof design. and shall be provided by metal, ties, spirals. or parts of the floorconstruction. Metal, ties or spirals so designed shall be placed near (not, morethaneight-bar diameters from) the pointof bend., The horizontal thrust to be resisted shall be assumed, as one and half times the horizontal components of, the nominal stress in the inclined portion of the bar., Offsetbarsshall be bentbefore they are placedin the, forms, Where column faces areoffset75mmormore,, splices of vertical barsadjacent to theoffsetfaceshall, be made by separate dowels overlapped as specified, in 26.2.5.1., , ii) no bar of the inner row is closer to the, , nearest compression face than three, times the diameter of the largest bar in, the inner row (see Fig. 10)., 4) Where the longitudinal bars in a compression member are grouped (not in, contact) andeachgroup adequately tiedwith, transverse reinforcement inaccordance with, 26.5.3.2, thetransverse reinforcement for the, compression member as a whole may be, provided on the assumption thateachgroup, is a single longitudinal bar for purpose of, determining the pitch and diameter of the, transverse reinforcement inaccordance with, , 26.5.3.2. The diameter of such transverse, , 2116 BIS/07-8, , d) Helical reinforcement, , 49

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IS 456 : 2000, , 27.1 Structures in which marked changes in plan, dimensions take place abruptly shall beprovided with, expansion onjointsat thesection where such changes, occur. Expansion joints shall be so provided that the, necessary movement occurs with a minimum, resistance at the joint. The structures adjacent to the, joint should preferably be supported on separate, columns or walls but not necessarily on separate, foundations. Reinforcement shall not extend across, anexpansion jointand thebreak between thesections, shall be complete.', , 27.2 The details as to the lenith of a structure where, expansion joints have to beprovided canbe detennined, after taking into consideration various factors. such as, temperature, exposure toweather. thetime andseason, ofthelaying of the concrete. etc. Normally structures, exceeding 45 m in lenith are designed with one or, more expansion joints. However in view of the large, number of factors involved in deciding the location., spacing and nature of expansion joints. the provision, of expansion joint in reinforced cement concrete, structures should be left to the discretion of the, designer. IS 3414 gives the design considerations,, wJtich need to be examined and provided for., , Alldimensions In millimetres., , Alldimensions Inmlllimetres., , Flo. 8, , Flo. 9, , 27 EXPANSION JOINTS, , TRANSVERSE REINFORCEMENT, , ..., '", , 1\\, , 'ND'VIDUAL GROUPS, Alldimensions in millimetres., FIG., , FrG. 11, , 10, , 50

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IS 456: 2000, , SECTION 4 SPECIALDESIGN REQUIREMENTS FOR STRUCTURAL, MEMBERS AND. SYSTEMS, 28 CONCRETE CORBELS, , 28.2.4 Resistanceto Applied Horizontal Force, , 28.1 General, , Additional reinforcement connected to the supported, member should be provided to transmit this force in, its entirety., , A corbel is a short cantileverprojectionwhichsupports, a load bearing member and where:, , 29 DEEP BEAMS, , a) . the distance av between the line of the reaction, to the supported load and the root of the corbel, is less than d (the effective depth of the root of, the corbel); and, , 29.1 General, , a) A beamshall be deemedto bea deep beam when, , b) the depth at the outer edge of the contact area, of the supported load is not less than one-half, of the depth at the root of the corbel., , the ratio of effective span to overall depth., , ~, , is less than:, 1) 2.0 for a simply supported beam; and, , The depth of the corbel at the face of the support is, determined in accordance with 40.5.1., , 2) 2.5 for a continuous beam., b) A deep beam complying with the requirements, of 29.2 and 29.3 shall be deemed to satisfy the, provisions for shear., , 28.2 Design, , 28.2.1 Simplifying Assumptions, The concrete "and reinforcement may be assumed to, act as elements of a simple strut-and-tie system, with, the following guidelines:, , 29.2 Lever Arm, , The lever arm z for a deep beam shall be detemined a~, below:, , a) The magnitude of the resistance provided to, horizontalforce shouldbe not less than one-half, of the design vertical load on the corbel, (see also 28.2.4)., , a) For simply supported beauts:, , z, , b) Compatibility of strains between the strut-and.., tie at the corbel foot should be ensured., , = 0.2 (I + 2D), , when I, , ~, , I, , -, , D, , ~, , 2, , ~, , 2.5, , or, , z = 0.61, , It should be noted that the horizontal link requirement, described in 28.2.3 will ensure satisfactory serviceability performance., , I, , when - < 1, l), , b) For continuous beams., , z = 0.2 (I + 1.5 D), , 28.2.2 Reinforcement Anchorag«, , when 1 S -, , I, , D, , or, , At thefrontfaceof the corbel, the reinforcement should, be anchored either by:, , z =0.5 I, , /, , when - < 1, D, where / is the effective span taken as centre to centre, distance between supports or 1.15 times the clearspan,, whichever is smaller, and D is theoverall depth., , a) welding to a transverse bar ofequal strength -, , in this case the hearing area of the load should, stop short of the faceof the supportby a distance, equal to the cover of the tie reinforcement, or, b) bending buck the bars to form a loop - in this, case the bearing area of the load should, not project beyond the straight portion of, thebarsforming themain tension reinforcement,, , 19.3 Reinforcement, , 29.3.1 Positive Reinforcement, The tensile reinforcement required to resist positive, bending moment in any span of a deep beam shall:, , 18.1.3 Shear Reinforcement, , a) extend without curtailm-..~r1t between supports;, b) be embedded beyond the face of each support,, so that at the face of the support it shall have a, development length not less than 0.8 LtJ; where, L,j is the development length (see 26.2.1). for, the design stress in the reinforcement; and, , Shear reinforcement should be provided in the form, of horizontal links distributed in the upper two-third, of the effective depth of root of the corbel; this, reinforcement should be not less than one-half of the, area of the main tension reinforcement and should be, adequately anchored., 51

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IS 456: 2000, , c) be placed within a zone of depth equal to, 0.25 D - 0.0' I adjacent to the tension face of, the beam where D is the overall depthand I is, the effective span., 29.3.2 Negative Reinforc,ment, a) Termination of reinforcement -, , Por tensile, reinforcement required to resist negative, bending moment over a support ofa deep beam:, 1) It shall be permissible to tenninate notmore, than half of the reinforcement at a distance, of O.~ D from the face of thesupport where, D is as defined in 29.2;and, 2) The remainder shall extend over the full, span., b) Distribution-When ratio of clear span to, overall depth is in the range 1.0 to 2.5. tensile, reinforcement over a support of a deep beam, shall be placed in two zones comprising: ', 1) a zone ofdepth0.2D. adjacent to the tension, face. which shallcontain a proportion of the, • . tension steel given by, , O.S, where, , (~ -, , o.s), , =, =, , 2), , I, clearspan. and, D, overall depth., a zone measuring 0.3 D on either side of, the mid-depth of the beam, which shall, contain the remainder of the tension steel,, evenly distributed., For spantodepthratios lessthanunity. the, steel shall be evenly distributed over a, depthof 0.8 D measured from the tension, face., , 29.3.3 Vertical Reinforctmt1l1, If forces are applied to a deepbeam in sucha way that, hanging action is required. barsor suspension stil'NPS, shallbe provided to carry all the forces concerned., , 19.3.4 Side Face Reinforcement, Side face reinforcement shall comply with require.., ments of minimum reinforcement of walls (ste 32.4)., , 30 RIBBED. HOLLOW BLOCK ORVQIDEDSLAB, 30.1 General, , This covers the slabs constructed in one of the ways, described below:, a) As a aeries of concrete ribswithtoPPinlcaston, , forms which may be removed aftertheconcreto, has set;, b) As a series of concrete .ribs between precast, blocks which remain part of the completed, , ItNcture; the top of the ribs may be connected, by a toPpinlofconcrete of thesame strenath as, that usedin the ribs; and, , c) With a continuous top and bottom face but, containing voids of rectangular, oval or, othershape., 30.2 Analysis or Stnacture, , The moments and forces due to desian loads on, continuous slabs maybeobtained by themethods liven, in Section 3 for solid slabs. Alternatively, the slaba, may be designed as a seriesof simply supported spans, provided they arenotexposed to weather or corrosive, conditions; wide cracks may develop at the supports, and the engineer shall satisfy himselfthat these will, not impair finishes or lead to corrosion of the, reinforcement., 30.3 Shear, , Where hollow blocks are used, for the purpose, of calculating shear stress. the rib width may be, increased to takeaccount of the wan thickness of the, block ononesideof therib; with narrow precast units., the width of the jointing mortar or concrete may be, included., 30.4 Deflection, Therecommendations fordeflection inrespect of solid, slabs maybeapplied toribbed. hollow blockor voided, construction. Thespan to effective depthratiosliven, in 23.2 for a flanged beam are applicable but when, calculating the final reduction factor for web width., the rib width for hollow blockslabs may be assumed, to include the walls of the blocks on both sidesof the, rib. For voided slabsand slabsconstructed of box or, I-section units. aneffective ribwidth shall be calculated, assumins all material below the upper flange of the, unitto be concentrated in a reetanaular rib hlvins the, same cross-sectional areaand depth., 30.5 Sizeand Poeltlonof Rib•., , In-situ ribs shall be not less than 65 mm wide. They, shall be spaced at centres not greater than 1.~ apart, and their depth. excluding any topping, shall be not, more thanfour times their width. Generally ribs shall, be formed alons eachedge parallel to the spanof one, way slabs. Whenthe edge is built into a wall or rests, on a beam, a ribat leastas wideas the bearing shall be, fonned alons the ed,e., , m, , 30.6 Hollow Blocks and Formen, , Blocks and fonners may be of any suitable material., Hollow clay tiles for the filler type shall conform to, IS 39~ 1 (Part I). When required to contribute to the

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IS 4S6: 2000, , structural strengthof a slab they shall:, a) be made of concrete or burnt clay; and, b) have a crushins strength of at least 14 N/mm2, measured on thenetsection when axially loaded, in the direction ofcompressive stressin theslab., , toll' measured centre to centre of supports., b) Middl~ strip - Middle stripmeans a desisn strip, , bounded on each of its opposite sides by the, column strip., c) Panel-« Panel means that part of a slabbounded, on each of its four sides by the centre-line of a, columnor centre-lines of adjacentspans., , 30.' ArraDlemeDt of Reinforcement, The recommendations liven in 26.3 resardinl, maximum distance between bars apply toareas ofsolid, concrete inthisfonn ofconstruction. Thecurtailment., anchorage and cover to reinforcement shall be as, described below:, a) At least SO percent of the total main, reinforcement shall be carried through at the, bottom on to the bearinl and anchored in, accordance with 36.2.3.3., b) Wherea slab.which iscontinuous oversupports,, has been designed as simply supported,, reinforcement shallbeprovided overthesupport, to control cracking. This reinforcement shall, have a cross-sectional area of notless thanonequarter that required in the middle of the, adjoining spans and shall extend at least onetenth of the clear span into adjoining spans., c) In slabs with pennanent blocks, the side cover, to the reinforcement shall not be less than, 10 mm. In all other cases. cover shall be, provided according to 26.4., , 31.2 Proportlonlnl, , 31.2.1 Thickness of Flat Slab, The thickness of the flat slab shall be generally, controlled by considerations of spanto effective depth, ratios given in 23.2., For slabs with drops conforming to 31.2.2. span to, effective depth ratios liven In 23.2 shall be applied, directly; otherwise the span to effective depth ratios, obtained in accordance with provisions in 23.2 shall, bemultiplied by0.9. For this purpose. thelongerspan, shall be considered. The minimum thickness of slab, shall be 12S mm., , 31.2.2 Drop, The drops whenprovided shall be rectangular in plan., and have a lengthin each direction not less than onethirdof the panellengthin thatdirection. For exterior, panels. the width of drops at right angles to the noncontinuous edgeandmeasured from thecentre-line of, the columns shall be equal to one-half the width of, drop for interiorpanels., , 30.8 Precuts Joists and HoUow Filler Blocks, , 31.2.3 Column Heads, , The construction with precast joists and hollow, concrete filler blocks shall conform to IS 6061 (Part, 1) and precastjoist and hollowclay filler blocksshall, confonn to IS 6061 (Part 2)., , Where column heads are provided, that portion of a, column head which lies within thelargestrightcircular, cone or pyramid that has a vertex angleof 90°and can, be included entirely within the outlines of the column, and the column head, shall be considered for design, purposes (Stt Fig.12)., , 31 FLATSLABS, 31.1 General, , 31.3 DetermlnatioD of Bendinl Moment, , The term flat slab means a reinforced concrete slab, , 31.3.1 Methods 01 Analysis and Desig", It shall be pennissiblc to design the slab system by, one of the following methods:, a) The direct design method as specified in 31.4., and, b) The equivalent frame method as specified, in 31.5., In each case the applicable limitations given in 31.4, and 31.S shall be met., , with or without drops. supported generally without, beams. by columns with or without flared column, heads (see Fig. 12). A flat slab may be solid slab or, may haverecesses fonnedon the softlt ~o thatthe soffit, comprises a series of ribs in two directions. The, recesses may be fonned by removable or permanent, filler blocks., ', 31.1.1 For the purpose of this clause, the following, definitions shall apply:, ., a) Column strip - Column strip means a design, strip having a width of 0.2S ' 2, but not greater, than 0.25 'ion each side of the columncentreline, where I. is the span in the direction, moments are beingdetermined, measured centre, tocentreof supports and' 2 is thespantransverse, , 31.3.2 Benc#ng Moments in Panels with Marginal, , Beams or Walls, Wherethe slab is supported by a marginal beam with, a depthgreaterthan 1.5timesthe thickness of the slab., or by a wall, then:, S3

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IS 456 : 2000, ....-~........--r- CRITICAL SECTION 'OR, , SHUR IMMfDIATlLY, ADJACENT TO COLUM, , 12A SLAB WIT Hour DROP & COLUMN, WITHOUT COLUMN HEAD, CRITICAL SECllON, , FOR SHEAR, , 12 B SLAB WITH DROP & COLUMN, WITH COLUMN HEAD, , , ,--I'., , ,,', , /", , ANY CONCRITE IN THIS ARIA, TO BE NEGLECTED IN THE, CALCULATIONS, , 12 C SLAB WITHOUT DROP" COL UMN, WITH COLUMN HEAD, NOTE - D. is the diameterof column or column head to be considered for desi... and d ia effective depth of alab or drop II, IIpproprillte", FlO., , 12 CRJ11CAL SEC110NS FOR SHEAR IN FLAT SLABS, , a) the total loadto be carried by the beamor wall, shall comprise those loadsdirectly on the wall, or beam plusa uniformly distributed loadequal, to one-quarter of thetotalloadon theslab,and, b) the bending moments on the half-column strip, adjacent to the beam or wall shall beone-quarter, of the bending moments for the fll'St interior, column strip., , 31.3.3 Transfer of Bending Moments to Columns, When unbalanced gravity load, wind, earthquake, or, otherlateral loadscausetransfer of bending moment, between slab and column, the flexural stresses shall, be investigated using a fraction, a of the moment given, by:, 1, , a-~, -l+~ aJ, 3, , fa,, , where, , a., , = overall dimension of tile critical section, , a2, , for shear in the direction in which, moment acts,and, overall dimension of the critical section, for shear transverse to the direction in, which moment acts., , =, , A slab width between linesthatare one andone-half, slab or drop panel thickness; 1.5 D, on each side of, thecolumn or capital may be considered effective, D, being the size of thecolumn., Concentration of reinforcement overcolumn headby, closer spacing oradditional reinforcement may beused, to resist the moment on this section:, 31.4Dlreet Destp Method, , 31.4.1 Limitations, Slabsystem designed bythedirect design method shall, fulfil the following conditions:, a) There shall be minimum of three continuous, spans in eachdirection,, b) Thepanels shallbe rectangular, and the ratioof, the longer span totheshorter spanwithin a panel, shallnot be greater than2.0,, c) It shall be permissible to offsct columns to a, maximum of 10 percent of the span in the, direction of the offset notwithstanding the, provision in (b),, d) The successive span lenllhs in each direction, shall not differ by more than one-third of the, longer span. The end" spans may be shorterbut, not longer than the interior spans, and

