Handbook+for+structural+engg_SP+-+6(5)+-+1980

8/10/2019 Handbook+for+structural+engg_SP+-+6(5)+-+1980

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BIS 2007

B U R E A U O F I N D I A N S T A N D A R D S

MANAKBHAVAN, 9 BAHADURSHAHZAFARMARG

NEWDELHI 110002

SP : 6(5) - 1980

(Reaffirmed 2001)

Edition 2.1

(1984-03)

P ri ce Group 15

HAND BOOK

FOR

STRUCTURAL ENGINEERS

5. COLD-FOR MED, L IGHT -GAUGE STE ELSTRUCTURES

( First Revision )

(Incorporating Amendment No. 1)


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HANDBOOK

FOR


NO. 5


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BIS 2007

B U R E A U O F I N D I A N S T A N D A R D S

MANAKBHAVAN, 9 BAHADURSHAHZAFARMARG

NEWDELHI 110002

P ri ce Group 15

HANDBOOK

FOR


5. COLD FORMED, L IGHT-GAUGE STEELSTRUCTURES

( First Revision )


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1980 B U R E A U O F I N D I A N S T A N D A R D S

Edi tion 1 1970Edi tion 2 1980

(Second Reprint AUGUST 1989)

UDC 624.014.2.04 (026)

SP : 6(5) - 1980


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C O N T E N T S

PAGE

0. FOREWORD 9

SECT I ON 1 C OMMENT AR Y

1. SCOPE 15

2. INTRODUCTION 15

3. CURRENTSHAPES 15

4. DECKSANDPANELS 18

5. MATERIAL 19

6. DEFINITIONS 197. LOADS 22

8. DESIGNPROCEDURE 23

8.1 General 23

8.2 Properties of Sections 23

8.3 Effective Design Width 26

9. ALLOWABLEDESIGNSTRE SSES 32

9.1 Compression on Unstiffened Elements 32

9.2 Laterally Unbraced Beams 35

9.3 Webs of Beams 38

9.4 Compression Members 40

9.5 Combined Axial and Bending Stress 43

10. WALLSTUDS 44

11. CHANNEL ANDZ-BEAMS 46

11.1 General 46

11.2 Connecting Two Channels to Form an I -Beam 46

11.3 Bracing of Single-Channel Beams 49

11.4 Bracing of Z-Beams 50

12. CONNECTIONS 52

12.1 General 52

12.2 Welding 53

12.3 Bolting 54

12.4 Spacing of Connection in Compression Elements 55


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13. MISCELLANEOUS 56

13.1 Usually Wide, Stable Beam Flanges 56

13.2 Shear Lag 56

13.3 Flange Curling 57

13.4 Application of Plastic Design to L ight-Gauge Structures 57

SECTION 2 DESIGN TABLES AND DESIGN CURVES

1. SCOPE 61

2. DESIGNOFSTI FF EN EDCOMPRESSIONELEMENTS ELEMENTSWITHOUTINTERMEDIATESTI FFENE RS 61

3. DESIGNOFSTI FF ENEDCOMPRESSIONELEMENTS MULTIPLESTI FF ENEDELEMENTSANDWIDESTI FFE NEDELEMENTSWITHEDGESTI FF EN ERS 62

4. STI FF ENE RSFORCOMPRESSIONELEMENTS 71

5. COMPRESSIONONUNSTIFFENEDELEMENTS 71

6. LATERALLYUNBRACEDBEAMS 72

7. SHEARSTRE SSESINWEBSOFBEAMS 76

8. AXIALLYLOADEDCOMPRESSIONMEMBERS 78

TABL ES

TABLE 1 STI FF ENED COMPRESSION ELEMENTS L IMITING WIDTHTHICKNESS RATIO w/tlim BELOW WHICH ELEMENT ISFULLYEFFECTIVE 61

TABLE 2 REDUCTION FACTOR, , FOR COMPUTING EFFECTIVEAREAOFSTI FFENERS( Aef= Asf) 62

TABLE 3 M INIMUM MOMENT OF INERTIA OF EDGE STI FFE NE R( Imin/t

4 ) 71

TABLE 4 M INIMUM DEPTH OF SIMPLE L IP EDGE STI FFE NERS( dmin/t ) 72

TABLE 5 COMPRESSION ONUNSTIFFENEDELEMENTS 72

TABLE 6 VALUESOFCOEFFICIENTS 74

TABLE 7 BENDINGCOEFFICIENTCb 76


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SECT ION 3 DESIGN EXAMPLES

1. SCOPE 87

EXAMPLENO. 1 SECTIONAL PROPERTIES 87

EXAMPLENO. 2 INTERMEDIATESPAN ROOFDECK 89

EXAMPLENO. 3 IMPROVEDROOFDECK 92

EXAMPLENO. 4 BEAMSTRENGTHCALCULATION 96

EXAMPLENO. 5 AXIALLY LOADEDCOMPRESSIONMEMBER 101

EXAMPLENO. 6 WALL STUDBRACED BYWALL SHEATHING-AXIALCOMPRESSIONMEMBER 103

EXAMPLENO. 7 WELDED COLD-FORMED L IGHT-GAUGE STEELROOFTRUSS 106

APPENDIX A COMPOSITION OF STRUCTURAL ENGINEERINGSECTIONAL COMMITTEE, SMBDC 7 119

APPENDIX B L ISTOF IMPORTANTSTANDARDS ANDCODES OFPRACTICES PUBLISHED BY THE INDIANSTANDARDSINSTITUTION I N TH EFIELDOFSTEELPRODUCTION, DESIGNANDUSE 120


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0. F O R E W O R D

0.1This Handbook, which has been processed by the StructuralEngineering Sectional Committee, SMBDC 7, the composition of whichis given in Appendix A, has been approved for publication byStructural and Metals Division Council and Civil E ngineering DivisionCouncil of ISI .

0.2 Steel, which is a very important basic raw material for industriali-zation, had been receiving attention from the Planning Commissioneven from the very early stages of the countrys First Five Year Planperiod. The Planning Commission not only envisaged an increase inproduction capacity in the country, but also considered the question ofeven greater importance, namely, the taking of urgent measures for the

conservation of available resources. I ts expert committees came to theconclusion that a good proportion of the steel consumed by the structuralsteel industry in India could be saved if more efficient procedures wereadopted in the production and use of steel. The Planning Commission,therefore, recommended to the Government of India that the IndianStandards I nstitution should take up a Steel Economy Project andprepare a series of Indian Standard specifications, handbooks, and codesof practices in the field of steel production and utili zation.

0.3 Over several years of continuous study in I ndia and abroad, andthe deliberations at numerous sittings of committees, panels and studygroups, have resulted in the formulation of a number of I ndianStandards in the field of steel production, design and use, a list ofwhich is given in Appendix B.

0.4 In comparison with conventional steel construction which util izesstandardized hot-rolled shapes, cold-formed, light-gauge steelstructures are a relatively new development. To be sure, corrugatedsheet, which is an example of such construction, has been used formany decades. However, systematic use had started in the UnitedStates only in the 1930s and reached large-scale proportions only afterthe Second World War. I n E urope, such large-scale use is beginningonly now in some countries.

0.5The design of light-gauge structural members differs in manyrespects from that of other types of structures. Since its principles arerelatively new, they are as yet not usually taught in engineeringinstitutions. The important methods, referring to such design havebeen formulated in IS : 801-1975, to which reference has been madethroughout.

0.6 Intelligent and economical use of a code by a designer may be madeonly if he has a thorough understanding of the physical behaviour of


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the structures to which the code applies, and of the basic informationon which the code is based.

0.7This handbook which deals with the use of cold-formed, light-gaugesections in structures was first published in 1970 and was based on the1958 edition of IS : 801. With the revision of IS : 801 in 1975, a revisionof the handbook was taken. This revision has been prepared in threesections:

0.7.1 Section 1 contains a systematic discussion of IS : 801-1975 andits background, arranged by fundamental topics in a manner useful tothe practicing designer. This portion should enable the engineer notonly to orient himself easily with the provisions of IS : 801-1975 butalso to cope with design situations and problems not specificallycovered in I S : 801-1975.

0.7.2 Section 2 contains considerable supplementary information ondesign practices in the form of tables and design curves based on provi-sions of IS : 801-1975.

0.7.3 Section 3 contains a number of illustrated design examplesworked out on the basis of provisions of IS : 801-1975 and usingvarious tables and design curves given in Section 2.

0.8This handbook is based on, and requires reference to the followingIndian Standards:

Section 1 Commentary

Section 2 Design tables and design curves

Section 3 Design examples

IS : 800-1962 Code of practice for use of structural steel in generalbuilding construction ( revised )

IS : 801-1975 Code of practice for use of cold-formed light gauge steelstructural members in general building construction( first revision )

IS : 811-1965 Specification for cold-formed light gauge structural steelsections ( revised )

IS : 816-1969 Code of practice for use of metal arc welding for generalconstruction in mild steel ( first revision )

IS : 818-1968 Code of practice for safety and health requirements in

electric and gas welding and cutting operations (firstrevision )


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0.9This edition 2.1 incorporates Amendment No. 1 (March 1984). Sidebar indicates modification of the text as the result of incorporation ofthe amendment.

