i!3:2210-1988 Indian St&Mhrd Criteria for Design Of

8/14/2019 i!3:2210-1988 Indian St&Mhrd Criteria for Design Of

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I!3:2210-1988Indian St&mhrdCRITERIA FORDESIGN OF REINFORCED CONCRETE SHELLSTRUCTURES AND FOLDED PLATES( First Revision )First Reprint JANUARY 1992

-UDC 62401245 - 04 : 624074/42BUREAU OF INDIAN STANDARDSMANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARGNEW DELHI 110 002Gr 7 November 1989.IIS :2210 - 1988Indian StandardCRITERIA FORDESIGN OF REINFORCED CONCRETE SHELLSTRUCTURES AND FOLDED PLATES( First Revision )

0. FOREWORD0.1 This Indian Standard ( First Revision) wasadopted by the Bureau of Indian Standards on I5November 1988, after the draft finalized by theCriteria for Design of Special Structures SectionalCommittee had been approved by the Civil EngineeringDivision Council.0.2 Shells and folded plates belong to the class ofstressed-skin structures which, because of theirgeometry and small flexural rigidity of the skin,tend to carry loads primarily by direct stresses actingin their plane. Wherever shell is referred to in thisstandar$ it refers to thin shell. On account of

multiphclty of the types of reinforced concrete shelland folded plate structures used in present daybuilding practice for a variety of applications demandingroofing of large column-free area, it is notpracticable to lay down a rigid code of practice tocover all situations. Therefore, this standard laysdown certain general recommendations for theguidance of the designers. .*0.3 Cylindrical shells have been in use in buildingconstruction for the past six decades. Well developedtheories exist for their analysis. Labour-savingshort cuts, such as, charts and tables for their

design, are also available.0.4 Although shells of double curvature, with theexception of domes, have been introduced on a largescale comparatively recently into building construction,these are likely to be used more and more infuture. Being non-developable surfaces, they aremore resistant to buckling than cylindrical sheTlsand in general, require less thickness. This savingin materials is, however, often offset by the dativelyexpensive shuttering required for casting them.Among the doubly-curved shells, the hyperbolicparaboloid and the conoid have, however, theadvantage of less expensive shuttering because their

ruled surfaces can be formed by straight plankshuttering.0.5 Folded plates are often competitive with shells


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for covering large column-free areas. They usuallyconsume relatively more materials compared toshell but this disadvantage is often offset by thesimpler framework required for their construction.0.6 This standard was first published. in 1962. Thepresent revision is based on the developments in thedesign of shell and folded plate structures subsequently

and to include more rigorous methods of analysiswhich have become available to enforce morerational criteria of design.0.7 For the purpose of deciding whether a particularrequirement of this standard is complied with, thefinal value, observed or calculated, expressing theresult of a test or analysis, shall be rounded off inaccordance with IS : 2-1960*. The number ofsignificant places retained in the rounded off valueshould be the same as that of the specified value inthis standard.*Rules for rounding off numerical values (revised ).

1. SCOPE1.1 This standard lays down recommendations forthe classification, dimensional proportioning, analysisand design of cast in situ, reinforced concrete thinshells and folded plates. This standard does notdeal with construction practices relating to thesestructures which have been separately dealt inIS : 2204-1962*.2. TERMINOLOGY2.0 For the purpose of this standard, the followingdefinitions shall apply.2.1 Asymmetrical Cylindrical Shells - Cylindricalshells which are asymmetrical about the crown.

*Code of practice for construction of reinforced concreteshell roof.2.2 Barrel Shells - Cylindrical shells which aresymmetrical about the crown (see Fig. 1 ).2.3 Butterfly Shells - Butterfly shells are thosewhich consist of two parts of a cylindrical shelljoined together at their lower edges (see Fig. 2).2.4 Chord Width - The chord width is the horizontalprojection of the arc of the cylindrical shell.2.5 Continuous Cylindrical Shells - Cylindrical shellswhich are longitudinally continuous over thetraverses (see Fig. 3 ).NOTE - Doubly-curved shells continuous in one or bothdirections may be termed as continuous shells.2.6 Cylindrical Shells - Shells in which either thedirectrix or generatrix is a straight line.1FIG. 1 SINGLE BARREL SHELLFIG.2 B ~ITERFLYS HELLFIG. 3 MULTIPLE BARREL SHELL22.7 Edge Member - A member provided at theedge of a shell.NOTE - Edge members increase the rigidity of the shelledge and h&p in accommodating the reinforcement.