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IS 456: ZOOO, , Exteriornegative designmoment:, , e) The deSiSD liveloadshallnotexceedthreetimes, the desian dead load., , --.O.6S, , 31.4.2 Total Design Moment/ora Span, , 1+-, , ac, , 31.4.11 In the direct desip method, the total design, moment for a span shall be determined for a strip, bounded laterally by the centre-line of the pane) on, eachsideof the centre-line of the supports., 31.4.2.2 The absolute sumofthepositive andaverase, ne,ative bendina momenta in each direction shall be, takenu:, Win, Mo ·, 8, , a c is the ratio of flexural stiffness of the exterior, columns to the flexural stiffness of the slab at a joint, , taken in the direction moments are being determined, and is liven by, , EX, a • =:.a., , s, = sum of, , the flexural stiffness of the, columnsmeetingat thejoint; and, K. = flexural stiffness of the slab, expressed, as moment per. unit rotation., , = total moment;, W = design load on an area '2 '.;, , M", , In = clearspan extending from face to face of, , '2, , 31.4.3.4 It shall bepermissible to modify thesedesign, moments by up to 10percent. so 10nlas the totaldesign, moment, M., for the panel in the direction considered, is not less than that required by 31.4.1.1., , columns, capitals, brackets or walls, but, not less than 0.651.;, length of span in the direction of Mo ; and, , = length of span transverse to ' r, , 31.4.3.5 The negative moment section shall be, designed toresist the IB1Jcr of the twointerior negati ve, design moments determined for the spans framing into, a common support unless an analysis is made to, distribute the unbalanced momentin accordance with, the stiffness of the adjoining parts., , 31.4.2.3 Circular supports shall be treated as square, supportshaving the same area., 31.4.Z.4 When the transverse span of the panels on, eitherside of thecentre-line of supports varies, 12 shall, be taken as the averageof the transverse spans., 31.4.Z.5 Whenthespan adjacent and parallel to anedge, is being considered, the distancefrom the edge to the, centre-line of the panel shan be substituted for lz, in 31.4.2.2., , 31.4.4 Distribution of Bending Mo~,.ts Across the, Panel Width, Bending moments at critical cross-section shall be, distributed to the column strips and middle strips as, , 31.4.3 Negativ« and Positive DesignMoments, , specified in 31.5.5as applicable., , 31.4.3.1 The negative desiBn moment shall be located, at the face of rectangular supports, circular supports, being treated as square supports having the same, area., 31.4.3.2 In an interior span, the total design moment, Mu shall be distributed in the following proportions:, 0.65, Negativedesign moment, Positivedesign moment, 0.35, , 31.4.5 Moments in Columns, , 31.4.5.1 Columns builtintegrally withthe slabsystem, shall bedesigned to resistmoments arisingfrom loads, on the slab system., 31.4.5.1 At an interior support, the supporting, members above and below the slab shall be designed, toresistthe momeat M givenby thefollowing equation,, indirectproportion to theirstiffnesses unless a general, analysis is made:, , 31.4.3.3 In an end span, the total design moment M", shall be distributed in the following proportions:, Interior negativedesign moment:, , 0.7S _ O.l~, 1+-, , M, , =O.OS, , (W, , d, , +O.Sw, )111: -w~, 1, , I; I:', , 1+al:, , at, , where, , Positivedesign moment:, , Wei' WI, , 0.63-, , •, , where, , where, , 'I =, , K, , e, , O.2~, , '2, , 1+ac, , = design, , dead and live, respectively, per unit area;, , = length of span transverse to the, direction of M;, , 5S, , loads

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IS 456: 2000, I., , =, , ac, , =, , w;.I'l, , b) Eachsuchframe maybeanalyzed in itsentirety,, or, for vertical loading, each floor thereofand, the roof may be analyzed separately with its, columns being assumed fixed at their remote, ends. Where slabsarethusanalyzed separately,, it may be assumed in determining the bending, moment at a givensupport thattheslab is fixed, at any support two panels distant therefrom, provided the slab continues beyond the point., c) For the purpose ofdetermining relative stiffness, of members. the moment of inertiaof any slab, or column may be assumed to be that of the, gross cross-section of the concrete alone., d) Variations of moment of inertiaalong the axis, oftheslabonaccount of provision ofdropsshall, be taken into account. In the case of recessed, or coffered slab which is made solid in the, region of thecolumns. thestiffening effectmay, be ignored provided the solid part of the slab, doesnotextendmorethan0.15 'eI' intothespan, measured from the centre-line of the columns., Thestiffening effect offlared column heads may, be ignored., , length of the clear span in the, direction of M, measured face to face, of supports;, , IK, , --&'I' where Kc and K. areas defined, K., , in 31.4.3.3; and, and I:. referto the shorterspan., , 31.4.6 Effects of Pattern Loading, In thedirectdesign method. when theratioof liveload, to dead loadexceeds O.S :, a) thesumoftheflexural stiffnesses of the columns, above and below the slab. IKe' shall be such, that ex. is notlessthantheappropriate minimum, value ex. IltIa specified in Table t 7. or, b) if the sum of the flexural stiffnesses of the, columns. IKe' does not satisfy(a). the positive, design moments for the panelsball bemultiplied, by the coefficient P. given by the following, equation:, , 31.5.2 Loading Pattern, 31.5.2.1 When the loading pattern is known. the, structure shall be analyzed for the load concerned., , ex. is theratioof flexural stiffness of thecolumns above, and below the slabto the flexural stiffness of theslabs, at a joint taken in the direction moments are being, determined and is givenby:, , Table17Minimum PermissibleValues of exc, (Clause 31.4.6), , ImpoHd LoadIDelld Load, , ex = IKe:, c, , (1), , IK, , •, , where Kc and K. are flexural stiffnesses of column and, slab respectively., , 31.5 Equivalent Frame Method, , 31.5.1 Assumptions, The bending moments and shear forces may be, determined by an analysis of the structure as a, continuous frameand the following assumptions may, be made:, a) The structure shall be considered to be madeup, of equivalent frames on column lines taken, longitudinally and transversely through the, building. Each frame consists of a row of, equivalent columns or supports, bounded, laterally by the centre-line of the panelon each, side of the centre-line of the columns or, supports. Frames adjacent'and parallel to anedge, shall be bounded by the edge and the centreline of the adjacentpanel., , Ratlo~, , VII. ora...., , (2), , (3), , II, , O.S, , O.S to 2.0, , o, , 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 3.0, , 0.5, , 0.6, , 0,8, , 0.7, 0.7, 0.8, , 1.0, 1.25, 2.0, O.S, 0.8, , 1.0, 1.2S, 2.0, 0.5, 0.8, , 1.0, 1.25, 2.0, , 1.2, 1.3, 1.5, 1.6, 1.9, 4.9, 1.8, , 2.0, 2.3, 2.8, 13.0, , 31.5.2.1 When the live load is variable but does not, exceed three-quarters of the dead load. or the nature, of the live load is such that all panels will be loaded, simultaneously, the maximum moments may be, assumed to occurat all sections whenfull design live, loadis on the entireslab system., , S6

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IS 456: 2000, , 31.5.2.3 For other conditions of live load/dead load, ratioand when all panelsare not loadedsimultaneously:, , greater than three-quarters of the value of 12, the, length of span transverse to the direction, moments are being determined, the exterior, negative moment shall be considered to be, uniformly distributed across the length, 31.5.5.3Column strip: Positivemomentforeach span, , a) maximum positive moment near midspan of a, panel may be assumed to occur when threequarters of the full design live load is on the, panel and on alternate panels; and, , '2', , b) maximum negative moment in the slab at a, , For each span. the column strip shall be designed to, resist 60 percent of the total positive moment in the, panel., , support may be assumed to occur when threequarters of the full design live load is on the, adjacent panels only., , 31.5.5.4 Moments in the middle strip, , 31.5.1.4 In no case shall design moments be taken to, be less than those occurring with full design live load, on all panels., , The middle strip shall be designed on the following, bases:, a) That portion of the design moment not resisted, by the column strip shall be assigned to the, adjacent middle strips., b) Each middle stripshall be proportioned to resist, the sum of the moments assigned to its two half, middle strips., c) The middlestrip adjacentand parallelto an edge, supported by a wall shall be proportioned to, resist twice the moment assigned to half the, middle strip corresponding to the first row of, interior columns., , 31.5.3Negative Design Moment, 31.5.3.1 At interior supports, the critical section for, negative moment, in both the column strip and middle, strip, shall be taken at the face of rectilinear supports,, but in no case at a distance greater than 0.175 II from, the centre of the column where II is the length of the, span in the direction moments are being determined,, measured centre-to-centre of supports., 31.5.3.2 At exterior supports provided with brackets, or capitals, the critical section for negative moment in, the direction perpendicular to the edge shall be taken, at a distance from the face of the supporting element, not greater than one-half the projection of the bracket, or capital beyond the face of the supporting element., 31.5.3.3 Circular or regular polygon shaped supports, shall be treated as square supports having the same, area., , 31.6 Shear in Flat Slab, 31.6.1 The critical section for shear shall be at a, distance d/2 from the periphery of the column/capital/, drop panel,perpendicular to the planeof the slab where, d is the effective depth of the section (see Fig. 12)., TIle shapein plan is geometrically similarto the support, immediately below the slab (see Fig. 13A and 13B)., NOTE - Forcolumn sections withre-entrant angles. thecritical, section shall be takenas indicated in Fig. 13Cand 130., , 31.5.4 Modification ofMaximum Moment, Moments determined by means of the equivalentframe, method, for slabs which fulfil the limitations of 31.4, may be reduced in such proportion that the numerical, sum of the positive and average negative moments is, not less than the value of total design moment M", specified in 31.4.2.2., , 31.6.1.1 In the case of columns near the free edge of, a slab, the critical section shall be taken as shown in, Fig. 14., 31.6.1.~ When openings in flat slabs are located at a, distance less than ten times the thickness of the slab, from a concentratedreaction or when the openings are, located within the column strips. the critical sections, specified in 31.6.1 shall be modified so that the part of, the periphery of the critical section which is enclosed, by radial projectionsof the openings to the centroid of, the reaction area shall be considered ineffective, (.\"ee Fig. 15), and openings shall not encroach upon, column head., , 31.5.5 Distribution of Bending Moment Across the, Panel Width, 31.5.5.1Columnstrip: Negativemomentat an interior, support, At an interior support, the column strip shall be, designed to resist 7S percent of the total negative, moment in the panel at that support., 31.5.5.2 Column strip:Negative momentatanexterior, support, a) At an exterior support. the column strip shall be, designed to resist the total negative moment in, the panel at that support., b) Where the exterior support consists of a column, or a wall extending for a distance equal to or, 2116 815/07-9, , 31.6.2 Calculation ofShear Stress, The shear stress tv shall be the sum of the values, calculated according to 31.6.2.1 and 31.6.2.2., 31.6.2.1 The nominal shear stress in flat slabs shall be, takenas V I b d where V is the shear forcedue to design, load, bit is th~) periphery of the critical section and d is, the effective depth., 57

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15456: 2000, , r-------l, , 'a:': '';', ':, ., ., .., t: ••::' . ., II, ~~. ';, :~:, , I, , •, , I, , , •• ', , CRITICAL, SECTION, , I, , .., , L_, , I, , SUPPORT, , d/2, , ~tT, , SUliPORT SECTION, COLUMN ICOLUMN HEAD, , 13A, SUPPORT, SECTION, , rr-, -l., d/2, , SUPPORT, SECTION, , CRITICAL, SECTION, , [, , I ., ,'..•:, ) d/2, ;......, ""'.', •, I •.1"", ~:~":'.,~, ., r :.. ~I, ., I, d/2, L - ;i;-1, '4 \., , ", , ".", , t, , NOTE - d i. the effec:tive depthof the nat slab/drop., , FlO. 13 CarneAL SScnONS IN PLAN FOR SHEAR IN fLAT SLABS, , FREE, CORNER, , ~'ReE, , L.-r eDGE, , I, , I, , I, I, , I, , ~.' •••'., , ., , "".~., , 'VCRITICAL, seCTION, , :~· ...., •. ~:~~, ;., ~~ ;, ~,", , ...... ', , I ~__, , d/2, , L __ ~ _, , ~/~-- T, , CORNeR, , COLUMN, , CRITICAL, SeCTION, , 148, , " A, , Fro. 14 EFFEcr OF FRBB BOOBS ON CRrneAL SBC110N FOR SHEAR, , 31.6.2.2 When unbalanced gravity load, wind,, earthquake or other fo~s cause transferof bending, moment betweenslab and column. a fraction (I - ex), of the moment shall be considered transferred by, eccentricity of the shear about the centroid of the, critical section. Shearstresses shall betaken all varying, linearly about the centroid of the critical section. The, , value of a shall be obtained from the equation given, in 31.3.3., , 31.6.3 Permissible ShearStress, 31.6.3.1 When shear reinf~ment is not provided., the calculated shearscress at the critical section shall, not exceed k."C~., , S8

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IS 4~6: 2000, .......---4M--, , OPENING, , SUBTRACT FROM, PERIPHERY, , r-I, , i, , ,, II, , COLUMN, , OPENING, , COLUMN, , ..L, d/2 , . - - -, , :':~:~' . :~~:; ~~~'J~~~~, , j, , ..................11I6, , J :, , «n, , en, , r, , ~tr, , ,, , i, , L, , I, I, , :'-CRITICAL, I, SECTION, , I, , ''''·.~~:.~''':-+-AI, 0'-'·".', , L, , I, 1, I, , ,, , __.II, , - -, , 15 A, , 158, , PENlNG, , ,,, , I, , I, , I, , I, I, , I, I, , ,, , t, I, , ...-, , I, , ,, , :, , CRITICAL, SECTION, , Il.., , ~, ,., · : ..•.. ; . ., 0, , ..', , I, T, , --, , ~ oj, • ':'." "..:, il~:· '!: ~., , COLUMN, , I, , "--CR ITICAL, I, SECTION, JI, , "---- ...--..J, , • REGARD OPENING, AS FREE EDGE, , 1St, , 15 D, , FlO., , 15 EFFECf OF OPENINGS ON CRmCAL SEmON FOR SH£AR, , where, k., , 2 times the slab thickness, except where a slab is of, cellular or ribbed construction., , =(O.S + Pc) but not greaterthan 1, Pc beingthe, ratio of shortside to longside of the column!, capital; and, , tt, , 31.7.1Area ofReinforcement, , When drop panels ~ used. the thickness of drop panel, for determination of areaof reinforcement shall be the, lesserof the following:, a) Thickness of'drop, and, b) Thickness of slab plus one quarter the distance, between edge of drop and edge pf capital,, 31.7.3 Miniml4nl Length ofReinforcement, a) Reinforcement in flat slabs shall have the, minimum lengths specified in Fig.16. Larger, lengths of reinforcement shallbe provided when, required by analysis., b) Where adjacent spans are unequal. theextension, of negative reinforcement beyond each face of, the common column shall be based on the longer, span., e) The lengthof reinforcement for slabs in frames, not braced against sideways and for slabs, resisting lateral loads shall be determined by, analysis but shall not be less than those, prescribed in Fig. 16., , =0.25 [l;; in limit state method of design,, , and 0.16 [l;; in working stress method of, design., 31.6.3.2 When the shear stress at the critical section, exceeds the value given in 31.6.3.1, but less than, 1.S 1:( shear reinforcement shall be provided. If the, shear stress exceeds I.S 1 c the flat stab shall be, t, , redesigned. Shear stresses shall be investigated at, successive sectionsmoredistantfromthe supportand, shear reinforcement shall be provided up to a section, where the shear stress does not exceed 0.5 t c . While, designing the shear reinforcement, the shear stress, carried by the concreteshall be assumed to be 0.5 t~, and reinforcement shall carry the remaining shear., 31.7 Slab Reinforcement, , 31.7.1 Spacing, , The spacing of bars in a flat slab, shall not exceed, , S9