0.10 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 be rounded off in accor-dance with IS : 2-1960*. The number of significant places retained inthe rounded off value should be the same as that of the specified valuein this standard.

0.11 In the preparation of this handbook, the technical committee hasderived valuable assistance from commentary on the 1968 edition ofthe specification for the Design of Cold-Formed Steel StructuralMembers by George Winter published by American Iron and SteelInstitute New York.

IS : 875-1964 Code of practice for structural safety of buildings:Loading standards ( revised )

IS : 1079-1973Specification for hot-rolled carbon steel sheet and strip( third revision )

IS : 1261-1959Code of practice for seam welding in mild steel

IS : 4000-1967Code of practice for assembly of structural joints usinghigh tensile friction grip fasteners

*Rules for rounding off numerical values ( revised ).


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SECT I ON 1 COMMENT AR Y


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1. SCOP E

1.1This section contains a systematic discussion of the provisions ofIS : 801-1975.

2. INTR ODUCTI ON

2.1 Light gauge members are cold-formed from steel sheets or strips.Thickness for framing members (beams, joists, studs, etc) generallyranges from 1.2 to 4.0 mm; for floor and wall panels and for long spanroof deck from 1.2 to 2.5 mm, and for standard roof deck and wallcladding from 0.8 to 1.2 mm. These limits correspond to normal designpractice, but should not be understood to restrict the use of material oflarger or smaller thickness. In India light gauge members are widelyused in bus body construction, railway coaches, etc and the thickness

of these members vary from 1.0 to 3.2 mm.2.2 Forming is done in press brakes or by cold-rolling. Light gaugemembers can be either cold-formed in rolls or by press brakes from flatsteel generally not thicker than 12.5 mm. For repetitive mass produc-tion they are formed most economically by cold-rolling, while small quan-tities of special shapes are most economically produced on press brakes.The latter process, with its great versatility of shape variation makes thistype of construction as adaptable to special requirements as reinforcedconcrete is in its field use. Presently light gauge members are producedin India both by press brake system (for use in small quantities) and bycold-forming (for use in large quantities). These members are connectedtogether mostly by spot welds, cold riveting and by special fasteners.

2.3The cold-formed members are used in preference to the hot-rolledsections in the following situations:

3. CURR ENT SHAP ES

3.1 In contrast to hot-rolling, the cold-forming processes coupled withautomatic welding permit an almost infinite variety of shapes to be

a) Where moderate loads and spans make the thicker hot-rolledshapes uneconomical, for example, joists, purlins, girts, rooftrusses, complete framing for one and two storey residential,commercial and industrial structures;

b) Where it is desired that load carrying members also provideuseful surfaces, for example, floor panels and roof decks, mostlyinstalled without any shoring and wall panels; and

c) Where sub-assemblies of such members can be prefabricated inthe plant, reducing site erection to a minimum of simpleoperations, for example sub-assembly of panel framing up to3 4 metres and more for structures listed in (a), standardizedpackage shed type utili ty buildings, etc.


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produced. The requirements for the sections generally manufacturedin India are given in IS : 811-1965. But the freedom of designers is notlimited to the use of sections listed in that standard. This is because agreat variety of usages require a corresponding variety of shapes.However the designer is advised to seek the advice of themanufacturers or fabricators before specifying special sections.

3.2 Shapes for Structural Framing Many of the shapescurrently in use are shown in Fig. 1.

3.3 Shapes 1 to 21 in Fig. 1 are outlines similar to hot-rolled shapes,except that in shapes 2, 4 and 6 lips are used to stiffen the thin flanges.These shapes are easily produced but have the disadvantage of beingunsymmetrical. Shapes 7 to 11 are to be found only in cold-formedconstruction, they have the advantage of being symmetrical. Shapes 7,8, 10 and 11 are adapted for use in trusses and latticed girders; thesesections are compact, well stiffened and have large radii of gyration inboth principal directions. Shape 9, lacking edge stiffeners on thevertical sides is better adapted for use as a tension member. Shapes 12and 13 are used specifically as girts and cave struts respectively, inall-metal buildings shape 12 being the same as shape 4 which is alsoused for pur lins. The above members are all one-piece shapes producedmerely by cold-forming.

3.3.1 When automatic welding is combined with cold rolling, it ispossible to obtain additional shapes. Shapes 14 and 15 are two varietiesof I shapes, the former better adapted for use as studs or columns, thelatter for joists or beams. Two of the most successful shapes, namelyshapes 16 and 17 are further adaptations of shapes 14 and 15. Bydeforming the webs and by using projection spot welding, curved slots

are formed which provide nailing grooves for connecting collateralmaterial, such as wall boards and wood floors. Shapes 18 and 19represent closed members particularly favourable in compression theformer primarily for columns, the latter for compression chords oftrusses. Shape 20 shows one of a variety of open web joists, with chordsshaped for nailing, and shape 21 shows sections similar to the chords ofshape 20 connected directly to form a nailable stud.

3.3.2The shapes in Fig. 1 do not exhaust the variety of sections now inuse. There is no doubt that design ingenuity will produce additionalshapes with better structural economy than many of those shown, orbetter adapted to specific uses. In the design of such structuralsections the main aim is to develop shapes which combine economy ofmaterial (that is a favourable strength weight ratio) with versatilityease of mass production, and provision for effective and simple

connection to other structural members or to non-structural collateralmaterial or both of them.


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4. DECK S AND PANEL S

4.1 Some typical roof decks, floor and roof panels, siding, and curtainwall panels as they have developed during the last 20 years in USAand are beginning to find application, duly modified, in other countriesare shown in F ig. 2.

4.2 Standard roof decks are usually 58 mm deep, with a rib spacing of130 mm and are used on spans between purlins up to 5m. Ascompared to corrugated sheet they have the important advantage thatthe flat surface makes it possible to apply insulation and built-uproofing. L ong-span roof decks are used for spans up to 6 m and more,which means that purlins in most cases may be dispensed with. Chiefapplication is for industrial buildings, but also for other structureswith relatively long roof spans, such as for schools.

4.3 Floor and roof panels are made to cover spans from 3 to 10 m. Theyare usually cellular in shape and permit a wide variety of ancil lary uses.Thus, acoustic treatment is obtained by perforating bottom surfacesand installing sound absorbing elements, such as glass fibre insulation,in the cells. Electrification of the entire floor is achieved by permanentinstallation of wiring in the cells, which permits floor outlets to beplaced wherever desired. Recessed lighting may be installed in the

spaces between cells, etc. The flooring proper is installed on alight-weight concrete fil l (50 to 75 mm) placed on top of the floor panels.

F IG. 2 FLOORANDROOFDECKS, ANDWALLPANELS


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4.3.1 Curtain walls consist either of single-sheet siding or of cellularinsulated wall panels.

4.4 Advantages of these systems are light weight which reduces thecost of main framing and foundations; speed of erection; absence ofshoring or other temporary supports for floors and roofs; immediateavailability; adaptability to later changes and additions; andsuitability to perform enumerated ancillary functions.

4.5 In the design of these members, structural efficiency is only one ofthe many criteria since the shape should also be selected to minimizedeflections, provide maximum coverage, permit adequate insulation,and accessibility of cells for housing conduits, etc. Optimum strength,

that is, optimum strength-weight ratio, therefore, is desired onlyconditionally, that is, in so far as it is compatible with the otherenumerated features.

4.6 I t is evident from this discussion that the shapes used inlightgauge construction are quite different from, and considerablymore varied than, those employed in hot-rolled framing. Inconsequence, an appropriate design code, such as IS : 801-1975 andIS : 800-1962 should enable the designer to compute properties andperformance of practically any conceivable shape of cold-formedstructural members.

5. MATERI AL

5.1 Structural steel sheet used for production of member should

conform to IS : 1079-1973.

6. DEF INI TI ONS

6.1 Stiffened Compression Element A flat compression element,for example, a plane compression flange of a flexural member (Fig. 3A,3B and 3C) or a plane web or flange of a compression member, of whichboth edges parallel to the direction of stress are stiffened by a web,flange stiffening lip, intermediate stiffener or the like conforming tothe requirement of 5.2.2of IS : 801-1975.


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6.2 Unstiffened Compression Elements A flat element which isstiffened at only one edge parallel to the direction of stress (Fig. 4).

6.3 Multiple Stiffened Elements and Subelements An elementthat is stiffened between webs, or between a web and a stiffened edge(Fig. 5), by means of intermediate stiffeners which are parallel to thedirection of stress and which conform to the requirements of 5.2.2ofIS : 801-1975. A subelement is the portion between adjacent stiffeners

or between web and intermediate stiffener or between edge andintermediate sti ffener.