2.8 End Frames or Traverses - End frames ortraverses are structures provided to support andpreserve the geometry of the shell.


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where a and b are the semi-major and semi-minor axes,respectively, and d is the slope of the tangent at the point.2.16 Rise - The vertical distance between the apexof the curve representing the centre line of the shelland the lower most springing.2.17 Ruled Surfaces - Surfaces which can begenerated entirely by straight lines. The surface is

said to be singly ruled if at every point, a singlestraight line only can be ruled and doubly ruled ifat every point, two straiglt lines can be ruled.Cylindrical shells, conical shells and conoids areexamples of singly ruled surfaces; hyperbolic paraboljids and hyperboloids of revolution of one sheetare examples of doubly ruled surface ( see Fig. 6 ).2.18 Semi-Central Angle - Half the angle subtendedby the arc of a symmetrical circular shell at thecentre.2.19 Shells - Thin shells are those in which theradius to thickness ratio should not be more than 20.

2.20 Shells of Revolation - Shells which are obtainedwhen a plane curve is rotated about the axis ofsymmetry. Examples are segmental domes, cones,parab Jloids of revolution, hyperboloids OI revolution,etc ( see Fig. 7 ).2.21 Shells of Translation - Shells which areobtained when the plane of the generatrix and thedirectrix are at right angles. Examples are cylindricalshells, elliptic paraboloids, hyperbolic paraboloids,etc ( see Fig. 8 ) ,2.22 span - The span of a cylindrical shell is thedistance between the centre lines of two adjacentend frames of traverses (see Fig. 1 ).

3. NOTATIONS3.1 For the purpose of this standard, unless otherwisedefined in the text, the following notationsshall have the meaning indicated against each:a =B ZZb =D sd =Ec =Es =F =f = ro=lh =semi-major axis of an elliptical shell;chord width;semi-minor axis of an elliptical shell;flexural rigidity;thickness of shell;Modulus of elasticity of concrete (longterm );Modulus of elasticity of steel;stress function which gives the in-planestress in doubly-curved shells whenbending is also considered;

characteristic strength of concrete;critical buckling stress;rise of shell;


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3f cc =H =permissible compressive stress frombuckling consideration;total depth of shell, measured from thecrown of the shell to the bottom of the

edge member;L =Mx =span;bending moment in the shell in thex-direction;My = bending moment in the shell in they-direction;iuxy =2x2 IkNJW J

NXP, NVPandN XYP 1P =twisting moment in the shell;= real membrane stresses in the shell;= projected membrane forces;permissible buckling load per unit areaof the surface of doubly-curved shells;n =. -&- .6x SZ4 =Sy;

S"Zr = 62;S

Zs =6x.6yit8z . =wR = radius;& = radius at crown;R, and Rx = principal radii of curvature at anypoint on the surface of shell;s = shear stress;Tx = normal stress in the x-direction;TV = normal stress in the y-direction;Wx, WV and Wx = real forces on unit area ofthe shell in the x, y and zdirection;IV = de&&on in the direction of z-axis;X, YandZ = fictitious forces on unit projectedarea of the shell in the X, y and zdirections;X, y and z = axes of co-ordinates;Q, = stress function used in the membraneanalysis of doubly-curved shell;9 = angle of inclination of tangent to thecurve at any point;+c = semi-central angle of a symmetricalcircular cylindrical shell;

P and K = Aas Jakobsens varameters forV =V =


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cylindrical shells; _Poissons ratio; and4. CLASSIFICATION OF SHELLS4.1 General - Shells may be broadly classified assingly-curved and doubly-curved. This is basedon Gauss curvature. The gauss curvature of singlycurvedshells is zero because one of their principal

curvatures is zero. They are, therefore, developable.Doubly-curved shells are non-developable and areclassified as synclastic or anticlastic according astheir Gauss curvature is positive or negative.4.1.1 The governing equations of membranetheory of singly curved shells are parabolic. It is-elliptic for synclastic shells and hyperbolic foranticlastic shells. If z = f (x, y) is the equationto the surface of a shell, the surface will be synclastic,developable or anticlastic according as s2-rf 40 where t, s and t are as defined in 3.1.4.1.2 There are other special types of doubly

