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है”ह”ह

SP 6-3 (1962): ISI Handbook for Structural Engineers -Part-3 Steel Columns and Struts [CED 7: Structural Engineeringand structural sections]

SP : 6 ( 3 ) - 1962

HANDBOOKFOR

STRUCTURAL ENGINEERS

3. STEEL COLUMNS AND STRUTS

BUREAU OF INDIAN STANDARDS

STRUCTURALENGINEERS' HANDBOOK

No. :I

Gr 12

SP : , ( J) • 1M2

HANDBOOK'OR

STRUCTURAL ENGINEERS

3. STEEL COLUMNS AND STRUTS

BUREAU OF INDIAN STANDARDSMANAK BHAVAN, 8 BAHADUR SHAH ZAFAR MARG

NEW DELHI 110002

BUREAU OF IIPIAI STAIDARDS

First EdltJonEighth Reprint

1962May1999

UDC 624.21.9 : 624.075.2 : 669.14

C Copyright 1962

BUREAU OF INDIAN STANDARDSThis publication is protected under the Indian Copyright Act (XIV of 1957) andreproduction in whole or in part by any means except with written permission of thepublisher shall be deemed to be an infringement of copyright under the said Act.

Printed in India by Simco Printing Press, Delhi; andPublished by the Bureau of Indian Standards, New Delhi (India).

CONTENTSPAGE

FOREWORD ...SYMBOLSABBREVIATIONS

SECTION I GENIRAL

1. INTRODUCTION

2. COLUMN DESION FORMUL~ AND SPECIFICATIONS

SICTION II DISIGN OF CENTIlALLY LOA DID COLUMNS

3. INTRODUCTION

4. SHORT CoLUMNS WITH SMALL LoADS

5. SHORT COLUMNS WITH LAROE LoADS

6. LoNO COLUMNS WITH SMALL LoADS

7. LONG CoLUMNS WITH INTERMEDIATE LoADS

SICTION III COLUMNS IN MULTI-ITORIY aUILDINGS

8. INTItODUCTION

9. BUILDING COLUMN DESIGN FOR DEAD PLUS LIVE LoADS

SECTION IV MILL aUILDING COLUMN WITHCRANE GANTRY

71114

15

17

2021

25

29

33

38

38

10. INTRODUCTION 54..11. STEPPED MILL BUILDING CoLUMN WITH CRANE GANTRY 54-

SICTION V CONCLUDING REMAIIO CONe.RNINGCOLUMN DIIIGN

12. EPPlClEHCY 0' CoMPRESSION MEMBERS 67

TABU I ALLOWABLE AVERAGB STRuas FOR AXIAL CoMPUlSION 69

TABLE II ApPROXIMATE R.ADli OF GYRATION 71ApPENDIX A INDIAN STANDARDJ ON Paonucrrox, DE!ION AND USE

0' STEEL IN STRUCTURES 72ApPBNDIX B CoM.OIImoN OP STRUCTURAL t:NOI~EBRING SECTIONAL

CoIOllTrKIt. SMDC 7 74

5

FOREWORD

This handbook, which has been processed by the Structural EngineenngSectional Committee, SMDC 7, the composition of which is given in Appen­dix S, has been approved for publication by the Structural and MetalsDivision Council of lSI.

Steel, which is a very important basic raw material for industrialization,had been receiving considerable attention from the Planning Commissioneven from the very early stages of the country's First Five Year Plan period.The Planning Commission not only envisaged an increase in productioncapaciry'In the country, but also considered the question of even greaterimportance, namely, the taking of urgent measures for the conservation ofavailable resources. Its expert committees came to the conclusion that agood proportion of the stee! consumed by the structural steel industry inIndia could be saved if higher efficiency procedures were adopted in theproduction and use of steel. The Planning Commission" therefore, re­commended to the Government of India that the Indian StandardsInstitution should take up a Steel Economy Project and prepare a series ofIndian Standard Specifications and Codes of Practice in the field of steelproduction and utilization.

Over six yean of continuous study itt India and abroad, and the delibera­tions at numerous sittings of committees, panels and study groups, 'haveresulted in the formulation of a number of Indian Standards in the fieldof'stee! production, design and use, a list of which is included in Appendix A.

The basic Indian Standards on structural steel sections are:IS: 808·1957 SPECIFICATION POR ROLLED STEEL BLUI, CHANNBL AND

ANOLE SBCTIONS ( Since revised and split up into parts )IS: 811-1961 SPECIFICATION FOR. COLD FORMED LIOHT GAUOE STRUC­

TURAL STKBL_SBarlONS ( Since revised)IS: 1161-1958 SP&CIPICATION POR STaHL TUBEI lIOR STRUCTURAL

PURPOSItI ( Second revision published in 1968)IS: 1173-1957 SPECIFICATION FOR ROLLED STEaL SECTIONS, To HARS

( Since revised )IS: 1252-1958 SPECIFICATION POR ROLLED STEEL SECTIONS, BULB ANOLa.IS: 1730-1961 DIMENSIONI FOR STEET~ P:,ATE, SHEET AND SnIP FOR

STRUCTURAL AND GENERAL ENOINEERING PuRPOSES (Since revisedand spUt up into parts)

IS: 1731-1961 DomNilONS FOR STEEL FLATS FOR STRUCTURAL AND

GaNERAL ENGln...INO PuRPOSES ( Since revised)IS: 1732-1961 DIMENSIONS POR ROUND AND SQ,UAIlB STEEL BARS FOR

STRUCTURAL AND GBNERAL ENGINEERING PuRPoau ( Since revised )The design and fabrication of steel structures is covered by the following

basic Indian Standards:IS. 800-1956 CoDa OP PaAarlCB I'OR USB OP 8nuaruIlAL STaaL IN

• GSN&IlAL BU~INOCoNlTllUCTlON ( Since reviled )

7

.. IlANDUOOIt 10. lTaUCTUaAL aHOIN••U: naaL QOLUMNI AND natrn

IS: 801-1958 CODE OP PRACTICE POR USB OF COLD FOIUdD LIGHTGAUGB STEBL STRUCTURAL MBUBERS IN GBNERAL BUILDINO CON­nRuarlON ( Since revised)

IS: 806-1957 CODK OF PRACTICB POR USE OP STUL TUBES IN GENERALBUILDING CoNSTRUCTION. (Since revised)

IS: 816-1956 CoDS OF PRACTICE FOR USE OF METAL £\RC WELDING FORGENERAL CoNSTRUCTION IN MILD STEEL ( Since revised)

IS: 819-1957 CODB OF PRACTICE FOR RBSIITANCB SPOT WELDING PORLlOHT ASSEMBLIES IN MILD STBBL

IS: 823- CODS OF PROCEDURE FOlt METAL ARC WELDING OF MILDSTEEL ( Under preparation) ( Printed in 1964 )

IS: 1024- ConE OP PRACTICE FOR .WELDING OF STRUCTURES SUBJECTTO DYNAKIC LoADING ( Under preparation) (Printed in 1968 )

IS: 1261-1959 Oons OF PRACTICE FOR SBAM WBLDING IN MILD STEEL

IS: 1323-1959 CoDE OF PRACTICE FOR OXy-ACItTYLENE WELDING PORSTRUCTURAL Won IN MILD STEBL ( Since revised )

lSI undertook the preparation of a number of design handbooks. Thishandbook, vzhich is the third in the series, relates to steel columns andstruts. The first one on structural steel sections was published in March1959. The second handbook) which deals with steel beams and plategirders, is being simultaneously published along with this handbook. Otherhandbooks proposed to be published in the series in due course are expectedto cover the following subjects:

1) Apphcation of plastic theory in design of steel structures2) Designing and detailing welded joints and connections3) Design of rigid frame structures in steel4) Economy of steel through choice of fabrication methods5) Functions of good design in steel economy6) High strength bolting in steel structuresi) Large span shed type buildings in steel8) Light-weight open web steel joist construction9) Multi-storey steel framed structures for offices and residences

10) Roof trusses in steelII) Single-storey industrial and mill type ..buildinp in steel12) Steel transmission towers ·13) Steelwork in cranes and hoists14) ~tru~f:ura1 use of light gauge aecnoDi15) Structural usc of tubular sections

Metric system hu been adopted in India and all quantities, dimensionsand design ~p1el have been given in this tyltem.

8

tOa.woaD

This handbook is not intended to replace text books on the subject. Withthis object in view, theoretical treatment has been kept to the minimumneeded. Special effort has been made to introduce only modern and practi­cal methods of analysis and design that will result in economy in utilizationof steel.

The-information contained in this handbook may be broadly summarizedas follows:

a) Explanation of the secant formula adopted in IS : 800-1956,b) Design examples in a format similar to that used in a design office,c) Commentary on the design examples, andd) Tables of important design data.In accordance with the main objectives, those types of columns and strut

designs that lead to the greatest weight saving in steel have been emphasized,as far as possible.

The calculations shown in the design examples have all been workedout using the ordinary slide rules. The metric sizes of rivets and platesincorporated in the design examples are likely to be the standard metricsizes which would be produced in this countr-y. Indian Standards for theseproducts are under preparation.

This handbook is based on and requires reference to the following publica­tions issued by lSI:

IS: 226·1958 SPECIFICATION FOR STRUCTURAL STEEL ( Second revision)( Fifth revision published in 1915 )

IS: 800-1956 CoDE OF PRACTICE FOR USB OF STRUCTUP..AL ~TEItL INGENERAL BUILDING CONSTRUCTION ( Since revised)

IS: 806-1957 CaDit OP PumiCE FOR USE OP STEEL TUBKS IN GENERAL

BUILDING CONSTRUCTION (Since revised )IS: 808-1957 SPECIFICATION FOR ROLLED STEEL BEAY, CHANNEL AND

ANGLB SECTIONS ( Since revised and split up into parts)IS: 816-1956 CODE OF PRACTICB FOR USB OF METAL ARC WELDING FOR

GENERAL CONSTRUCTION IN !\{ILD STEEL ( Since revised)IS: 875-lgs7 CODE OF PRACTIOE POR STRum °JRAL SAFETY OF BUILDINGS:

LoADING STANDARDS ( Since revised)IS: 1161·1958 SPECIFICATION FOR STEEL TUBES FOR STRUCTURAL PUR­

POSES ( Second revision published in 1968)lSI HANDBOOK FOR STRUCTURAL ENGINEERS : 1. STRUCTURAL STaEL

SECTIONSlSI HANDBOOK FOR STRUCTURAL ENGINEBRS ON SINGLE-STOREY INDU­

STRIAL AND MILL TVPE BUILDINGS IN STEEL ( Under preparation)lSI HANDBOOK FOR STRUCTURAL ENGINBBRS ON USE OF STEEL TUBES AS

STRUCTURAL MATBRIAL ( Under preparation)lSI HANDBOOK FOR STRUCTURAL ENGINBERS ON MULTI-STOREY STEEl.

FRAMED STRUCTURES ( Under preparation)

9

• IIAJC.-ooK POa IftvcruaAL .......... : IftaL OOLUIOII AND .....un

In the preparation of thi~ handbook, the technical committee has derivedvaluable assistance from Dr Bruce G. Johnston, Professor of Structlll'a1Engineering. Univenity of Michigan, Ann Arbor. Dr Bruce G. Johnstonprepared the preliminary draft of this 'handbook. This assistance wasmade available to lSI through Messrs Ramseyer & Miller, Inc, Iron &:Steel Industry Consultants, New York, by the Technical Co-operationMillion to India of the Government of USA under their Technical Assis­tance Programme.

The photographs in this handbook have been provided through thecourtesies of American Institute of Steel Construction, New York, andButler Manufacturing Co, Kansas City, USA.

No handbook of this type can be made complete for aU times to come atthe very first attempt. As designers and engineers begin to use it, theywill be able to suggest modifications and additions for improving itl utility.They are requested to send such valuable suggestions to lSI which will bereceived with appreciation and gratitude.

10

SYMBOJ.,S

Symbols used in this handbook shall have the meaning assIgned to themas indicated below:

A Area of section; Greater projection of the base plate beyondthe column

a Distance between the main components in a laced or battenedsection or width of rectangular stress block in bearingplate design

B Lesser projection of the base plate beyond the column

b Flange width

d Depth of a section; In rivet groups, the diagonal distancebetween two rivets: Spacing of battens in a battenedsection

til' External diameter of a tube

d. Internal diameter of a tube

E Young's modulus

E, Tangent modulus

I Eccentricity

ICii Eccentricity ratio

F l Longitudinal shear

F. Permissible axial stress

F ~ Permissible bending stress

F, 1M: Permissible stress in direct compression

.fo == Calculated axial stress

f" Calculated bending stress

.I~ Stress at proportional limit

If' Calculated average shear stress in the section

I Moment of inertia

I.... Moment of inertia about .A-A axis

1.. Moment of inertia about B-B axis

l:t Moment of inertia about X-X axis

I., Moment of inertia about V-V axis

] ]

III HAIID800It 'OIl ITRVcn:aAL .NOISZr..S : STEEL ('.()L\.~ A~D nat.n

1.. c::

K z::

L -I _.I. -I. a::::

1/, -M -M".

~{.. ==

p -P".IfII

Q -

RA

R. -R. -r -

'.. s:::::::

'min -'. ==

" -S -, -

If =='tD -J" -J', =IV

Moment of inertia of a column section between mth and nthfloor levels

Coefficient of effective length

Actual length

Effective length (=KL)Effective length about X-X axis

Effective length about Y-Y axis

Slenderness ratio

Bending moment

Total bending moment in the column section at mth floorlevel

Distribution of the bending moment at the mth Boor levelin the column section between mth and nth ftoor levels

Axial load

Axial load in the column section between mth and 11th floorlevels

Static moment about the centroidal axis of [he portion ofcross-sectional area beyond the location at which thestress is being determined

Reaction at A

Component of the rivet strength in X-X direction

Component of the rivet strength in Y-Y direction

Radius of gyration

Radius of gyration about B-B axis

Minimum radius of gyration

Radius of gyration about X-X axis

Radius of gyration about Y-Y axis

Shear

Thickness of base plate or splice plate; Flange or webthickness

Flange thickness

Web thickness

Total shear resultant on cross-section

Shear force per unit length

Pressure or loading on the under-side of the base plate

12

x - Distance of the rivet from a reference point along X-X axis

y Distance of the rivet from .a reference point along Y-Y axis

Z = Section modulus

Z~ - Section modulus about X-X axis

Z. Section modulus about Y-Y axis

Zmtl - Section modulus of the column section between mth and nthfloor levels

.6 Deflection

~ Centre line

@ .- At

> = Greater than

< Less than

~ Not greater than

~ Not less than

~ Approximately equal to

Therefore

13

ABBREVIATIONS

Some important abbreviations used in this handbook are listed below:

UBit.