F IG. 3 STI FFE NEDCOMPRESSIONELEMENTS

F IG. 4 UNSTIFFENEDCOMPRESSIONELEMENTS


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6.4 Flat Width Ratio The flat width ratio of a single flat

element is the ratio of the flat width w, exclusive of edge fillets, to thethickness t( seeFig. 6 ).

6.5 Effective Design Width Where the flat-width wof an element

is reduced for design purposes, the reduced design width bis termed asthe effective width or effective design width (Fig. 7).

F IG. 5 MULTIPLESTI FF EN EDELEMENTANDSUB-ELEMENT

F IG. 6 FLATWIDTHRATIO

F IG. 7 EFFECTIVE DESIGNWIDTH

w

t----


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6.6 Torsional Flexural Buckling A mode of buckling in whichcompression members can bend and twist simultaneously (Fig. 8).

6.7 Point Symmetric Section A section symmetrical about apoint (centroid), such as a Z section having equal flanges (Fig. 9).

6.8 Yield Stress, F yThe cold-rolled steel sections are producedfrom strip steel conforming to IS : 1079-1973, the yield stresses of thesteels are as follows:

7. L OADS

7.1 For general guidance as to the loads to be taken into account in the

design of structures, reference should be made to IS : 800-1962 andIS : 875-1964.

( The cross section shown dotted after buckling )

F IG. 8 TORSIONALFLEXURALBUCKLING

F IG. 9 POINTSYMMETRICSECTION

Grade Yield Stress( Min )

St 34 2 100 kgf/cm2

St 42 2 400 ,,

St 50 3 000 ,,

St 52 3 600 ,,


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8. DESIGN PR OCEDURE

8.1 General All computations for safe load, stress deflection andthe like shall be in accordance with conventional methods of structuraldesign except as otherwise specified herein.

8.2 Properties of Sections The properties of sections(cross-sectional area, moment of inertia, section modulus and radius ofgyration) shall be determined in accordance with the conventionalmethods of structural design.

8.2.1 Computation of properties of formed sections may be simplifiedby using a method called linear method in which the material of thesection is considered concentrated along the central line of the steel

sheet and the area elements replaced by straight or curved lineelements. The thickness element t is introduced after the linearcomputation has been completed.

The total area of the section is found from the relation Area =L t t'where L tis the total length of all the elements. The moment of inertiaof the section is found from the relation I =I ' t' where I ' is themoment of inertia of the central line of steel sheet.

The section modulus is computed as usual by dividing I or ( I ' t' )by the distance from neutral axis to the extreme and not to the centralline of extreme element.

First power dimensions such as x, yand r(radius of gyration) areobtained directly by the linear method and do not involve the thicknessdimension.

When the flat width wof a stiffened compression element is reducedfor design purposes, the effective design width b is used directly tocompute the total effective length Leffectiveof the line elements.

The elements into which most sections may be divided for applica-tion of the linear method consist of straight lines and circular arcs. Forconvenient reference, the moments of inertia and location of centroid ofsuch elements are identified in F ig. 10.

8.2.2The formula for line elements are exact, since the line as suchhas no thickness dimensions; but in computing the properties of anactual section, where the line element represents an actual elementwith a thickness dimension, the results will be approximate for thefollowing reasons:

a) The moment of inertia of a straight actual element about itslongitudinal axis is considered negligible.


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F IG. 10 PROPERTIESOFL INE ELEMENTSContinued


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(expressed in radians) =0.017 45 (expressed in degrees and decimals thereof)l = R

C1 =

C2 =

I1 =

I2 =

I3 =

I4 =

G =centre of gravity

F IG. 10 PROPERTIESOFL INEELEMENTS

b) The moment of inertia of a straight (actual) element inclinedto the axis of reference is slightly larger than that of thecorresponding line element, but for elements of similarlength the error involved is even less than the error involvedin neglecting the moment of inertia of the element about itslongitudinal axis. Obviously, the error disappears when theelement is normal to the axis.

c) Small errors are involved in using the properties of a linear arcto find those of an actual corner, but with the usual smallcorner radii the error in the location of the centroid of thecorner is of little importance, and the moment of inertiagenerally negligible. When the mean radius of a circularelement is over four times its thickness, as for tubular sections

and for sheets with circular corrugations, the error in usinglinear arc properties practically disappears.

R sin---------------------

R 1 cos---------------------------------------

sin cos+

2----------------------------------------------------------

sin 2-------------------------- R

3

sin cos

2---------------------------------------------------------- 1 cos

2----------------------------------- R3

sin cos+

2---------------------------------------------------------- R3

sin cos

2---------------------------------------------------------- R3


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A typical worked out example is given in Section 3.

8.3 Effective Design Width Consider a plate simply supported ontwo edges and loaded as shown in Fig. 11.

As the load qis gradually increased, the stress will be uniform, At a

stress equal to the critical stress namely fcr = ... (1)

(where = Poissons ratio and t =thickness) the plate at the centre willbuckle. The stress distribution is as shown in Fig. 12A.

As the load qis gradually increased the unbuckled portion of theplate resists the loads and the distribution of stress is as shown in Fig.12B. Failure occurs at a stage when the stress at the supported edgereaches yield stress Fyand the distribution of stress at this stage is as

shown in Fig. 12C.

For design purposes the total force is assumed to be distributed over

lesser width with uniform stress. This reduced width is called theeffective design width of plate (seeFig. 13 ).

FIG. 11 F IG. 12

E

3 1 2 b t 2-----------------------------------------------------


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The simplest form for effective width expression is obtained byequating yield stress

This expression, known as Von Karman equation, based onexperiments has been modified by Winter as

Substituting for Eas 2 074 000 kgf/cm2

F IG. 13

Fy = , or

, or

...... (2)

b =1.9 t ...... (3)

IS : 801-1975 is based on the latest expression adopted by AISI Code 68

which is given as ...... (4)

...... (5)

2E

3 1 2 b

t---

2-----------------------------------------------

b

t---

2=

2E

3 1 2 Fy---------------------------------------

b

t--- = 1.9

E

Fy------

Efmax----------- 1 0.475 t

w---- E

fmax-----------

b

t--- 1.9=

E

fmax----------- 1 0.415

t

w----

E

fmax-----------

b

t---2 736

f--------------- 1598

w t f--------------------------=


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8.3.1 Formulae for load and deflection determination:

The stiffened compression elements fail when the edge stress (thatis, the stress on the effective area) reaches the yield point. In order tocompute the failure moment Multof a beam it is necessary to calculatethe section modulus at a stress equal to the failure stress, that is theyield stress, and multiply it by the yield stress.

The factor of safety for bending members =1.67 that is Fy =1.67 fbwhere fbif the basic design stress.

I t may be confusing to the designer to calculate allowable bendingmoment at section modulus at Fyand then multiply by fb. To avoid thisconfusion, the effective width expression for load determination ismodified by replacing fby 1.67 fso that the designer can substitute ffor determining the effective width and thus calculate the sectionmodulus and multiply the section modulus by fagain.

Therefore, the expression for effective width for load calculation isobtained as follows by substituting 1.67 finstead of fin expression (5):

The expressions (9) and (5) are rounded off and modified to arr ive atthe expression given in 5.2.1.1of IS : 801-1975.

Load determination:

Mult =Sat Fy fy ...... (6)

Mult =Sat Fy 1.67Fb ...... (7)

Mallowable =

= ...... (8)

= ...... (9)

...... (10)

MultFactor of safety-------------------------------------------

Mult

1.67------------ Sat Fy fb=

b

t---

2 736

1.67 f-------------------- 1

598wt---- 1.67f

---------------------------=

2 117

f---------------

1462

w

t---- f---------------------

b

t--- 2 120

f--------------- 1

465

wt---- f

---------------=


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Deflection determination:

The flanges are fully effective when b =w; substituting in theexpression (10) as b =w;

By simplifying the expression (12)

This is a quadratic equation in and solving

In a similar way for deflection determination can be

obtained from expression (11) as,= which is modified as

= in IS : 801-1975

8.3.2 Effective Widths for Square and Tubular Sections Thesesections being rolled under strict quality control, a higher value ofeffective widths are permitted to be in agreement with theexperimental results.

8.3.3 Multiple Stiffened Elements and Wide Stiffened Elements withEdge Stiffeners The elements with large flat width ratios becomeuneconomical because they have only very small effective widths. I n such

cases the elements may be stiffened with stiffeners as shown in Fig. 5.In cases when flat width ratio of subelement exceeds 60 because of the

...... (11)

...... (12)

...... (13)

This is modified as =

b

t---

2 710

f---------------

1600

w

t---- f----------------

=

w

t----

2 120

f---------------

1465

w

t---- f----------------

=

w

t----

2 2 120

f---------------

w

t----

985 800f

--------------------- 0=+

wt----

w

t----=

1 431

f---------------

wt----

lim

1 435

f---------------

wt----

lim

wt----

lim

1 813

f---------------

wt----

lim

1 850

f---------------


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shear lag effect, the effective design width and also the effective area ofthe stiffener should be reduced as given in 5.2.1.2of IS : 801-1975.