curved shells, such as, funicular shells, which aresynclastic and anticlastic in parts and corrugatedshells which are alternately synclastic and anticlastic.The gauss curvature for such shells is positivewhere they are synclastic and negative where theyare anticlastic.4.2 The detailed classification of shell structures isgiven in Appendix A.5. MATERIALS5.1 Con&&e - Controlled concrete shall be usedfor all shell. and folded plate structures. Theconcrete is of minimum grade M20. The qualityof materials used in concrete, the methods of proportioning

and mixing the concrete shall be donein accordance with the relevant provisions ofIS : 456-1978*.NOTE-High cement content mixes are generallyundesirable as they shrink excessively giving rise tocracks.5.2 Steel - The steel for the reinforcement shall be:a) mild steel and medium tensile steel bars andhard-drawn steel wire conforming to IS : 432(Part I)-1982 and IS : 432 (Part 2)-1982t;b) hard-drawn steel. wire fabric for concreteTi$forcement conforming to IS : 1566-19821;c) high strength deformed bars conforming toIS : 1786-1985s.5.2.1 Welding may be used in .reinforccment inaccordance with IS : 456-1978*.*Code of practice for plain and reinforced concrete( third revision ).tSpecification for mild steel and medium tensile steel barsand hard-drawn steel wire for concrete reinforcement:Part 1 Mild steel and medium tensile steel bars (thirdr cvisfon ) .Part 2 Hard-drawn steel wire (third revision).SSpecification for hard-drawn steel wire fabric forconcrete reinforcement (second revision ).

#Specification for high strength deformed steel bars andwires for concrete reinforcement ( rhfrdrevlsfon).4


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Non + Diaphragms 4Fu IG- 4 FOLDED eP LnAoYi S bOWO,6A CONbID68 HYPERBOLIC PARABOLOID6C HYPERBOLOID OF REVOLUTION OF ONE SHEETFIG. 6 RULED SURFACES6

Is : 2210 - 19887A SEGMENTAL DOME78 PARABOLOID OF REVOLUTIONFro. 7 !fhLU OF REVOLUTION8A ELLIPTIC PARABOLOID88 HYPERBOLIC PARABOLOIDFIG. 8 SHELLS OF TRANSLATION7IS : 2210 - 19886. LOADS6.1 Unless otherwise specified, shells and foldedplates shall be designed to resist the following load

combinations:a) Dead load,b) Dead load + appropriate live load or snowload,c) Dead load + appropriate live load -I- windload, andd) Dead load + appropriate live load + seismicload.6.2 Dead loads shall be calculated on the basis ofthe unit weights taken in accordance with IS : 875(Part I)-1987*.6.3 Live loads, wind loads and snow loads shall betaken as specified in IS : 875 (Parts 2 to 4)-1987*.

6.4 Seismic loads shall be taken in accordance withIS : 1893-1984t.6.5 Where concentrated loads occur, special considerationsshould be given in analysis and design.7. SELECTION OF DIMENSIONS7.1 Thickness7.1.1 Thickness of Shells - Thickness of shellsshall not normally be less than 50 mm if singlycurvedand 40 mm if doubly-curved. This requirementdoes not, however, apply to small precast concreteshell units in which the thickness may be lessthan that specified above but it shall in no case beless than 25 mm (see IS : 6332-19842).7.1.1.1 The reinforcement shall have a minimumclear cover of 15 mm or its nominal size whicheveris greater.7.1.2 Shells are usually thickened for some distancefrom their junction with edge members andtraverses. The thickening is usually of the orderof 30 percent of the shell thickness. It is, however,important to note that undue thickening is undesirable.In the case of singly-curved shells, the distanceover which the thickening at the junction ofthe shell and traverse is made should be between038 4R.d and 076 1/rd, where R and d are the

radius and the thickness, respectively. The thickeningof shell at straight edges shall depend on the*Code of practice for design loads (other than earthquake)


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for building and structures:Part 1 Dead loads (second revision ).Part 2 Imposed loads (second revision ).Part 3 Wind loads (second revision ).Part 4 Snow loads (secotlri revision ).tCriteria for earthquake resistant design of structures(fourth revision ) .