Area in square centimetresLength in centimetresLength in metresLength in rnillirnetresLoad in kilogramsLoad in kilograms per metreLoad in kilograms per square centimetreLoad in kilograms per square metreLoad in tonncsMoment in centimetre-kilogramsMoment in centimetre tonnesMoment in metre kilogramsMoment in metre tonnesMoment of inertia expressed in centimetre to the

power of fourSection modulus expressed in cubic centimetresStrength of weld in tonnes per centimetre

Other AbbreviadoD8

AlrightBasement levelCentre to centreDead load,Floor

lndian Standard Angie Section conforming to andas designated in IS : 808-1957

Indian Standard Beam Section conforming to andas designated in IS : 808-1957

Indian Standard Channel Section conforming toand as designated in IS : 808-1957

Live loadOutside diameter

14

em l

emmmmkgkg/mkg/cm~

kgjm't

em-kgcrn-trn-kgm·t

em l

em'tlcm

OKBc/cDLFl

ISA

ISLB, 18MB, etc

ISLe, ISMC, etcLLOD

SECTION I

GENERAL

I. INTRODUCTION·

1.1 A column is a structural member whose primary function is to transmitcompressive force between two points in a structure. The subject of columnstrength has retained the interest of mathematicians and engineers alike formore than 200 years since Euler's famous contributions to column theory of1744 and 1757.

1.2 A column is loaded and performs its useful function in compression,hut, when overloaded, beyond its working strength, it does not generally failby direct compression. Failure may be due to excessive bending or in somecases by bending combined with twisting, depending on the slenderness ratioof the compression member. If a short compression member is subjectedto an axial load of sufficient magnitude, it will rail by decreasing in lengthand bulging, or may rail because of excessive shearing stresses if the materialis brittle. If, on the other hand, a long slender strut is subjected to arelatively small axial load, the strut is in stable state and if it is displaced bya small amount due to some disturbing force, the member will straightenitself when that disturbing force is removed. For a certain increased valueof the axial force, however, the member is in a state of neutral equilibriumand will remain deflected even after the removal of the disturbing force.This axial load is called the buckling load. The column will behave in thesame way it: instead of a disturbing force there is a bent and/or twistedconfiguration existing in the member, Thus, as the length of the columnincreases, the cross-sectional area being. constan-t. the load requited toproduce the various types of failure decreases. Therefore, columns arecommonly classified as short and long columns. Even though this divisionmay be arbitrary and there ~ no absolute way of determining the exactlimits for each classification, for convenience ofdiscussion in design examplesof columns in this handbook this classification is being adopted.

1.3 The Euler load is the buckling load which will hold a completelyelastic column in a bent position. An infinitesimal tendency to changefrom a straigltt to a bent or buckled shape will, at the Euler load causethe column so to bend. If we consider the inelastic stress-strain curveof the material, the compressive load capacity without any bending is thetangent-modulus load, Shanley having showed that if any load larger thanthe tangent-modulus load is applied the column will start to bend.

1.4· Thus, the tangent-modulus load provides a strength criterion for theideally straight and centrally loaded column. In this connection, astatementpublished in Bulletin No.1 of Column Research Council (of 'USA) may be

·Part of the introduction is abstracted from the talk on 'Basic Column Strength' presentedby Dr. Bruce G. Johnston at the Fourth Technical Session of Column Research Counciland publish~d in the Proceedings of ~f.)", 1944.

15

.............. (1)

lSI HANDBOOIt roa STauC"li1uL ENOINUas : ITEEL COLl:M..tu AND STRun

quoted:'It is quite generally accepted that the column strength may be

determined with satisfactory accuracy by the use of the tangent-modulusmethod applied to a compressive stress-strain curve for the material, ifthe material throughout the cross-section of the column has reasonablyuniform properties and the column does not contain appreciable residualstresses. The strength of a column may be expressed by:

P ""ErA = (~L) i

wherepA ~ average stress in the column,

E.,. := tangent modulus (slope ofstress-strain curve) at stress i'fA, and

!CL= equivalent slenderness ratio of the column.',

1.5 In the elastic range, E; == E, and this substitution in equation (1) reducesit to the Euler column formula. Equation (1) may be written:

KL = ./ E.", V PIA (2)

1.5.1 In equation (2), if E.,.=E and PIA=f. (stress at proportional limitof material), the KL/, so evaluated is the minimum slenderness ratio forwhich the elastic buckling occurs.

1.6 Since the failure of the column, excluding the possibility of torsion,is a matter of bending, one may catalogue the following two general categoriesof 'effects' that influence bending behaviour in real columns. These resultin departure from the ideal column strength estimated by the tangent­modulus theory.

a) Accidental factors that caus« bending in the· column to take placebelow the tangent-modulus load:

1) Lateral loads,2) End eccentricity, and3) Column curvature or twist and non-homogeneity of material.

b) Fa':tolS that modify "sislanu to bnuJing:1) Residual stress (may increase or decrease strength);2) Variation in inelastic stress-strain characteristics, either

inherent in the material or as a result of prior tensile over­strain in all or various parts of the column.

3) Shear strength;4) Local buckling;

16

I&C11OIC I : OaMULAL

5) Shape of CI'OII-sectionj and6) Lateral or end restraints (may increase strength).

1.6.1 One item bas been left out of the foregoing outline, that ill compres­sive load, which in itself reduces bending stiffness. When an 'ideal' columnbuckles at the Euler load it remains perfectly straight up to that load, then,under an infinitesimal increment of load, suddenly buckles with indefinitedeflections within the range wherein the assumptions inherent in the Eulerderivation are valid. It would appear as if such an 'ideal' column suddenlyhad lost all of its bending stiffness, since the slightest touch would cause itto take any bent-position desired. This is not the case. Relatively smallaxial load has little effect on bending stiffness, as measured by EI, but ata gradually increasing rate, the bending stiffness reduces and as the Eulerload is approached the rate of loss is quite rapid. The bending stiffnessdoes become zero when the Euler load is reached but the variation is acontinuous function of load even though the buckling itself is a discontinuousprocess.1.7 If any generalization at all can be made about the list of facton thataffect the strength of a column it is obvious that it is impractical tointroduce them all in any mathematical way into anyone column formula.On the other hand, various investigaton and designers in the past havetended to over-emphasize one factor without a good enough look at theothers. One is reminded of the old folk tale of the blind men, feelingvarious parts of an elephant, with each different man coming to a differentconclusion as to what an elephant really was. The uncertainty 81 to whata column really is has been increased by virtue of the fact that even inlaboratory tests there are usually several factors affecting column strengthas determined by the testing machine. In attempting to explain any singletest by a mathematical formula, it is quite possible through over-empbasisof anyone factor in any particular trial 'theory', unknowingly or otherwise,to compensate for the effect of other factors that may co-exist in the teststhat may be omitted from the particular theory that is on trial. Thus. onemay take a given set of test data on concentrically loaded hinge-end columnsand show that the test results agree with the secant formula, assumingaccidental initial eccentricities of the required amount to make the theory

. fit the telt 6r, on the other hand, agree with an initial curvature theory byam,ming an initial curvature of the required maximum amount. Thus.there may be no proof at all that either eccentricity or curvature was thedominating factor that should have been used in the theory.

2. QOL11MN DESIGN FORMUlA: AND SPECIFICATIONS2.1 A! has been stated, the tangent-modulus formula provides the mostproper theoretical basis for relating the stress-strain properties of a metalto the ideal column strength of the same metal. However, for designpurposa~tc customary to determine any point on the column strengthcurve, · y in the case of a structural steel, as that load which will

17

III HANDBOOK roa rraUCTtJaAL &NOIHUItI : STaaL COLUMNS AND lTRun

cause initial yielding in an eccentrically loaded column of that particularlength. The eccentricity is arbitrarily assumed so as to give agreementbetween the resulting strength formula and many column tests. This isthe basis for the permissible working stresses given in IS : 800-1956. Theactual formula (reduced from the column strength curve by a factor ofsafety of 1-67) is given in Appendix D of IS : 800-1956 and is referred toin Table I of that standard. It is noted that the assumed eccentricityisin dimensionless terms : .

ec;a = 0·15

Tables I and XIII of IS : 800-1956 give permissible average stress forvarious 1/, ratios for structural steel and high strength structural steel res­pectively. As noted in Appendix D of IS : 800-1956, when 1/, is greaterthan ISO. the allowable stress given by the secant formula is modified bya reduction factor which, in effect, introduces an increasing factor of safetywith I/r as the value of 150 is exceeded.

2.2 To facilitate interpolation, for each integer value of lIt from 1 to 180,Table I (," p. 69) presents permissible stresses in agreement with '.1.2 andTable I of IS : 800-1956, for structural steel conforming to IS : 226-1958.

2.3 The cross-sectional shape of various columns commonly used. in practiceis given in Table II (see p. 71). Also shown are approximate values of 'radiiof gyration for these sections. In the-case of the rectangular and circularsections. the values indicated are closely approximate to the correct valuesbut for the built up section there, may be a considerable ftuctuationbecause of the variation in relative cross-sectional dimensions.

2.4 To minimize steel requirements in column design, one should keepthe effective llr as small as possible so as to use the niaterial at the greatestpossible stress. The length is given in the general design drawing and tiledesigner should select the cross-section that will provide the largest possibleradius of gyration without providing more area than is needed. Since

, = J ~ t the largest radius of gyration is obtained when the material is

farthest from the centroid. For constant area this means that the materialgets thinner and thinner as the column size increases for any particular typeofcross-section. This leads ultimately to such thin walls for any given columncross-section that local bpckling becomes a problem and it is local bucklingthat ultimately limits the size to which one may go. In some cases, inorder to ·get the material as far as possible. from the neutral axis, especiaUywhen only a small load is to be carried and the total area is small, anglesor channels are used. together with lacing or batten/latel to hold them inposition as shown in Table II. The lacing bars an batten p.lates are notload ca.-rying elements. They function primarily to hold the load carryingportions of the column in their relative positions and provide points. ofintermediate sup~rt for each separate part of the built-up,column. Thus,

18

I&CTION I : OuaaAL

for minimum st-eel requirements, batten plates and lacing ban are econo­mical only if the increase in permissible Itren for the load-carrying membenpermits a greater reduction in weight than is added by lacing or battens.

2.5 A column designed as centrally loaded may be accidentally loadedeccentrically or may start to bend. In such cases, there will be variablebending moments induced because ef'the eccentricity between the centroidalaxis of the column and the resultant line of action of the applied load.As a result of the varying bending moment that is induced there will berelated shearing forces in the plane of the cross-section and the lacing,batten plates, or other connecting elements should be designed to be adequateto resist this shearing force. In 21.2 of IS : 800-1956, this is arbitrarilytaken as 2·5 percent of the direct load for which the column is designed.In the case of very short columns, the shearing force is induced primarilyby the eccentricity of load whereas in long columns, it is primarily inducedby bending. Some authorities consider that the connecting parts should bedesigned for the shear that would be developed when the column has finallybuckled at its full load and in buckling has reached the yield point.

2.6 An important determining factor in the design of a column is the 'effec­tive length' as influenced by end restraint conditions. There are two typesof restraints, namely, position restraint or restraint against movementpe~ndicular to the ~xis of the column and direction restraint or rest~ntaplDst angular rotation at the end of the column. Each type of restraintmay exist about either or both axes and the conditions at the opposite endsof the column may be different. A complexity of possible combinationsresults but some of the more usual conditions of restraint are J?ictured inAppendix G (Fig. 1 to 15) of IS : 800-1956. Design examples will illustratethe use of these figures which provide interpretation of 18.1 and Table Vof IS : 800-1956.2.7 Maximum permissible slenderness ratios are given in 18.2 and Table VIof IS : soo.I956 and minimum thickness of local elements is given interms of ratios of width to thickness in 18.4 and in Tables VI and VII ofthat standard.

2.8 The design of a column base slab is also covered in this Handbook. as provided-in 18.8 of IS : 800-1956.

2.9 Additional reductions in permissible stress for single struts or discon­tinuous struts are provided in 18.9 of IS: 800-1956 with allowable stressesfor single angle struts given in Table X of that standard.

2.10 If bending moments are introduced into the column at axial loadsbe10\\" the buckling load, the column is sometimes called a 'column-in­bending' and rules for design of such members are given in 9.5 ofIS : 800-1956 covering bending and axial stresses. The bending momentin a beam-column may be introduced either by lateral load, or by endeccentricity and the assumed allowances for end eccentricity are givenin ILl aftd Table IX of IS : 800-1956.

19

SECTION II

DESIG'N O'.ClNTRALLY LOADED COLUMNS

s, INTaODUCDON

3.1 11ae crou-sectional shape of a centrally loaded column dependa verylargely OIl whether the column is long or short and whether it carria asmall or Jjrge load. Therefore, design examples will show alterDativeselectioDl suitable for the following load and length conditions:

al Short columns with .man loads,b Short columns with large loads,c Loug columns with small loads, andd Long columns with intermediate loads.

3.2 The design examples will be discussed under me fonowing headingspertaining to the column type rather than the length and load category:

a Circular cress-section,b Single angle,c Double &nJle,d H-beam WIth welded cover plates,

. e Single cell box,Lacedcolumns, and

gl Batten plate columns.

3.3 In summary, the design problem of a centrally loaded column includesthe following steps:

a) Make an initial approximation of the average allowable streuF.;b) Determine the required area to carry the load at the estimated

allowable stress A=-P/Fc;

c) Select a column section that will provide the estimated requiredarea along with as large as possible a radius of gyration consistentwith clearance requirements and minimum thickness limitations;

d) Calculate the radius of gyration;e) Determine the effective slenderness ratio based on the estimated­

effective length according to 18.1 of IS : 800-1956;C) Determine allowable stress from Table I as based on 1.1.2 of

IS: 800-1956; andg) Repeat steps (a> to (f), if necessary, with' a revised estimate of

allowable column stress.

3.4 In makinK the yreliminary estimate of allowable stress, reference mavbe made to Table with a rough approximation of the probable lIre Inthe case of very ahort columns, or columns of any reasonable lengt& withvery heavy loads, the IJ, ma}: always be made reasonably small. In sucha case the allowable stress will vary but little and a good estimate may bemade at the outset.

20

(~.p.25)

4. IIIORT COLUMNS WITH SMALL LOADS4.1 Col.... 01 CIreaIar ero..-Secdoa (SII De8Ip ........ 1)­The circular cross-section may be either a solid round or a hollow cylindricaltube. Any circular cross-section has the same radius ofgyration abo~t everycentroidal axis and the thin wall hollow tube provides the most effectivepossible disposition of material for a circular column that has the sameequivalent length with respect to all axes. For a more complete discussionof tubular members, reference should be made to lSI Handbook for Struc­tural Engineers on Use of Steel Tubes as Structural Matero.l (underpreparation) .

Local buckling will not occur in the walls of a circular tube until verylarge ratios of radius to thickness are introduced. For practical purposes,allowing for imperfections in manufacture, it is customary to require thatthe tube radius be no more than about 65 times the wall thickness. Thus,for a tube having minimum permissible wall thickness of 6·3 DUD the maxi­mum radius should be about 400 rom. Minimum wall thickness permittedfor tubes not exposed to weather is 3·2 mm (SII6.3 of IS : 806-1957).

Circular columns are especially recommended for exposed use in regionsof heavy wind. The wind forces on such columns are minimized and areindependent of direction.