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IS 456: 2000, , 31.7.4 Anchoring Reinforcement, a) All slab reinforcement perpendicular to a, discontinuous edge shall have an anchorage, (straight, bent or otherwise anchored) past the, internal face of the spandrel beam. wall or, column, of an amount:, 1) Forpositive reirforcement - not less than, 150 mm except that with fabric reinforcement having a fully welded transverse wire, directly over the support, it shall be, permissibleto reduce this length to one-half, of the width of the support or SO mm,, whichever is greater; and, 2) Fornegative reinforcement - such that the, design stress is developed at the internal, , face, in accordance with Section 3., b) Where the slab is not supported by a spandrel, beam or wall, or where the slab cantilevers, beyond the support. the anchorage shall be, obtained within the slab., 31.8 Openings In Flat Slabs, , Openings of any size may be provided in the flat slab, if it is shown by analysis that the requirements of, strength and serviceability are met. However, for, openings conforming to the following. no special, analysis is required., a) Openings of any size may be placed within the, middle half of the span in each direction., provided the total amount of reinforcement, required for the panel without the opening is, maintained., b) In the area common to two column strips, not, more than one-eighth of the width of strip in, either span shall be interruptedby the openings., The equivalent of reinforcement interrupted, shall be added on all sides of the openings., c) In the area commonto one columnstripand one, middle strip, not more than one-quarter of the, reinforcementin either stripshall be interrupted, by the openings. The equivalent of reinforcementinterrupted shall be addedon all sides, of the openings., d) The shearrequirements of 31.6shall be satisfied., 32 WALLS, , as perempirical procedure givenin31.2.The minimum, thicknessof walls shall be 100rom., 32.1.1 Guidelines or design of walls subjected to, horizontaland verticalloads are given in 32.3., 32.2 Empirical Desllll Method for Walls Subjected, to Inplane Vertical Loads, , 32.2.1 Braced Walls, Walls shall be assumedto be braced if they are laterally, supported by a structure in which all the following, apply:, a) Walls or vertical braced elements are arranged, in twodirections so as to providelateralstability, to the structure as a whole., h) Lateralforcesare resistedby shear in the planes, of these walls or by braced elements., c) Floor and roof systems are designed to transfer, lateral forces., d) Connections between the wall and the lateral, supports aredesignedto resista horizontal force, not less than, 1) thesimplestaticreactionsto thetotalapplied, horizontal forces at the level of lateral, support; and, 2) 2.5 percent of the total vertical load that the, wallis designedto CaJTy at the levelof lateral, support., 32.1.2 Eccentricity o/Vertical Load, The design of a wan shall take account of the actual, eccentricity of the verticalforcesubject to a minimum, value of O.OS t., The vertical load transmitted to a wall by a, discontinuous concrete floor or roof shall be assumed, to act at one-third the depth of the bearing area, measured from the span face of the wall. Where there, is an in-situ concrete floor continuous over the wall,, the load shall be assumed to act at the centre of the, wall., The resultant eccentricity of the total vertical load on, a braced wall at any level between horizontal lateral, supports, shall be calculated on the assumption that, the resultanteccentricity of all the verticalloadsabove, the upper support is zero., 32.2.3 Max;mrlm Effectiv« Height to Thickness Ratio, The ratio of effective height to thickness. Hwelt shall, not exceed 30., 31.2.4 Effective Height, The effectiveheight of a braced wall shall be taken as, follows:, a) Where restrained against rotation at both ends, , 31.1 General, Reinforced concrete walls subjected to direct, compression or combined flexure and direct, compression should be designed in accordance with, Section 5 or Annex B provided the vertical, reinforcement is provided in each face. Braced walls, subjected to only vertical compression may be designed, , by, , 61

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IS 456: 2000, J) floors, , 0.75 /1w or, , 2) intersecting walls or, similar members, whichever is the lesser., , 0.75 [J), , h) Where not restrained against rotation at hoth, ends by, , I) floors, , 1.0 II ow or, , 2) intersecting walls or, similar members, whichever is the lesser., , 1.0 L1, , II, , \Ii, , L,, , :;:;, , where, , = shear force due to design loads., , ~I, , d, , =, , wall thickness., , =, , n.R >< L~ where L", is the length of, the wall, , 32.4.2.. ] rJndc, no circumstances shall the nominal, shear stress r vw m walls exceed 0.17 t; in limit state, method and 0 12/. l in working stress method., , 32.4.3 Design Shear Strength of' Concrete, , the unsupported height of the wall,, , = the horizontal distance between centres, , The design shear strength of concrete in walls,, t n v ' without shear reinforcement shall be taken as, below:, , a) For Hw ILw~ 1, , of lateral restraint., , =(3,0 -Il, , K, , 32.2 . 5 Design Axial Strength. of Wall, , t(.w, , 111e design axial strength Pu~ per unit length of a braced, wall in compression may be calculated from the, following equation:, , where K1 is 0.2 in limit state method and 0.13, in working stress method., , P l 1W, , = 0.3 (t -, , Lesser of the ·~';·dlJf:~~, above and .I'ro'lJ, , where, e, , at TIght, , i. r w z:, , angles to the plane of the wall determined, in accordance with 32.2.2, and, , ., , L'cl]c'Jlafcd from, , (a'), , . .... (H .v / I..: ~ J ), .1(., ",: :r\: .:-----,--- .~----.- . -., . . . . (/-'\" / 1.... , _.. , ), , where K, ~, p.n4~ in Jir"it "f~~tt' n\(~1hod and, 0.03 in workinc st.rt~~.;s method. but shall be, , e'l :: addi tiona} eccentricity due to sle ndcrness effect taken as /-1 we' I 2 500 t., 32.~~, , Lw ) K,, , b) For I(./L w > J, , 1.2 e - 2e)fck, , = thickness of the wall,, = eccentricity of load measured, , w/, , not less than K~ ,\;~T~' in allY v.r-c. where K,, , Walls Subjected to Combined Horizontal, , is f),l.t; in linut state rnethod and 0.) 0 in, , and Vertical Forces, , working stress method., , 32.3.1 When horizontal forces are in the plane of the, wall. it may be designed for vertical forces in, accordance with 32.2 and for horizontal shear in, accordance with 32.3. In plane bending may be, neglected in case a horizontal cross..section of the wall, is always under compression due to combined effect, of horizontal and vertical loads., , ~~2 . 4.4. Design, , oJ' Shear Reiniorcemcnt, , Shear reinforcement shall he provided to carry a shear, equal to V "'\;w.t (OJ~ L.. . ).'In case of working stress, method Vl1 is replaced by V. The strength of shear, reinforcement shall be calculated d~ per 40.4 or B~S.4, with A"" defined as below:, l, , 32.3.2 Walls subjected to horizontal forces, , A, , \,, oI, , perpendicular to the wall and for which the design axial, load does not exceed 0.04 .f~k Ai' shall be designed as, slabs in accordance with the appropriate provisions, under 24, where Ait is gross area of the section., , -, , = P (0.8 L, w, , w), , t, , where Pw is determined as follows:, a) For walls where Hw ' Ly,:S 1. Pw shall be the, Jesser of the ratios of either the vertical, reinforcement area or the horizontal, reinforcement area to the cross-sectional area, of wall in the respective direction., , 32.4 Design for Horizontal Shear, , 32.4.1 Critical Section/or Shear, The critical section for maximum shear shall be taken, at a distance from the base of O.S Lw or 0.5 H..,, whichever is less., , b) For walls where HwI Lw > 1, PVi shall he the, ratio of the horizontal reinforcement area to, the cross-sectional area of wall per vertical, , metre., , 32.4.2 Nominal Shear Stress, The nominalshear stress t\lW in wallsshallbe obtained, as follows:, r yw = Vu / t.d, , 32.5 Minimum Requirements for Reinforcement, in Walls, , The reinforcementfor walls shall be providedas below:, 62

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IS 456: 2000, a) the minimum ratio of vertical reinforcement to, gross concrete area shall be:, , be taken as the following horizontal distances:, a) Where supported at top and bottom risers by, beams spanning parallel with the risers. the, distance centre-to-centre of beams;, , 1) 0.001 2 for deformed bars not larger than, , 16 mm in diameter and with a characteristic, strength of 415 N/mm2 or greater., , b) Where spanning on to the edge of a landing slab., which spans parallel, with the risers (see Fig., 17). a distance equal to the going of the stairs, plus at each end either half the width of the, landing or one metre. whichever is smaller; and, , 2) 0.001 5 for other types of bars., 3) 0.( :)1 2 for welded wire fabric not larger than, 16 mm in diameter,, b) Vertical reinforcement shall be spaced not, farther apart than three times the wall thickness, nor450mm., , c) Where the landing slab spans in the same, direction as the stairs. they shall be considered, as acting together to form a single slab and the, span determined as the distance centre-to-centre, of the supporting beams or walls. the going being, measured horizontally., , c) The minimum ratio of horizontal reinforcement, to gross concrete area shalt be:, 1) 0.002 0 for deformed bars not larger than, 16 mm in diameter and with a characteristic, strength of 415 Nzmm' or greater., , 33.2 Distribution of Loading on Stairs, , 2) 0.0025 for other types of bars., , In the case of stairs with open wells, where spans partly, crossing at right angles occur, the load on areas, common to any two such spans may be taken as onehalf in each direction a~ shown in Fig. 18. Where flights, or landings are embedded into walls for a length of, nor less than I 10 mm and are designed to span in the, direction of the flight. a 150 mm strip may be deducted, from the loaded area and the effective breadth of the, section increased by75 mm for purposes of design (see, Fig. 19)., , 3) 0.002 () for welded wire fabric not larger, than 16 rntn in diameter., d) Horizontal reinforcement shalt be spaced not, farther apart than three times the wall thickness, nor 450 mm., NOTE _.'. The minimum remforcement may not always be, sufficient to provide adequate resrsrance to the effects of, shrinkage and temperature, , 32.5.1 For walls having thickness more than 200 mm,, the vertical and horizontal reinforcement shall, be provided in two grids, one near each face of the, wall., , 33.3 Depth of Section, 111e depth of section shalt be taken as the minimum, thickness perpendicular to the soffit of the staircase., , 32.5.2 Vertical reinforcement need not he enclosed, by transverse reinforcement as given in 26.5.3.2 for, column. if the vertical reinforcement is not greater, than 0.0 I times the gross sectional area or where the, vertical reinforcement is not required for, compression,, , 34 FOOTIN(;S, 34.1 General, , 33.1 Effective Span of Stairs, , Footings shall be designed to sustain the applied loads., moments and forces and the induced reactions and to, ensure that any settlement which may occur shall be, as nearly uniform as possible. and the safe bearing, capacity of the soil is not exceeded (sa IS 1904)., , The effective span of stairs without stringer heams shall, , 34.1.1 In sloped or stepped footings the effective, , 33 STAIRS, , I, , I, , I, , 1K, , I, , I, , I, , I, , ~,, , ~, I, , • It-, , UP, , i, , ~x- •x4- GOING (G) ---+'v-i-v-l, FIG., , 17, , x, , y, , <1m, , <1m, , SPAN IN METRES, , G·X·Y, , <1m, , >'m, , G.X + 1, , >'m, , <1m, , G·Y·', , >lm, , >'m, , G., + 1, , ,---., , EFfECTIVr-: SPAN FOR STAIRS SUPPORTED AT EACH END IW, , LANDINGS SPANNING PARALLEL WnH THE RISERS, , 63

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IS 456: 2000, , UP, , .c, I, , 8 E AM, , !, , I, , I~N, ,, , w, , THE LOAD ON ARE, COMMON TO TWO, SYSTEMS TO 81£, TAKEN AS ONE, HAL,. IN EACH, DIRECTION, , I, , Flo. 18 LoADINO ON STAIRS WITH OPEN WELLS, , FlO., , 19 LoADINO ONSTAIRS, Bun.T INTO WAJ,.LS, , cross-section in compression shall be limited by tho, areaabovethe neutral plane, andtho angle of slopeor, depth andlocation of stepsshall besuchthatthe desip, requirements aresatisfied ateverysection. Sloped and, stepped footings that are designed as a unit shall be, constructed to assure action as a unit., , where, q" •, , 34.1.2 Thickness at the Edge 01 Footing, Inreinforced andplainconcrete footings, thethickness, at theedgeshallbe notless than 150mm forfootings, on soils, norless than300mmabove the topsof piles, for footings on piles., 34.1.3 Inthecaseof plainconcrete pedestals, theangle, between the planepassing through the bottom edgeof, the pedestal and the corresponding junction edge of, the column with pedestal and the horizontal plane, (see Fig. 20) shallbe governed by the expression:, , 34.2 Momenband Fore., 34.1.11n the case of footings on piles, computation, for moments and shears may be based on the, assumption that the reaction from any pile is, concentrated at the centreof the pile., , tan a, , leII., , =, , calculated maximum bearing pressure at, the baseafthe pedestal in N/mm2, and, characteristic stren,th of concrete at, 28 days in N/mm2•, , 34.2.2 Forthepurpose ofcomputin, stresses infootings, which support a round oroctagonal concrete column or, pedestal, the face of the column or pedestal shall be, taken as the side of a square inscribed within the, perimeter oftheround or octagonal column or pedestal., , 34.2.3 Bending Moment, , ~ 0.9pooq" +1, , 34.2.3.1 The bending moment at any section shall be, determined by passing through the section a vertical, , I.., , COLUMN, , I, I, , PLAIN, CONCRETE, , PEDESTAL, , Flo. 20, , 64

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IS 456: 2000, , plane which extends completelyacross the footing,and, computing the moment of the forces acting over the, entire area of the footing on one side of the said plane., 34.2.3.2 The greatest bending moment to be used in, the design of an isolated concrete footing which, supports a column. pedestal or wall, shall be the, momentcomputed in the mannerprescribedin 34.2.3.1, at sections located as follows:, a) At the face of the column, pedestal or wall, for, footings supporting a concrete column, pedestal, or wall;, , 34.3 Tensile Reinforcement, , The total tensile reinforcement at any section shall, provide a moment of resistance at least equal to the, bending moment on the section calculated in, accordance with 34.2.3., 34.3.1 Total tensile reinforcement shall be distributed, across the corresponding resisting section as given, below:, , a) In one-wayreinforcedfooting, the reinforcement, extending in each direction shall be distributed, uniformly across the full width of the footing;, , b) Halfway between the centre-line and the edge, of the wall, for footings under masonry walls;, and, , h) In two- way reinforced square footing, the, reinforcementextending in each direction shall, be distributed uniformly across the full width, of the footing; and, , c) Halfway between the face of the column or, pedestal and the edge of the gussetted base, for, footings under gussetted bases., , c) In two-way reinforced rectangular footing. the, reinforcement in the long direction shall be, distributed unifonnly across the full width of, the footing. For reinforcement in the short, direction, a central band equal to the width of, the footing shall be marked along the length of, the footing and portion of the reinforcement, determined in accordance with the equation, given below shall be uniformly distributed, across the central band:, , 34.2.4 Shear and Bond, , 34.2.4.1 The shear strength of footings is governed by, the more severe of the following two conditions:, a) The footing acting essentially as a wide beam,, with a potential diagonal crack extending in a, plane across the entire width; the critical section, for this condition shall be assumed as a vertical, section located from the face of the column,, pedestal or wall at a distance equal to the, effective depth of footing for footings on piles., , Reinforcement in central band width, 2, Total reinforcement in short direction = ~ + 1, , b) Two-way action of the footing, with potential, diagonal cracking along the surfaceof truncated, , where, , cone or pyramid around the concentrated load;, in this case, the footing shall be designed for, shear in accordance with appropriate provisions, specified in 31.6., , is the ratio of the long side to the short, , reinforcement shall be uniformly distributed in, the outer portions of the footing., 34.4 Transfer of Load at the Base of Column, , 34.2.4.2 In computing the external shearor any section, througha footing supportedon piles, the entire reaction, from any pile of diameter D (1 whose centre is located, D /2 or more outside the section shall be assumed as, p:oducing shear on the section; the reaction from any, pile whose centre is located Dr/2 or more inside the, section shall be assumed as producing no shear on the, section. For intermediate positions of the pile centre,, the portion of the pile reaction to be assumed as, producing shear on the section shall be based on, straight line interpolation between full value at D(1/2, outside the section and zero value at DI'/2 inside the, section., , The compressive stress in concrete at the base of a, column or pedestal shall be considered as being, , transferred by bearing to the top of the supporting, pedestalor footing.The bearing pressureon the loaded, area shall not exceed the permissible bearing stress in, direct cornpression multiplied by a value equal to, , K but not greater than 2;, , ~A;, , where, , 34.2.4.3 The critical section for checking the, development length in a footing shall be assumed at, the same planes as those describedfor bendingmoment, in 34.2.3 and also at all other vertical planes where, abrupt changes of section occur. If reinforcement is, curtailed, the anchorage requirementsshall be checked, in accordance with 26.2.3., , 2116 815/07-10, , ~, , side of the footing. The remainder of the, , 65, , AI, , =, , A2, , = loaded area at the column base., , supporting area for bearing of footing,, which in sloped or .stepped footing may, be taken as the area of the lower base of, the largest frustum of a pyramid or cone, contained wholly within the footing and, having for its upper base, the area actually, loaded and having side slope of one, vertical to two horizontal; and

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IS 456: 2000, For working stress method of design the permissible, bearingstresson fullarea of concreteshall be takenas, 0.25!c,,; for limitstatemethodof designthepermissible, bearing stress shall be 0.45 let., 34.4.1 Where the permissible bearing stress on the, concretein thesupporting or supported memberwould, be exceeded, reinforcement shall be provided for, developing the excess force, either by extending the, longitudinal bars into the supporting member, or by, dowels (see 34.4.3)., 34.4.2 Where transfer of force is accomplished by, reinforcement, the development length of the, reinforcement shall be sufficient to transfer the, compression or tension to the supporting member in, accordance with 26.2., 34.4.3 Extended longitudinal reinforcement ordowels, of at least O.S percentof the cross-sectional area of the, supportedcolumn or pedestal and a minimum of four, bars shall be provided. Where dowels are used, their, , diameter shall no exceed the diameter of the column, bars by more than 3 mm,, 34.4.4 Column bars of diameters larger than 36 mm,, in compression only can be dowelled at the footings, with bars of smaller size of the necessary area. The, dowel shall extend into the column. a distance equal, to the development lengthof the column bar and into, the footing, a distance equal to thedevelopment length, of the dowel., , 34.5 Nominal Reinforcement, 34.5.1 Minimum reinforcement and spacing shall be, as per the requirements of solid slab., 34.5.2 The nominal reinforcement for concrete, sections of thickness greater than 1 m shall be, 360 mmz per metre length in each direction on each, face. This provision doesnotsupersede therequirement, of minimumtensilereinforcement based on the depth, of the section.