*Code of practice for construction of floors and roofsusing Precast doubly-curved shell units (first revislon ).transverse bending moment. For doubly-curvedshells, this distance will depend upon the geometryof the shell and the boundary conditions as the extentof bending penetration is governed by thesefactors.7.1.3 Thickness of Folded Plates - The thicknessof folded plates shall not normally be less than75 mm.7.2 Other Dimensions7.2.1 CyIindrical Shells

7.2.1.1 The span should preferably be lessthan 30 m. Shells longer than 30 m will involvespecial design considerations, such as the applicationof prestressing techniques.7.2.1.2 The width of the edge member shallgenerally be limited to three times the thickness ofthe shell.7.2.1.3 The radius of shell structures shall beselected keeping acoustic requirements in view.Coincidence of the centre of curvature with theworking level should be avoided unless suitableacoustic correction is made. It is, however, importantto note that even where coincidence of centre of

curvature with the working level is avoided, acoustictreatment may be necessary iu certain cases.7.2.1.4 A single cylindrical shell whose span islarger than three times the chord width shall have atotal depth, H, between l/6 and l/l2 of its span(the former value being applicable to smaller spans).The rise in the case of a shell without edge membersshall not be less than l/l0 of its span.7.2.1.5 For a shell with chord width larger thanthree times the span, the rise of the shell shall notbe less than l/8 of its chord width.7.2.1.6 The chord width of shells shall preferablybe restricted to six times the span as otherwisearch action is likely to predominate.7.2.1.7 The semi-central angle shall preferablybe between 30 and 40.NOTE - Keeping the semi-central angle between theselimits is advisable for the following reasons:a) If the angle is below 40, the effect of wind loadon the shell produces only suction; andb) With slopes steeper than 40. backforms maybecome necessary.Within these limits the semi-central angle shallbe as high as possible consistent with the functionalrequirements.

7.2.2 Folded Plates - For folded plates of typeshown in Fig. 4D, the selection of depth may bebased on the rules applicable to cylindrical shells.


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With other shapes, such as, the V or the trough,the depth may be taken as about l/l5 of the spanfor preliminary designs.87.2.2.1 The angle of inclination of the plates tohorizontal shall be limited to about 40 for in-situconstruction in order to facilitate placing of concrete

without the use of the backforms.8. ANALYSIS8.0 General - Shells may be analyzed either bylinear elastic analysis based on theory of elasticity oryield line theory. Methods based on yield linetheory for shells are still the subject of research andexperimentation and, therefore, for the present, itis recommended that they may be used along withmodel tests to check the load carrying capacity.The finite element method has become a practicaland popular method of analysis for all types ofstructures. Many common and important features

of shell and folded plate structures that cannot beconsidered by classical methods can now be analyzedsatisfactorily by the finite element method. Forexample :4b)44e)f)dh)3

WmldPI9)r)Complex support or boundary conditions;Openings large enough to disturb globalstress distribution;Irregular surface geometry;Highly variable or localized loads;Tapering folded plates or boxes or silo andbunker bottoms;Branching shells;Large deformations;Heavy and eccentric stiffners;Thermoelastic strains;Elastoplastic, viscoelasticbehaviour;Material non-homogeneity;Irregular surface geometry;or any inelasticSudden changes in curvature;Shells under dynamic wind action; andPossible effect of settlement.

When one or more of these complexities occur inshell structures, it is advisable to use finite elementmethod, at least for a final acceptance of the design.


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Even normal shell structures of spans larger than30 m should be analyzed by finite element methodif it is expected that there would be serious andsignificant structural participation in the shell behaviourby the supporting units, such as, edge andintermediate beams, stiffners, and or intermediatetraverses ( specially flexible traverses ) cable supports,

columns, etc.For many shells, finite strip method ( FSM) ( aparticular form of finite element method ) of analysisis easier to apply and also more economical to usethan the finite element method. All types ofprismatic folded plates and cylindrical shells can beIS : 2210 - 1988handled by FSM since these shells can be discretizedinto long strip elements. Shells of revolution canalso be efficiently analyzed by this method, afterdiscretization of such shells into finite ring elements.Since FSM can be used even when the loads are not

uniform, it may be advisable to use the method evenfor simple shells that are amenable to analysis bycommon classical methods.The common classical methods of analysis ofshells are mentioned in the following clauses foruse for the analysis of common types of shells thatare without any of the complexities.8.1 Cylindrical Shells8.1.1 Analytical Methodr - The analytical methodsconsist of two parts, membrane analysis and edgedisturbance analysis.8.1.1.1 Membrane analysis - In the membraneanalysis, the shell is regarded as a perfectly flexible