In the following pages, designs of different types of sections used as shortstruts are compared for a small axial load. As a first example, tubularsection is taken up for illustration. Then the other types follow. It isto be noted that the required area of cross-section for the tube is leu thaneither the single or double angle struts designed.

4.2 ",Ie Aalle Strata (SI' De8ip kample 2) - The permissiblestress in single angle struts connected by a single rivet or bolt is penalizedby 18.9.1.1 of IS : 800-1956 because of the eccentricity of connection.But when connected by a weld or by two or more rivets or bolts in line alongthe angle af each end, the permissible stresses in accordance with Table Iof this Handbook or Table I of IS : 800-1956 are applicable without anyreduction, because of the end restraint effect that reduces the effect of

.eccentricity. The effective length I should be taken as equal to the lengthcentre to centre of connections.

4.3 Doable ~Ie Strau (se, De.... kample 3) - The double anglestrut is more effective and efficient than the single angle strut, Dot onlybecause of the greater permitted working stress, but alsobecause the anglesdo not tend to buckle about either oftheir individual principal axes in~of which the radius of gyration is the minimum. All other things beingequal, if the long legs are placed back to back, the beat balance ofradii ofgyration about the two axes of the combined section will be olftaiDed.Attention. is called to the required use of stitch rivets to cmure integralcombined action of the two angles.

21

• JlANl)M)()1t PO. ITaUC'n1aAL UOINUIlI : ITU.L COLUMNS A."fD STRUTS

- ----. - - - - - - - - .. - - - - _. - - - - --,..---------~-.....DellI" Ixample I ,_

ofTubular Strut I

Load P ::z 10 t

Length 1 :a 3 m

~,permiaible axial comprcuive suea F.:a: 1 000 ka/c:m'

A_ • ed ~ 10 000 10 'nn:ia requir n - -rDOO" em

Minimum wall thiekneu - 4 mm ($II 6.3 of IS : 806-1957)

TO 8O-mm nominal bore x-O-48.S; em (SII IS : 1161.1958)

Area A == 12-8 em'

Radius oIlYNtion - V~ -= 2·98 em

Allowable F, - 884 kg/ern l (III '.1.2 of IS : 800-1956and Table I ~ thisHandbook).

Allowable load - 884 x 12·8-II SOO ... or 11·3 t>10 t •••••OK.

22

'min

aCTION II: DUION OP CENTRALLY LOADED COLUMNI

0..;,. £aM",_ Z-Si,.,l. A,.". Serul

nil aa¥N Uu/ieGIIs JlVlral trial s,l«tioIU ktuling to an anlU tJaal provUUs a cajHlcily oj12·61.II is to".IMI tlUll OM ofeM triGl duif1U IuuJ to IHmodifwd becauu th6outslilndint withJalllliattus,atio oftJu tJIIIl.", UHJS excessiv«. For sin," anglt • -......_ ..struts, tIM maximum pmnitud withh/thickness ratio Desll" Example 1is 14 tu cortI/JtI',d with 16 for otJwr outstands, This IlimitalUm is usi,abk b,causl 1M singl, angle strut ofWJUJlly "","s 1M neares: to torsional huckling of any Sin". Anile Strut I,011.'s.1 mmabtr.- -- - - - - - - - - - - - - - - - - - - - - - - - -----------_.........- ...

(Equal legs for maximum 1min)

Auume two rivets at eaeh end.Allowable stresses in accordance with Table I and lL9.1.1 (b) of IS : 800-1956

Trw, for l/, = 120=300. ,=2·5 emOJ , ,

Allowable F, = 709 kg/eml (ut Table I of this Handbook)

Area required = I~:;:o =14·1 em l

Try ISA 100 100, 8 mm.A = 15·39 emt

'_In = 1·95 em

1/, = 300 = 154-1·95

Allowable F. =: 472 kg/emt

Allowable load = 472 X 15·39=7 250 kg-~o Good.Try ISA 130 130, 8 mm.

A =: 20·22 em-'min = 2·55 em

300llr =: rn = 118

Allowable F, z= 726 kg/em t

Allowable load == 726 x 20·22:: 14 700 kg -- over designTr;yISA 110 110, 8 rom .

.If == 17,02 emS= 2·14 em

3001/, == rn = 140

Allowable F, . :lIE 559 kg/eml

Allowable load = 359 x 17·02 =9 500 kg-~o Good.Therefore, ISA 130 130, 8 mm is the mOlt economical section because other sections

with required area and 'min have greater weigh; per metre.

Check outstanding}ISO -= 16'25> 14-No Good (S', ILt.! of IS: 800(1956)

Iq TEffective width - 14 x 8 -=112 nunEffective area - 17·3 em' (according to 11.4.1.1 of IS : 800(1956).o\IIowable F. .. -726 ka/an'AllowabIe IoMI - 0-726 x 17·5-12·6 t ......OK.

------------------------------------------------• OIl &hat Cor compudnl~rdathe full ana of tbe ouwandlna may be tUeD. in •.....CMe"' (........eeaceoi IS: 100-19-'6).

23

III HANDBOOK POR lTRucnJIlAL UfOINUltl: IT&&L OOLUIOII AND .TaL,..

D..... ...",. 3 - DoubH A,.,le S".",

(LM,Ir "" hid to bd etmn«tMJ 10 bolla sidu of tJ lo-mm gwSlI by two ';l1ItI)~---.....- ..

D_lln E.amp'e J Iof

Double Anile Strut I

Load and length are the same as Jriv~n in Design Examples 1 and 2

Tty 2 ISA 90 60, 6 mm.

A ICI 2 X 8·65= 17·3 em l

r. lIZ 2·86 em

r" == 2·55 em (from lSI Handbook for Structural Engineers:I. S~ctural Steel Sections)

l/'mID - 2~~ = lIB-No length reduction is auumed.

Allowable r, as 726 kg/eml [SI' IU.l.2 (b) of IS: 800-1956]

Allowable load lei 726 X 17·3 II:: 12 550 kg-over design

Try 2 ISA 80 50, 6 mm longer legs back to back.

A II:IZ 14·92 em-

'. == 2·54 em

'. cr 2-16 cm300

llr... - m -139

Allowable F, -= 565 kg/emf

Allowable load - 0·565 x 14·92-8-42 t-No Good.

Adopt 2 ISA 90 60, 6 mm only,

~'O.60.'"''

==L---Il.-.o"""

'_Ia of ~Dlle ISA CD 1·28 em.luimumc/coC.dtcbriveta - J·28xSO-64 em <_ 22.5 of IS:8QO;.1956)

(Ule @ SO em clc.)

24

SECTION II: DESIGN OF C!.NTRALLY LOADED COLUMNS

Double angle struts are frequently used in single plane truss constructionand it is common practice in the chords to put the short legs of unequalangles, back to back, on opposite sides of gusset plates, so as to provide theoverall truss with greatest stiffness against lateral bending out of the planeof the truss,

5. SHORT COLUMNS WITH LARGE LOADS

5.1 H-Beam with Welded Cover Plate (see Design Example 4)­The H-beam by itself is a very commonly used column cross-section and thedesign of a number of such columns is provided later in DesignExample 9 pertaining to a complete building column design. In the DesignExample 4 the load is considerably greater than that in the building designexample and it is necessary to add cover plates to the H-beam cross-section.This introduces the design of connecting welds as a function of requiredshear strength. '

5.2 Slagle Cell Box Section (see Design ExaDlple 5) - The single cellclosed box cross-section provides a very effective column, similar to the hollowtube, in that the material is disposed nearly as far as possible in all directionsfrom the central axis and it is convenient to provide about the same radiusof gyration about all axes. Although the built-up box section requiresmore work of fabrication, because of the longitudinal welds, it is made ofplates or channels that cost less than a cylindrical tube. As in the case ofthe cylindrical tube, a box section is immune from torsional buckling butshall be checked as to width/thickness ratios of plate segments.

25

III HANDBOOK ,oa IT1lUCTURAL ENGINEERS: STEE.L COLUMNS A~D STIlL,..

"..... Ese•• 4-SIaort s.n.u lorLq, ..4sUt1 Loab-H·B,.". willa JJ'fldtfl CoHr PIal..

TIw I.. is 500 t 01 50 ti""s of 1M' givm ;ft Dlsi,,. Examp" 1 but I'" 1"'Ith ,IIII4iItJ ,IttUfW til tilt. ""Ir,s. FOl" sutlra lare« l«J4 it is obvitnu llult 1/, will IN stIUIll a"d a 'ar" tIl,.,.6ItIIraI is tU.".,d at tiu start, As soon as tlr, basit L-----------....---IISHB s,ction is s61tcttd it ;.1 possibu to maU tJ dou Dnilit I.ample .. ,_¥JnXi"""Um of tlu rad;w ofg,ration SUtu llu 'OIJI' .... 1""'J "..., INput on suffici"'/~., wid. 10 maJu 1M '. of.......... RIji"ntt is mad, to Tabl« II to ,s,imtJu Des.p of Cover Platee 21M'.' Aft" a s,l,etioft ofplaus thatar, a/J!Wdimal,ly.. ,,,,,A to baltIIIU 'III ,adii of ,y,ation about r- ......._ ..

NM "tS, 1M oulsttUUli"l witlthltlaickfllss ,atitl H.1o"" tla, H-btam u clwktd a"d slMnJtl H less.. 16. rial restof th« calcullliions tn, s,1j ,Jt/JItmakwy. . '-- -.. - - -- ... - - - - - - - - - - - - - - - - - - - -'- - - - - - - - - - - - - - - .. - - -

P = 5OO-l 1:=3 mSmall 1/,-Trial F, = I 200 kg/em'

Area required :=~ =417 em'1200

I,!

~'-- -lr- 'If I

~._"c"'~

132 717 em4

Area = 117·9-+·2 X 146..409,9 em'

'" CIC Vl32 727 == 18 cm4iJ§:9(,_ steater than 18'5-no need to check)'. is Ina than predicted but probably O~.

ISHB 450, 92'-5 kgA = 117·89 em' '.-= 18'5 em ',==5,08 em

Add plates-inereac '. and '. to about 19

Predicted II' = ~ = 16 Predicted F.= I 228 kg/em'

500 000Area required = TI28:a 407·0 em'

rea supplied by 15HB 450 == !lU.em'Balance JaS 289,1 em'

289·1 ,.. -2- = 145 COli required per cover plate

Rdeninl fo Table II :Approx,. = 0·21 b 19=:0,21 b (0·21 is low ifplatea are wide)

19:. Assume b = 0,25 = 76 em

T'7 75X 2 em cover plate as in the sketch.Check outstanding width: thickness ratio

24= 2' ::: 12 less than 16 ...•.OK ($II 1.....1 of IS: 800-1956)

Check radius oof gyrationJ.-H Section == 3 045 em!

lof plates = 4 ~;3' = 129 672 cm~

26

SECTIO:-r II: DEIION OP CI.NTIlALLY LOADED COLU!4XS

2of2

Desl... "amp'e 4

D•••," of Cover Plat.W.ld.

W.lth ., _s;IIIIIIfor a sJua,of 2·S/Jn,mt of 1MaxUJIl«ul Of' J2·5 I. It is 10b, noud that1M continuous ....----------....WlltIs til ,,,,II ",d shou:d b, as grtat as 1M maximumwit/til of'M JlMts joint,d.- -- - -- - - - - - - - - - - - - - - - - - - - - ....._--------_.......-..

0'115 tfem per weld greater than Y. -0-11t/cm .....OK•

Clear .cIia&aAce between welds 220-11iiCb. or ihiOn"t plate :II: i§:f' - 16·05> 161 but may be penaitkcL

Ute (I" X. em @ 30 em clc intermittent.

I,'r "= 31~ = 16·67 F.= I 227 kg/em.

. 500000 .Area required =-~ =408 em' (near enough to 409·9 emt provided)

.....OK.D,s;',. tDlin«ti,., wtldsfor sAto, of 2'5 /JIt't,,,t OfP (.ft, 12.2.1 of IS: 800-1956)

Y = 0·025 X 500= 12·5 t

Shearing force per unit length, V, = !.plz of H..Beam = 40 3-4-9·9 ~ 40 350 em!

J. of plates == 161 352 em·Total I. Zt: 201 702 em~

a.- == 146x 23,5=3 431 em'12'5x3431 ,

Y, == 201 702 X 2t ==0,11 tJcm per weld

Cover plate 2 em thick requires minimum fillet weld of 6·0 nun (m Table I and1.2.2 of IS: 816-1956)

Shear value for weld per em length -= 0·6 x O'70: X 1.()2S:::'C 0'43 t/cm per weld

Tr:1 0·1)( 8 em @ 90 em e/e intermitttnt.83lf X 0-49 =

. ~:

, 1

27

III HANDBOOK POR STRUCTURAL ENOINEERI: STEEL COLUMNS AND STRvn

t

.....---17c. ----..

d

I::I6e"

1.-.---------I-:'J-.,J.....---b---...I,

Trial u"ion25-mm plate)Area of 2 plates 46 X 2·5 em =m 230 eml

Area of 2 plates S6x 2·5 em == 180 em.

Total ::I 410 em'

5x36I1. of the two 36-cm plates = -12- :c; 19 500 em.

1. of the two 46-cm plates == 46 X 5 x 19·25' == 85 200 emt

104 700 em·

• /i047OO, =:V~ =16em

3001/, =: 16==19

Allowable F, Ell 1 225 kg/emt

Area required ... 5f2:-408 cm1o=area provided..•••OK.

Ule diaphrapDI or capl @ eachend to seal out air and hold the erosa-section ahape.

------------------------------------------------• n...tlc.l~uan lbape boa teedoa II more eea.omical but Ia the pnleDt cue, &he loacI ~~ dae N ~~ ..... ", ......... tberel'ore. Cor any b:creue iD,. the efFect OIl ..............1. aDd pracdCaIlylaO ecoDOIDy II aCbieYed.

28

I&C'I'IOIC D: omaN O. CBNTIlALLY LOAD&D OOLUIINI

6. LONG COLUMNS wrra SMALL LOADI

..1 J.-. ~."oa MemIIer for Small I..-.l (- ......B._pie 6) - t is generally efficient to use laced channel sectioaI ~rlong compression members carrying a small load. Therefore, in the c:IeIiJrnexampe illustrated also, it is tint expected that laced channels would proviClca suitable cross-section. However, a closed box section turns out to be thelogical development subsequent to the initial trial of a laced channelsection.