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IS 456: ZOOO, SECTION 5 STRUCTURAL DESIGN (LIMITSTATE METHOD), 35 SAFETYANDSERVICEABILITY, REQUIREMENTS, 35.1 General, In the method of design based on limit state concept,, the structure shall be designed to withstand safely all, loads liable to act on it throughoutits life; it shall also, satisfy the serviceability requirements, such as, limitationson deflectionand cracking.The acceptable, limit for the safety and serviceability requirements, before failure occurs is called a 'limit state' . The aim, of design is to achieve acceptable probabilities that, the structure will not become unfitfor the use for which, it is intended, that is, that it will not reach a Iimit state., 35.1.1 All relevant limit states shall be considered in, design to ensure an adequate degree of safety and, serviceability. In general, the structure shall be, designed on the basis of the most critical limit state, and shall be checked for other limit states., 35.1.2 For ensuring the above objective, the design, should be based on characteristic values for material, strengths and applied loads, which take into account, the variationsin the materialstrengthsand in the loads, to be supported. The characteristic values should be, based on statistical data jf available: where such data, are not available they should be based on experience., The 'design values' are derivedfrom the characteristic, values through the use of partial safety factors, one, for material strengths and the other for loads. In the, absence of special considerationsthese factors should, have the values given in 36 according to the material., the type of loading .and the limit state being, considered., , 35.2 Limit State 01CoDapse, The limit state of collapse of the structure or part of, the structure could be assessed from rupture of one or, more critical sections and from bucklingdue to elastic, or plastic instability (including the effects of sway, where appropriate) or overturning. The resistance to, bending,shear,torsionand axial loads at every section, shall not be less than the appropriate value at that, section produced by the probable most unfavourable, combination of loads on the structure using the, appropriate partial safety factors., 35.3 Limit States of ServiceabUlty, , 35.3.1 Deflection, Limiting values of deflections are given in 23.2., , 35.3.2 Cracking, Cracking of concrete should not adversely affect the, appearance or durability of the structure; the acceptable, , limitsof crackingwould vary withthe typeof structure, and environment. Wherespecificattention is required, to limit the designedcrack width to a particular value., crack width calculation may be done using formula, given in Annex F., The practical objective of calculating crack width is, , merely to give guidance to the designer in making, appropriate structural arrangements and in avoiding, gross errors in design, which might result in, concentration and excessive width of flexuralcrack., The surfacewidthof the cracks should not, in general,, exceed 0.3 mm in members where cracking is not, harmfuland does not have any serious adverseeffects, uponthe preservation of reinforcingsteel nor upon the, durability of the structures. In members wherecracking, in the tensile zone is harmful either because they are, exposed to the effects of the weatheror continuously, exposedto moistureor in contactsoil or groundwater,, an upperlimitof 0.2 mm is suggestedfor the maximum, width of cracks. For particularly aggressi ve, environment, such as the 'severe' category in Table 3,, the assessed surface width of cracks should not in, general,exceed 0.1 mm., 35.4 Other Limit States, , Structures designed for unusual or special functions, shall comply with any relevant additional limit stale, consideredappropriateto that structure., 36 CHARACTERISTIC AND DESIGN, , VALUES AND PARTIALSAFETYFACTORS, 36.1 Characteristic Strength of Materials, , The term 'characteristicstrength' means that value of, the strengthof the materialbelowwhichnot more than, 5 percent of the test results are expected to fall. The, characteristic strength for concrete shall be in, accordance with Table 2. Until the relevant Indian, Standard Specifications for reinforcing steel are, modified to include the concept of characteristic, strength, the characteristic value shall be assumed as, the minimum yield stress 10.2 percent proof stress, specified in therelevant Indian Standard Specifications., 36.2 Characteristic Loads, , The tenn 'characteristic load' meansthat valueof load, which has a 9S percent probability of notbeingexceeded, during the life of the structure. Since data are not, available to express loads in statistical terms, for the, purpose of this standard, dead loads given in IS 875, (Part 1). imposed loads given in IS 875 (Part 2), wind, loads given in IS 875 (Part 3), snow load as given in, IS 875 (Part 4) and seismic forces given in IS 1893, shall be assumed as the characteristic loads., , 61

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IS 456: 2000, 36.3 Design Values, , 36.4.2PartialSafety Factor Ym for Mateiral, Strength, , 36.3.1 Materials, , 36.4.2.1 Whenassessing thestrength of a sttucturcor, structural memberfor the limit stale of collapse. the, values of partial safetyfactor. -r.. should be taken as, I.S for concrete and US forsteel., , The design strength of the materials.!.J is givenby, , where, , NOTE - y. values are .a1ready incorporated ill the, equations and tables aiven ill this .tandard for limit state., , = characteristic strength of the material, , f, , design., , (see 31).1). and, , Ym, , 36.4.2.2 Whenassessing the deflection, the material, properties such as modulus of elasticity should be, taken 8S those associated with the characteristic, strength of the material., , = partial safety factor appropriate to the, material and the limit state being, considered., , 36.3.2 Loads, , 37 ANALYSIS, , The design load. FI! is given by, , 37.1 Analysis of Stnacture, , Fd=FYr, , Methods of analysis as in 22 shall be used. The, material strength to beassumed shallbecharacteristic, values in the determination of elastic properties.of, members irrespective of the limit state being, considered. Redistribution of thecalculated moments, may be madeas givenin 37.1.1., 37.1.1. Redistribution of Moments in Continuous, Beamsand Frames, The redistribution of moments may be carried out, satisfying the following conditions:, a) Equilibirum between the interal forces and the, extemalloads is maintained., h) Theultimate moment of resistance provided at, any section of a member is not less than 70, percent of the moment at that sectionobtained, from an elastic maximum moment diagram, covering all appropriate combinations of loads., c) Theelastic moment at anysection in a member, due to a particular combination of loads shall, , where, F, , =, , Yf, , = partial safety factor appropriate to the, , characteristic load (see 36.2).and, nature of loading andthelimitstatebeing, considered., , 36.3.3 Consequences ofAttainingLimit State, , Where theconsequences of a structure attaining a limit, state are of a serious nature such as huge loss of life, and disruption of the economy. higher values for Yf, and Ym thanthosegivenunder36.4.1 and36.4.2may, be applied., 36.4 Partial Safety Factors, 36.4.1 PartialSafety Factor Yf for Loads, , The values of Yf givenin Table 18 shall normally be, used., , Table 18 Valuesof Partial Safety Factor Yf for Loads, (Clause.t 18.2.3.1.36.4.1 andB-4.3), Load Combination, , .., , (I), , DL+/L, DL+WL, , Unlit State 01 CoIIapIe, , DL, , IL, , WL, , DL, , IL, , (2), , (3), , (4), , (5), , (6), , 1.0, , I.S, I.S or, , ., , 091), , DL+/L+ WL, , Limit Statel of, SenlceabUllJ, , ..., , ..., 1.2, , 1.0, , 1.0, , 1.S, , 1.0, , --, , 1.0, , WL, (7), , 1.0, 0.8, , 0.8, , NOTES, 1 Whileconsidering earthquake effects. substitute EL for WL, 2 For lhe limitstatesof serviceability. thevoluca or 1, liven in thistableareapplicable forshan termeffects.Whileasses.inathe, loftg term effectsdueto enep thedead load and that part of the live loadlikelyto be permanent mayonly be conlidered., n This valueis to be considered whenstability apinst overturning or stressrevenal il critical., , 68

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15456: 2000, not be reduced by more than 30 percentof the, numerically largestmomentgivenanywhere by, the elastic maximum moments diagramfor the, particular member. covering aU appropriate, combination of loads., d) At sections where the moment capacity after, redistribution is less than that from the elastic, maximum moment diagram. the following, relationship shall be satisfied:, , b) The maximum strain in concrete at the, , outennostcompression fibreis takenas 0.003 5, in bending., c) The relationship between thecompressive stress, distribution inconcrete and the sttainin concrete, may be assumed to be rectangle. trapezoid., parabola or any other shape which results in, prediction of strengthin substantial agreement, with the results of test. An acceptable stressstrain curve is given in Fig. 21. For design, purposes. the compressive strengthof concrete, inthe stnaeture shallbe assumed to be 0.67times, the characteristic strength. The partial safety, factor y. = 1.5 shall be applied in addition to, this., , 5L+ 8M SO.6, d, , 100, , where, Xu, , = depth of neutral axis., , =, , d, effectivedepth. and, 6M, percentage reduction in moment., e) In structures in which the structural frame, provides the lateral stability. the reductions in, moment allowed by condition 37.1.1 (c) shall, be restricted to 10 percentfor stnactures over 4, storeysin height., , NOTE - Pordie streu·llrlin CUM ill rrlJ. 21 die deaip, stressblock plIIUIDClerI_ IS follows ('flfI Pia. 22):, , =, , • 0.36lot' x., , Area ofsuessblock, , Depthof celItle of colllplalive force, • 0.42 x., fromthe extreme fim ift compression, , when:, = chancteriatic c:omprasive lballth ofconcme. lIIlCI, , I~, , x. = depCh of neutnl WI., , 37.1.2 AnalysisofSlabs Spanning in lWo Directions, at RightAngles, , 38 LIMIT STATE OF COLLAPSE: FLEXURE, , d) The tensilestrengthof the concreteis ignored., e) The stresses in the reinforcement are derived, from representative stress-strain curve for the, type of steel used. 'JYpica1 curves are given in, Fig. 23. For design purposesthe partial safety, factor Ym • equal to 1.15 shallbeapplied., , 38.1 Assumpdons, , f) The maximum strain in the tension reinforce-, , Yield line theory or any other acceptable method, may be used. Alternatively the provisions given in, Annex D may be followed., , ment in the section at failure shall not be, less than:, , Design for the limit state of collapse in flexure shall, be basedon the assumptions given below:, a) Plane sections nonnal to the axis remain plane, after bending., , --!:t.+0.002, 1.15E., where, , _.r-------t, , f, = characteristic strengthof steel. and, , fa, , E,, , (H7fCk, , t, , III, III, III, , Ill:, , 0.67 fck Irm, , t-, , III, , 0·002, , = modulus of elasticity of steel., , T, , O'42X u, , Xu, , ~, , 0·03S, , STRAIN-, , FIG., , 21 STRESS-STRAIN CURVE R>R CONCREm, , FIG., , 69, , 22 STRESS BLOCK PARAME'I1!RS, , O·36fc k Xu

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IS 456: 2000, , calculated eccentricity is larger, the minimum, eccentricity should be ignored., 39.3 Short Axially LoadecI Me.ben in, COlDpnaloD, The member shall be designed by considering the, assumptions given in 39.1 and the minimum, , eccentricity. When the minimum eccentricity as, per 25.4 does not exceed O.OS times the lateral, dimension, the members may be designed by the, followins equation:, , . PI, where, Pu, , I.., , 39.6 Members Subjected to Combined Axial Load, , and Biaxial BenellD., The resistance of a member subjected to axial force, and biaxial bending shall be obtained on the basis of, assumptions given in 39.1 and 39.2 with neutral axis, so chosen as to satisfy the equilibrium of load and, moments abouttwoaxes.Alternatively suchmembers, may be designed by the following equation:, + [, ]a. S, [~]a., Al, Atu~1, M uy, , = 0.4'et .A + 0.67f, .A, c, , •, , ux1, , Ie, , = moments about x and y axes, , axial load on the member., , = characteristic compressive strensthof the, characteristic strength ofthecompression, reinforcement, and, , is relatedto PulPtJI, where Py Z =0.4S let · Ac + 0.7S 1,. Ale, For values of Pu'PUI 0.2 to 0.8, the valuesof a. vary, linearly from 1.0to 2.0.For values less than0.2, aa is, 1.0; for values greater than 0.8. Q. is 2.0., , =, , 39.4 Compression Memben with ReDeal, Relnforcemeat, , 39.7 Slender Comp....lon Memben, , The strength of compression members with helical, reinforcement satisfyin. the requirement of39.4.1shall, be taken as 1.0~ timesthe strensth of similarmember, with lateralties., 39.4.1 Theratioof the volume of helical reinforcement, to the volume of the core shall not be less than, 0.36(A.IAc-l)f*'f,, where, A., pss area of the section,, , fa, , The design ,of slender compression members, (see 25.1.1) shall be based on the forces and the, moments determined froman analysis of thestructure,, including the effect of deflections on moments and, forces. When the effect of deflections are not taken, Into account in the analysis. additional momentgiven, in 39.7.1 shall be takenintoaccountin the appropriate, direction., 39.7.1 The additional moments M. and M.'I shall be, calculated by the ~ollowinl fonnulae:, , =, = areaof the core of the helically reinforced, , columnmeasured to the outside diameter, of the helix,, , M = PyD, , concrete, and, , M, , characteristic strength of the helical, reinforcement but not exceeding, , where, Pu, , 41~N/mm2., , 39.5 Memben Subjected to Combined Axial, , la, , Load aDd Unlulal BeDeIlD,, Amember subjected to axial force anduniaxial bending, shall be desisned on the basisof 39.1 and 39.3., , .y, , {!a.}2, , 2000 D, , u, , • characteristic compressive strensthof the, , I, =, , due to design loads,, maximum uniaxial moment, capacity foranaxialloadof Pu', bending about x and y axes, respectively, and, , Q., , Ale == area of longitudinal reinforcement for, columns., , Ac, , =, , MU l t MaYI, , = Area of concrete,, , t, =, , •, , where, , concrete,, Ac, , 10, , •, , ..M..{!.2.}2, 2000 b, , = axial loadon the member,, =effective length in respect of the major, axis., , 'ey, D, , NOTE - The deli... of member lubjecttocombined uialload, and uniuial bendin. will involve leftIlhy calculation by trill, and error. In orcI. to overcome these difticuldes intonacuoD, diql1UDl may beUIed. The. havebeenprepand aDd published, by 8 IS in •SP : 16 Deilin aida for reinforced concreto to, IS456'., , =effective lenlth inrespect of the minor axis., =depth of the cross-section at right angles, to the major axis, and, , b, , = width of the member., , Fordesignof section, 39.5or 39.6as appropriate shall, apply., 71