membrane which is infinite in extent and is assumedto carry loads by means of forces in its plane only.This analysis gives the two normal stress resultantsNx and NY in the longitudinal and the transversedirections and the shear stress resultant Nxv.8.1.1.2 Edge disturbance analysis - Shells, inpractice, are always limited by finite boundarieswhere the boundary conditions demanded by themembrane theory are not obtained with the resultthat a pure membrane state would seldom exist.Edge disturbances emanate from the boundaries,altering the membrane state and causing bendingstresses in the shell. These are accounted for bye,carrying out the edge disturbance analysis. Usuallyedge disturbance analysis is confined to disturbanceemanating from straight edge as any disturbanceemanating from curved edges is damped quite fast.Even in the case of disturbance from straight edges,the bending stresses would get damped out morerapidly in shells having chord width larger than thespan and would seldom travel beyond the crown,with the result that the effect of the further edgemay be ignored without appreciable error.The superposition of the membrane and the edgedisturbance stresses gives the final stress pattern in

the shell.8.1.1.3 Tables for the analysis of circular cylindricalshells - Simplifications in the analysis -of


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shells are possible by systematizing the calculations 4making use of tables compiled for this purpose(see Appendix B ).8.1.2 Applicability of the Methods of Analysis8.1.2.1 Cylindrical shells with k ratio less thanrr shall be analyzed using any of the acceptedanalytical methods (see Appendix B ).

9IS : 2210 - 1988In such shells, if P exceeds 10 and K exceeds 015,the effect at any point on the shell of the disturbancesemanating from the farther edge may beignored, whereP-812 - R" w RL- dand K = -L PFor shells with P less than 7 and K less than 012,

the effect of the disturbances from both the edgesshall be considered. Shells with P values between 7and 10 and K between 012 and 015 are relativelyinfrequent. However, should such cases arise, theeffects of both the edges shall be considered.8.1.2.2 Cylindrical shells with L/R greater thanor equal to n may be treated as beams of curvedcross section spanning between the traverses and theanalysis carried out using an approximate methodknown as the beam method (see Appendix B)which consists of the following two parts:a) The beam calculation which gives thelongitudinal stress resultant N, and the shear

stress resultant NXY, andb) The arch calculation which gives the transversestress resultant NY and the transverse momentMY.8.1.3 Continuous Cylindrical Shells8.1.3.1 Analytical methods - In the analyticalmethods, the problem of continuous shells is solvedin two stages. In the first, the shell is assumedto be simply supported over one span andall the stress resultants worked out. In the secondstage, correcg;ns for continuity are worked out andare superimposed on the values corresponding to thesimply supported span. Long cylindrical shells canbe analyzed by approximating the cylindrical profileby a folded plate shape and applying well knownanalysis methods for continuous folded plates (seeAppendix B).8.1.3.2 Beam method - Solution of continuousshell with -$ 2 ?r is simpler by the beam method.The bending moment factors are obtained by solvingthe corresponding continuous beam. Thereafter,analysis can be continued as in 8.1.2.2.8.2 Donhly-Curved SheIIs8.2.1 Membrane Analysis - In the membraneanalysis, it is assumed that the shell carry loads by

in-plane stress resultants and usually only deepdoubly-curved shells behave like membranes. Thegoverning equations for membrane analysis of doublycurved


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vertical loads, in a membrane state of stress, theydevelop only pure compression unaccompanied byshear stresses. Thus theoretically no reinforcementwill be necessary except in the edge members. Smallprecast funicular shells without any reinforcementexcept in edge beams are suitable for roofs andfloors of residential, industrial, and institutional

buildings (see IS : 63321984* ). For roofs of largersize, in situ construction may be resorted to; in suchshells, provision of reinforcement is necessary to takecare of the effects of shrinkage, temperature andbending.*Code of practice for construction of floors and roofsusing precast doubly-curved shell units (fist revision ).108.4 Folded Plates - The structural action of foldedplates may be thought of as consisting of two parts.the slab action and the plate action. By the slabaction, the loads are transmitted to the joints by the

transverse bending of the slabs. The slabs, because oftheir large depth and relatively small thickness, offerconsiderable resistance to bending in their own planesand are flexible out of their planes. The loads are,therefore, carried to the end diaphragms by thelongitudinal bending of the slabs in their own planes.This is known as plate action. The analysis offolded slabs is carried out in two stages.83.1 Transverse Slabs Action Analysis - Thetransverse section of the slab, of unit length, isanalyzed as a continuous beam on rigid supports.The joint loads obtained from this analysis arereplaced by their components in the planes of the