29

III HA~D800~ PO. ITaUCTtJRAL ENOIND..: Itt&L COLUMNS AltD ITaUTI

IofJ

D...", I.amp'. 6

..... ....pI~ 6-Lo", CornpreuionM~fer • S..." LoU

..... ltJatJ is smalland 1M column ltmt, 1M sltutint point in this des;,n is till ,..,...,.,., ,... ,. 1/, ,atio btlow tM maximum ptrmissi61, VtIlw of 180. The ;,.;lio1 4SSUWtMI~simi illJtIIt corrtsptmding to an llr of180. 0,. this .... ..._ ...1MriI. ,., ISLe 150, 14'41cg cluuaMls art found to" llllifl-Itwy and Ilvir capacifY is_found at one, to 6, 1- -1

"..,., IJwa "guirtd. HOWlvtr, the jlangts ar, tH Tria. Deslln w.th Lacedc..".,."JorfabrUation to mak, ,;r:tl,d lacing""', /MsilJu b«ilUSI of IN insufficient clearanc« j", Channels6dVv", th« rivets. ISje 150,9'9 kg 'MnMlstill IriIdMIlfound to bejwt sufficient.----~-------------------------------------~-~~~-Load p==10 t; Effective length 1= 10 m (No bracing possible)

Tbe problem is to obtain maximum r with minimum sectional area.Vie 2 channels or 4 angles with battens or lacing ban.rrMl INs;,n c"·sin, ChtlllMlsMinimum depth of channel for I/r= 180 is determined as follows:

,_ == 0-36d* =rmln

~.:tl = 180; tl= 15·5 em

Try ISLe 150, 14'4 kgA=:2 x IB·36em'==36·72 em''. == 6·16 em

:\'OTE - By choosil18 6. '. can be made equal 10 '.

10001/,_ = &i6==162

Allowable F. == 427 kg/em' (m Table I)Allowable load = 0'427 x 36·72::::: 15·7 t-over daip

Tr::v ISj C 150. 9'9 kgA=:2 x 12·65em'=25·3 eM''. = 6·16 em

1 0001/,- -= '&16== 164

Allowable F. = 416 kc/cm 'Allowable load == 0·416 X 25·3 == 10·5 t •••••OK..

Approx b to make " -='. (sa 21.1.1 and ILLI ofIS: 800-]956)

0·40 6 c:: 6·166 = 15·4 em Adopt 61:::16 em

Ch~ck till of web

dlt = 150-2 x 5·6=:38 <45 (_lLU of~·6 IS: 800-1956)

Check '.I, :m 2 x 12·65 (8-1·66)'+2 X 37·9

-= 1 090 em'

" _A / 1 090 == 6·55 em ...••OK."V . 25.9

Battenlor 1acinp are required. (These will not be designed here. Ep.,.,. ottbeIedesipa win be given under 7.)--~-----~~--~--~----------~----~-------~---~----...Table II OIl .... 71.

30

UCTION U: DEIIOH OF CENTRALLY LOADaD COLL~

2.f3

0.1... E.ample ,LtJa.,s OT haUntS will ... 10 " WId in CtJSI tA,.sip "SltMt J is tUIo/J;'tl. &tum;", to till on,intJIul«tion qf two ISI£ J50, it is obvitnu IMI tlte blst ....--r--------...wo" is Is lUI thes« in tltefiorm 01' tI closldboxS;1I&, ",is Flha 0.11" with Welded~ ~ Channel. a•• Box,limi1UJlls tIw nec,ssity to WI battln plaus or lating

ba1s, wlaieh in tltnns,lzo,s carry no lotJd, Y'l tulti 1o 1M ...----------........- ..to/ol s.1 ,'quir,m,nl. Thl widtJalthidcnlss ratio of the ,"b of a compression mlmHr mtI)' P tU

Ai," as 80 but only 45 t is alloWld tIS cont,ibutinf to wifulload capacil)'. The wtb of the ISLeJ50 is satisfactory in thi»"s/JI"andtill dettJils of uildingup channels with b(J(k-up stripsto prouitMa .ulIisf«tory weld (111 shown "",. The llr is found to bejust under J80 and the column ctlJNl&il.1of tit, box section is about 25perc,nt more than tha: required.-~--------------------------------------------~

.\5 an alternative, if a solid welded box is desirable:

Try ISLe 150, 14·4 kg

A 2 x 18,36=36,72 em:

r- 6·16r,

I, 2:< 18·36 (7·j-2·38)'+2 X 103·2

1 169'0 em!

1Scm

Lr. :._>Vl 169'0=5'64 em

36·72-

1/,. = 1000=177'15·64

C2038cm F, 350 kg/em'

7·5cm p 0·330 x 18·36 x 2

~s~;STR'P

DETAIL AT A

J2·83 t greater than 10 t ..•.. OK.

Size of weld= thickness of flange a tend

(7·8- 62,. tan 1·5°)

7'80-0,92

-= 6·88 mm

Weld to be continuous

W HANDBOOK FOR ITRUcrultAL E.NOINItI.RS: STEEL COLC)lNI AND STaUTI

F• .. ,.., "","lin (10 m) trtlllS7ltillint G srull Dell... hample' Jl«MI (ff, "9, 9 10 10 I) tU illllais lXampl6, 1M hollow .f9IiltJlii.l "'" is comJHlrtJbl6 10 1M box,d cluztaMl· Alternatl•• D.IIII with •.... Tube·------- - - - - - - - - - - - - -- - - - - - ...._-------_........- ..TrW INn". Using Tub,s

Tr;,1S nominal bore 150 ($II IS: IIt'I-1958) 16·51 em OD by 5-4 rom wan thiclme.

A == 27·1 eml

, - 5·65 em

1 0001/, - 5.65

.. 177 (Border line Cor 1/, of main memben)

Allowable F. - 353 kg/em l

Allowable load - o-S53x27·1

- 9·6t

Because of small loads, a tube or closed box is obviously economical of Heel. Laced« battened column of amaller 1/, would be of comparable wa,ht becaUIC: or non-ltrellanyiDs material.

32

SECTION n: DUION OF C&MTaALLY LOAD&D COLUMNa

7. LONG COLUMNS WITH INTERMEDIATE :tOADS7.1 LacecI Colama. (SII De.......pl. 7) - For either very heavy orvery light loads the use of solid box or hollow tube columns seems moreeconomical of steel but for intermediate loads the i&£ed or batten platecolumn may be selected. The lacing ban or battenjlate serve to hold theload carrying portions of the column in position an shall be designed forthe shear requirement as previously explained, Lacing ban are moreeffective.than batten plates in resisting shear since they cause the column toact as a truss.

7.2 .ttea Plate Co11llll1l. (su De.......p1e 8) - It is to be notedthat the batten plate column, according tQ 22.1.2 of IS : 800.1956, shallnot be used where the compression members are subjected in the plane ofthe battens to eccentricity of loading.

33

III HANDBOOK FOR ITaVCTURAL POINDU: S.TEEL COLUM~I A:sn STRl"'CS

D..... Esompl~ 7-Le,., Compr",ion MIJfIMr for Inln'lfIflli.ol, Lotul

'T1tI load is 100 t and 1M lnagth 11 m. A .fortunate jwelimiru:wy IstimtJle of lIN tWnGl't--issibll slress as btJJed on em Istimaud 1/, of 92 Itmtsout to be alright and two c/um,..ls lit,

~ly Sllected with a caPacity jwt a littl« 0"", ...----------....---1• $~d loadof Jq~ t. F.I~,s of 1M .,han",ls Deslln Example 7 I." IIIntId out to lat'/Ilate nvellllg of lae,,,, bars.TtIIM II provi*s tift eslimeu as to how fa, apa,t ....----......-----... of1M duJnnlls should H btl€/c-to-btl€/c to balancl the radii S.lectlon of Section 2ofvr4lilm about 1M X.X and Y-Y axes.- - - - - - - - - - - - - - - - - - - - - - - - - - ....----------...--4

Load p= lOOt; Effective length I = 11 m

LM,dClaalWls - (Probably ISLe 300, 33'1 kg or ISLe 400, 45·7 kg channels required)

Preliminary estimate , c::: 30·0 x 0·4 = 12 em

llr = I :~ "'" 92; Allowable F. = 950 Itg/em'

11'11

AUowable F,Allowable load

A = 49'47x2=98'94cm'13·72 em-by choosing 6,

'tl may be made equal to '"1 10013.72 = 80·41 036 kg/em'1·036x 98·94-102·5 t .....OK.

Spacing .hould provide equal/I,_ and 1/,,,ASl\lme'it ;:z: 0·6 b (set Table II)

13·72b c:: ""0=6=22'9 em

Try II -= 22 emI, ~ 2 X 49·47 (11'0+2'41)'

+2 X 395= 18 581 an·'., ::a: Vl8 581/98·94 =- 13·7 em

11,_ _ 1 100 == SO.5J3:7

Allowable F, 1 OS5 kg/eml ••••• OK.Allowable load :::: 1·035X g&.94

100·8 t .•••. OK.Single lacing ban @ 60 0 to the axis of the member.Check 1/, of channel between lacing connections.

1= 32x2=37cmy3

'" of ISLe 350, 38·8 kg==2·82 em371/,. lIZ: fftD;J3·1 <0·7 x80 ..... OK• (SII 21.' of IS : 800-1956)

7011"1'1

b ---......1 Ar~a =- .!-OO~ =105 em'. 950- ----4---- Try two ISLe 350, 38·8 kg laced as shown in theI sketch.

22c:",-t----------t------

34

SECTION II: DaslON OF C1NTRALLY LOADED COLUMNS

2of2D••lln of Laclnp

D.11ft Example 7H", Ih6 principtJl tUsip problnn is 1M dlsip of1M ltuin{ btlts. A trial layout wing jlal bars isSMWft Willa tJ1J ..,11 of 60° b,1wun sucussive bars.1-----------_Ths l/r of 1M indir.,idual chtmnll bllw,m lacing and·oMlditnu is d,ck,d and found 10 IH well b,/ow themaximum JIm1Iissibu limit. .------------....--41

1M us, ofjlat bars for lacing is usuallysuitable _for very muzll columns bUI ,II" jltUb., '"41 h,cJuuag,tllo anglls or ClumMI SIC'ions for larln columns and varioru schmw, sueh til X br«ill,may6, inlrodut,dtofill 1Mr,quirmamts. A lae,dcolumn wingangustIS ladn, bMS will 1M tlaipldin DIng,. Exampll 10 for tJ sllpp,d mill building column' can;yinf tJ C1tIM lDtuJ. Tlu IIIuilIstr""th tmtl rivet Vdlues ar, cMcUd and ar, found to hi atl,qllall. Compr,ssio,. strl1l,11I is ..cOnlrolling factDr.

Ti6 plaUsar, r,quit-,dat 'lUla nul but theirdesi,,. is tM StJtM asfor bat",. plalucovn,tl b.7 olin-MI;w DlSign Example 8. '-------------~-----~-----------------------~---Lacing BMS

Minimum width .. 50 nun (su 21.3 of IS: 800-1956)370

Minimum thicknesa a: 40 -9·25 mm (SII 21.4 of IS: 800(1956)

Try SOx 10 rnm bar-,. - 0·289 em

371/,. Ia ro:28§-= 128< 145 .... • OK (- 21.2.S orIS: 800-1956)

F. - 644 kg/eml

Allowable load - 644 X 5-=3 220 qShear capacity, 2 ban (one on either aide)

- S·22x2xO·866.-S·58 t >2·5 percent ~ the

load or 100 (-2·5 t) ••••.OK.

Check teDIile .treDfth - l6-mm rivet17-1D1D rivet bole

1 (5·0-1·7) 1420xG-866x2 - 8·1 t>2·S t. - - - .OK.1·7'

One l6-mmahop rivetJDisiDlIe abear - 1-025 X T X. - 2-32 t

BeariDI - 2 S60x 1·7x 1 - .. t

..... shear' acmma. 2·32 X 2>2-5 t shear·capacity required ••••• OK.Supplyde pla.·fleacb ad-cIeaip II~ • for batteDpJMee·1iaDedpB......·L

35

III HANDBOOK FOR STRUCTURAL ENGINEERS: STEEL COLUMNS AND ITIltrn

D_i&ra &ampl_ 8-Ale.r"". D.'i&n U.i,., B.,." PI... '0 Reploee Lori",1M crosl-_tiM m4kI up is th6 IIIIM asfar tit, liIud column in D,si". &ampll 7, Mnu tAu 1IIId

nol" "/JIaud.lrtitially, tlat code JWovision is followld and tM battnas arl/JUt in wWa ,. mMimums/Nl&inl b,twun """esl rivlls .MJ tIS to /WovUh lUI "... ~-...