8.3.4 Stiffeners for Compression Elements In order that a flatcompression element may be considered a stiffened compressionelement it shall be stiffened along the edge with stiffener of sufficientrigidity. The minimum moment of inertia required to stiffen the edge hasbeen calculated approximately and the expression under 5.2.2.1 ofIS : 801-1975 has been arrived at. The experimental results give a closefit to the values obtained from the expression. Whereas an edge stiffenerstiffens only one compression element, an intermediate stiffener stiffensthe two compression elements on either side of the stiffener. Theminimum moment of inertia required for an intermediate stiffener is

proposed as double the moment of inertia of an edge stiffener.

Tests have shown that in a member with intermediate stiffeners theeffective width of a subelement is less than that of an ordinary stiffened

element of the same ratio, particularly if exceeds about 60. This

may be understood from the discussion in the following paragraphs.

In any flanged beam the normal stresses in the flanges are the resultof shear stresses between web and flange. The web, as it were, originatesthe normal stresses by means of the shear it transfers to the flange. Themore remote portions of the flange obtain their normal stress throughshear from those closer to web, and so on. I n this sense there is adifference between webs and intermediate stiffeners in that the latter is

not a shear-resisting element and therefore does not originate normalstresses through shear. On the contrary, any normal stress in thestiffener should have been transferred to it from the web or websthrough the intervening flange portions. As long as the subelementbetween web and stiffener is flat or only very slightly buckled (that is

with low ) this shear proceeds unhampered. In this case, then, the

stress at the stiffener is equal to that at the web and the subelement is

as effective as a regular stiffened element of the same ratio.

However for large ratios the slight buckling waves of the sub-

element interfere with complete shear transfer and create a shear lag,consequently the stress distribution in a multiple stiffened element,

when the ratios of the subelements exceed about 60, can be thought

wt----

wt----

wt----

wt----

wt----

wt----


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31

of as represented in F ig. 14. That is, since the edge stress of asubelement is less at the stiffener than at the edge, its effective width

is less than that of corresponding stiffened element (with same

ratios). Also the efficiency of the stiffener itself is reduced by this lowerstress; this fact is best accounted for by assigning a reduced effectivearea to the stiffener.

Correspondingly the effective widths of subelements are identical

with those obtained from 5.2.1.1of IS : 801-1975 only where is less

than 60. For larger ratios these effective widths are reduced accor-

ding to the formula 5.2.1.2of IS : 801-1975. Also in view of the reducedefficiency of the intermediate stiffeners as just described, theireffective area for determining properties of sections of which they arepart, is to be determined from the formula for Aeff. It should be noted

that the usually slight reduction in efficiency provided by 5.2.1.2 ofIS : 801-1975 does not detract from the very considerable gainstructural economy obtained by intermediate stiffeners.

Provisions (a), (b) and (c) of 5.2.2.2 of IS : 801-1975 reflect thedescribed situation, namely, that the intermediate stiffeners, due toshear lag across slightly waved subelement are not as effective as

complete webs would be. Consequently, if a number of stiffeners wereplaced between webs at such distances that the resulting subelements

F IG. 14 MULTIPLESTI FF EN EDELEMENT

wt----

wt----

wt----


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32

have ratios of considerable magnitude, there would be a rapidly

cumulative loss of effectiveness with increasing distance from the web.

Provisions (a) and (b) in essence provide that if of the subelements

exceeds ,that is, if they are in the slightly buckled state so that

the shear transfer is interfered with, only such intermediate stiffenerswhich are adjacent to web shall be regarded as effective. On the otherhand if stiffeners are so closely spaced that the subelements show no

tendency to slight buckle , the

entire element including stiffeners will be fully effective. This is whatprovision (c) also specifies for such closely stiffened elements aneffective thickness tsfor computing, when needed, the flat width ratioof entire element (including stiffeners). I t is easily checked that this tsis the thickness of a solid plate having the same moment of inertia asthe actual, closely stiffened element.

9. ALL OWABL E DESIGN STRE SSES

9.1 Compression on Unstiffened Elements An unstiffened

compression element may fail in yielding if it is short and its ratio is

less than a certain value.

The elastic critical local buckling stress for a uniformly compressedplate is

For a long rectangular plate with a free edge and supported on threeedges the value of K=0.425. When the restraining effect of the connec-

ted edge is considered Kcan be taken as 0.5. The limit of ratio below

which the steel will yield can be found out by equating

asE =2 074 000 kgf/cm2and =0.3.

I f the steel has sharp yielding and the element is ideally plane, theelement will fail by yielding below this limit. In practice the element

fcr

=...... (14)

Fy = ...... (15)

Substituting for Eand = ...... (16)

wt----

wt----

wt----

lim

that is,wt---- is less than

w

t----

lim

wt----

K 2E

12 1 2

wt----2

----------------------------------------------------

wt----

0.5 2E

12 1 2 wt----

2----------------------------------------------------

wt----

.

F y---------------


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33

will buckle below this theoretical l imit and it has been found at a valueof about 0.55 times this value will be suitable for practical cases and

hence the limit is fixed as in 6.2 of IS : 801-1975. As the

cold-forming process sets up residual stresses this also reduces theproportional limit. By assuming a proportional limit of 0.65 Fy the

limit of at which elastic buckling starts can be found out as

0.65 Fy =

Substituting E =2 074 000 kgf/cm2and =03,

=

This limit is taken as in 6.2(b) of IS : 801-1975. For the

stresses within the limit of = to = that is the

region of inelastic buckling line Bin Fig. 15. Straight line variation isassumed and the equation is worked out as follows:

Let the equation to straight line be

f=m +c

0.6 Fy =m +c

and 0.383 Fy =m +c

= ...... (17)

at = Fa = =0.6 Fy

at = Fa =

Fy------------

wt----

0.5 2E

12 1 2 w

t----

e

2--------------------------------------------------------

wt----

e0.5

2E

7.8 1 2 Fy--------------------------------------------

wt----

e

1 200

Fy---------------

1 210

Fy---------------

wt----

Fy-----------

wt----

1 200

Fy---------------

wt----

wt----

530

Fy----------- Fy

1.67-----------

wt---- 1 200

Fy--------------- 0.5

2E

12 1 2 1 210

Fy---------------

2

1.67

----------------------------------------------------------------------------------- =0.383F

530

Fy-----------

1 210F y

---------------


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34

Solving these equations:

Hence substituting in the equation, the expression for allowablestress is obtained as:

Fa =Fy

This is rounded off as the expression given in IS : 801-1975

For ratio from 25 to 60 the allowable stress is obtained as dividing

the expression by a factor of safety of 1.67

m = 0.000 32Fy and

c = 0.769 Fy

Fa =Fy ...... (18)

F IG. 15 UNSTIFFENEDELEMENTFAILURE STRESSESANDALLOWABLE

STRESSESFOR0 <


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35

that is, Fa =

The expression given in 6.2(d) of IS : 801-1975 is .

For sections other than angle sections the allowable stress

expression is obtained by joining the point cand d. As for large

ratios there is sufficient post buckling strength factor of safety which

is taken care of in the post buckling strength and the point dis takenin the buckling curve.

9.2 Laterally Unbraced Beams The critical moment for a beamsimply supported at the two ends and subjected to two end couples is

Therefore, the critical stress for lateral buckling of an I beamsubjected to pure bending is given by

cr =

=...... (19)

By fitting a straight line between the limits w/t = 25 and

equation to straight line is obtained as

60, the

...... (20)

Mcr =...... (21)

For I beams Cw =

and Iy =

The equation (21) becomes Mcr =

=

...... (22)

= ...... (23)

0.5 2E

12 1 2 w/t 2 1.67-----------------------------------------------------------------------------

561 250

w

t----

2---------------------

562 000

w

t----

2---------------------

wt----

1390 20wt----

L---- EI yGJ 1

2ECw

GJ L 2-------------------+

b3td2

24---------------

b3t6

--------

L---- E IyGJ

2E2

L2

-------------Iyb

3td

2

24---------------+

L---- E IyGJ L

----2Iy

2.E2d

2

4------+

Mcr

Sx----------

Mcr

Ixd 2-----------

-------------------- d2 IxL--------------- E Iy GJ

2E 2

L2------------- Iy2

d2

4------+= =

2

d

2

E

2

2L2--------------------

IyGJ

I x2 Ed2

------------------- L

2

2------ I 2

y4I 2x-----------+


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36

For thin-walled sections the first term appearing in the square rootis considerably less than the second term and hence neglecting thefirst term, we get

Where Sxcis the section modulus with respect to the compressionflange and Iycis the moment of inertia of compression flange about YY-axis that is

I t may be noted that the equation applies to the elastic buckling ofcold-formed steel beams when the computed theoretical bucklingstress is less than or equal to the proportional limit pr. But if the

computed stress exceeds the proportional limit then the beam will failby inelastic buckling. For extremely short beams the maximummoment capacity may reach full plastic moment Mp. A study byGalambos* has shown that for wide flanged beams Mp =1.11 My.