slabs and these are known as plate loads.8.3.2 In Plane Plate Action Analysis - Under theaction of plate loads obtained above, each slab isassumed to bend independently between the diaphragms,and the longitudinal stresses at the edgesare calculated. Continuity demands that thelongitudinal stresses at the common edges of theadjacent slabs be equal. The corrected stresses areobtained by introducing edge shear forces.8.4 Expansion Joints - The expansion joint shallconform to provisions laid down in IS : 456-1978*.In the case of folded plates, it is recommended thatthe joint may be located in the ridge slab. In thecases of large spans where it is not feasible to provideexpansion joints, effects of shrinkage shall betaken care of in the design.8.5 Openings in Shells - Openings in shells shallpreferably be avoided in zones of critical stresses.Small openings of size not exceeding five times thethickness in shells may be treated in the same wayas in the case of reinforced concrete structures. Forlarger openings, detailed analysis should be carriedout to arrive at stresses due to the openings.9. ELASTIC STABILITY9.1 Permissible Stresses

9.1.1 Permissible stresses in steel reinforcement,and concrete for shells and folded plates shallbe in accordance with the provisions given in


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longitudinal or transverse stresses are criticalfrom Considerations of elastic stability.The value of modulus of elasticity of concreteto be used in the above formulae for calculating thebuckling stresses should be the value for long termmodulus including the effect of creep also.11

IS : 2210 - 19889.4 Buckling in Doubly-Carved Shells - Forspherical shells, the permissible buckling load perunit area of surface, P,,,,, from considerations ofelastic stability, is given by:whereEC d and R are as defined in 3.1.For other types of doubly-curved shells, thepermissible buckling load per unit area of surface,Pperm shall be calculated from the formula:PEcda

wm= R,R,whereR, and R, are principal radii of curvature atany point, and EC and d are as definedin 3.1.9.5 Bwkhg in Folded Plates - The folded platemay be replaced by the corresponding cylindricalshell where possible and the appropriate formulaused to check for elastic stability.10. DESIGN OF TRAVERSES10.1 Types of Traverses - Traverses may be soliddiaphragms, arches, portal frames, trusses orbowstring girders. For shells with large chord widths,

it is advantageous to have trusses in the form ofarches, trusses or bowsting girder.10.1.1 Traverses may be placed below or abovethe shells. Where a clear soffit is required, speciallyto facilitate the use of movable formwork, they maybe in the form of upstand ribs.10.1.2 The simplest diaphragms for folded platesare rectangular beams with depth equal to theheight of the plate. The diaphragms are subject tothe action of the plate loads on one-half of the spanof the folded plate.10.2 Load on Traverses - Traverses shall be designedto carry, in addition to their own weight,reactions transferred from the shell in the form ofshear forces, and the loads directly acting on them.For preliminary trial designs, however, the total loadon half the span of the structure may be consideredas a uniformly distributed vertical load on thediaphragm.10.3 Design - The shear forces transferred on tothe end frames from the shell shall be resolved intovertical and horizontal components and the analysismade by the usual methods. Owing to the monolithicconnection between the traverse and the shell,the latter participates in the bending action of the

traverse. The effective width of a cylindrical shellthat acts aL1lg with the traverse may he assumedas GX! *./m to 076 1/a, on either side in the case


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of intermediate traverses and on one side in the caseof end ones; the higher value being applicable to auinfinitely rigid rib that can prevent the shell fromrotating and the lower value to a flexible rib. Wheresolid diaphragm traverses are used, adequatereinforcement to distribute shrinkage cracking shallbe provided throughout the area of the traverses.