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18456: 2000, Table 19 DesIp Shear ~tre"'" 01Concrete, 't c ' NI.....r, (Cltuues4O.2.1. 40.2.2. 40.3. 40.4. 4O.S.3. 41.3.2. 41.3.3 and41.4.3), l00~, , ,.., , btl, , CoDcnte, Gnde, ,, , -, , MIS, , M20, , M2S, , M30, , M3S, , M40IIld above, , (l), , (2), , (3), , (4), , (5), , (6), , (7), , ~0.t5, , 0.28, 0.35, 0.46, , 0.28, 0.36, 0.48, 0.56, 0.62, 0.61, 0.12, , 0.29, 0.36, 0.49, , 0.29, 0.37, , 0.29, , 0.25, 0.50, 0.1S, 1.00, 1.2S, I. SO, 1.1S, 2.00, 2.25, 2.50, 2.7S, , 0.54, 0.60, 0.64, 0.68, 0.11, , 0.7S, 0.79, 0.81, 0.82, 0.82, , 0.11, 0.11, 0.11, 0.71, , 3.00, nnd, , 0.71, , 0.82, , 0.37, 0.50, 0.59, 0.61, 0.73, 0.18, 0.82, , 0.50, 0.59, 0.66, 0.11, 0.76, 0.80, 0.84, 0.88, 0.9t, 0.94, , 0.$1, , 0.64, 0.10, 0.14, 0.78, 0.82, 0.85, , 0.88, 0.90, 0.92, , 0.86, 0.90, 0.93, 0.96, 0.99, , 0.96, , 0.30, 0.38, 0.51, 0.60, 0.68, 0.74, 0.79, 0.84, 0.88, 0.92, 0.95, , 0.98, , 1.01, , above, , NOTE - The termA Is the arell of lonaltudinll1ten.lon reinforcement which conllnues at IClISt oneeffective depth beyond the section, bein, considered exc;pt at supponwhere the full areaof tension reinforcement maybe usedprovided thedetllilina confonn.to 16.1.1, and26.1.3, , Table 10 Maximum Shear Stress, f c, , _ll ,, , N/mmJ, , ( Cia",,, 40.2.3. 40.2.3.1. 4O.S.1 arad 41.3.1 ), Concrete, Gncle, , MIS, , M20, , M2S, , M30, , M3S, , 2.5, , 2.', , 3.1, , 3.S, , 3.7, , c) Inclined stirrups., Where bent-up bars are provided. their contribution, towards shear resistance than not be more than half, thatof the total shearreinforcement., Shear reinforcement shallbe provided tocarry a shear, equal to Vu - f'~ bd The atrenath of ahcar reinforcement V... shall be calculated u below:, , where, A, , V, , •, , II:, , des ian shear strenath of the concrete., , Iv, , Ir, , 0.8.7 Iy.-\vd ( ., ), sma + cosa, sv, , a, , c) For 5in,1e bar or 5in,Ie group of parallel bars., all bent-up at thesame cross-section:, , 21H1815/07_11, , e,, b, , b) Forinclined stirrups or a series of barl bent-up, at different cross-sections:, VU1, , III, , s., , _, 0._87...;./',1...A,...;.y~d, U1 •, , 'tv, , total cross-sectional area ofstirrup legs, or bent-up ban within a distance s.', specina of the stirrups or bent-up bars, alona the lenath of themember,, nc)tninal shear SIre.S,, , ••, , a) For vertical stirrupa:, , d, , 73, , M40, lIIId, IIbove, 4.0, , II:, , •, , breadth of the member which for, flan.ed beams, shall be taken as the, breadth of theweb b••, characteristic ItrenJthof thestirrup or, bent-up reinforcement which shall not, be taken Jreaterthan 41~ N/mm 2,, III, anale between the inclined stirrup or, bent- upbarandthe axis of the member., notless than 4'°. and, :; effective depth., , III, , =

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IS 456: 2000, NOTES, , is given by:, , 1 Where more(hanone type of shear reinforcement is used, to reinforcethe same portion of the beam. the total shear, resistance shallbecomputed asthesumof the resistance, for the varioustypes separately., 2 Theareaof the stirrupsshallnot belessthan the minimum, specified in 26.5.1.6., , AI' = ayb (Tv - 2d fJa,) I 0.87/" ~ O.4ay b/O.87 ~, , Thisreinforcement should be provided within themiddle, three quarters of (lv' wherea y is less than d. horizontal, shear reinforcement will be effective than vertical., , 40.5 Enhanced Shear Strength of Sections Close, to Supports, , 40.5.3 EnhancedShear Strength Near Supports, (SimplifiedApproach), , 40.5.1 General, Shear failure at sections of beams and cantilevers, without shear reinforcement wiIJ normally occur on, plane inclined at an angle 30° to the horizontal. If the, angle of failure plane is forced to be inclined more, steeply than this [because the section considered, (X - X) in Fig. 24 is close to a support or for other, reasons}, the shear force requiredto produce failure is, increased., The enhancement of shear strength may he taken, into account in the design of sections near a support, by increasing design shear strength of concrete to, 2d reI a; provided that design shear stress at the face, of the support remains less than the values given in, Table 20. Account may be taken of the enhancement, in any situation where the section consideredis closer, to the face of a supportor concentrated loadthan twice, the effective depth. d. To be effective. tension, reinforcement should extend on each side of the point, where it is intersected by a possible failure plane for a, distance at least equal to the effective depth, or be, provided with an equiv rlent anchorage., , The procedure givenin 40.5.1and40.5.2 may be used, for all beams. However for beams carrying generally, uniform load or where the principal load is located, farther than 2d from the face of support, the shear, stress may be calculated at a section a distance d from, the face of support. The value of t c is calculated in, accordance with Table 19 and appropriate shear, reinforcement is provided at sections closer to the, support, no funher check for shear at such sections is, required., 41 LIMIT STA1'E OF COLLAPSE: TORSION, 41.1 General, , In structures, where torsion is required to maintain, equilibrium, members shall be designed for torsion in, accordance with41.2,41.3 and41.4. However. for such, indeterminate structures where torsion can be eliminated, by releasing redundant restraints. no specific design for, torsion is necessary, provided torsional stiffness is, neglectedin the calculation of internal forces.Adequate, control ofanytorsional cracking isprovided by theshear, reinforcement as per 40., N()TE - The approach to design in this clause is as follows:, , 40.5.2 Shear Reinforcementfor Sections Close to ., Supports, , Torsional reinforcement is not calculated separately from that, required for bending and shear. Instead the lotal longitudinal, reinforcement is determined for a fictitious bending moment, which is a function of actual bending moment and torsion;, , If shearreinforcement is required. the total areaof this, , NOTE - The shearcausing failure is thatocting on, section X-X., FIG., , 24 SHEAR FAILURE NEAR SUPPORTS, 74

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IS 456: 2000, similarlyweb reinforcement is determined for 3 fictitious shear, which is a function of actual shear and torsion., , where, '~I is the torsional moment, D is the overalldepth, of the beam and b is the breadth of the beam,, , 41.1.1 The design rules laid down in 41.3 and 41.4, , shall apply to beams of solid rectangular cross.. section., However, these clauses may also be applied to flanged, beams, by substituting bw for b in which case they are, generally conservative; therefore specialist literature, may be referred to., , 41.4.2.1 If the numerical value of M l as defined, , in 41.4.2 exceeds the numerical value of the moment, A1 longitudinal reinforcement shall be provided on, ,, 11, , the flexural compression face, such that the beam, can also withstand an equivalent M e2 given hy, , 41.2 Critical Section, , Me2 == M, - Mu ' the moment M~.2 being taken as acung, in the opposite sense to the moment Mu ', , Sections located less than a distance d. from the face, of the support may be designed for the same torsion as, computed at a distance d, where d is the effectivedepth., , 41.4.~', , Transverse Reinforcement, , 41.3 Shear and Torsion, , Two legged closed hoops enclosing the corner, longitudinal bars shall have an area of cross-section, , 41.3.1 Equivalent Shear, , A~\", , given by, , Equivalent shear, Vc ' shall be calculated from the, formula:, , A, sv, , :::; _, 7:J SV, +, Vu s v, _.., hi lil (O.H7 j~), 2.5 eft ((J.~7./; ) ,, , hut the total transverse reinforcement shall not be less, than, where, (f\.e - f c, , V," = equivalent. shear,, Vu = shear,, 1·u = torsional moment, and, b, , 0.87 J~, where, , = breadth of beam,, , The equivalent nominal shear stress., , .lb.s,., , 'tv.., , in this case, , shall be calculated as given in 40.1, except for, , substituting \'u hy Vc' The values of r vc shall not exceed, the values of tt' mall given in Table 20., , "1:,, , torsional moment,, , '<I _., s,. =, , shear force,, , bi, , 41.3.2 If the equivalent nominal shear stress, 't\'l' docs, not exceed tl' given in .ablc 19, minimum shear, , d,, , .~., , 0-, , spacing of the stirrup reinforcement., centre-to-centre distance hctwccn Ct uner, bars in the direction of the width., centre-to-centre distance between corner, , bars,, , reinforcement shall he provided as per 26.5.1.6., , h, , 41.3.3 If t v\. exceeds t, given in Table 19. both, longitudinal and transverse reinforcement shall he, , -, , breadth of the member,, , t, .-, , characteristic strength of the stirrup, reinforcement,, , 41.4 Reinforcement in Members Subjected to, Torsion, , tw, , equivalent shear stress as specified in, , 41.4.1 Reinforcement for torsion, when required, shall, consist of longitudinal and transverse reinforcement,, , '(..., , provided in accordance with 41.4., , 41.3.1, and, , 41.4.2 Longitudinal Reinforcement, , In all normal cases. the deflection of a flexural member, will not he excessive if the ratio of its span to its, effective depth is not greater than appropriate ratios, given in 23.2.1. When deflections arc calculutcd, according to Annex C, they shall not exceed the, permissible values given in 23.2., , where, , = bending moment at the cross-section, and, t: (. I + !J, u, , shear strength of the concrete as rt.~r Table, It) ., , 42.1 Flexural Members, , M d =Mu +M,, , M. =, , -, , 42 LIMIT STATI~ OF SF:RVll~EABII.4IT\':, n E:I~~I.lE<.:'rl ON, , The longitudinal reinforcement shall he designed to, resist an equivalent bending 1l10111Cnl, Md - given by, , Mu, , -, , lb·), , 1.7, , 75

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IS 456: 2000, , •, , 43 LIMIT STATE OF SERVICEABILITY:, CRACKING, , 43.2 Compression Members, , Cracks due to bending in a compression member, subjectedto a design axial load greater than O.2fc.. Ac', whereJet, I" is the characteristiccompressivestrength of, concrete and Ac is the area of the gross section of the, member, need notbe checked. A member subjected to, lesser load than 0.2 let Ac may be considered, as flexural member for the purpose of crack control, (see 43.1)., , 43.1 Flexural Members, , In general,compliance with the spacing requirements, of reinforcement given in 26.3.2 should be sufficient, to control flexural cracking. If greater spacing are, required, the expectedcrack width should be checked, by formula given in Annex F., , "I)

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IS 456: ZOOO, , ANNEXA, (Clause 2), , LIST OF REFERREDINDIAN STANDARDS, nIle, , IS No., , 269 : 1989, , Specification for ordinary, Portland cement, 33 grade (fourth, , IS No., 1642: 1989, , Code of practice for fire safety, ofbuildings (aenn) : Details of, construction (first I'tvilio1l), , 1186: 1985, , Specification for high strength, deformed steelbarsand wiresfor, concrete reinforcement (third, , revision), , 383 : 1970, , Specificationfor coarse and fine, aggregates from natural sources, for concrete (second revision), , 432 (Part 1) :, , Specification for mild steel and, medium tensile steel bars and, hard-drawn steel wire for, concrete reinforcement: Part 1, Mild steel and medium tensile, steel bars (third revision), , 1982, , 4SS: 1989, , Specification for Portland slag, cement (fourth revision), , 516 : 19S9, , Method of test for strength of, concrete, , 875, , Codeof practicefor designloads, , (other than earthquake) for, buildingsand structures :, , ntle, , m'uioll), , 1791 : 1968, , Specification for batch type, concrete mixers(StCoM revision), , 1893 : 1984, , Criteria for earthquake resistant, design of structures (fourth, nvision), , 1904: 1986, , Code of practice for design and, construction of foundations in, soils : General requirements, (third revision), , 2062 : 1992, , Steel for general structural, purposes (fourth Tn'uion), , 2386 (Part 3) :, 1963, , Methods of test for aggreptes for, concrete: Part3 Specific pavity,, density, voids, absorption and, bulking, , 2502: 1963, , Code of practicefor bendingand, fixing of bars for concrete, reinforcement, , (Part 1) : 1987, , Dead loads - Unit weights of, building material and stored, materials (second revision), , (Part 2) : t 987, , Imposed loads (second revision), , (Part 3) : 1987, , Wind loads (second revision), , (Part 4) : 1987, , Snow loads (second revision), , (Part S) : 1987, , Special loads and load, combinations (second revision), , 2S05: 1980, , Concrete vibrators-Immersion, type - General requirements, , 1199: 1959, , Methods of sampling and, analysis of concrete, , 2506: 1985, , 1343 : 1980, , Code of practice for prestressed, concrete (first revision), , General requirements for screed, board concrete vibrators (first, revision), , 2514 : 1963, , 1489, , Specification for Portland, pozzolana cement :, , Specification for concrete, vibratingtables, , 2751 : 1979, , Recommended practice for, welding of mild steel plain and, , (Part 1) : 1991, , Fly ash based (third revision), , (Part 2) : 1991, , Calcined clay based (third, revision), , 1566 : 1982, , 1641 : 1988, , deformed bars for reinforced, construction (first Tn'ision), 3025, , Specification for hard-drawn, steel wire fabric for concrete, reinforcement (second revision), Code of practice for fire safety, of buildings (general): General, principles of fire grading and, classification (first revision), , Methods of sampling and test, (physical andchemical) forwater, and waste water:, , (Part 17) : 1984, , Non-filterable residue (total, suspendedsolids) (first ~vision), , (Part 18) : 1984, , Volatile and fixed residue (total, filterable and non-filterable) (first, revision), , 77

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IS 456: 1000, IS No., , Title, , IS No., , Title, , (Part 22) : 1986, , Acidity (first revision), , (Part 3) : 1972, , Concrete reinforcement, , (Part 23) : 1986, , Alkalinity (first revision), , (Part 4) : 1972, , Typesof concrete, , (Part 24) : 1986, , Sulphates (first revision), , (Part S) : 1972, , Pormworkfor concrete, , (Part 32) : 1988, , Chloride (first revision), , (Part 6) : 1972, , Equipment,tool and plant, , 3414 : 1968, , Code of practice for design and, installationofjoints in buildings, , (Part 7) : 1973, , 3812 : 1981, , Specification for fly ash for use, as pozzolana and admixture (first, revision), , Mixing, laying, compaction,, curing and other construction, aspect, , (Part 8) : 1973, , Properties of concrete, , (Part 9) : 1973, , Structuralaspects, , (Part 10) : 1973, , Tests and testing apparatus, , (Part 11) : 1973, , Prestressedconcrete, , (Part 12) : 1973, , Miscellaneous, , 395I (Part 1) :., 1975, , Specification forhollow claytiles, for floorsand roofs: Part 1Filler, type (first revision), , 403I(Part S):, 1988, , Methods of physical tests for, hydraulic cement : Part S, Determination of initialand final, setting times (first revision), , 4082 : 1996, , Recommendations on stacking, and storage of construction, materialsand componentsat site, , 6909: 1990, , Specification for supersulphated, cement, , 7861, , Code of practice for extreme, weatherconcreting :, , (Part 1) : 1975, , Recommended practice for hot, weather concreting, , (Part 2) : 1975, , Recommended practice for cold, weather concreting, , (second revision), , 4326: 1993, , 4656: 1968, 4845 : 1968, , Code of practice for earthquake, , resistantdesign and construction, of buildings (second revision), , 8041 : 1990, , Specification for form vibrators, for concrete, , Specification for rapid hardening, Portland cement(second revision), , 8043 : 1991, , Definitions and terminology, relating to hydrauliccement, , Specification for hydrophobic, Portland cement(second revision), , 8112 : 1989, , Specification for 43 grade, ordinary Portland cement (first, revision), , 9013 : 1978, , Method of making, curing, and determining compressive, strength of accelerated cured, concrete test specimens, , 9103 : 1999, , Specification for admixtures for, concrete (first revisiom, , 9417 : 1989, , Recommendations for welding, cold worked bars for reinforced, concrete construction (j; rst, , 4925 : 1968, , Specification for concrete, hatching and mixing plant, , 4926: 1976, , Specification for ready-mixed, concrete (second revision), , S816: 1999, , Method of test for splitting, tensile strength of concrete, (first revision), , 6061, , Codeof practiceforconstruction, of floor and roof with joists and, filler blocks:, , (Part 1) : 1971, , With hollow concrete filler, blocks, , (Part 2) : 1971, , With hollow clay filler blocks, (first revision), , 6452: 1989, 6461, , r~\lision), , Specification for high alumina, cement for structural use, , 11817 : 1986, , Classification of joints in, buildings for accommodation of, dimensional deviations during, construction, , 12089: 1987, , Specification for granulatedslag, for manufactureof Portland slag, cement, , 12119 : 1981, , General requirements for pan, mixers for concrete, , Glossary of terms relating to, cement:, , (Part J) : 1972, , Concrete aggregates, , (Part 2) : 1972, , Materials, 78