This means that extreme fibre stress may reach an equivalent value

of 1.11 fywhen =0, if we use the elastic section modulus Sxc.

As in the case of compression members, effective proportional limitcan be assumed as one half the maximum stress that is

cr =

=

= ...... (24)

To consider the effect of other end conditions coefficient Cbis addedand

cr = ...... (25)

*Inelastic lateral buckling of beams. T. V. Galambos. J ournal of Structural DivisionASCE Proc. Volume 89, No. ST 5 October 1963.

pr = (1.11 Fy) =0.555 Fy ...... (26)

The value of corresponding is obtained as

2d

2E

2L2-----------------

Iy

2 Ix----------

2Ed

2L2-----------------

I y

2 Sxd

2---

-------------------------

2Ed

SxL2

---------------- Iy

2-----

2Ed

SxcL2

------------------ Iyc=

IycIy

2-----=

2E CbSxcL

2

d I yc------------------

--------------------

L Sxcd I yc

------------------

12---

L2Sxc

d I yc----------------


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37

The stress against is shown in Fig. 16.

The equation for the stress in the inelastic region is obtained by fitting

a parabola f=Fy between the points aand c.

At point a, = 0 and f=1.11 Fyand

at point c, = and f=0.555 Fy. Substituting these,

the value of Ais found as 1.11 and that of Bas 3.24.

or ...... (27)

F IG. 16

2E Cb

L 2Sxc

d I yc------------------

-------------------- 0.555 Fy=

L2Sxc

d I yc------------------

2E Cb

0.555 Fy------------------------

1.8 2E Cb

F y---------------------------------= =

L

2Sxc

d I yc------------------

A1B----

Fy

fcr------

L2Sxcd I yc

------------------

L2Sxcd I

yc

------------------1.8 2E Cb

Fy

-------------------------------


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38

For the allowable stresses in 6.3 of IS : 801-1975, the stresses areobtained by dividing the following expression by the factor of safety1.67. For the inelastic range the expression is

9.2.1The Z-shaped sections, when they are loaded parallel to web theydeflect laterally due to unsymmetrical bending, if not properly braced.

Hence to be on conservative side the value as given in 6.3(b) ofIS : 801-1975 are assumed.

9.3 Webs of Beams

9.3.1 In regard to webs, the designer is faced with somewhat differentproblems in light gauge steel construction than in heavy hot-rolledconstruction. I n the latter, the webs with large h/tratios are usually

The value of at which the stress f=Fyis found out as

Fy =Fy ,

solving

f=Fy ...... (28)

In this expression to be on safe side the factor 1 is taken instead of 1.11

and the expression in the elastic range is f= ...... (29)

By dividing the expressions in (28) by 1.67,

Fb =

for the range greater than and

> . When that is elastic range

Fb =0.6 ...... (30)

F or < allowable stress is naturally =fb

L2 Sxc

dIyc------------------

1.111

3.24-----------

Fy2E Cb

-------------------- L2 Sxc

d I yc------------------

L 2SxcdI yc

------------------ 0.362E CbFy

--------------------=

1.0

1

3.24-----------

Fy

2E Cb--------------------

L 2Sxc

d Iyc------------------

2E Cb

L 2 Sxc

d I yc------------------

----------------------

23---Fy

F 2y

5.4 2ECb---------------------------

L 2 Sxc

d I yc------------------

L2Sxcd Iyc

------------------ 0.362E Cb

Fy--------------------------------

1.8 2E CbFy----------------------------- L

2 SxcdIyc------------------

1.8 2E CbFy-----------------------------

2E Cb

L 2Sxcd I yc

------------------

--------------------

L2SxcdI yc

------------------0.36 2ECb

Fy-------------------------------

Fy

1.67-----------


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39

furnished with stiffeners to avoid reduction of allowable stress. Incontrast in cold-formed construction large h/tratios are the rule ratherthan the exception. At the same time the fabrication process, as a rule,makes it difficult, though not impossible, to employ stiffeners. Underthese conditions the problem is that of so limiting the variousallowable web stresses that adequate stability is obtained without theuse of stiffeners.

9.3.2 The web of a beam may be considered as a simply supportedplate subjected to shear only. The elastic stress at which a simply

supported plate subjected to shear is cr = where

his the smaller dimension and t, the thickness.

Substituting for the value of E =2 074 000 kgf/cm2and =0.3;

The yielding stress in shear is known to be times that of yield-

ing stress in tension Fys = .

In the yielding case, that is for smaller h/tratios, a lesser factor ofsafety is permitted and is equal to 1.44.

This is given as the maximum limit in 6.4.1(a) of IS : 801-1975.

cr = =

Assuming a factor of safety equal to 1.71. Allowable stress in elasticshear buckling is:

= ...... (31)

This value is given in 6.4.1(b) of I S : 801-1975 as Fv =

...... (32)

Hence for smaller h/tratios, that is, when the sheet fails by yielding

by shear, the allowable stress = = 0.4Fy ...... (33)

For the non-linear portion, that is, between yield and elastic buck-

ling, an allowable stress of Fv= is permitted and the limit of

h/tratio is kept less than ...... (34)

5.35 2E

12 1 2 h/t 2---------------------------------------------------

5.35 9.87 2 074 000

12 0.91 h/t 2-------------------------------------------------------------- 10 028 980

h/t 2------------------------------

10 028 980

1.71 h/t 2----------------------------------

5 864 904

h/t 2--------------------------

5 850 000

h/t 2--------------------------

1

3---------

Fy3

-------

Fy

3 1.44--------------------------

1 275 Fyh/t

4 590

Fy---------------


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40

9.4 Compression M embers

9.4.1 General The basic difference between a compression memberin hot-rolled section and cold-formed section is that, in cold-formedlight gauge sections, as the width-thickness ratios of componentelements of cross section are large, these elements will be undergoinglocal buckling also. Hence it is necessary to incorporate the localbuckling effects in the allowable stress expressions. This is done byincorporating a factor Qin the allowable stress expressions.

9.4.2Axial Stress in Compression In light gauge sections because ofthe possibility of local buckling a factor Q which is less than 1 isassociated with the yield stress Fyand if we substitute QFyfor Fyinthe well known axial compressive expression, the expressions given

in 6.6of IS : 801-1975 can be obtained.9.4.2.1To find the value of Q

a) For stiffened elements For members composed entirely ofstiffened elements:

Pult =AeffFywhere

Pultis the yield load

Comparing with the expression yield stress =Q.Fy

Q = for stiffened element whereAeff

is the effective area

of all stiffened elements computed for basic design stress.

b) For unstiffened elements When the member consists ofunstiffened elements the yield load or ultimate load is the criticalstress multiplied by the area of cross section.

that is Pult =fcr Awhich is rearranged as

Where fcand fbare the allowable compressive and bending stressesrespectively comparing with the expression

Yield stress =Q.Fy

= ...... (35)

Q = ...... (36)

ult

A---------- eff

A---------- Fy

Aeff

A

----------

Pult

A----------

fcrFy------ Fy

1.67 fc1.67 fb------------------ Fy

fcfb---- Fy===

fcfb----


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41

c) For members consisting of both stiffened and unstiffenedelements The member consisting of both stiffened andunstiffened elements will attain its failure load when the weakerof the unstiffened elements buckles at the critical stress. At thestress Aettwill consist of unreduced area of unstiffened elementsand effective area of the stiffened elements computed for fcr.

Pult =fcr Aeffwhich is rearranged as

That is product of QunstiffenedQstiffened9.4.2.2The allowable stress in axial compression

a) Factor of safety The factor of safety for compression membersis taken as 1.92 which is about 15 percent larger than the basicsafety factor of 1.67 used in most part of the specification. Thisincrease is to compensate for the greater sensitivity of the com-pression members to accidental imperfections of the shape oraccidental load eccentricities.