(/, 1j'lO ma.rimum ., O' 7 timls 1M 1/, of1M mnnb" Deilin Example • ItU .. w"'''. TIll II' df 50 UJOJJ4 .:,nmt and tht 1- .....

~~~~~~~~.~ ~" .. is Wdc,tl/., 1M trI01MIt "Stdliltg.frMn 1M DeslE of a.tten 2sJwr of 2·5 iJ'rena' o{ till u* l«uJ UJlUeh in this pacln..e4U is 2·5 I. .A WIIIJ&t com/JtJriMa sMwS that th6.6tJtlera pl4u collllM "tplires less total CtmllUWr stlllfor bdttms tJum aMS 1M lac,tlcol",""for laan,btUs.

1m 6·4 mm ($1122.4 of IS: 800-1956)

,a·o -

._-------_.--.....

. ._--&0._

Shear S == 0·025 X 100=2'5 t

Maximum spaCing)" _ 50 X 2·82 ac 141 em (su 22.5 of IS: 800-1956)be~eennearntriveb

M· · the kn 3201?lmUOl IC ell - 50

Use 71-mm plate.T~ 4 rivetl on each side.

Rivet group.,- Ie: 2 (151+51) - 500 eml

tl ca 175 em, .... 32em

••,10·0 .......--...

.....----- .".0 c.- C TO C IMTINI ----.....

Loqitudinal mear (.- 22.2.1.1 of IS: 800-1956) :

F 2·5x 175 _ 6-84 tI - 2x32

Moment (SIC 22.2.1.1 of IS: 800-1956) :.M _ 2·Sx 175 109. t

2x2 em

1-" •107.5JSheu - ~ - 1'71 t

IeDcIioc .traI-~ -~ - 3'27 t

Raultant load - V3·27'+1·711 - 3·64 t. ·2·Sx7·1 x2~

BeuiDI value of 22 mm nvet - 100 x 1 000- 3·80 t>S·64 t .•••• OK.

-;i+i,~~-~~~-------------------------------

36

SECTION II: DUIGN OF CENTIlALLY LOAnKO COLUMNS

1,. or" 10 IIUW' IJuu local .f4il"" of IhI nuaUl Deslan "amp'e • 2uwnJxmItW .ar b4tlna 'OMItINtIS doIs not «"'" ..... •du 10 loedl tombiMdsfrus tlw 10 blndu., (41 (J ,,11I" .pac"••f a.ttenl .fof 1M 2'~ Jllrunl transwrs, shM6 in lJ4ttms) tIIIII .-....ce4 2axial lHl, 1M $IdioM 111' ,hld,d and 1M to'"ctmllJiltld fi/w. stress is limilld to 1 575 kllmal b.1 1-----------...-...,1duM, tfw sJHIMI of bGttms.

- -ch;ek~-~ndinK ;~ i;th;dt~ (tho~h-th; i~ ~;t p;";i~i';l; ~td';; ~IS: 800-1956, it is considered necessary).

Moment = 1·25X 72·5 = 90·6 em-t

Z. (on channel) 1:1I 52 em' '·as. '·JSt

f. = I 250X 72·5 == 1 740 kg/em'52

Average colUOlnf. :::: 1 035 kg/em'CombiDcclf.+f.loca1ly =- 2 775 kg/em'

Non - er-..ectioo Z. - 52 ani wu UNd.R.educed spacing is required to allow I 575 kg for local

combined Itrea.1 575-1 035 tm 540 k,/an' •

is available for local bendinas.

Thespacing n:quiredia1s: X 145 = 45 em

With this lower spacilll adopt 2 rivetl of 22 mm at10 em c/c instead of 4 of 22 mm at 10 em cleo~ 6GUM sJNM:inl

Check rivet IttuI:

F1 = 2;5:~5 -= 2-15t

M = 2-~: ~5 34-6em-t

MOIl """. rioI':2·15

Shear :.: -2- == 1·1 t

M·6x5"Bending at 2'X5i az 3-46 t

Resultant load V (3·46)1+(1·1)'3·64 t<3·8 t beanna value

of 22 mm rivet .....OK.Weilb t comparison -laced Wf'nu battened

Laced-4 ban == 4 X 1X 42X .5 em'per 37 an of column

:=I 17·7 kg/mI~ of column(taking density of structural steel as

0·00785 q/cml )

Battened-2 platn := 2 X 20 X 42 X 007em'per 5.5 em of column

16·8ka/m length of column

37

SECTION III

COLUMNS IN MULTI-STOREY BUILDINGS

.. INTRODUCTION

8.1 For a general treatment of the design of steel frames for multi-storeybuildings, reference should be made to lSI Handbook for StructuralEngineen on Multi-Storey Steel Framed Structures (under preparation)wherein the problem of multi-storey building column design will be treatedin greater detail with reference to both vertical loads and lateral wind loads.

8.2 In the design example to follow, the details regarding distributionof load to a typical building column for dead plus live load only are given.Special design aspects related to column splices, eccentricitx of floor load,and base plate design are included. Several typical budding columnsare shown clearly at the left side of Fig. l , The column splices shouldbe noted.

9. BtJILDlNG COLUMN DESIGN FOR DEAD PLUS LIVE LOADS(SII .... Esample 9)

9.1 The building column in question will be designed for a full silt-storeyheight of a building that includes a set-back. In the top four storeys, thecolumn is at the exterior of the building with corresponding eccentricitiesof load, and in the first two and basement storeys it becomes an interiorcolumn with centric load. The basement column will be designed as acased column.

9.2 In calculating the loads on multi-storey building columns, reference ismade to IS : 875-1957. From Table I of IS : 875-1957 the loading istaken at 500 kg/rn l ofarea and the imposed roof load is taken as ISOkg/raJ.Reference is 'aIio made to the reduction in imposed floor load on columnsu given in 5.1 of IS: 875-1957. A uniformly distributedIoad of400 kg/ml for weight of floon plus 100 kg/m'A for partitions is assumed onaU ftoon. The fint floor is designed for a heavier live load of 1 000 kg/m!.and a total dead load of 750 kg/mi.

38

tiECr:r10 N III: CCLtoMNS I~ YVLTI-ITOIUtY BUILDINGS

, ~~it;~:~;~~¥f\:"!~~~~~~""'"

1; ; ,,,~,~"r.U~~" ·''-:- ~;.. ' .--"'~~fE..·l·?" .' .r.: ',:}~;~i~~r::>,.~':'~:; :'~", :

r:~J,~~~;~:L, ~.f.' '.:;. .:t' ':>'1! '"

.:...,

. .-.',:

I,ffr.~~ ~:~'~~

~:..~,; .

39

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~ECTION III: COLUMNS IN ~ULT1-STOREY BUILI>IN05

Dulin Example' 2

ofDetails of Loads 14

r-6IT'-r-smi1

7·5m

JFLOOR IlL LJ. REDUCED I.L COMBINATIOf\ ..\LTERNATIt

OF LoADS AS CoLUMN·REDUCED DESIGN LoAD

[(2) + (4)]

(1) (2) (3) (4) (5) (6)

Roof 3·625 3·375 3·37.5 9·000 9·00..

6th Fl 18·000 11·250 10·125 28·125 37'125

5th FI 18·000 11·250 9·000 27·000 64'125

..th FI 18'()()() 11·250 7·87.) 25·87r) 90·00

3rd PI 23·625 14·62:-) 8'77.1 32·40() 122·40

2nd FI 22·300 22·j()() 11·250 33'7~O 156'15

1st Fl 33·700 4:'),000 22·500 .16·200 212·3:;

(All values in 1l1..-tric tonnes.)

~-~--------~------~---~~--~~----------~-------~~• Doa DO& InclucWcInd weitht or columns.

41

151 HANDBOOK FOR STRUCTURAL ENGINEERS: STEEL COLUMNS A~D ITIlUTS

Sinc« thetopcolumn runsfrom ,levation71·0 to77'5, Dellln ••ample t JlM design load is estimated al approximauly midway1------------..between tlu .fifth floor and ,oof with an approximate Column a.tween 5th ofallowance of 190 kglm fo~ the weight of this ~rtion Floor and Roof 14of IhI column together with encasement. As UI thlcas, of a centrally loaded column the darting point ...-----------...---1is a trial average load but this is reduced in rough. proportion to thl amount of eccentr"ieifY that is,x/JIcted. In thI case of building columns, the calculation of eccmtricifY is based on IL6 of1$: 800-1956. At th« sixth floor and at the roof, one-third of tM total load is inlroduud with aneccmtricifY. This may be verified by referenc« to th« connection details shown on Sheet 2 wlrere itmay b, seen that two-thirds of the load above th4 set-back is introduud cmtrally to tM column webc~tions and one-third comes in eccentricity through the seat angleconneclwn to the column jltmge.At 1M sixthJlDOr level, theeamnic moment is assumed equally divided above andbelow th6sixtJajloor.II is tohi noud that no redutt",n in live loadis made in calculating tlu localeccentric moment.

The column has been checked in the last sluet at the sixth floor leVlI andthn, is no ,..d to cheekit 411M rooflewl since theeccent, it column moment there is lessthanjust abowor below thI sixth floor.

II ts to be noud that in calculating ,hi dfectwekngtJa of tMs, columns, tIaI sleruJmuss ratio is 'auntIS 067 times tM sleruJmuss ratio cmtr,-to-unlre of floors. This is in accordance willa Fig. J ofAppnuJix G Qf IS: 800-1956. .AltJaough only one Ham frames into1Mcolumn jlange 011 OM siu.tIwr, an two beams providing direction fixity in the WlaJc plaM ofbending.

Assu",. 3 column splices as shown ill 1Msketch. Also nou lhal 1M splices are O'5 m above 1M,.,.,st jloorlevels.------------------------------------------------

Top Column-5th Floor to Roof

= 950 kg/ems

Approximatedesign load -- 38 t (from Sheet I)

Area required -- 38 000/950- 40 cm l

Try ISHB 150, 34·6 kg

A = 44-08 em'Z. = 218·1 em'

J-- .!.Of LOAD

r::r.-; • I, (THII CAUSU~ _ ..... ICClNTlttCITV)

~O'LOAOTop and seat connection of roof beam to column flange introduces 1/3 roof load with

eccentricity as explained in the commentary above.(See 18.6.1 of IS : 800-1956)

e = ;·5+2·0==9·5 em (seat usumed to be unstiffened bracket with1=2 em)

Moment at Load at roof levelroof level M a :;;; 3 X e

9·00- -3- X 9·5 = 28·5 cm·t

Moment ., .29.25 x 9·56th Roor level M. := 3 X 2t = 46·3 cm·t

------------------------------------------------• No reduction in live load in c:alcu1a~ local ecceatric IDOI'MDt. ThUi 29·2.5 i. obtalnod by aclcUa,the..m. iD 2Dc1 aDd3rd col 01' table oIloada In Sheet2.

t s. IU.I (b) oilS : 1OO-19~.

42

UOTION m: COLUMNI IN JlULTI-srORBY BUILDINGS

D••lp Example t

Column Between5th Floor and Roof

..of14

lIb = 0·67 x 3'5 x 100 ~ 1220

F. ~ 1 575 kg/em' (see 9.2.2 of IS: 800-1956)

_ 46·3 x 1 000 _ ,f. - 218'1 -212 kg/em

'. = 3·35 em, effective

II - 0·67 x 350 -70'. - 3·35 -

F. := 1 098 kg/em' (_ 9.1.2 of IS: 800-1956)

Axial load p _ *190x ~3~I'75) -38'125 t

38 125f. :::: 4+08

:a::: 865 kg/em'

865 212 •Therefore, I 098 +1m := 0·922 < 1 ..... OK.

T'7ISHB ISO, 30·6 kg

A J::1I 38·98 em'

Z. ;::I 205·3 em'

M. = 46·3 cm-t

0·67 X 350 Ilib ::a 20 = 12; F.= 1 575 kg/em

f. = 46·3~~.~ =225 kg/em.

Q ...... il:B 0'67 X 350 ==68,.-..,.~ em, '. 3.44-

F, == 1 106 kg/em'

38125f. - r:s:98 ==980 kg/em'

f. r 980 225;:; + ~ c. rror+rm== 0·884 +0·143 lIS 1·027> I ..... not permitted

•• U.lSHB 150,34·6 q.- ;~-liGkij';br;r-.ddid~~ ~.; ;t~~ ';p~o-ndd-h~;-of So;,-(;, :;.;;.;.; -..­......).

43

III HANDBOOK FOR ITIlUCTURAL ENOlNEEltS: STEEL COLUMNS .'ND STRUTS

5of14

De.lln Example'

Column Between3rd and 5th Floon

TM dlsip of tlu column bdwem t1l6 third andfifth jlotWs split,s is similar to thatfor the top column 1------------41slttion tU already given with the exception of thebmJing moment diJt,ibution at 'M fifth floor. A,·tording to 18.6.2 of IS: 800-1956 ijtJu differencein III is gr,G'" than 1,5, thI "cmlrit moment is to I" ....----------.....--..distrihuud in proportion to 'h, III of 1M up"" and lower column sections resplCtively. &ttlllSl of1M UMquQl distribution, 1M bmding moment in the column at the fifth .floor level is W(" IJum tiltAlfourth./loor, but thl stress condition at thl fourth .floor lel',l goterns thedesign beceus« o,t1M IfWIUraialload.

Column-J,d to 5th Floor

Area required _.

Assume f. = 900 kg/ems

4th floor load = 90·0 t

Add weight of column = 1·3 t-Approximate design load = 91·3 t

91·3x 1000900

=101,5 em'

1/6 -

Effective 1/,'1 ==

Try' ISHB 400, 77·4 kg

A = 98·66 em',

r'l z= 5·26 em,

350 x 0·6725

350 x 0·675·26

Ze ~- 1 404·2 em"

b = 25·0 em

=- 9'4, F.;": 1 575 kg/emt

=44-6, F. = 1 187 kg/em'

M.. (without reduction) (assuming t == 2'0 em a.~ before) =-= 29·25 (20+2)3x2

Therefore)

- 107·25 em' t

P q ~ 90'00+ (200 x 12,25)· 92.57 t1 ()()()

f t107'25 xl 000 --76.t: k / '• - 1 404.2 -:) g em

= 92·57 X 1 000 = 938 k / If. 98.66 gem

938 76·5fl87+T'575 = 0·84<1 .....OK.

But· try smaller sections ;

With f. - I 187 kg/em' as obtained in the lut trial

92·57an area of TI87X I 000 :=: 78 enl l i!l required approximately.

-~------~--------~---------------~---------~-~--• TbiIiI.~weipt due to column and ill encuiDt concrete (or aleJlJth o( 12·25 m - 5·5)( S (tor 4th,~... aDd.. loon) plYi S'5x 1/2Corthe 3rei 8001',the ~cUOD coneidend MiDI midway betwecD 'rei aacl4ttiIoor .......t 1I.-I07-a..., IIeonsidered ADd Dot M.. u it I. only 45·5em" U could be teeD froID &beet14.

5ECTJOS III : COLt!MNS IN )IVLTI-STOR£Y BUILDINGS

"ir- )orC':.ol~o c~

, s.o cm ~__-=-="--H ~

L~ I \J-

D••II" Examp'e 9

Column Between3rd and 5th Floor.

6of14

-- 82·9 em' t

- 96 kg/em'

= 1 154 kg/em'

'" = 5·29 ern

= 0·67,,< 3:;0 ~44'45·29

= 175 em· t

fll _..

I 188 kg/em'29'25 (15+2)

3x2F. ~-: 1 575 kg/em'

82·9 x I 000863·3

92·57 X 1 00080·25

Z;e -- 863·3 ern", Effective 1/"F. --

M •• -

Tr}' ISHB 300, 63·0 kgA = 80·2.i em",

f. --I 154 96

Therefore, I 188+rm = 0·973+0·061 rtzz 1·034> 1 ..... not permitted

:. Adopt next heavier section ISHB 350, 67·4 kgCheck 4-5 section due to probable greater moments

19 159·7 }lull ~ ~ = 55·0 The ratio between tbe two isgreater than 1·5 ($II lLI.2 of

I ••ll ==- 1 635·6 -= 4.7 IS: 8OO-1956~350

Total moment at 5th floor

29·25x (17'5+2) = 190·1 em· t3

The distribution to the column below4P" 55x 190·1

== 59·7175x I 000Iv > I 094-8 -,,, 160 kg/em'

/, at 5th floor

Effective l/,. =z

·66x 1 00085.91 == 768 kg/em

l

350x 0·675·304-

F. == I 189 kg/em l

768 160Therefore, f1ii§+f575 == 0·747 < 1 ..... OK.

Use ISHB 350, 67·4 kg-~-~---~----~~-~-------~--~----------~~~~~---~--• (14·125+ 1·9-66).

45

III HASDBOOK FOR STRUCTURAL ENGINEEltS : STEEL COLUMNS AND STRUTS

Ire asipin, the column hllwma 1M firsl and the D••lan Example 9 7tltirtl jI«w splic,s, it is _foawl illitWI" thdI th, first ....----------1to uetmtljl«w slgment will null COVlr pltJl,s b,caus,IM Column Betw..n ofr'fUfr,d ar'd is ,r'aln tlum 1M.dr,. of ~"tion of4,,! lit and 3rd 'Ioon 14IntlUIIt Standard rolkd uctuna tWaalabil. ThISjJrooUU$ an opportunit,y for ",allf' SUfi 'COllOm" and .....---------.........- ••1M rolutl uction is #lIcud on till basis of 1M r,quirements betwem tM second and llaird .floor wilJatIN plan 10 tuld cover platls bltwma tIN first and s,cond floors onl". TM mortIINt .. to,cemtrieif1 etndd /Jet'1afI/JS H maimum dt IJw firstfloor l,vel as th, liueloaJalfirstjlOtJr is maiMumHUt, J 000 kllm' and mcu1mama ,ccm"icit.1 is cawedWMn live load on one sideof tlaljl«w is uroaNI a' 1M DtAn the full 1 000 kglm' and llat ratio of III ahove andbelow this.floor is dlai" p'''''IIum 1·5 so""', 1MmD1M1Its Gr,/JrD/JO'ftiDrwd aecordingly. This will he clr6chdlaln whiZ, jinididntth6 uelUmftw (DIII1M /-2 (see S",,, 10). Having checked in this sheet ,hi second to thi,tJjloor Sf"""as tldlqutJII, 1M additional MIa "pir""'''' for CDVtr pial's in ttu first andsecondjloor is MtmninMIin SIwI I.

ColMmn-1st to SrdFloor

For maximum steel economy: Try selection for 2...3 and add cover plates in 1-2 only.

PI-a ~ 122-4+ 190X7+21~~+24() (1'75) = 125·6 t

Alaume F. = I 100 kg/em'

A :::2 125·6x I 000 114 em'1 100 ::

Tt:7 ISHB 450, 87·2 kg

A =r 111·14 em'

~ ....., .t JrtJ jIMw ,.",.

Ittler Sheet 1_to.d calculation at 3rd floor.~tric load &om the left aide:

DL 250X 7·5)t 6/2 X -I/S - 1 875 kg

LL J50X 7·5X 6/2 X 1/3 .. 1 125kg-3 000kg110m the riaht aide:

DL500x7'5x6/2xl/3 -,3750qU500x7·Sx6/2xl/3 - 3750.-7500.Therefore, net load caUlinc escentric moment:

7·5-3-0 - 4-5 t

But thewont cue is wbeDthe Uve lC*l is DOt aetiDI OD the left aide on the roof.11MII die maximum ecceatric moment M.-f5·625 (22-5+2)

-138 em- t

SECTION III: COl.l:MNS IN ~UL'fI·STOREY BUILDINGS

•of14

Column aetweenlit to 3rd Floor.

Des.,n Example ,Calculation of column between first and third flooris eontinUld from Sheet 7 and the additional require- 1------------1mt"ts/:or column betwetn ,first and second floor arework, out in this shiel.

- - - - -- - - - - - - - - - - - - - - - - - - - - ._---------_.....- ....

32 em l

f. -

A. the moments of inertia of column section above and below the floor differ by morethan 1·5 times the lesser, the moment due to eccentricity will be distributed in the ratio of 1.

. 1.... 39 211The share ot column 3-2 JII+l

u--= 39 211+ 19 160 ~ 0·67

M u ::-~ O'67x 138 ::.c:. 92,5 em' tZ« =- 1 742·7 ern" (of ISHB 450, 87'2 kg)r" = 5·18 em

Effective llr" = (350/5'18) 0·67 ~.:- 45,:)F. == 1 184 kg/em'

lIb -- ~ =-~ 1425F" -~ 1 575 kg/em'

*125'6 x 1 000111.14 - I 130 kg/cnlt

92·5x I 000 _ 21 742.7 --- 53 kg/em

Area of ISHB 'i-50, 87,2 kg ==Are. of plates required ==

Try ~ platet'20 x o·a em:A:=

f. -1 130 53

Therefore, TT8i + T575 - 0·988< 1 ..... OK.

AtIdUiMIJl 'lpi,nnnats ""WlIII floors 1-2Co'-t--lllltl Jrd floor

Select for axial load from lit to 2nd floor and then check for eccentricity at 3rd floor.AaumeF. ---= 1 160~g/cml

Pn - 156'15+ 190X7.0+210~~i~t240(3.5+5/2) - 160'4t

A::r 160·4 X 1 000 == 138em'1 160

111·14 em-26·86 em'

1. (HB).. 2 985·2 cm·1,. plate == 1 067 em'

Tota11. ~ 4 052 em'

.d - 32+111·14 - 143·14 em" ::a y''"i0'52=a 5·33 em, • i'4§':i4

0·67 X 5001/,_ a: 3.§§ :: 62·8, F, = 1 129 kg/em'

CaJ*ityaa 1·129x 143·14 == 161·6 t> 160'~ t tTentatively .....OK.

••1Iaeet 7.t 11M .....t due to eocentridty II Dot considered yet hen in the deslp orsection for colWILD 1.2•••

ddI will .. cIoDe ill Sheet10.

47

lSI HANDBOOK tOR STRU~"'URAL ENGINEER!: STF.EL COLU"~S .~~D STR\.'TS

,of14

De.lln Examp'e tContinued from Sheet 8. the design of tilt COIlt,­

plated column segment between the first and second 1-------------.­floors is similar 10 prerious Design Example " for Column a.tw.en lit aftflaxial loads. 2nd Floor. and In auement

The basement Jet/jim of the column is 'cased' andmay be designed by a direct procedure because the ....------------....--1undth. of the corer /)/all'.\ may be selected in at/vance. The radius of gyration is tJam thlnmintdaccording to 18.10 of IS: HOO-l.95(j on the basis of concrete encasement. Thus llr. is pt:etktmnilVdand direct I altulation I1U!l' be madeas 10 the required thickness ofCOl'eT plaus 10 be addedto the (ho~en

ISHB 450, 117·:! kg.

Stop 0·8 ern plate at 0'2 rn above 2nd floor level.

Design intermittent welds same as in Design Example 4

l)fJign BasementSa/ion: Column cased with concrete (see 18.10 of JS : 800-1956)