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IS 456: 1000, IS No., , IS No., , Title, , 12269 : 1981, , Specification for S3 grade, ordinary Portland cement, , 12330: 1988, , Specification for sulphate, resisting Portland cement, , 12600 : 1989, , Specification for low heat, Portland cement, , 13311, , Methods of non-destructive, testing of concrete:, , Title, , (Pan I) : 1992, , Ultrasonic pulse velocity, , (Pan 2) : t 992, , Rebound hammer, , 13920: 1'993, , Code of practice for ductile, detailing of reinforced concrete, structures subjected to seesmic, forces, , 14687 : 1999, , Guidelines for falsework for, concrete structures, , 79

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IS 456: 2000, , ANNEX B, (Clauses 18.2.2,22.3.1,22.7.26.2.1 and 32.1), STRUCTURAL DESIGN (WORKING STRESS METHOD), , 8-1 GENERAL, , c) The stress-strain relationship of steel and, concrete, underworking loads,is a straight line., , B-l.1 General Desiln Requirements, , d) The modular ratio m has the value 280., , The general design requirements of Section 3 shall, apply to this Annex., , 30'cbc, , wherea c~hc is permissible compressive stress due, to bending in concretein N/mm2 as specified in, Table21., , 0-1.2 Redistribution of Moments, , Exceptwherethe simplified analysis usingcoefficients, (see 22.5) is used, the moments over the support" for, any assumed arrangement of loading, including the, deadload moments may each be increased or decreased, hy not more than 15 percent, provided that these, modified moments over the supports are used for the, calculation of thecorresponding moments in the spans,, , NOTE- The expression given for m panially takes into, account long-termeffects such as creep. Therefore this In, is not the same Wi the modular ratio derived bDSC~d on the, valueof Ef: givenin 6.2.3.1., , B-2 PERMISSIBLESTRESSES, B-2.1 PermL.sible Stresses in Concrete, Permissible stressesfor the variousgradesof concrete, shall he taken as those given in Tables 21 uno 23., , 8-1.3 Assumptions for DesilD of Members, , In the methods based on elastic theory, the following, assumptions shall be made:, , NOTE - For increase in strength with Qie 6.1.1 shall be, upplicable.The values of permissible stres~ shall he nbruined hy, interpolation betweenthe gradesof concrete., , ill At any cross-section. plane sections before, bending remain plain after bending., , B-2.1.1 DirectTension, For members in direct tension, when full tension is, taken by the reinforcement alone, the tensilestressshall, be not greater than the values given below:, , b) All tensile stresses arc taken up by reinforcement, and none by concrete. except as otherwise, specifically permitted., Grad« til, COli, , f,.,, , M I(), , M I~, , M20, , M2~, , M~O, , M3~, , M40, , M4~, , 1.2, , 2.0, , 2.8, , 3.2, , 3,6, , 4.0, , 4.4, , 4.8, , M~O, , It, , T",I.fUt Stress,, Nllnlll', , The tensile stress shall be calculatedas, , F, , 0-2.2 Permissible Stresses in Steel Reinforcement, , A". +mA. t, , Pennissiblc stresses in steel reinforcement shell not, exceed the values specified in Table 22., , f, , where, FL, , 8-2.2.1 In flexural members the value of 0'.. given in, Table 22 is applicable at the centroid of the tensile, , = total tension on the member minus pre-, , reinforcement subject tothecondition thatwhen more, than one layer of tensile reinforcement is provided,, , tension in steel. if any, before concreting:, A\:, , ~.2, , = cross-sectional areaot'concrete excludina, , the stress at the centroid of the outermost layer shall, not exceed by more than 10percent the value given in, , any finishing material and rcinforcina, stee]:, , n,, , == modular ratio: and, , A.., , = cross-sectional area of reinforcing steel, , TobIe 22., 8-2.3 Increase in Permlaslble Stresla, Wherestresses dueto wind(orearthquake) temperature, and shrinkage effects are combined with those due to, dead, live and impact load, the stresses specified in, Tables 21 22 and 23 may be exceeded upto a limit of, , in tension., n-1.1.% Bond Stressfor Deformed Bars, , t, , In the case of defanned bars conforming to IS 1786,, the bond stresses given in Tahle 21 may be increased, by 60 percent., , 33.!. percent. Wind and seismic forces need not be, , 3, considered as acting simultaneously., , 80

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IS 456: 2000, , Table 21 Permissible Stresses in Concrete, (Clauses B·l.3. B·2.1. B-2.l.2.B-2.3 and B·4.2), All values in Ntmml ., , <Yrade 01, Concrete, , Permissible Stress In Compression, , (1), , Permissible Strea, , Bending, , Direct, , In Bond (Averale) for, Plain Bars In Tension, , (2), , (3), , (4), , <,, , 0", , M 10, , 3.0, , 2.5, , M 15, , 5.0, , 4.0, , M20, , 7.0, , 5.0, , 0.8, , M2S, , 8.5, , 6.0, , 0.9, , M30, , 10.0, , 8.0, , 1.0, , 1.1, , 0.6, , M 35, , 11.5, , lJ.O, , M40, , 13.0, , 10.0, , 12, , M45, , 14.5, , 11.0, , 1.3, , M 50, , 16.0, , t2.0, , 1.4, , NOTES, , I The values of permissible: shear stress in concrete are given in Table 23., 2 The bond stress given in col 4 shall be increased by 25 percent for bars in compression., , multiplication of the appropriatemaximumpermissible, stress as specified under B-2.1 and B-2.2 by the, coefficient C, given by the following formula:, , B-3 PERMISSIBLE LOADS IN COMPRESSION, MEMBERS, B-3.1 Pedestals and Short Columns with Lateral, Ties, The axial load P permissible on a pedestal or short, column reinforced with longitudinal bars and lateral, ties shall not exceed that given by the following, equation:, , C, r, , where, C,, , I",, b, , where, 0n, , =, , permissible stress in concrete in direct, compression., , A,., , =, , cross-sectional area of concrete, excluding any finishing material and, reinforcing steel., , 0"", , =, , permissible compressive stress for, column bars, and, , A",, , =, , cross-sectional area of the longitudinal, steel., , = reduction coefficient:, = effective length of column; and, = least lateral dimension of column;, , for, column with helical reinforcement, b is, the diameter of the core., , For moreexact calculations, the maximum permissible, stresses in a reinforced concrete column or part thereof, having a ratio of effective column length to least lateral, radius of gyration above 40 shall not exceed those, which result from the multiplication of the appropriate, maximum permissible stresses specified under B.2.1, and 0-2.2 by the coefficient C, given by the following, formula:, , NOTE - The minimumeccentricity mentioned in 25.4 may he, deemed to be incorporated in the above equanon., , Cr, , B-3.2 Short Columns with Helical Reinforcement, , =1.25 _, , le~, IbO'min, , where i miP is the least radius of gyration., , The permissible load for columns with helical, reinforcementsatisfying the requirementof 39.4.1 shall, be 1.05 times the permissible load for similar member, with lateral ties or rings., , B-3.4 Composite Columns, a) Allowable load - The allowable axial load P, on a composite column consisting of structural, steel or cast-iron column thoroughly encased in, concrete reinforced with both longitudinal and, spiral reinforcement. shall not exceed that given, hy the following formula;, , B-3.3 Long Columns, The maximum permissible stress in a reinforced, concrete column or part thereof having a ratio of, effectivecolumn length to least lateraldimensionabove, 12 shall not exceed that which results from the, , 2116815/07-12, , =1.25 _.!SL, 48b, , 81

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IS 456: 2000, Table 22 Permissible Stresses in Steel Reinforcement, (Clauses 8-2.2, 8-2.2.1, B-2.3 and B..4.2), No., , l2), , (l), i), , ii), , Permissible Stresses In N/mm2, , Type of Stress In Steel, Reinforcement, , SI, , Tension ( 0"1 or, , Mild Steel Ban, Conforming to, Grade I of, IS 4J2 (Pan I), , MediumTensile, Steel Conforming to IS 432, (Port 1), , forming to IS 1786, (Grade Fe 41S), , (3), , (4), , (5), , 011), , a) LJp (0 and including, 20 mm, , 140, , b) Over 20 rom, , 130, , Compression in column, , I, , Half the guaranteed, yield stress subject, to a maximum of 190, , High YieldStrength, , Deformed Bars Con-, , 230, , 230, , 130, , 130, , 190, , bars (all), , iii), , Compressionin bars in a, bean) or slab when the compressive resistanceof the, concrete is taken into account, , iv), , Compressionin bars in a, beam or slab where the, compressiveresistance, of the concrete is not, taken into account:, , The calculated compressive stress in the surrounding concrete multiplied by 1.S times, the modularratio or 0.: whicheveris lower, , a) Up to and including, , 20mm, b) Over 20 mm, , 140, , I, , Half the guaranteed, yield stress subject, to a maximum of 190, , 190, , J90, , 130, , NOTES, 1 For high yield strengthdeformedbars of Grade Fe SOO the permissible stress in direct tension and flexural tension shall be Oj~.f~., The permissiblestresses for shear and compression reinforcement shall be as for GradeFe 415., 1 For welded wire fabric conformingto IS 156fl, the permissible value in tension CJIII is 230 Nzmm'., 3 For the purpose of this standard, the yield stress of steels for which there is no clearly defined yield point should be taken to be, 0.2 percent proof stress., 4 When mild steel conforming to Grade II of IS 432 (Part I) is used, the permissible stresses shall be 90 percent of the permissible, stressesin col 3,or if the designdetailshave already beenworkedout on thebasisof mildsteelconformingto GradeI of IS 432 (Pan, I); the area of reinforcement shall be increased by 10 percent of that required for Grode I steel., , where, , 20 percent of the gross area of the column. If a, hollow metal cote is used, it shall be filled with, concrete.The amount of longitudinal and spiral, reinforcement andtherequirements as to spacing, , = permissible stress in concrete in direct, , (J cc, , compression:, At" = net area of concrete section; which is, , (J, , ~., , =, , of bars, details of splices and thickness of, protectiveshelloutside the spiral, shall conform, to require- rnents of 16.5.3. A clearance of at, least 75 mm shall be maintained between the, spiral and the metal core at aJl points, except, , equal to the gross area of the concrete, section - AIC - Am;, permissible compressive stress for, column bars;, , A = cross-sectional area of longitudinal bar, ~(.', , (J me, , =, , that when the core consists of a structural steel, H-column, the minimum clearance may be, , reinforcement;, allowable unit stress in metal core, not to, , reduced to 50 mrn,, , exceed 125 N/mm 2 for a steel core, or, 70 N/mm2 for a cast iron core; and, , Am = the cross-sectional areaof thesteel or cast, , c) Splicesand connections ofmetalcores- Metal, cores in compositecolumns shall be accurately, milled at splices and positive provisions shall, , Metal core and reinforcement - The crosssectional area of the metal core shall not exceed, , another. At the column base. provisions shall be, , iron core., , b), , be made for alignment of one core above, , 82

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IS 456: 2000, made to transfer the load to the footing at safe, unit stresses in accordancewith 34. The base of, the metal section shall be designed to transfer, the load from the entire composite columns to, the footing. or it may be designed to transfer, the load from the metal section only. provided, it is placed in the pier or pedestal as to leave, ample section of concrete above the base for the, transfer of load from the reinforced concrete, section of the column by means of bond on the, vertical reinforcement and by direct, compressionon the concrete. Transferof loads, to the metal core shall be provided for by the, useof bearingmembers, suchas billets,brackets, or other positive connections, these shall be, provided at the top of t.he metal core and at, intermediate floor levels where required. The, column as a wholeshall satisfy the requirements, of formula given under (a) at any point; in, addition to this, the reinforced concrete portion, shall be designed to carry, according to a-3.1, or B-3.2 as the case may be, all floor loads, brought into the column at levels between the, metal brackets or connections. In applying the, formulae under B-3.1 or 8-3.2 the gross area of, column shall be taken to be the area of the, concrete section outside the metal core, and the, aJlowable loadon the reinforced concrete section, shall be further limited to 0.28.t::k times gross, sectional area of the colurnn., , b) TIleresultant tension in concrete is not greater, than 35 percentand 25 percentof the resultant, compressionfor biaxial and uniaxial bending, respectively, or does not exceed three-fourths,, the 7 day modulus of rupture of concrete., NOTES, , 1a, , =, , lu.• 1, , P, for columnswithties where P. A. and, A,. +1.5mA-.., ', , A... definedin B-3.1and m is the modularratio., , 2, , O'l. huIII, , :::, , ZM, , where M equals the moment and Z equals, , modulus of section. In the caseof sectionssubjectto moments, in twodirections, the stress shall becalculated separately nod, added algebraically., , 8-4.2 Design Based on Cracked Section, If the requirements specified in 8-4.1 are not satisfied,, the stresses in concrete and steel shall be calculated, by the theory of cracked section in which the tensile, resistance of concrete is ignored. If the calculated, stresses are within the permissible stress specified in, Tables21, 22 and 23 the section may be assumed to be, safe., NOTE- The maximum stress in concrete and steel may be, found fromtablesandchartsbasedon thecrackedsectiontheory, ordirectly by determining the no..stresslinewhichshouldsatisfy, the following requirements:, a), , The direct load shouldhe equal to the algebraic sum of, the forces on concreteand steel,, , b) The moment of the external loads about any reference, lineshouldbeequalto the algebraic sumof the moment, of the forces in cancrete (ignoring the tensile force in, concrete) and steel about the same li~. "and, , d) Allowable Load on Metal Core Only - The, metal core of composite columns shall be, designed to carry safely any construction or, other loads to be placed upon them prior to their, encasement in concrete., , c), , B-4 MEMBERS SUBJECTED TO COMBINED, , The moment of the external loads about any other, reference lines should be equal to the algebraic sum of, the mOlneft1 of theforcesinconcrete (ignoring thetensile, forcein concrete)and steel about the same line., , AXIAL LOAD AND BENDING, B4.3 Members Subjected to Combined Direct, Load and Flexure, , 8-4.1 Design Based on Uneracked Section, , A member subjected to axial load and bending (due to, eccentricity of load. monolithic construction, lateral, forces, etc) shall be considered safe provided the, following conditions are satisfied:, , Members subjected to combined directloadand flexure, and shall be designed by limit slate method as in 39.5, afterapplying appropriate load factors as given inTable, 18., , a Ct, cal, , a), , ace., , +, , (1 chc,cal, , ~, , 1., , B-S SHEAR, , 0cbc, , B-S.l Nominal Shear Stress, , where, ace,e,l!, , The nominal shear stress r v in beams or slabs of, unifonn depth shall be calculated by the following, equation:, , = calculated direct compressive stress, in concrete,, , <Tce, , = permissible axialcompressivestress, in concrete,, , ach~,f.~aal, , = calculated bending compressi ve, , tv, , stress in concrete, and, ache, , V, , =-, , bel, , where, , = permissible bending compressive, , V = shear force due to design loads,, , stress in concrete., 83