The expressions for the compression stress in the elastic

range is based on Euler critical stress fcr = where Kis

the effective length factor. For the inelastic range a parabolicvariation is assumed. The limit of inelastic buckling is taken as0.5 Fy. As the cold worked members have residual stresses thelimit of proportionality assumed 0.5 Fy. For light gauge members

the effective Fy =Q.Fyand hence the limit of slenderness ratio atwhich elastic buckling starts is obtained as

0.5 Q.Fy =

Therefore

This limit is denoted by the symbol , where Cc =

Yield stress =Q.Fy

Q = ...... (37)

or ( KL /r )2 = = ...... (38)

Pult

A----------

fcrFy------

AeffA

---------- Fyfcfb----

AeffA

---------- Fy==

fcrFy------ =

fc

fb----

AeffA

----------

2E

KL /r 2-------------------------

2E

KL /r 2-------------------------

2E

0.5 Fy.Q-----------------------

2 2EQ.Fy--------------

KL

r--------

limit2 2E Q.Fy-----------------=

Cc

Q----------

2 2EF y

----------------


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42

The expression in the inelastic range is obtained by taking theequation for parabola as

By substituting these two conditions, the value of A =1 and B =4,

The expressions are:

1) for inelastic range f=Q.Fy1

2) for elastic range f=

f=Q.Fy

between the limit at = 0; f= Fyand

at KL /r= = ; f =0.5 Fy

f=Q.Fy ...... (39)

F IG. 17

A1B----

QFy

fcr-------------

KLr--------

Cc

Q-------- 2 2E

Q Fy---------------

1 1

4---

Q.Fy

2E

KL /r 2-------------------------

-------------------------

Q.Fy

4 2E----------------

KL

r--------

2

2E

KLr

--------2

---------------------


44/127

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43

The allowable stresses are obtained by dividing the above expressions

by the factor of safety 1.92 that is for KL/r


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44

or eccentricity to be magnified in the ratio which is known as the

magnification factor. This additional deflection causes additionalbending moment. Hence the interaction formula for such cases is

the factor can also be written as

where PEis the Eulers load and FEis the Euler stress. If the bendingmoment is acting about both the axes then the chord term also enters.

namely

For smaller axial loads that is 0.15, the term is very small

compared to 1 and hence the magnification factor is taken as 1 itself.These give the expressions given under 6.7of IS : 801-1975. Cm is acoefficient to take into consideration the end moments in the members.

10. WAL L STUDS

10.1 Cold-formed steel studs in walls or load carrying partitions areoften employed in a manner different from that used in heavy steelframing, but similar to that used in timber construction of residentialbuildings. Such studs are faced on both sides by a variety of wall materialsuch as fibreboard, pulp board, plywood and gypsum board. While it isthe main function of such wall sheathing to constitute the actual outerand inner wall surfaces and to provide the necessary insulation, they alsoserve as bracing for the wall studs. The latter, usually of simple ormodified I or channel shape with webs placed perpendicular to the wallsurface, would buckle about their minor axes, that is, in the direction ofthe wall at prohibitively low loads. They are prevented from doing so bythe lateral restraint against deflection in the direction of the wallprovided by the wall sheathing. If the lateral support is correctlydesigned, such studs, if loaded to destructions wil l fail buckl ing out of the

wall, the corresponding buckling load obviously represents the highestload which the stud may reach. The wall sheathing therefore contributesto the structural economy by maximising the usable strength of the stud.

1.0

1 PA

PE-------

-----------------

faFa------

fbxF bx---------+

Cm

1fa

F ex----------

------------------------------

1

1P

A

PE

-------

----------------

1

1faF

E

-------

----------------

fby

1 faF ey----------

----------------------------

Fby

a

Fa------

faFe------


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45

10.2The necessary requirements in order to assure that the wall shea-thing provide the lateral support necessary for the described optimumfunctioning of the studs are stipulated in 8.1of IS : 801-1975. In orderthat collateral wall material furnish the support to the studs to which itis attached, the assembly (studs, wall sheathing, and the connectionsbetween the two) shall satisfy the following three conditions:

10.2.1The first of these conditions is satisfied by8.2(b) of IS : 801-1975.This stipulates that the slenderness ratio a/r2for minor-axis bucklingbetween attachments (that is, in the direction of the wall) shall not exceedone-half of the slenderness ratioL/r1for major-axis buckling, that is, outof the wall. This means that with proper functioning of attachmentsbuckling out of the wall will always occur at a load considerably below

that which would cause the stud to buckle laterally betweenattachments. Even in the unlikely case if an attachment was defectiveto a degree which would make it completely ineffective, the buckling loadwould still be the same for both directions (that is, a/r2 =L /r1), so thatpremature buckling between attachments would not occur.

10.2.2 In regard to conditions (b) the rigidity of the wall material plusattachments is expressed as its modulus of elastic support kthat is,the ratio of the applied force to the stretch produced by it in thesheathing-attachment assembly.

The minimum modulus kwhich shall be furnished by the collateralmaterial in order to satisfy condition (b), above, that is, to preventexcessive buckling of the stud in the direction of the wall. It definesthe minimum rigidity ( or modulus k ) which is required to prevent

from lateral buckling a stud which is loaded by P =A.Fy, that is,stressed right up to the yield point of the steel.

a) The spacing between attachments (screws, nails, clips, etc) shallbe close enough to prevent the stud from buckling in the direc-tion of the wall between attachments.

b) The wall material shall be rigid enough to minimise deflection ofthe studs in the direction of the wall which, if excessive, could leadto failure in one of the two ways, namely, (1) the entire stud could

buckle in the direction of the wall in a manner which would carrythe wall material with it, and (2) it could fail simply by beingoverstressed in bending due to excessive lateral deflection.

c) The strength of the connection between wall material and studmust be sufficient to develop a lateral force capable of resistingthe buckling tendency of the stud without failure of the attach-ment proper by tearing, loosening, or otherwise.


47/127

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46

It may be seen from 8.1(c) of IS : 801-1975 that the requiredmodulus of support kis directly proportional to the spacing of attach-ments a.

10.2.3 I t remains to satisfy condition (c) above to the effect that thestrength of the attachment of wall material to stud shall be sufficientso that it will not give way at a load on the stud which is smaller thanits carrying capacity. This is achieved by means of provision (d) of 8.1of IS : 801-1975.

10.3Theory indicates that an ideal (straight, concentric) stud which iselastically supported at intermediate points (such as by wallattachments) will not exert any force on these attachments until itreaches its buckling load. In contrast, analysis and test indicate that

intermediately supported real, that is, imperfect studs (crooked,eccentric) do exert pressure on their support increasingly so that theload on the stud is increased.

I t may be noted that a value L /240 has been provided to allow forthe imperfections.

11. CHANNE L AND Z-BEAMS

11.1 Among hot-rolled sections, I -shapes are most favourable for use asbeams because a large portion of the material is located, in the flanges,at the maximum distance from the axis. In cold-formed construction,the only two-flange shapes which may be formed of one single sheet(without welding or other connection) are the channel, the Z-shape, andthe hat. Of these, the hat shape has the advantage of symmetry about

the vertical axis and of great lateral stability; its use is correspondinglyseparate webs which pose problems of access, connection, etc.

Channels and Z-shapes are widely used. Neither of them is symme-trical about a vertical plane. Since, in most applications, loads plate isapplied in the plane of the web, lack of symmetry about that planecalls for special measures to forestall structurally undesirableperformance (lateral deflection, twisting, etc). Appropriate provisionsfor this purpose are contained in IS : 801-1975.

11.2 Connecting Two Channels to F orm an I -Beam

11.2.1There are various ways of connecting two or more cold-formedshapes to produce an I -section. One of these is by spot-welding anangle to each flange of channel (see shapes 15 and 17 of Fig. 1 ).Another is to connect two channels back to back by two rows of

spot-welds (or other connectors) located as closely as possible to topand bottom flanges. The shapes 14 and 16 of Fig. 1 are sections of this


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47

sort. Provisions for the correct proportioning of the connecting weldsfor such shapes are given in 7.3of IS : 801-1975.

11.2.2 In view of lack of symmetry or anti-symmetry about a verticalplane the so-called shear-centre of a channel is neither coincident withthe centroid (as it is in symmetrical or anti-symmetrical shapes) nor isit located in the plane of the web. The shear-centre is that point in theplane of a beam section through which a transverse load should act inorder to produce bending without twisting. In a channel the shear centreis located at a distancemback of the midplane of the web, as shown inFig. 18. The distance mfor channels with and without flange lips isgiven in 7.3of IS : 801-1975. The internal shear forceVpasses throughthis point. Consequently, if the external load Pwas applied at the same

point (such as by means of the dotted bracket in Fig. 18) the two forceswould be in line and simple bending would result. Since loads in mostcases actually act in the plane of the web, each such load produces atwisting moment Pm, unless these torques are balanced by someexternally applied counter-torques, undesirable twisting wil l result.