Continue ISllll·F>O. B7·2 kg and usc cover plate 35 em wide.

-- 47·2

r. = 0·2 fb+IO) (selll.lOofIS : 800-1956)

-- 0·2 > 45 - 9 em

·0·85:-: 5009liT. -

F, -- I 182 kg/on'Load Pal = t21S·4 t

• Area required218·4x 1 000

185em'-1 182

_.

ISHB 450, 87·2 kg;..4 = 111·14

Plate area required -- 73'86 em-

15~.7.5 5tJ.

ri·;t~:;s.:;n·~~~.1;}?i;~t ;~~

~~;!~;;{~f~~·:JX::;~??~j1; f;~I

All dimensions in centimetres.

Add cover plates 35 Y 1·25 each,

.t ..- 87·5 em', Total A = 198·64 em' ..... OK.

Check mOITJ~nt at Ist floor level

Eccentric load from left side:

DJ.. 750x 7·5 X 6/'1 X 1/3 - .3 625 kg

LL assumed zero for maximum moment as before

Eccentric load for right side:

DL 750 X 7·5 X 61'i. X 1/3 = 5 625 kg

LL 1 000 X 7·5 X 6/2 X 1/3= 7 500 kg

13 125 kgl\Jet load causing maximum

moment = 13 125-5 625 = 7 500 kg------------------------------------------------• Base connection will not be desicncd for fixing direction.

T212.35+ (190)( 7'0) + (210)('7.~~40 (3'5+ Q) +360)(' 5 -218.4.

48

111+11•

= 0·61 times the total moment M 1 at Ist floor

5ECTIO~ III: COLt.:M~5 IN Mt:L TI-ITOREY BU1LDINOI

Column ...........m...t and lit Floor

Ignoring the concrete encasement

Total moment at 1st floor = 7·5 (22·5+1·23+2) = 193 em· t

Moment of Inertia of basement column section about X-X axis:

II. = ~q 211+87·5x(23·1)'

= 88 600 eint

Zla = 3 740 ema

Moment of Inertia of column section between the 1st and 2nd 800n:

111 = 39211 +32 X (22·9)1

= 56000 em!

Zit ~ 2 400 em'

Thus moments of inertia are varying .by more than 1-1/2 times the lesser.The share of column between

basement and 1st floor

~loment at lst floor distributed tocolumn between Ist and 2nd floor = 193 X O·39

::: 75·3 em· t

.1of14

lib =

Final check of the column section between 1st and 2nd floor (continued from Sheel 8)

0·67x 50025

= 13·4

F. = 1 500 kg/ems

Applying the interaction formula:

160·4 X 1 000 75·3 X 1 000143.14x 1129 + 2 430 X 1500 = 1> I ..... OK.

Check the section between basement and lit floor. In the light of 11.10.2.1 ofIS: 800-1956. the steel section alone should be considered as carrying the entire load. Thestiffening effect of concrete could be recognized to adopt allowable stresses of 1 500klJ/cml in bending and 1 182 kg/eml axial compression as determined in Sheet 9.

~,Ioment share of basement column := 193X 0·6 == 115·8 cm-t

218·4x I 000 IIS·ax I 000Therefore. 195.16 X 1182 .f- 3660 X 1 500 == 0-97< 1 ..... OK.

49

III HANDBOOK POa navcrvllAL ENGlNUIlI: ·STEEL COLUMNS AND ITRUTI

Dalp fI6 ... Plat. - TIwr, is JID pan;- Desl... bamp'. , IInd• ......, ("..,., ;roNlH.1' • l«k of~) ill ..... ...~ 1M ftJUltllstiOll tmJ~n 'au lIS ditlttion Dell", of ... Plata ofJ!w. T1Iis is tIw 10 II"I.~ IMI 1M l/~ is smtUl and Spllc. at 5th Floor 14III tn!1 UUI .. th, pmrtusal, stress WlU not ""'''1.1 4«Ud b.1 th, VtJriGtitm in llr thllt would " -------------..intlutltl by tlumfin, th, lUISI/IDle .~Iy_ Rt/min, 10 1 .2 of IS : 800-1956 1M"pUlIl .'11is ohltlinldon the 'lUis of 5 kgl",t hemi,., pressw, em tlrt concrete and th, btu, pltlu lllicbwssatc",ditlglD 1M spedfittJti.aformuu, isfouruJ to he2-93ma_- - .. - - - - ~ - - - - - - - - - - - - - - ... -, - -- ... - ... - - - - - ...... - ... - ... '- ~ - - .-. -

o

'1

SECTI(H AA

~T WELDAU. ROUND

5.

(All dimensions in centimetres.)

f-45 ---.

1to--- 35 -----1---~

7-547·5 7

I

(SI, 1....2 of IS : 800(1956)It is asaumM that the load is being

jistribut~d uniformly by the slab bale.Assume that concrete can take a

bearing pressure of 55 kg/em':Load == 218·4 t (SII Sheet 9)

Area .. 21S·4x 1 000 KS 3970 emt55

The load is auumed as distributedby the column with an area of47·5x 35em. For maximum economy in thethickneu of the slab bale ',', the projec­tiona '.,4' and 'B' should be elluaJ .. maybe seen from the formula given under11.1.2 of IS : 800-1956.

For suchequal projectiODl, try 58 X70em witn 11·5 em and 11-4 em projec­tions giving an area of .. 060em l _

W EO 218':~000 _ 54kg/cml

/ 3 X54( 11-41)t == TBO 11.51

- . =2·93cm

Use ba e plate 58x 70x 3 em.SPLICE AT 5TH FLOOR

The splice is to be checked for twoconditions, namely:

a) for moment caused by eccen­tricity, and

b) for axial load.CHECK for .moment capacity of the

splice with details as shown in thesketch.

Assume 16 mm rivets in ~7 mm rivet holes at 630 kg/em' tension for power drivenfield rivet (SII Table IV of IS : 800-1956).

Taking puge as 45 mm for the 80 X 80 mm angle ISA 8080 used for connection, thedistance between the rivets on either aide ia2(4·5)+15-24 em.

. 2x630x2·27x24· •Moment capacity == 1 000 K2 68·6 em· t

190·1-175 &:3 15-1 em- t (Sheet 5) ••••• OK.

If-CTION In:. OOLUMMI IN MULTI-ITOUY BU1LDlNOI

..41 et.:,if llttt ."", in-- tIIpI1I is J:.,.II. • D"',n "amp'e t 12~ . JJ- "'4' H us. to trMSj., IIu 1tHul.nu if"" -....utrtJlld on Shu' 14. If I1wrI is 1-----------1 ofd ,.,,. dum,t ill ~, it will 6, mor, ICOIIDtftittJl of Deslln of Splice at .4s.1 Ie itaIrotJuu GIl nul tl6tail, suth as is mown on 5th 'Ioor$'-' 11. In IIW aldil, tI UMuud WF sMp, is builtiIIIo tJw top of 1M column. This is c"'c/udjtJrsuJ/i&ient s',mgU& in sMtutwl Hndu." III if~ .",d slttwt HtJIII, to"asj" d U1&iform distribution of stress in the column lulow 1M sl'lie.. 1M iJdIUl~ lIS shDum UJIU ftnWl ,. 6, inatUquaU in sMa,. W,b doubler plaus could H tWlMJ, hi iI UJiJ¥ln tIII4 mtW, IttmtnnittJl in th6 ""snal cas, 10 thepen 'hi "tun slCtitm so tU to~ ..",,,-, CIJ/NI&iI.1. AlllmdtiDl{". WId" sluJped t,ansition section could6, introduud.----~-------~----------------~-~-~--~-----~-~~--Check for axial load.

The axial load may be considered as being transmitted to the column section below bythe specified sections acting like a short beam.

The load iJ auumed to be distributed uniformly at the bearing.

Total axial load at the fifth floor splice to be transmitted as detailed in Sheet 2 is58 t.

The se~tiODl designed are ISHB 150, 34·6 kg above and ISHB 350, 67'4 kg below theaplice.

The ftanIe width == 150 mm or 15·0 emThe depth of web between flanges .. 150- 2 X 9 =- 132 mm or 13·2 em

The total1ensth ofdistribution ::II 15+15+13·2 -43·2 cm

t-14'lan-i

13'2' 13'2t

tilifut

f f f f f f I'---v-----'

U·St 15t n.l.

L, n"cm -..J

ra

L~--,=s 15 e

,. 25 em

- (35-2·52)

== 52·68em

!I~~i5 ... 1l.5tEach flange takes up

lporinc the difference in thickneta between the web and flange of column section itmay he .-oDed that the distribution of load is proportional to length and with thisaaumpdon each flange transmits:

~ -= 13·2t43·2

The load beins tranamitted through web =- 38-2 X 13,2==11-6 t

The 8aage width of the lowercolumn aecbOD ISHB 550, 67·4 kg

Web depth between flanges

Web takes up 38-2 X 11·5

The loading is mown diagrammatically.

Maximum .hear - 11·,5 + 15x9'9 16 t33·8 -AI .ketched (IeCtion AA, _ Sheet 13)

if11-'41, 14em, aheararea 12X 0·83· .. 9·96 em l

16f·-R X 1 OOO

- 1 610./cml >allowable ahear Itraa945 ./cm'-No Good.--~---------------------~------~-----~-~----~--~• w.......0111118 550,17-4.. - HS.

51

• 1IAND8OO& FOR STRUCTURAL I!KQINURI: STEEL COLUMNS .",SD ITRun

Dellp Ixample ,

Desl", of Splice at5th Floor

Therefore, " should be increased suitably to give more shear area.

16 ()()() 1~ X m = 20'4 em, S41, 22 em

22tiJI = 0:83 <85 .. · · . OK (SII 20.7.1 of IS : 800(1956)

11·5x!!·8 J5x33-8Moment at centre ::= 2 + 2 x 4-

13·2x14·1 Il'6x14-1- .2 2x4

=- 144·2em- t

The teetion shown in the sketch i. the one resisting the moment of 144·2 em' t.

SECTION I\A

lIb 33·8=-25

== say, 1-5

F. == 1 500 kg/em l

l.offtanges =- 2x25x(.y.)1

Z _ 2x25x21 x21 x2• 2 x2 x 22

a= 503 em'(even ignoring web modulu.)

I' 144·2X 1 000I. - 50S

13.f14

- 287 kcleml < 1 500 kB/cm' . _. _. OK•...-T-bb ;.; ;.;.;.d ;..- If;.; ba..-- i'1~ - - - - - - - - - - - - - - - - - - - - - - - - - -

52

SECTION III: COLt;~NS IN MULTI-STOUY BUILDINOI

14.,14

Dellp 01 Spliceat Jrd 'Ioor

Del.... "amp'e'HeT' is. sIunDn " /JOssiIJle tlItlJil al IhI llairll JI«w$/Jlia """,. IItt r,huit" c"'" in column siu is null .... ..mough to /JIrIftil lUI of II simtJu b,ann, pIG" 10"tlllSfn 1M l«uJ, .4 similar spIkl will bl r'qui"dtil IN firstJlotW, Tlat bearing plote is dlsi""d as asimp" beam with all of the column loadconsnvatit'lly -------------...- ....utimtJIMI tIS being in th, column flanges. The colll1lUl bas, piau dlldil is shDum III ,....... ..prnriDlul.1t11siped at Sh8et J1. Only two tJtI£luw boltson tJu axis of 1M Wlb.,,.~.. 1Mcol.",.,. htu ., bien assumed to be dir,ction fix,d al 1M 1Hu.. ActluJU.1, ofetlWU, II~amtIIIItl ..,tlmctionfixity will bepresent~ ,specially in viIw ofIJIe conal" III&tJUmmI.

/Hs;'" ofSrd FlooT Splice

a, a.k for tuuu. load

Referrins to Sheet 5,the column load at3rd floor 92'57 t

Each ftaRKe, neglect­ing the lOad taken

92,57by web, tau, -2- = 46·29 t

:\Iomrnt =.-: 46·29:: 5 231· j

cmv t

: =V231300;.:6 - 5'35cm1 890 X 25 -

;from the usual flexure formula)

htS

.\1 == jZ=!T

BASEPlATE

Bearing valueAaunling l-cm thick splice plate:

b, CMdcfo!, tlte """Mlt

The moment at the 3rd floor in column 3-4 138-92'545·5 an- t

(su Sheet 8)

The rivets along the ftanges shown in the sketch should be designed for a momentcapacity of this 4~':l em- t

.-\lsuming 16 rnm power driven field rivet: Shear value == 2·27 X 945 kg= 2 140kg

l'7x2 125- kg= 3612 kg

SIwJ, l'allM controls

Two rivets on each side with lever arm of 4.1 em have a capacity of 2·14 X 45 X 2­193 em- t>45·j em' t ••.•• OK.

No further extra rivets required for packing.____ .. .-..-- .. - __ ... .-._ ... ~_ ........ ..,4a> ..... __

• S. lI.I oJ IS : 8OO.19~.

53

SECTION IV

MILL BUILDING COLUMN WITH CRANE GANTRY

II. 1NT1l0DUCTION

10.1 The stepped mill building column with crane cantry is an importantdesign probfein that combines a variety of important design quationa.The column is of non-uniform cross-section, it is a cbeam-eolumn' withboth eccentric and lateral loads introduced along its length, and it involvesa multiplicity of effective length questions. For the aDlWerI to matten ofeffective length, one is guided by Appendix G of IS : 800-1956. Thecolumn to be designed herein will be similar to that shown in Fig. 14 inAppendix G of IS : 800-1956.

10.2 There is a current practice of designing the column directly underthe crane girder independently of the column that supports the bull~.

There have been argument» and dUCUllions over this question and it 11

pointed out that the assumption ofseparate action requires special provisionsto attain it. It is recommended that the entire unit should be designed forintqral action. The column section in Design Example 10 is designed withthiI approach in this Handbook.

11. ITBPPBD MILL IItJILDING COLUMN WITH CRANE GANT!lY(_ .......pIe 10)

11.1 It hu to be undentood that the example for the crane pntry columnhal been designed with the assumption that the top of the column is fixedin poIition but Dot in direction. Therefore, this method or design.illustra­ted here may be followed only when these conditions are satisfied throughsuitable and adequate bracinp at the level of the top of the column. Otherexample. of columna where such conditions are not aatUfied will be dealtwith m lSI Handbook for Structural Engineen on Single-Storey Industrialand Mill Type Buildings in Steel (under preparation). Reference should,therdOre, be made to this Handbook for details and tuner discUllion of theproblem.

11.2 In com~n with a design based on completely separate actionof crane and bu~ column components, the consideration of the entirecolumn as a single umt with eccentric and lateralloada will result in heavierde.ign above the crane gantry and ~bly somewhat ~~~r design below.A certain amount of rigidi~ is desirable m a mill buildi because of theundesirable sway and vibration that may be induce:,~l the operation of thetravelling bridge crane. It is learnt that some • buildings in use inUSA have had to undergo extensive revisions with coady additions of steelbecause they were too flexible with regard to side away in the upper columnIqpnentl above the crane runway girder.

S&CTION IV: MILL BUILDING COLUMN WITH CILAN& GANTIlY

XI

II

Ix,

-85

A =- 80·25 eml

'.1 Ell 5·29 em

T . If; -~ 40 x 10'na .'. 80.25

I' . 9 X 100>: 1()IJ. ~ 863.3

For .\lax 1/, == './"F, = I OOS kg/eml

!.-! 6·75 X 100::;: 53

"1 12·7 Vt-j/"1 4·5 x 100~ 85

'.1 5·29

(This is maximum slender­n~ rario.)

Try ISHB 300, 63-0 kgZ.l ;::; 863·3 em','.1 = 12·7 em,.

0.•• Esarraple lo-S,~I'''' Mill BuiId'-l CoIuMB .ida er.... GaaryCNu-.1iInuJl ,lIvatiota til OM ofIIw &OlumIu WIuJs 1M,.,.• .,..,...,1INl......". TIM

m;U hiUift,,MIls at, tlSsumMllo hi 9 m ,Ie _ n.:.1Mt:06mm siu is 110I a.m III t iI iI~ 10,,, SfJmI /W,limitulty ,stinuzU M 10bnulitw .- _ ....momIIIts in ordn 10 G/JIWOtJ&Ia IM.fintJI tlui"a I1artnIIh "-I Ix ...0II miu of"i4ls. 1M lmwalloddis s/J«flild tU 10 .,.. II' ampJlnMll oj tJy crtltll f'UIUD41 "atiUm of 80,-tlIUllIris is oflIPJ»rlioMd Mlf to '(Jeh column. This slIM, SMwS Tria' Dell... .f Top 12",. ,.,h initial 'gUlss' tJS to R~ ktldiltt 10 an S..meatinitUJl tJ./JIWoximlJtwn of binding mommI in 1M to/Jcolumll sigmenl AS for which 1M actutJIIOdd is 1M utld Wlighl oj'" rJNIf lrws SYIUm JHw supmm-pos,d lotul, all Istimatldat 40 I. ,-

-----------~--------~----------------~---------SUH-d Mill Buildi", CDlumn with C,aM Gantry

For effective lengths, su Fig. 14 of Appendix G of IS: 800-1956Column se"""., A 10BTo makespreliminary selection, estimate bending momentl:

Estimate RA =- 1/2x4 :=r 2 tTrial M.~ = 2 X 4·5 :IS 9 m· t

Effective length considering XI·~ axil =- 1 5 L=- 1·5x4·5=- &·75 m (I.)

Effective length considering Y1-VI axis - 1-0 LZI: 4·~ m ('••)

55

lSI HANDBOOK FOR. STR.t,;CTt~JlAL ENGlSf.ERS: STEEL COLU)lNS A,.D STRLIS

2of12

Desl... Example .0

2nd Tria' Desl... ofTop Seament

__________________________ '------------....--4

TIw riJl ••tUm is ,Mck.d for its tMlIqu«y. Itis / ... ,.., IhI .lItlion is slightly rmtIn-dui".,d .... .....tIIUl siItu 1M 1IIMIWIIts df' only known ID a 'OUIhMgr. ¢ tl/JProxinultion, 1M trial of the noa MaL'in'16HB IS SUUU"d.

For determining maximum allowable bending stress for bending of the column aboutXl-Xli 111/6 is to be considered as the Beam-Column section is likely to buckle laterallyabout '11-y 1-

lIb430

-25

= 18

498 1 0401 003 + 1m = 0·495 +0·66

:a:: 1·133> 1 - Xo Good(se, 9.5 of IS : 000-1956)

~Ioment due to eccentricity has been neglected.

Improve trial section for .ABby adding trial eccentric moment.

Try ISHB 350, 72-4 kg.

56

SF,CTION IV: MILL Bl:ILDISG COLt:~~ ",°ITH CR.\~E G.-\~TRV

Jof12

Tllal DeliII' ofBottom S.,..,.nt

D.",n Example '071w first Irisl s,lIcticm for 'hi lown Jltnt of the(01.... U sltown ;11 cross-section and lhe RIOmnJt of ... ....Wrtu. &/Iblautl alJout A-A axis° On th« basisof 1M IrUJl _'ion, it is fJossiblt 10estimat« tht eccentricmtmIIJIt tINl this is dmtI initially as if tht top tJndhottom tJt .A tWJ C were pinned. This is still only a 1 ..-6__.-

roIllJa tl/'JWoximation of 1M actual moments which aft later dttn-m;Md by the moment distributiollJmK'tIvr, till SllMI 7.

approximation

= 80+40= 120 t= 650 kg/em'

120x 10'= li50= 185 em' (ignoring

eccentricity)Try 2-ISWB 450, 79·4 kg

A = 2xlOI015=202-3cml

Try the arrangement. as shown in thesketch M-M.Trial Utlw" u.u.Calculate lAd

I A A

Preliminaryas pinned

Ji

•'·IZc"'----..IA

= '2)( 1 106·7+ 101-15 (32-96)1 X 2

== 3413·4+220000M .20-35",-\ = 223 413 em t

!r1•• = 2 X 35 057-4-

AI ~C = 70 105em·~4-5", -l .12",~ Applied eccentric

14 80,. t moment = 80 x 32·96-40 X 15

~- - =2035cm-t

assuming 'C'I

/ I IL -S•• 410 -- "eOOaft~'2.1Ic"'--.4

A

SECTION MM

_-..~ ..... -

r......... ---'

, \15HI no

I _.

~I

2035R~ = 16-5x 101 :::I 1·23 t

2035x4·5= 16·Sx 100 = 5·55 m- t (This distribution is approxi­

mate assuming that theSection from ... to C isunifonn.)

r~ = 995 kg/em'

lIb - ~~ = 18F. = 1 57.1 kg/em'

40x 10'J. ~ -mr = 434 kl/cm l

kl -- 2 035 X 12 ._ 14.80 m· tlie - 16.5 X 100

Check revised selection suggested in Sheet 1 for AB for resisting these approximatemoments also,

18HB 350, 72·4 kg... = 92·21 em'r~ = 14·65 em'. - 5·22 emZ~ z:s 1 13106 enl'

J\la 1/, r:.; 1;'. = 450 = 86s:22

57

III HANllBOOX PO. ITRUCfURAL ENQINURI: STEEL COLUMNS AND STaUTI

..of12

Dell... Example IITIw iItiIitJl trial *sitn witJa ISHB 350, 72·4 leiis./otlU 100 SlMIl ami in 1M S'Ctm4 trial ISWB 500, 1------------195:2 i, J«t~ (IT' KUd. . This is found ~ IN Trial Dell", ofSlI&!t¥ItIry,. sl.ll 011 thI ~aslS of W!J ~ppr(J~ Bottom S••ment",.,.,., ,sllnuJlu, the s"hon propntr.es In thl mainII,...' Be au tUlmnined. 0" this jh~1I also,/qr1-----------...- .....I/wJrst IitM, IA6 tUtditional dirtct/0(" due to diad w,i,ht ofwalls, gi,ts, siding tmtl colunut is,slituIItJ tUUl tultkd 10 the axial load.

±19 m· t± 5m·t

19·23 m· t24·23 m· t

= 334600an'=- 70115 em'

775 kg/em l

331 kg/em-

i

f.

A

c

.-I...._a:IIJI......~...._~-_...-\I- •

2.

Total M.A = 9·0· +5·55t14·55 m· t14·55 X loa

1 131·6I 287 kg/em'

434 1 287995 + T575 = 0·437 +0·817

= 1·254> I-No Good.Try ISWB 500, 95·2 kg

A .= 121·22 em'Z. = 2091·6 em', '. = 4·96 em

450MtIJt Ilr === 4796 = 91