10.3.1 In the design of tied arches, it may benecessary to determine the elastic extension of the tiemember due to tension and the consequent effecton the horizontal thrust on the arch.10.3.2 The bottom member of a bowstring girder,or the tie in the case of a tied arch, is usuallysubjected to heavy tension. Welding or the provisionof threaded sleeve couplings (see 25.252 ofIS : 456-1978* ) or laps may be used for joints in thereinforcement rods. Where lapping is done, thelength of the overlap shall be as specified in therelevant clause of IS : 456-1978* and the composite

tension shall be restricted to 01 fck, where&k is thecharacteristics cube strength of concrete at 28 days.Where the composite tension exceeds 01 fck, theentire length of the lap shall be bound by a helicalbinder of 6 mm diameter at a pitch not exceeding75 mm. The joints in the bars shall always bestaggered. Prestressing the tension member offersa simple and satisfactory solution. The detailing ofinclined or vertical members of trusses or bowstringgirders and suspenders of tied arches should be donewith great care. The reinforcements in the tie oftied-arches shall be securely anchored at their ends.10.4 The traverses may be hinged to the columns,

except where the traverses and columns are designedas one unit, such as in a portal frame. Provisionshall be made in the design of columns to allow forthe expansion or contraction of traverses due totemperature changes.11. DESIGN OF EDGE BEAMS11.1 Edge beams stiffen the shell edges and acttogether with the shell in carrying the load of thesupporting system. They can either be vertical orhorizontal. Vertical beams are usually employed inlong cylindrical shells wherein the cylindrical actionis predominant. Horizontal beams are employed inshort cylindrical shells where transverse arch actionis predominant. It is preferable to completely isolatethe structural system of the shell structure withoutadding any other structure to it.In most of the shell forms, edge beams form partof the shell structure itself. An analysis of the shellstructure is carried out along with the edge beam.Analysis and design of edge beams should ensurecompatibility of boundary conditions at the shelledge. Analysis should take into account theeccentricities, if any, between the central line of theshell and the edge beam. Analysis should also takeinto account the type of edge beam, interior or

exterior, as well as supporting arrangement of theedge beam.Code of practice for plain and reinforced concrete


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( third revision ).12IS:2210-198811.1.1 Thickness - A width of two to three timesthe thickness of the shell subject to a minimum of15 cm is usually necessary for the edge beams.11.1.2 Reinforcements - Edge beams carry most

of the longitudinal tensile forces due to NX in theshell and hence main reinforcements have to beprovided for carrying these forces, It may benecessary to provide many layers of reinforcementin the edge beam. Design of reinforcements shouldensure that the stresses in the farthermost layer doesnot exceed the permissible stresses. Edge beamsshould also be designed for carrying its self-weight,live load on the part of the shell, wind load andhorizontal forces due to earthquakes.12. DESIGN OF REINFORCEMENT12.1 Shells - The ideal arrangement would be to

lay the reinforcement in the shell to follow theisostatics, that is, directions of the principal stresses.However, for practical purposes, one of thefollowing methods may be used:One is the diagonal grid at 45 to the &is c+f theshell, and the other the rectangular grid in whichthe reinforcing bars run parallel to the edges ofthe shell. The rectangular grid needs additionalreinforcement at 45 near the supports to take upthe tension due to shear.12.1.1 In the design of the rectangular grid forcylindrical shells, the reinforcement shall usually bedivided into the following three groups:

a) Longitudinal reinforcement to take up thelongitudinal stress Nx or Ny as the case maybe,b) Shear reinforcement to take up the principaltension caused by shear Nxy, andc) Transverse reinforcement to resist NY and My.12.1.2 Longitudinal reinforcement shall be providedat the junction of the shell and the traverse toresist the longitudinal moment M, . Where MX isignored in the analysis, nominal reinforcement shallbe provided.12.1.3 To ensure monolithic connection betweenthe shell and the edge members, the shell reinforcementshall be adequately anchored into the edgemembers and traverses or vice versa by providingsuitable bond bars from the edge members andtraverses to lap with the shell reinforcement.12.2 Folded Plates12.2.1 Transverse Reinforcement - Transversereinforcement shall follow the cross section of thefolded plate and shall be designed to resist the transversemoment.12.2.2 Longitudinal Reinforcement - Longitudinalreinforcement, in general. may be provided to takeup the longitudinal tensile stresses, in individual

slabs.12.2.3 Diagonal reinforcement may be providedfor shear.


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12.2.4 The section of the plate at its junction withthe traverse shall be checked for shear stress causedby edge shear forces.12.2.5 Reinforcement bars shall preferably beplaced, as closely as possible, so that the steel iswell distributed in the body of the plate. Nominalreinforcement consisting of minimum 8 mm diameter

bars may be provided in the compression zonesat about 200 mm centre-to-centre.12.3 General - The minimum reinforcement shallconform to the requirements of IS : 456-1978*.12.3.1 Diameters of Reinforcement Bars - Thefollowing diameters of bars may be provided in thebody of the shell. Larger diameters may be providedin the thickened portions, transverse and beams:a) Minimum diameter : 8 mm, andb) Maximum diameter : 4 of shell thickness or16 mm whichever issmaller.