11.2.3 I f two channels are joined to form an I -beam, as shown onFig. 19A each of them is in the situation shown on Fig. 19B and tendsto rotate in the sense indicated by the arrow on that figure. Thechannels, then, tend through rotation to separate along the top, butthis tendency is counteracted by the forces in the welds joining them.These forces Sw, constitute an opposing couple; they are shown onFig. 19B, which represents a short portion of the right channel, oflength equal to the weld spacings. This portion, delimited by dottedlines on F ig. 19A, contains a single pair of welds, and P is the totalforce acting on that piece of one channel, that is half the total beamload over the lengths. From the equality of moments:

F IG. 18 SHEARCENTRE OFACHANNEL

Pm =SwC, so that Sw =P(m/c ) ...... (44)


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48

11.2.3.1 I t is seen that the weld forceSwdepends upon the load acting

in the particular longitudinal spacing between welds S. If P is theintensity of load on the beam at the location of the particular weld, the

load on the channel is P = .

where

11.2.4 I t is seen that the required weld strength depends on the localintensity of load on the beam at that weld. Beams designed foruniform load actually are usually subjected to more or less uneven

load, such as from furniture and occupants. I t is, therefore, specifiedthat for uniformly loaded beams the local load intensity Pshall be

F IG. 19 CHANNELSSPOTWELDEDTOFABRICATEI-BEAM

Substituting this in equation (44) we have the required weld

strength Sw =...... (45)

Sw = required strength of weld,

s = longitudinal spacing of welds,

c = vertical distance between two rows of welds near or attop and bottom flanges,

p = intensity of load per unit length of beam, and

m = distance of the shear centre from middle plane of the webof channel.

ps

2------

mps

2c------------


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taken as three times the uniform design load. Concentrated loads orreactions pare actually distributed over some bearing length B; if Bislarger than the weld spacing s, than the local intensity is obviouslyp/B. I f, on the other hand, the bearing length is smaller than the weldspacing, then the pair of welds nearest to the load or reaction shallresist the entire torque (P/2 )m, so that Sw =Pm/2c. Since the mainformula above is written in terms of a load intensity p, it i s convenientto use an equivalent intensity for this case which is p =P/2s; thecorrectness is easily checked by substituting this value in the generalequation 44 ( seealso7.3of IS : 801-1975 ).

11.3 Br acing of Single-Channel Beams

11.3.1 I f channels are used singly as beams, rather than being paired

to form I-sections, they should evidently be braced at intervals so as toprevent them from rotating in the manner indicated in F ig. 18. Forsimplicity, F ig. 20 shows two channels braced at intervals against eachother. The situation is evidently much the same as in the compositeI -section of Fig. 19A, except that the role of the welds is now played bythe braces. The difference is that the two channels are not in contact,and that the spacing of braces is generally considerably larger than theweld spacing.

In consequence, each channel will actually rotate very slightlybetween braces, and this will cause some additional stresses whichsuperpose on the usual simple bending stresses. Bracing shall be soarranged that (a) these additional stresses are sufficiently small sothat they will not reduce the carring capacity of the channel (ascompared to what it would be in the continuously braced condition),

and (b) rotations are kept small enough to be unobjectionable (forexample, in regard to connecting other portions of the structure to thechannels), that is, of the order of 1 to 2.

11.3.1.1 Corresponding experimental and analytical investigationshave shown that the above requirements are satisfied for mostdistributions of beam loads, if between supports not less than threeequidistant braces are placed (that is, at quarter-points of the span orcloser). The exception is the case where a large part of the total load ofthe beam is concentrated over a short portion of the span; in this case anadditional brace should be placed at such a load. Correspondingly, 7.3ofIS : 801-1975 stipulates that the distance between braces shall not begreater than one-quarter of the span; it also defines the conditions underwhich an additional brace should be placed at a load concentration.

11.3.2 For such braces to be effective it is not only necessary that theirspacing is appropriately limited but also that strength is suffice to


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provide the force necessary to prevent the channel from rotating. I t is,therefore, necessary also to determine the forces which will act inbraces such as shown in F ig. 21A. These forces are found if oneconsiders (as shown in the figure) that the action of a load applied inthe plane of the web (which causes a torque Pm) is equivalent to that

same load when applied at the shear centre (where it causes no torque)plus two forces f=Pm/h which, together, produce the same torque Pm.As is sketched in F ig. 21B, each half of the channel may then beregarded as a continuous beam loaded by the horizontal forces fandsupported at the brace points. The horizontal brace force is then,simply, the appropriate reaction of this continuous beam. Theprovisions of 8.2.2of IS : 801-1975 represent a simple and conservativeapproximation for determining these reactions, which are equal to theforce Pbwhich the brace is required to resist at each flange.

11.4 Bracing of Z-Beams Most Z-sections are anti-symmetricalabout the vertical and horizontal centroidal axes. In view of this thecentroid and the shear centre coincide and are located at the mid-pointof the web. A load applied in the plane of the web has no lever arm about

the shear centre ( m =0 ) and does not tend to produce the kind of rotationa similar load would produce on a channel. However, in Z-sections the

FIG. 20 BRACEDCHANNELS


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principal axes are oblique to the web (Fig. 22). A load applied in the planeof the web, resolved in the direction of the two axes, produces deflectionsin each of them. By projecting these deflections into the horizontal and

FIG. 21 LOADACTINGAT THESHEARCENTRE ITSEFFECTSONTHEBRACES

F IG. 22 PRINCIPALAXESINZ-SECTIONS


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vertical planes it is found that a Z-beam loaded vertically in the plane ofthe web deflects not only vertically but also horizontally. I f suchdeflection is permitted to occur then the loads moving sideways with thebeam, are no longer in the same plane with the reactions at the ends. Inconsequence, the loads produce a twisting moment about the lineconnecting the reactions. In this manner it is seen that a Z-beam,unbraced between ends and loaded in the plane of the web, deflects late-rally and also twists. Not only are these deformations likely to interferewith a proper functioning of the beam, but the additional stresses causedby them produce failure at a load considerably lower than when the samebeam is used fully braced. Appropriate experimental and analyticalinvestigation has shown that intermittently braced Z-beams may beanalysed in much the same way as intermittently braced channels. I t is

merely necessary, at the point of each actual vertical load P, to apply afictitious load f. It is in this manner that the provisions applicable tobracing of Z-shaped beams in 8.2of IS : 801-1975 have been arrived at.

NOTE Since Z-shapes and channels are the simplest two-flange sections which canbe produced by cold-forming, one is naturally inclined to use them as beams loaded inthe plane of the web. However, in view of their lack of symmetry, such beams requirespecial measures to prevent tipping at the supports, as well as relatively heavybraking to counteract lateral deflection and twisting in the span. Their use isindicated chiefly where continuous bracing exists, such as when they areincorporated in a rigid floor or roof system, so that special intermittent braking maybe required during erection only. For such erection condition in 8.2of IS : 801-1975may be chiefly useful. For conditions other than these, serious consideration shouldbe given to hat sections. These have the same advantages as channel and Z-sections(two-flange section produced by simple cold-forming) but none of their disadvantages.

They are, in fact, in some respects superior to I -sections.

12. CONNECTI ONS12.1 General A considerable variety of means of connection findsapplication in cold-formed construction. Without any claim for comple-teness, these may be listed as follows:

a)Welding which may be sub-divided into resistance welding,mostly for shop fabrication, and fusion welding, mostly for erec-tion welding;

b)Bolting which may be sub-divided into the use of ordinaryblack bolts without special control on bolt tension, and the useof high-strength bolts with controlled, high bolt tension;

c)Riveting while hot riveting has little application inlight-gauge construction, cold-riveting finds considerable use,particularly in special forms, such as blind rivets (for application

from one side only), tubular rivets (to increase bearing area),high shear rivets, explosive rivets, and others;


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12.2.2.2 When plug welds are made with pre-punched holes, thelength of the fillet weld for computing weld strength is identical withthe perimeter of the hole. When the hole is burned and the weld madein the same operation, a frequent process (which is more aptlydesignated as puddle-welding), a conservative procedure is to computethe perimeter for a hole of diameter 6 to 10 mm less than the visiblediameter of the puddle.

12.2.2.3 I t should be added that the welding of thin steel sheetrequires a high degree of skill and welding technique. Welders whohave successfully passed the usual proficiency tests for welding ofheavy sections, as a rule, are not capable without special additionaltraining and experience to produce satisfactory welds of light-gaugemembers. Moreover, the welding together of two sections of radicallydifferent thicknesses, such as the welding of light-gauge panels orjoists to ordinary, heavy steel beams or girders, again requires specialtechniques. A well-trained, skilled welder usually will acquire anddevelop these special techniques with a reasonable amount of practice,but such practice should be acquired not on the job, but in advance on

special practice welds, and under competent supervision.12.3 Bolti ng

12.3.1Black Bolts in Ordinary Connections The nature oflight-gauge, cold-formed construction generally precludes the use ofturned and fitted both. The provisions of 7.5of IS : 801-1975 therefore,are written for black bolts in oversize holes (usually 1.5 mm oversizefor bolts of 12 mm diameter and larger, and 0.75 mm for smaller bolts).