~~~~--~-~---_·_~-~~~=9~~~m~~ =2~77~

lib = 450 ~1825

F. = 1 575 kg/em I

AIIUIDinr revised· section M-M as in the sketch.Applied eccentric moment is 80 X 40·46- 40 X 15= 2 637 em· t

5·5Approximate moment to.AS -= 2637 x 2"015 = 714 em· t ($II Sbttt 3)

40 X IQI121·222(900+ 714) X 10'

2091·6331 775958 +1m = 0·346+0·49 0·84< I ..... OK.

4 t Use ISWB 500, 95·2 kg for section AB .•_ Cluck stress in Be (see Shu' J)

IT Due to 4 tonnes lateral load.. ( Approx moment at C= ± (2 X 16-5-4x 13)

Approx moment at B=±(2x4'5-4x 1)Approximate moment

at B due to vertieal1oad=26·37-7·14Total Mu moment at B

IAA = 2 X 1 706·7 +2 X 101·15 X 4{)-461J.. = 2 X 35 057·4Estimate additional dead weight:

at middle of se~ent BC-assume column spacing of8·5 m girts+slding @ 25 kJr/ml=0·025xS·Sx 10·5 =- 2·24 tcolumn AB @ 95-2 kg/m=O 0952 X 5 := 0-476 tcolumn Be @ 200 kg/m (say) =0·200 X 6 ::a~

Total :a: 4·0 t

- ; i.-~ 1.- i s-"s';;';; i.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

58

SECTION IV: MILL BtnLDINO COLUMN WITH CRANE GANTRY

5ef12

D••lln Exampl. .1

Trial Deslln ofBottom S••ment

Qmliluting IN antIl.1sis on Shell 4, il is found thai1M 1IUJUa sedUm now a/J/JIars ovtr-tksign6d muJ tJ 1------------....-1sm4lllr s,ction is trietl. The CtJlfUlations ar, are/JItilion of tJupr,vUnu slwet and the smaller sectionis found to bl salis/tutory.--------------------------1----------_.......- ..