12.3.2 Spacing of Reinforcement - The maximumspacing of reinforcement in any direction in the bodyof the shell shall be limited to five times the thicknessof the shell and the area of unreinforced panelshall in no case exceed 15 times the square ofthickness.NOTE - These limitations do not apply to edge memberswhich are governed by IS : 456-1978+.*Code of practice for plain and reinforced concrete( r/rid revision ).13APPENDIX A( Clause 4.2 )

DETAILED CLASSIFICATION OF STRESSED SKIN SURFACESStressed Skin Surfaces? IPolded+Pla*es!1Doubly-CurvedNon-developable1IbSingly-CurvedDevelopableIIGauss CuAature ZeroMembraneEquationParabolicISyncLticGauss Curvature PositiveMembrane EquationEllipticAnticiastic

Gauss Curvature NegativeMembraneEquation


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HyperbolicOther Special TypesII I ISh&sRe%u- Translationtion

4 +i+ J j.Alternately Partly Syn- MiscellaneiSynclastic. & clastt;;d ous TypesRuledAntic/astrcAntielasticSurfacesII .Ii 1 i

YFs %ls RskdRevo- Trans- faceslution lation4 & ICal?C&i;drical ConicalandExamplesIncludingNorthrSW?sdricallight 8~;;;;;;Y

i5iJ,Sl&lS Shellsof ofRevo- Translutionlation, + 4CircularDomes,Paraboloids,EllipsoidsofRevolution,etcElliptic$6so-CircularYoyd;bo-F;iaTu-ShellsHyperboloidsof Re- Ivolution of

One Sheet,HyperbolicParaboloids,


20/22


21/22


22/22

ax axe a2 +a ?; aay )F-_z=(J Ty -e,b) For shells of constant curvature, that is, forshells for which r, s and t are constant, aboveequations simplify to:Et V4F +[t $$ - 2sazy+$$ 1 c = 0 ! (7)ax a21w 3

-z= 0 Mxy = -0(1-v) sFIG. 9 SIGN CONVENTIONF OR STRESSFBA ND MOMENTSI N A SHELL ELEMENT16Bmrma of IBdiu St8mdard8BIS is a statutory institution established under the Bureau of Indian Stan&r& Act, 1986 topromote harmonious development of the activities of standardization, marking andqualitycertification of goods and attending to connected matters in the country.BIS has the copyright of all its publications. No part of these publications maybe reproducedin any form without the prior permission in writing of BIS. This does not preclu

de the free use,in the course of implementing the standard, of necessary details, such as symbols and sizes, typeor grade designations. Enquiries relating to copyright be addressed to the Director( Publications ), BIS.Revbiom of Idian StandardsIndian Standards are reviewed periodically and revised, when necessary and amendments, ifany, are issued from time to time. Users of Indian Standards should ascertain that they are inpossession of the latest amendments or edition. Comments. on this Indian Standard may be

sent to BIS giving the following reference:Dot : No. BDC 38 (3329)Amendments Ismed Since PublicationAmtnd No. Date of Issue : Text AffectedBUREAU OF INDIAN STANDARDSHeadquarters :Manak Bhavan, 9 Bahadur Shah Zafar Marg, New Delhi 110002Telephones : 331 01 31, 331 13 75 Telegrams : Manaksanstha.( Common to all Offices )Regional Offices,: TelephoneCentral : Manak Bhavan, 9 Bahadur Shah Zafar MargNEW DELHI 110002I 311 01 31331 13 75Eastern : l/14 C. I. T. Scheme VII M, V. I. P. Road,.ManiktolaCALCUTTA 70005437 86 62Northern : SC0 445-446, Sector 35-C, CHANDIGARH 160036 53 38 43Southern : C. I. T. Campus, IV Cross Road, MADRAS 600113 235 02 16Western : Manakalaya, E9 MIDC, Marol, Andheri ( East )BOMBAY 4000936 32 92 95Branches : AHMGDABAD, BANGALORE, BHOPAL, BHUBANESHWAR, COIMBATORE,PARIDABAD. GHAZIABAD, GUWAHATI, HYDERABAD, JAIPUR, KANPUR,PATNA, SRlNAGAR. THIRUVANANTHAPURAM.

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