These provisions of safeguard against the following four types offailure observed in tests, generally with a safety factor of the order of2.5, which was selected in view of the significant scatter in these tests.

12.3.2 High Tensile Friction Grip Bolts

12.3.2.1The use of such bolts for connections in hot-rolled steel workhas become very common in a number of countries. Such connections

FIG. 23 THROAT OFAFILLETWEL D


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differ in two respects from those made with ordinary black bolts:

a) the material from which these bolts are made has about twice thetensile strength of ordinary, black bolts; and

b) the nuts of such bolts are torqued to prescribed amounts whichresult in a minimum bolt tension of 90 percent of the proof load ofthe bolt (the proof load is about equal to the proportional limit ofthe bolt).

One of the chief advantages of these connections is that theyeliminate connection slip which would occur if these same connectionswere made with unfinished black bolts. They also increase the shearstrength of the connection ( seeIS : 4000-1967 ).

12.3.2.2In order to investigate the possible advantages in the field oflight-gauge steel construction of using high-strength bolts with

controlled high bolt tension, a number of tests have been made onconnections of this type, with the bolts and bolt tensions (torques)complied with the regulations governing the use of such bolts in heavysteel construction as in I S : 4000-1967.

12.3.2.3 I t has also been found in these tests that the use of hightensioned bolts will effectively eliminate connection slip at designloads regardless of whether the faying surfaces are bare, painted, orgalvanized. This may be of importance in situations where smalldeformations in connections may cause relatively large distortions ofthe structure, such as in knee-braces of portal frames, in rigid jointconstruction generally, and in many other situations of the like.

12.3.2.4This brief summary will indicate the economic possibilities ofhigh strength bolting in light-gauge construction. These may be utilizedonly if special bolts are available, and special assembly techniques arestrictly adhered to, such as specified in the quoted specifications.

12.4 Spacing of Connection in Compression Elements I fcompression elements are joined to other parts of the cross section byintermittent connections, such as spot welds, these connections shallbe sufficiently closely spaced to develop the required strength of theconnected element. For instance, if a hat section is converted into a boxshape by spot welding a flat plate to it, and if this member is used as abeam with the flat plate up, that is in compression ( seeF ig. 24 ), thenthe welds along both lips of the hat should he placed so as to make theflat plate act monolithically with the hat. If welds are appropriately,spaced, this flat plate will act as a stiffened compression element with

width wequal to distance between rows of welds, and the section canbe calculated accordingly.


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13. MISCEL L ANEOUS

13.1 Usually Wide, Stable Beam Flanges Compression flanges oflarge w/tratio tend to lose their stabil ity through buckling. However, ifflanges are unusually wide they may require special consideration evenif there is no tendency to buckling, such as in tension flanges. Twomatters need consideration for such elements; shear lag, which depends

on the span-width ratio and is independent of the thickness, and curlingwhich is independent of the span and does depend on the thickness.

13.2 Shear Lag In metal beams of the usual shapes, the normalstresses are induced in the flanges through shear stresses transferredfrom the web to the flange. These shear stresses produce shear strainsin the flange which, for ordinary dimensions, have negligible effects.However, if flanges are unusually wide (relative to their length) theseshear strains have the effect that the normal bending stresses in theflanges decrease with increasing distance from the web. Thisphenomenon is known as shear lag. I t results in a non-uniform stressdistribution across the width of the flange, similar to that in stiffenedcompression elements, though for entirely different reasons. As in thelatter case, the simplest way of accounting for this stress variation in

design is to replace the non-uniformly stressed flange of actual widthwby one of reduced, effective width subject to uniform stress.

FIG. 24 PLATESPOT-WELDEDTOHATSECTION


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hinges. I t has been established in recent research at Lehigh Universityand elsewhere that in order for a flange section to performsatisfactorily in connection with plastic design, limitations shall beimposed on w/tand h/fratios which are significantly more stringentthan those in use in conventional design. I f this is not done, membersat plastic hinges will prematuraly buckle locally and the carryingcapacity computed by plastic methods will not be reached.

13.4.4 I t is evident from this that most shapes now in use in light- gaugesteel structures, since they have w/tratios considerably in excess ofconventional hot-rolled shapes, are not capable of developing plastichinges satisfactorily and of maintaining them throughout the requiredrotations without local buckling. It follows that plastic design methodsare not applicable to light-gauge construction in its present form, unless

such construction is surrounded with additional safeguards of the kindwhich are now in the process of development for hot-rolled structures.What is more, it is obvious that those shapes most typical of light-gaugesteel, such as panels and decks, by their very nature require large w/tratios which preclude satisfactory performance under plastic designconditions. This is not to say that, through appropriate research anddevelopment, cold-formed sections suitable for structural framing (asdistinct from panels and decks) could not be developed with sufficientsection stability to be amenable to plastic design.

13.4.5 I t should be noted that these reservations apply to the fulldevelopment of plastic hinges. There are a number of unsymmetricalsections in light-gauge steel construction, such as many roof decks,where the neutral axis is much closer to the compression than to thetension flange. In such sections the (stable) tension flange yields first,

but failure does not occur at that load at which such yielding begins.Only when yielding has spread over much of the section, including thecompression side will the member fail at a load considerably higherthan that which initiated tension yielding. This development has beenused as early as 1946 for the successful interpretation of tests onstiffened compression elements. I t is this ability of unsymmetricalsections to redistribute their stresses through plastic action whichaccounts for the excess of their strength over and above that computedon the conventional, elastic basis. In such more limited connectionsplastic analysis is needed for a full understanding of structuralperformance even of some thin-wall sections.

13.4.6 However, since light-gauge structures of the presently currenttypes (a) usually have compression flanges too thin to develop plastichinges without local buckling, and (b) are usually not of thecontinuous-beam or rigid-frame type; the application of plastic designto light-gauge steel structures is much more restricted and of lessconsequence than in hot-rolled construction.


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SECTION 2 DESIGN TABLES AND DESIGN CURVES


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1. SCOP E

1.1This section contains various design tables and design curves,required in design of structures using light-gauge steel sections inaccordance with the provisions of IS : 801-1975.

2. DESIGN OF STIFFENED COMPRESSION ELEMENTS

EL EMENTS WITHOUT INTERMEDIATE STIFFENE RS

2.1The limiting width thickness ratio ( w/tlim ) for compression elementsbelow which the element is fully effective ( b =w ) has been tabulated inTable1 both for nontubular and tubular section for the load anddeflection determination. The values of w/tlimhave been calculated inaccordance with the formulae contained in 5.2.1.1of IS : 801-1975.

2.2 Nontubular Section Design curves, worked out in accordancewith the provisions of 5.2.1.1 of IS : 801-1975, for the load and

deflection determination of nontubular members have been given inFig. 25A, 25B, 26A and 26B.

TAB LE 1 ST IF FENED COM PRESSION EL EMENTS L I MI TI NG WIDT HTHICK NE SS RAT IO w/tli mBELOW WHICH EL EMENT IS FULLY E FFECTIVE

STRE SSINCOMPRESSION

ELEMENTf, kgf/cm2

NONTUBULARSECTION TUBULARSECTION

For Load Deter-mination

For Deflec-tion Deter-mination

For Load Deter-mination

For Deflec-tion Deter-mination

100200300400500600700800900

1 0001 1001 2001 3001 4001 5001 6001 7001 8001 9002 0002 100

143.5101.482.8571.7564.1858.5854.2450.7347.8345.3843.2741.4239.838.3537.0535.8834.8033.8232.9232.0931.31

185.00130.72106.8192.5082.7475.5269.9265.4061.6658.5055.7853.4051.3149.4447.7646.2544.8643.6042.4441.3740.36

154.0108.8088.9177.0068.8762.8658.2154.4451.3348.7046.4344.4542.7141.1539.7638.5037.3436.2935.3334.4433.60

199.0140.71114.8999.589.081.2475.2170.3666.3362.9360.057.4555.1953.1851.3849.7548.2646.9045.6544.543.43


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2.3 Tubular Sections Design curves, worked out in accordancewith the provisions of 5.2.1.1 of IS : 801-1975, for the load anddeflection determination of tubular member have been given inFig. 27A, 27B, 28A and 28B.

3. DESIGN OF STIFFENED COMPRESSION ELEMENTS MULTI PL E STIFFENE D EL EMENTS AND WIDE STIF FE NEDEL EMENTS WITH E DGE STIFFE NERS

3.1 Values of , the reduction factor for computing the effective area ofstiffeners, as contained in 5.2.1.2of IS : 801-1975 are given in Table 2for w/tratio between 60 and 150.

TAB LE 2 REDUCT ION F ACTOR , , FOR COMPUTI NG E FFECT IVE AREA OFSTIFFENE RS ( A

ef

= Aef

)

For 60


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4. STIF FE NER S FOR COMPRE SSION ELE MENTS

4.1 Clause 5.2.2.1

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