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IS 456: 2000, b, , = breadthof the member, whichfor flanged, sections shall be taken as the breadth of, , B-S.Z.l.1 For solid slabs the permissible shear stress, in concrete shall be kfc where k has the value liven, , the web, and, , below:, , d = effective depth., , Ovemlldepth 300ar 275 2SO 22S 200 175 150(1", ofslab, mm more, less, k, 1.00 1.05 1.10 1.1S 1.201.25 1.30, , B-S.l.1 Beamsof Varying Depth, In the case of beams of varying depth, the equation, , NOTE- This does not apply to l1at slabs for which31-' shall, apply., , shall be modified as:, , 8-5.2.2 Shear Strength of Members Under Axial, Compression, For members subjected to axial compression P., the permissible shear stress in concrete t c given, in Table 23, shalt be multiplied by the following, factor:, , v ± Mlanfj, f, , v, , =, , bd, , d, , where, t y ' V, band d are the same as in B-5.1,, , M =, ~, , ~ =1+~' but not exceeding 1.5, , bending moment at the section, and, , A.fc:k, , = angle between the top and the bottom, edges of the beam., , where, , p = axial compressive force in N,, , The negative sign in the formula applies when the, bending moment M increases numerically in the same, direction as the effective depth d increases, and the, positivesign when the momentdecreasesnumerically, in this direction., 8-5.2 Design Shear Strength, , A,, , =, , Ie.., , = characteristic compressive strength of, concrete., , grossareaof theconcrete sectionin mm',, , and, , 8-5.2.3 With Shear Reinforcement, , or Concrete, , When shear reinforcement is provided the nominal, shear stress f c in beamsshall not exceed f c ..... given in, Table 24., , 8-S.2.1 The permissible shear stress in concrete in, , beams without shearreinforcement is given in Table 23., , Table 23 Permissible Shear Stress in Concrete, (Clauses B-2.1,B-2.3, 8-4.2, 8-5.2.1, B-S.2.2, B-s.3, B-S.4, 8 ..5.5.1, 8.5.5.3,, , l00~, , B·6.~.2.B-6.3.3, , and 8-6.4.3 and Tabl~ 21), , Permissible Shear Stress in Concrete, t c' N/mm J, , bd, , Grade of Concrete, , MIS, , M20, , M2S, , M30, , M3S, , M40, , and above, (I), , (2), , (3), , (4), , (S), , (6), , (7), , 0.20, 0.23, , S O.IS, , 0.18, , 0.18, , 0.19, , 0.20, , 0.20, , 0.25, , 0.22, , 0.22, , 0.23, , 0.23, , 0.23, , O.SO, , 0.29, , 0.30, , 0.31, , 0.31, , 0.31, , 0.32, , 0.7S, , 0.34, , 0.3S, , 0,36, , 0.37, , 0.37, , 0.38, , 1.00, 1.25, 1.50, , 0.37, , 0.39, , 0.40, , 0.41, , 0.42, , 0.42, , 0.40, , 0.42, , 0.44, , 0.45, , 0.45, , 0.46, , 0.42, , 0.45, , 0.46, , 0.48, , 0.49, , 0.49, , 1.7~, , 0.44, , 0.47, , 0.49, , O.SO, , 0.52, , 0.52, , 2.00, , 0.44, , 0.49, , O.SI, , 0.53, , 2.25, 2.S0, , 0.44, , 0.~3, , o.~s, , 0.'4, 0.'6, , 0.55, 0.56, , 0.S7, 0.58, , 0.S7, , 0.60, , O.SS, 0.57, 0.60, 0.62, 0.63, , 2.7S, , 0.44, , 0.51, 0.51, 0.51, , 3.00 and, , 0.44, , o.s:, , 0.44, , o.sa, 0.60, 0.61, , above, NOTE- A. is thatareaof longitudinal tension reinforcclncnt which continues at leastoneeffedivc deplhbeyond the lettian beiDI, considered exceptat support.~ wherethe full area of tension reinforcement may be usedprovided the detai1inlconfotml to 26.2.2and, 26.2.3., , 84

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IS 456: 2000, , 8-5.2.3.1 For slabs, T shall not exceed half the value, of f t mal given in Table 24., , greater than 230 N/mn1, , y, , 2, ,, , = angle between the inclined stirrup or, , ex, , bent-up bar and the axis of the member,, not less than 45u • and, , B-S.3 Minimum Shear Reinforcement, , When t y is less than t c given in Table 23. minimum, shear reinforcement shall be provided in accordance, with 26.5.1.6., , = effective depth., , d, , Nf)TE -- Where mort.than one type of shear reinforcementis, used to reinforce the same portion of the beam. the Iota) shear, , B-5.4 Design of Shear Reinforcement, , resistance shall be computed as the sum of the resistance for the, various types separately. The area of the stirrups shall not be, , When tv exceeds t, given in Table 23, shear, reinforcement shall beprovidedin any of the following, , less than the minimumspecified in 26.5.1.6., , forms:, , 8-5.5 Enhanced Shear Strength of Sections Close, to Supports, , a) Vertical stirrups,, b) Bent-up bars along with stirrups. and, c) Inclined stirrups., , 8-S.5.1 General, Shear failure at sections of beams and cantilevers, , Where bent-up bars arc provided, their contribution, towards shear resistance. shall not be more than half, that of the total shear reinforcement., , without shear reinforcement will normally occur on, plane inclined at an angle 30" to the horizontal. If the, angle of failure plane is forced to ~c inclined more, , Shear reinforcementshall beprovided to carry a shear, equal to V- 'tc.bd. The strengthof shear reinforcement, V!' shall be calculated as below:, a) For vertical stirrups, , steeply than this Ibecause the section considered, (X - X) in Fig. 24 is close to a support or for other, , vs, , = O'sv, , reasons], the shear force required to produce failure is, increased., The enhancement of shear strength may be taken, into account in the design of sections near a support, hy increasing design shear strength of concrete, ',., to 2d r/a,. provided that the design shear stress at, the face of support remains less than the values, given in Table 23. Account may be taken of the, enhancement in any situation where the section, considered is closer to the face of a support of, concentrated load than twice the effective depth, d., To be effective, tension reinforcement should extend, on each side of the point where it is intersected hy a, possible failure plane for a distance. at least equal to, the effective depth, or be provided with an, equivalent anchorage., , Asv d, Sv, , h) For inclined stirrups or a series of bars bent..up, at different cross-sections:, , ~, , = C1sv ~v d (sin a + cos a), Sv, , c) For single bar or single group of parallel bars,, all bent-up at the same cross-section:, ~, , =G., , v, , Asv SiD ex, , where, , Asv, , = totalcross-sectional areaof stirrup legs, or bent-up bars within a distance,, , 8-5.5.2 Shear Reinforcement for Sections Close to, Supports, , = spacing of the stirrups or bent-up bars, along the length of the member,, , ~~y, , tc, , =, , b, , = breadth of the member which for, flanged beams, shall be taken as the, breadth of the web bwt, , =, , (J"y, , If shear reinforcement is required, the total area of this, is given by:, , design shear strength of the concrete,, , permissible tensile stress in shear, reinforcementwhichshall not be taken, , =, , A" avb ( f v, , .., , 2d fJav )/O.87fy ~ O.4a v b /O.R~f), , This reinforcement should be provided within the, middle three quarters of avo Where Q v is less than .l., horizontal shear reinforcement will be more effective, than vertical., , Table 24 Maximum Shear Stress, "r ma.' N/mm1, (Clauses 8-5.2.3. 8·5.2.3. t, 8..5.5,1 and B-6.3.1), Concrete Grade, , \'m••' N/mm, , 1, , M )~, , M20, , M2~, , MJO, , 1.6, , 1.8, , 1.9, , 2.2, , 85, , ~1, , 2.J, , 40 and above, , 2.5

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IS 456: 2000, , v, , 8-5.5.3 Enhanced Shear Strength Near Supports, (Simplified Approach), , = shear., T = torsional moment, and, b = breadth of beam., , The procedure given in D-S.S.l and 8-5.5.2 may be, used for all beams. However for beams carrying, generally uniform load or where the principal load is, located further than 2 d from the face of support, the, shear stress may be calculated at a section a distance d, , from the face of support. The valueof, , tc, , The equivalent nominal shear stress, 'Ye' in this case, shalJ be calculated as gi yen in B-5.1, except for, , substituting V by Ve • The values of 1'vc shall not exceed, the values of 'c max given in 'fable 24., , is calculated, , B-6.3.2 If the equivalent nominal shear stress, , in accordance with Table 23 and appropriate shear, reinforcement is provided at sections closer to the, , support, no further check for such section is required., 8-6 TORSION, 8-6.1 General, , In structures where torsion is required to maintain, equilibrium, members shall be designed for torsion in, accordance with8-6.2, 8-6.3 and 0-6.4. However, for, such indeterminate structures where torsion can be, eliminated by releasing redundent restraints, no, specific design for torsion is necessary provided, torsional stiffness is neglected in the calculation of, internal forces. Adequate control of any torsional, cracking is provided by the shear reinforcement as, per B-S., , 8-6.4 Reinforcement in Members Subjected to, Torsion, B-6.4.1 Reinforcement for torsion, when required,, shall consist of longitudinal and transverse, , reinforcement., B-6.4.2 Longitudinal Reinforcement, The longitudinal reinforcement shall be designed to, resist an equivalent bending moment, Mr l , given by, Mel :::M+Mr, where, M = bending moment at the cross-section, and, , NOTE- The approachto design in this clause for torsionis as, follows:, , Torsional reinforcement is not calculated separately from, that required for bending and shear. Instead the total, longitudinal reinforcement is determined for n fictitious, bending moment which is a function of actual bending, , Ml = T, , moment and torsion; similarly web reinforcement is, , (J+D/b), , 1.7, , ,where T is the torsional, , moment, D is the overall depth of the, beam and b is the breadth of the beam., B-6.4.2.1 If the numerical value of Ml as defined, in 8-6.4.2 exceeds the numerical value of the moment, M longitudinal reinforcernent shall be provided on, the flexural compression face, such that the beam can, also withstand an equivalent moment Mt.2 given by, Mez Ml-M, the momentMe2 being taken as acting in, the opposite sense to the moment M., , determinedfor a fictitious shearwhichis Il function of IlCtual, shear and torsion., , 8-6.1.1 The design rules laid down in 8·6.3, and 8-6.4 shall apply to beams of solid rectangular, cross-section. However, these clauses may also be, applied to flanged beams by substituting bw for b, in, which case they are generally conservative; therefore, specialist literature may be referred to., , t, , =, , B-6.2 Critical Section, , 8-6.4.3 Transverse Reinforcement, , Sections located less than a distance d. from the face, of the support may be designed for the same torsion as, computed at a distance d, where d is the effective, depth,, , Two legged closed hoops enclosing the corner, longitudinal bars shall have an area of cross-section, A.y ' given by, , -,v =bId)T,s;"+ 2.5dV'Sv(J,v, , A, , B-6.3 Shear and Torsion, , (Jay, , B-6.3.1 Equivalent Shear, , (tv. - t c) b.s, a.v, , formula:, •, , b, , • where, , T = torsional moment., , where, ~, , t, , but the totaI, , 1, , transverse reinforcement shall not be less than, , Equivalent shear, Ve shall be calculated from the, , v = V+1.6 T, , 'rye does, , not exceed fe' given in Table 23. minimum shear, reinforcement shall be provided as specified, in 26.5.1.6., 8-6.3.3 If 1'ye exceeds 1'\; given in Table 23, both, longitudinal and transverse reinforcement shall be, provided in accordance with B-6.4., , = equivalent shear,, , V, , 86, , =, , shear force., , y

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IS 456: 2000, , ANNEX C, (Clauses 22.3.2, 23.2.1 and 42.1), CALCULATION OF DEFLECTION, Col TOTAL DEFLECTION, , For continuous beams, deflection shaJl be calculated, using the values of It' lit 'and Mr modified by the, following equation:, , C-I.l Thetotaldeflection shallbe takenasthe sumof, the short-term deflection determined in accordance, with C-2 and the long-term deflection, in accordance, with C-) and C-4., , Xe = k. [ XI +2 Xl] + (I - k l ) Xo, where, , C-2 SHORT-TERM DEFLECTION, , Xe = modified valueof X,, XI' Xl = values of X at the supports,, XII = valueof X at mid span,, k, = coefficient givenin Table 2S, and, X valueof It'I" or Mr as appropriate., , C-2.1 The short-term deflection maybecalculated by, the usual methods for elastic deflections using the, short-term modulus of elasticity of concrete, E( and, an effective moment of inertia leff given by the, following equation:, , =, , I, , C-3 DEFLECTION DUE TO SHRINKAGE, C-3.! The deflection due to shrinkage a.. may be, computed from the following equation:, 2, , ae. = k3 Y'cs 1, where, I,, , where, k, is a constant depending upon the suppon, . conditions,, O.S for cantilevers,, 0.125 for simply supported members., 0.086for members continuous at one end,, and, 0.063for fully continuous members., , = moment of inertiaof the cracked section,, , M,, , = cracking moment, equal to ferYtI", , where, , I., is the modulus of rupture of concrete,, I g, is the moment of inertia of the gross, , section about the centroidal axis,, neglecting the reinforcement, andY,is the, distance from centroidal axis of gross, section. neglecting the reinforcement, to, extreme fibre in tension., M = maximum moment under service loads,, z = lever arm., .r = depth of neutral axis., d = effective depth., b w = breadth of web.and, b, breadth of compression face., , e, v; is shrinkage curvature equal to k. =t, where, , f:ea is theultimate shrinkage strainof concrete, , (Set 6.2.4)., , k., , =, , =0.72 x, , P,~ s 1.0for 0.25 s P.- Pc < 1.0, , = 0.65 x, , 1',~ s 1.0 for PI - r, ~ 1.0, , 1',, , 1',, , Table 2S Values of Coefficient,k,, (Clause C-2.1), 0.5 or less, , 0.6, , 0.7, , 0.8, , 0.9, , 1.0, , J.I, , 1.2, , 1.3, , 1.4, , o, , 0.03, , 0.08, , 0.16, , 0.30, , 0.50, , 0.73, , 0.91, , 0.97, , 1.0, , NOTE -, , *1, , is given by, , where, MI' M!, , Mf , . M,.!, , = supportmoments. lind, , = lixed end momenta., , 88

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IS 456: 2000, where, , where P=~andP=~, 'bd, , c·, , ai.cc(pmn) = initial plus creep deflection due to, permanentloads obtained using an, elastic analysis with an effective, modulus of elasticity,, , bd, , and D is the total depth of the section, and I is the, length of span., C-4 DEFLECTION DUE TO CREEP, , E, , ce, , C-4.1 The creep deflection due to permanent loads, , and, , aL'C(fICI'II') may be obtained from the following equation:, , 2116 818/07-13, , = ~., 9 beingthe creepcoefficient,, 1+8', , ai(.,erm), , 89, , = short-term, , deflection due to, permanent load using Ec •

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IS 456: 2000, , ANNEX D, (Clauses 24.4 and 37.1.2), SLABSSPANNING IN TWO DIRECTIONS, , o-i RESTRAINEDSLABS, , D-I.6 Ata discontinuous edge,negative moments may, arise. Theydepend on the degreeof fixity at the ~ge, of theslab but, in general,tensionreinforcement equal, to SO percent of that provided at mid-spanextending, 0.1 I into the span will be sufficient., , 1)-1.0 When the comers of a slab are prevented from, lifting, the slab may he designedas specifiedin D-I.l, to D-l.11., D-1.1 The maximum bendingmoments per unitwidth, in a slab are given by the following equations:, , D-t.7 Reintorcement in edge strip, parallel to that, edge, shallcomplywith the minimum given in Section, 3 and lhp. requirements for torsion given in D-t.S, to 1)..1.10., , u, =ax wi;, My, , :::(X, , )', , wlx2, , D·UI Torsion reinforcement shall be providedat any, corner where the slab is simply supported on both, edges meeting at that comer. It shall consist of top, and bottom reinforcement, each with layers of bars, placed parallel to the sides of the slab and extending, from the edges a minimum distance of one-fifth of, the shorterspan.The area of reinforcement in each of, these four layers shall be three-quarters of the area, required for the maximum mid-span moment in the, slab., , where, , u. and <Xy art:coefficients given in Table 26,, w, , M., My, , = total design load per unit area,, = moments on strips of unit width, , spanning I. and ly respectively,, and, I, and I y = lengths of the shorter span and, longerspan respectively., , D-l.2 Slabsareconsidered all divided ineachdirection, into middlestrips and edge strips as shown in Fig. 25, the middle strip being three-quarters of the widthand, each edge strip one-eightof the width,, 0-1.3 The maximum moment... calculatedas in 0.1.1, apply only to the middle strips and no redistribution, shall be made., {)-1.4 Tensionreinforcement providedat mid-span in, the middle strip shall extend in the lower part of the, slab to within 0.25 I of a continuousedge, or O. J5 lof, a discontinuous edge., 0-1.5 Over the continuous edges of a middle strip,, the tensionreinforcement shallextendin the upperp,art, of the slab a distanceof O. J5 1fromthe support.and at, least 50 perceent shall extend a distance of 0.3 I., , ,_.--t:t---I, , r~ T-'--Iii, , I, , •I, MIOOLE STRIP, , l-i 1 ~, 25A, , 1E0G, 1ST, , I, I, I, , oJ- Ly -----J j, FOR, , SPAN, , 0-1.9 Torsion reinforcement equal to half that, described in D-t.S shall be provided at a corner, contained by edges over only one of which the slab is, continuous., , D-l.tO Torsion reinforcements need not be provided, at any comer containedby edges over both of which, the slab is continuous., , V, , D-1.11 Torsion I. is greater than 2, the slabs shall, be designed as spanningone way., 0-2 SIMPLY SUPPORTEDSLABS, D-Z.1 When simply supported slabs do not have, adequate provision to resist torsion at comers and to, prevent the corners from lifting, the maximum, , r, , Ly, , -,, , l "------!'!!'!.~---~-. ~, . ~. ., , .1, L-----.-sToi----- ~, MIOOL.I STRP, , l-, , ~, , 258, , FOR SPAN ~, , PIO. 25 DIVISION Of SLAB IN1U MIDl>LE AND EOOE STRIPS, , 90, , .+,

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IS 456: 2000, Table 26 Bending Moment Coefficients for Rectangular Panels Supported on, Four Sides with Provision for Torsion at Corners, (Clau.fcs, , Case, , Type of Panel and, , No., , Mumenls COlLctldered, , D- J .1, , alit}, , 24.4. 1), , Short Span, , (~oemcient5 fl., , (Values, , Leng Span, , or 1,11. ), , Coemclenltt, , (2), , (I), , Interior P(",~/.~:, Negative moment at continuous edge, Positive rnornentat nlid-span, 2, , 4, , ~, , (,, , On« Ltm~ EtiNt Discontinuous:, Negative moment at continuous edge, Positive moment at mid-span, , 1.2, , 1.3, , 1.4, , 1.5, , 1.75, , 2.U, , (3), , (4), , (~), , (6), , (7), , (8), , (9), , ClO), , O.O's1, O.OJ9, , 0.053, 0.041, , 0.060, , 0.065, 0.049, , 0.032, 0.024, , (II), , O.()32, , 0.037, , 0.024, , 0.028, , O.04J, 0.032, , (lOJ6, , O.OJ7, , O.04J, 0.OJ2·, , (Ul48, O.(H6, , 0.055, 0.041, , (l.O57, , 0.064, , 0.06&, , 0.037, , 0.019, , 0.044, , 0.048, , 0.052, , 0.028, , 0.044, O.03J, , OJl~2, , n.OS1, , 0.063, , ()J)44, , 0.047, , Ooll67, OJ}51, , 0.077, , n.()J9, , O.O~9, , 0.085, O,()65, , 0.028, , 0.084, 0.063, , 0.091, 0.069, , ().{n~, , O.()47, , 0.045, , O.fl28, , O.cn7, (),02H, , O.()~I, , ()'O~7, , Negative moment at continuous edge, , 0.047, , O.05J, , (Ul60, , o.oe.. s, , n.n71, , 0.075, , Positive moment .&1 null-span, , O.(n~, , 0.040, , O.()4~, , O.()4<J, , ().O~J, , ().O~6, , TwoShort EtlJ.:e'.~ /Ji.\TO,,,i'UIfIUS:, Nc~ativc moment at continuous edge, Positive moment at mid-span, , n.045, , O,()49, , o.n56, 0.043, , 0.059, 0.044, , 0.065, , 0.069, , ().()~7, , 0.052, 0.040, , 0.060, , ().(n~, , 0.045, , 0.049, , (U)~2, , O.()J~, , (Un~, , O.04J, , 0,051, , 0.057, , 0,{.>63, , 0.068, , 0.080, , O.08R, , ().cn~, , 0.057, O.04J, , n.064, , 0.071, , O.07lJ, , O.USO, , O.O~:l, , 0.051, , O.fKlO, , 0.084, n.064, , ().()l) J, , n.04S, , 0.069, , OJ)'}?, 0.073, , 0.043, , Positive moment at .....d-span, , ().tl4~, , O.O~I, , ().O~9, , (l.(Xl~, , 0.071, , 0.076, , 0.087, , 0.096, , O.04~, , Fo"I' EdJ.:I·.\' Discontinuous:, Pll\itivl~ moment at mid-span, , ().()~(;, , 0,064, , 0.072, , 0.079, , O.08S, , 0.089, , 0.107, , ().O~6, , 0.047, , Two /""IIg Hd~('." Discontinuous:, O,()4~, , '1'1,,·(,(, 1:·tI,t:t',\' [)i,f",mt;NulIlI.\·, (Ollt' l.oll}!, , Edg« Continuous):, , Ncgntive moment at continuous edge, , Pn'\ltivc moment at Il'lid-silan, , X, , 'I'., , 1.1, , Two Adjllft'''' Edges Discontinuous:, , Negative moment at continuous edge, Positive moment at mid-span, 7, , ~, , 1.0, , One Slulrl EtIJ.!e Continuous:, , Negative moment at continuous edge, Positive moment at mid-span, ], , for All, Values of, , (l,, , ,.., , Thrc« EII~("'t Di.'t((lIlt;""o,,..., Shorl Edge,' Conunuous) :, , «(Jill', , O.()~7, , Negative moment at eonunuous edge, , 9, , 0.100, , and u x and a y are moment coefficients, given in Table 27, , moments per unit width arc given by the following, equation:, , =a, ~'" I;, .,, My =a y ,,\./;, , D-2.I.l A;t least 50 percent of the tension, reinforcement provided at mid-span should extend, to the supports. The remaining 50 percent should, extend to within 0.1 II or 0.1 ly of the support. as, appropriate., , Mx, where, , M \ . M Y• ~v91 • .l'I are same ~\S those in D-I.l,, , Table 27 Bending Moment Coefficients for Slabs Spanning in Two Directions at, Right Angles, Simply Supported on Four Sides, tClausc D-2.1), 1,/1,, a, , ., , (Iv, , 1.0, , 1.1, , I.:!, , 1.3, , 1.4, , I.~, , 1.7~, , 2.0, , 2.5, , vo, , O,()62, , 0.074, , ()'()84, , O.09J, , O.()l)9, , 0.104, , o.us, , (l.IIS, , 0.122, , 0.124, , O.(l62, , 0.061, , O.OSl), , ().()~~, , o.os:, , 0.046, , n.O]7, , 0.029, , 0.020, , (lO14, , 91

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IS 456: 1000, , ANNEX E, (Clmue 25.2), , EFFECTIVE LENGTH or COLUMNS, E.l Intheabsence ofmoreexactanalysis, the effective, length ofcolumns inframed structures may be obtained, , E.2 Todetermine whether a col\JIDD is I DO sway or, a swaycolumn, stability indexQmay becomputed u, , from the ratioofeffective lengthto unsupported length givenbelow:, 'et l' givenin FiS.26 whenrelative displacement of the, ends of the column is prevented and in Fil. 26 when, relative lateral displacement of the ends is Dot, prevented. In the lattercase, it is recommendded -that . where, ~D, Bum of axial loads on all column in the, the effective length ratio 1,,11 may not be taken to be, ~., storey,, less than 1.2., A., elutically computed first order lateral, NOTES, deflection,, 1 Aprea 26 and 27 are reproduced from -The Structural, H., totallatera1 forceactiDlwithintheitorey,, EnaiDCCJ" No.7, Volume 52, July 1974by the penniuioa, and, of the Council of the In.titutioD of Structural Enpaeen,, h. = height of the storey., U.K., If QS 0.04,thenthecolumn in theframe may betaken, IK, as no sway column, otherwise the column will·be, 2 In Pip. 26 and 27.1l. ud III ale equal to IK, c+ b, considered as sway columnn., where the lummatioD is to be done for the memben, £.3 For normal usagelSSuminl idealized conditions., framin. intoa joiat at top andbottom respectively; and Kc, the effective length I" of in a given plane may be, and K.. bein, the flexural stiffness for column and beam, assessed on the basisof Table 28., respectively., , =, =, =, , U, , HINGED 1·0, , .........- . . -..............-, , w-.....,~, , ..............., , ~I, , FIXED, D, , III, , M, , ;:, FlO. 26 EFncnvI LBNant RATIOS POI A COLUMN IN A PRAMI. wrrH NOSWAY, 92

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IS 456: 2000, , HINGED1.0, , 0.7, , t, , ~1, , 0.6, , II:--+--+-~~_~r--~, , O.S .......--+--~--+-~, , 0.3, 0.2, 0.1, , FIXED, , 0, 0, , 0.2 0.3, , 0.1, , ~2, , c, , w, , .., , 0.' 0.5 0.6 0.7 0.8 0.9 1.0, , )(, , u::, , Flo., , 27, , EFFF.('-IVE LENGTH RI\TIOS FOR A COLUMN IN A, , FRAMEWITHOUT RESTRI\INT AGAINST SWAY, , 2116 BISl07-14, , HINGED

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IS 456: 2000, , ANNEX F, (Claus" 3.5.3.2 and43.1), , CALCULATION OF CRACK WIDTH, Provided that the strain in the tension reinforcement, is limitedto 0.8F/ E•• thedesip surface cock width., whichshould not exceed the appropriate valueJiven, in 35.3.2 may be calculated from the following, equation:, Design surfacecrack width, , where, a",, , neutral axis., = the maximum compressive stress in the, concrete., the tensile stressin the reinforcement. and, E. the modulus of elasticity of the reinforcement, Alternatively. as an approximation. it will normally, besatisfactory tocalculate thesteelstresson thebasis, ofa cracked section andthenreduce thisbyan amount, equal to the tensile force generated by the triangular, distributions. having a value of zero at the neutral axis, and a value at the centroid of the tension steel of, llol/mm2 instantaneously. reducing to 0.55 N/mm2 in, thelong-term. acting overthetension zonedivided by, the steel area. Forarectangular tension zone. thisgives, , I., , t. =, =, , =distance from thepointconsidered to the, surface of the nearest longitudinal bar., , C.., , =minimum coverto the lonJitudinal bar;, , Em, , =average steel strain at the level considered., , h, , = overall depthof the member. and, , x, , =thedepthfromthecompression faceto the, , x, , b (h-x)(a-x), £m, , =depth of the neutral axis., , = £1, , -, , 3E.A.(d-x}, , where, , The average steelstrain em maybe calculated on the, , =, , A., areaof tension reinforcement., b = width of the section at the centroid of the, tension steel., , basisof the following assumption:, The concrete and the steel are bothconsidered to be, fully elastic intension andincompression. The elastic, modulus of the steelmaybetaken as 200 kN/mm2 and, the elasticmodulus of the concrete is as derived from, the equation givenin 6.2.3.1 bothin compression and, , in tension., , £1, , Theseassumptions are illustrated in Fig.28., where, h, the overall depthof the section., , =, , = strain at the levelconsidered. calculated, , a, , =, , d, , =, , ignoring the stiffening of the concrete in, the tension zone., distance from the campression faceto the, pointat which the crack width is being, calculated. and, effective depth., , Ie, , './Ee, , I, h, , ~""'--ST"88, , • A. •, SECTION CRACKED, , IN CONC'fETE, , 1 N'",,,,Z IN SHORT TERM, O'SS HI'" ",2 IN LONG TERM, , STRESS, , STRAIN, , FIG., , 28, , 95

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IS 456: 2000, , ANNEX· G, (ClGu,,38.1), , MOMENTS OF RESISTA.NCE FOR RECTANGULAR AND, T·SECTIONS, G·O The momenta of rosistance of rectanlular and, T-Iectionl baled onthe .I.umptlona of38.1 areaiven, in this annex., ., , exceeds the Ilmitllil value, M u. compr•••lon, " the followln,, reinforcement may be obtained from, equation:, , G·l RECTANGULAR SECTIONS, whore, , G-l.l SectloM Without COmprelllOD, , Relntorcement, , Mu • My 16m' d are lame u in G·I.l,, f.,. desiln strell in compre.lion reinforcement correlpondiol to a strain of, I, , The momerrt of resistance of rectanlular section., without compression reinforcement should be obtained, as follows:, a) Detennine the depth of netutral axia from the, followin, equation :, , ·0.0035, , .xu• mu, , 3 • 0.87 Ix Asc, d, , where, , 0.36 kkb.d, , Xu. JIIIII, , b) If the value of xuld is less than the limiting, value (see Note below 38.1), calculate the, moment of resistance by the following, expression :, , Mu =0.87 f y ~l, , AI&:, d', , •, , depth of compression reinforcement, from compression face., The total area of tension reinforcement shall be, ==, , obtained from the following equation :, , Astir), dll( -bdfek, , If the value of xuld is equal to the limiting, value. the moment of resistance of the section, is given by the following expression:, , Mu tUm, , the limitinl value of Xu from 38.1., , = areaofcomp'e8Sioo reinfcrcement, and, , A.=A. 1 +A1t2, , where, c), , (xu,mu -d'}, , A•l, AM 1, , ~, =0.36 -xu.dmax- ( 1 -0.42 -xu,dmax- )bd Jek, , d) If XuI d is greater than the limiting value. the, , G-Z FLANGED SECTION, , section should be redesigned., In the above equations., .xu, depth of neutral axis., d, effectivedepth,, characteristic strength of reinforce.., .t.y, ment,, , G-2.1 For xu< Dr' the moment of resistance may be, calculated from the equation givenin G-l.1 •, G·2.2 The limiting value of the moment of resistance, of the section may be obtained by the following, equation whenthe ratio Dr I d does not exceed0.2 :, , =, =, =, , = area of tension reinforcement., , t:, , =, , = area of the tensile reinforcement for a, , singly reinforced section for Mg. Um', and, AIt... = Alie f.Ie.: I 0.871.'I ", , 2, , Alit, , :: area of the total tensile reinforcement•, , 2, =0· 36~(1-0, I' b d, Mu, d, ·42 Xu ,max, d ) Jek, w, , characteristic compressive strength, of concrete., , b, , -, , +0.4Sfek (b f -bw)Df (, , width of the compression face., , d-pt), , Mu.lin, -- limiting moment of resistance of, , a section without compression . where, Mu., reinforcement, and, , xu. ;iI"~, , = Iimitingvalueof, , Xu, , =, bw =breadthof the web, and, , bI, , from 39.1., , G-l.2, , Section with Compression Reinforcement, , Where, , me ultimate moment of resistance of section, , andt.c are same as in G-l.1., breadth of the compression face/flange,, , oXu.mtAI• d, , D, = thickness of the flange., , 96

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IS 456: 2000, , G-Z.Z.I When the ratlo Dr/el exceeds 0,2, the moment, of resi~tllnce of the section may be calculated by the, following equation:, Mil =0.36 XU.;I'" (1-0.42 XU'~lllIJl, , )/ek bwd, , r-h)Yr(d-t ), , +0.45hk(b, , w, , 2, , where )', = (0, JS Xu + 0.65 D,.), but not greater than, DI , and the other symbols ore Maine I1S in 0-1.1, , nnd G·Z.2., , 0-Z.3, For xHI "U~_ > x" > D the moment of resistance, ., muy be calculated by the equation" given in G-Z.2, when J) Ix does not exceed 0.43 and a·Z.2.1 when, f, ", . ,, •, •, n/xLI exceeds, 0.43; In both caMe" substituting XU' ma_, ny xu', J, , ,

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