~ ---- 10·86cm ----~A----- -----r-------....-

40+80+4 _ If. --- 202.3 x l()l ~615 kg/cm

I' -- 2423x50'46 l fU 364 k I' 1863J. -- 334 600 x v- ~ g em Jr•• -= . ern

Effective 1/, -- 0.8~;'~3200 =55 (see Fig. 14 in Appendix G of IS: 800-1956)

F. -- I 159 kg/em'} r IS· 00-1956F. = 1 500 kg/em' rom . li .

16:~9 + 13~ = 0·529+0·243=0·772 <I-·ovrr design

Try smaller sections 2-ISLB 450, 65·3 kgCheck width/thickness ratio of web (set 18.4.2 of IS: 800-1956)

d-2i, = 450-2 X 13·4­= 423·2 mm

t. = 8·6 mm423·2

I d/t. = s:6 = 49>45

I :. Effective width ~ 45 t..-: 38·7 cm

8-&---- - -- + ---- -----It- 8 Width reduction = 423-387

I = 36 mmArea reduction -- 3·6 X 0·86

-- 3·09 em'

r•• = 18·20 em, Effective Ilr

LEffective area

-~- - - - - - - --- - --'=-=-:"'---1 of section --" 83·14-3·09""3cm .. - 80·05 em'

A Total :== 2xRO·05=160·)cml

I AA = 2 X 853+2 x 83·14· x 40'43' = 273 500 em'I •• :::= 2x27 536 = 55072 em'

0·85 X I 20018-20

=56F. = 1 156 kg/em'F. = 1 500 kg/em'

- 775 kg/em'f. =124x 10'

160·12423x48·93

I' = X 10' ~ 435 kg/em'J' 273500

l''l~ + 14:& = 0·67+0·29 = 0·96<1 •...• OK.

Now make accurate check on moments Uling moment distribution method consic:lerial.AB-BC U tepU'ate members,--------~-~~---------------~~------~---~~~-----~• FuJI... III calCUlatiOD orteetion properti-.

59

IS( HASOBOOK FOR STReCn·R.-\L £~GlNE.ERS: STEEL COLUM:'IlS .-\SO STRl'TS

6of12

Ana'ys.1 of Forc••and Moments

D_lln Examp'e 10..4 sMisf«1lwy tksitn Juu,;", bem IIIT;wtl ., on thehtuis ef tJ/J/n'Dximatt moments, Ilteu moments art tttIUI 1--------------1calcultultl mM't tJeactly. The Hardy Cross ..V,tMtJf!f moment tliJtrib"tion is wed. It is tltsired 1odelmnine the bending moments in lhe column for anarbilrtW.1 momenl introduced at B,. also,for an arbitrary 1-----------------.lateralfore, introduced at B. By keeping these separate it will be possible /0 handle combinationsof loaJ mor« readi{y. In tht initial analysislor moment introduced at B, an artificial imaginaryrestraint is prot'ided to hold B against ialttal movement. On the basis of the resulting momentscaused by an equal and opposite restraining force and superposing it on the initial solution, the tfftctof restrain: is removed and the desired solution is obtained. The analysis for lateralforce at B isstarud by assuming a displacement at B with no rotation. Rotation is IMn permitted and qfttrdistribution ofmoments, theforce consistent with thes« moments is determined. Then, by proportion,tIuJ mommts!ar unitforce at B may heevaluated. Finally, there aresummarizedthe bending momentsdUl to a unit laera! force at B and due to a hundred units of moment at B. .Vow, reft";ng hackto Shut 4, 1Mactual moments caused by the eccentric moment and lateralforce art tz'alUdted and tItecomhiNd maximum moment is given at the bottom of the next sheet.------------------------------------------------Analysis for eccentric load-Apply unbalanced

(-) moment of 100 m- t at B

II.'" 52 290 cm~8 ,- 273 500 c",il. ~

I \L.-A.TI'tCIA\ AnUAINT

J---4·5"'~ 12m ---

~­==-:..tDistribution factors at B:

= 0·27687

•.•.. (ii)C,

::3 87+228

= 0·724

} ..... (iii)

For AB

ForBC

== 0·775 E~

StifFness of AB} 3 52 290(one end be- ::.:: --;rx-- ::::: 87ing hinged) 450

Be:c: 273 500 = 2281200

Assuming restraint at B, a total applied moment of -100 m- t is distributed as

M aA = -27,6 m· t }Mile = -72·4 m· t ..... ~i)

and Mea = -36,2 m· t

~= 6·2 t ~ t4·572'4+36·2

Shear in BC= 12 = 9'1 t ~ t

Applied restraint -= 9'1-6,2 - 2-9 t ! at B

AI~__""'''

Aft4lysis Itw tlisplactment witla 110 rot4tiDn:3 E16 3 X 52 290£.6-

M." -~ == 450'

M.o - ~ - 6x27! 700ED, = 1.140 EA,-. 1 200' u

Shear in AB=

60

DCTIOH IV: MILL aUlLDtNO COLUMN WITH CRAIU OANTIlY

,of12

Desl... Example .1

Ana'ysll of Forcesand Momenta

1HMl .. VGlws .,,.,..,. (iii) in SllMI 6, "latilm­

s,. ....... ru"aiIaiIII/or" til B tJNI thI fMrMlU 1------------11iIt JItWIitms BA, Be _ CB "'9 " worked out 4S

,u. ill tAu ",.- - - - - - - - ------ - -- - - -- - - - - - ..._----~----_ ...-....

B

I 00276 0·724 I c

Fised eDd...ts (FEM)DittributiouCanoy onr

FilIal momeaII

-77·5 +114-10-1 - 26·4

-87·6 V U +87-6

+114

- IS·2

+ 100·8

MameDt cUllribudoalor I wait or force at B t

Shear 87"' Shear87·6+ 1OG-8

- 4=5~ t t~

--l~

- Ig.S, - 15·7 t

87-6 +87.-6 +1000819-5+15.7 - -2o~ ~ 1i=J+'in

-2·' -+2·' - +2·87

••••••• •••Ci.)

... OIl th1I..wt, the reladODlhip~ the applied moment at B and ftfta.I distributed ......... dueto daeapplied moment without any artificial ratraJot at B for lateral movement may be worked out.

AppliC'd moment - 100m· t

B c

+27·9

+36-2

-8·S

+27·6 +72·4

+7·2 - 7·2

+34·8 +65·2

a) Diltn1Ndoa with I'aU'aiDt at 1J (­Sheet 6)

b) Por releulnl the rattalat or 2·9 t ~<_ Sheet 6) (rom the relation (iv)1--------_··--.. - -I ----- --- 1

Fioal dlatributioD for 100 units ofIDCIIIIeDt at B

••••••• 0 •• (v)

From thae ...... the &naIdiltributioo 01momenta in the problem under desiln here could be warkeclout.

AppIiecllOAdJ are:.) lateral load 01 ±4 t at B (_ Sheet 4)b) momeat 01 ±41t1·cat Bc) 1D00000t due to ecceDuicity - -26·4 m· t (J" Sheet 4)

B cF 01' :i:4 t lateral load at BFor :t4 IDe tat BPCA -26-4 .0 t (due to eccentricity)

-;:10•=F 1·4+ 9·2

± 10 (from iv)=f 2·6 (from v)+ J7·2 (from v)

± 11-48=f 1·12+ 7·1

Maximum c:ombiDcd IDOIDeDt +20·6 +24·6

t Shear -24·6+ 17·~

12- s·s,

61

III HMiDBOOK Foa STIlUCTtJaAL ENOlNUIlS: ITUL COLUMNI AND STRUTS

•D_lln Example 10

- 985 Ita/em'

T1t6 situs eonJitwn in 1M U/JIJIr SI~ All and'M ,.", Sl,.,.' Be is cht~ketl andftnlllll to h, jwt 1------------1,GliJf«llJry. of

1M tUsip of the conntetion to 'rans/" t1aI vertical Flna' D••lln of Column 12lotul from AS to Be lind 10simultaneowly tab care of1MbnuJi,., mommt at tlu j_net"" POUtt is now inoesti- ,..-----------...--..,aud. As a startingpoint, thl vertical lOdd of41·5 t is trans/erre.withDut comidnation of bendingmtn'1Imt withtM addition of the ISLB 300, 37·7 leg to act as a diaphragm and to provide a relUtion10 1Mcolumn uetion directly undn the "'ant rtmWl!)' girder. Horizontal diaphragms are introdutedal/JOsilions marked(4) inthefigureandthemoment capacity of these is checked. Sine, tJaI diaphragms41' mM, or less jlexible in tile vertical dir"tion, these rivets are assumed to carry on?>, tJ hori~01ItclcomJNmml of load. The moment capadly of thes« diaphragms is insufficient anti tulditional rivlts., aJiUJ altml linl B-B to provide extra momen! capacity as calculated in Sheet 9. TM "PlLstil.", plaM B-B are assumed to be ,ood for vertical component of stress on(,. Sinu 1Mmommt ann 01 the rivets in th« horizontalplaneand those in thevertical planesar«aboutequsl 'MyM' 4SSlllUtl til shar« tqualfy Ptr rivet in tlalload.--~--------------~-----------------------~-----~Il.wlll~ S"UI

Upper leI'DleDt AB-IS\\"B .300, 95·2 Itl,., 20-6 X loaJa 2091-6

.331 985958+ n75 - 0·972< I • • • • • OK.

Lower IelD'Cftt BC--2 ISLB 450, 65·3 q (1ft Sheet 5)r. 24·6 x 103 X 48'9! 4K.3 k / •J. - 273 700 - J a em

1~~ + I :~: - 0'961<1 ••••• OK.

U. l-lSLB 450, 65·3 k,.~ ".. AB 10BC-Fusl MUitln " ••/. -t",," J.a MI.1.

Load OIl AB-40+0'96 (waU)+a.476 (1eIlwt)-41·5 t ('9)RaetioD .. the two IILB 450, M·' q lItCtiou (00 linea B-B and A.A) would be balC the total vertical

bel if the colUIIID All were I)'IIIIDetrical iii pIue with napect to the columa Be.

UHf OF ACTIONOF V!RTlCAl l~O

-l)()()"""--t-----......-

.......---- '1Om",--

~:":~a ·_··lEND T,! 'LAT£

Thia beiDa not the cue C- the diqram­mat1cal spUce)

THiae momentl OIl lIDe ,A-,A:

550lleactioD at B-B - 100 x41·S-28·5 t

ReactiOD at .4-A - 41·5-28·5-IS t

The sheat' at C-Cfor which the joint betweeD~ or ISLB 300. 57·7 k~ and ISWB 500,95·2 kl isJ lubjected to is abo - 13 t

r" 20 mm rivet on web of'ISLB 450, 65,' kl

Val\ae 10 beariDI - 2·1 x 2·360 x()o86- 4'27"

Value in tinlle _~ x 1'025aMar 4-

- '·55 t

:. Value or qle ahear CODtrollat B-B:

-I' • _.!--I 28·S 8• DlAPHltAnM. No. VI nvetl reqUIRU - --s:g--

u....... riv.at B-B~ 8aqe oIlSWB SOO, 95·2q to web ollSLB 450, 65·Sq.- - - - - - .. -. .., - - - - _-_ - - - - - - - - - - - - - __ - - - - - - - - ell .. ~ _

.... f. t .... s,

62

5ECJ10N IV : MILL BUILDING COLUMN WITH CRANE GANTRY

Dulin Example .1 ,

ofD••I,n of Splice 12

At A-A tmde-c

No. of rivets required ~ = 3·673·55

Use six 20-mm rivets at A-A and C-C, connecting flange of ISLB 300, 37·7 kg to webof ISLB 450, 65·3 kg and the other flange of ISLB 300, 37·7 kg to the flange of ISWB500, 95·2 kg respectively,

Transfer of Bending Moment

Although rivets considered in the last sheet at A-A and B-B provide some momentresistance, check moment capacity at diaphragms 4-4 only.

~l

Value in single shearof 5-16 rom rivets 1J' X 1.7'on each side --4- X 1·025

2·32 t

Non - Maximum moment adds to Itr'eII in liDeB-B.

Increase the number of rivets of 20 mmdiameter connecting flange of ISWB500, 95·2 kg and web of ISLB 450,65·3 kg in the vertical plane to 11.

II - 8 3 rivets good forvertical strell only

2 460 cm·t(III Sheet 7)

604 cm· t

SOcm

3 x80x 3·55

854>604 em· t.•...OK.

Moment tobe resisted

10 rivets carry10 X 2·32 23·2 t;

Lever arm 80 cm

Rivets good for horizontal stress only.

Moment capacity of diaphragms (4)(through the ten rivets)

23·2 x80= 1856 em· t

Balance

Lever arm sameas for diaphragm!

Moment

BOcm

I.II·I.I

I· •I. •

I. •

•

63

lSI HANDBOOK .·OR STRCCTURAL ENGISEERS: STEEL COLUMNS .-\NO STRUTS

"of12

De.l... Example .1Dftlp of Lacln, In

Bottom S..ment

n. ,..., 6t1ts fo, lJu layout shown 011 Shill 9 a"dt«W hIA lIS lomprlUUI, struts tmtIlmsitln mmabns. 1-----------...TIw tIiInntel httween this tmtl 1M /Jr1Vious lacingtIuip UtIIft/M IltUkr centric ltNUl (DIS;,,. Exampl,7)is • tJtIJitiotud SMa,. i,IIJw,d by 1M l4lwal lOdd and~ oJ wrti,;al load tluat is added 10 tl¥ .-----------....--..2'5 Jlnmd ofaxial load.~~---~----~-----------~-------~---------~-._~--~DIs;'" ofLating

Try 45 0 layout as shown in Sheet 9

Check local ...!-_; r of ISLB 450, 65·3 kg =. 3·2 em = '1-1'1'·1

I - 110 em

..!J.... 110_'1-1 = 3·2

3.j<O·7x56 (of main member) ..... OK.

35<50 ..... OK (s« 21.6 of IS : 800-1956)

F.Capacity of 2 angles

Sh,ll'Load due to applied moment = 3·5 t (s,t Sheet 7)

2·5 percent of axial load = 0·025 X 125 = 3·12 t (see 21.2.1 of IS : 800-1956j-Total = 6·62 t

Force ia1 the lacing = 6·62 x Vf =-= 9· 36 t

TV' IS.&. 10073, 6'0 mm with two rivets at each end.

A = ]0·15 ems

rmin = 1·59 em

Eff~ct:\e length = 80x V2 = 113 ern (jee 21.23 OL

IS : 800-1956)

113Ilr -- T59 = 71 < 145..... OK (se,21.2.3

of IS : 800-1956)

= 1 090 kg/em' (Table I of IS : 800-1956,

= 2>< 1·090~: 10-14 -- 22-1 t >9·36 ..... OK,but over design

Try ISA 7045, 5·0 mmA = 5·32 ern!

'min ~ 0·96 em

1/, _. 113 118< 145 ..... O}{.0:96=Capacity of 2 angle sections = 2 X 0,726;,5,52 = 8·05 t<9·64 t-~o Good.

c» ISA 7045, 6·0 mmA = 6·56 em', ..\pprox capacity as before = 0·726 X 2 X 6·56

= 9'5 t •••••OK.'min = 0·96 em

~,Uaerour 20-mm rivets value = 4x3·55· = 14-2 t>9·36 t ••••• OK.

• s. Sheet 8.

64

S~CTIUN IV: MILL IU.;ILUINO COLl:~'~ WITH (.;RANE GANTRY

IIof11

Design Example 10

Desisn of Tie Plate

1S : 800- J956 calls JOT end tie plaits OJl cotipres­slon members equal in length to the lateral breadtheleof riiet groups attaching the tie to the main com- 1--------------1ponents. 'Tilt layout shown at the centre of the sheetindicates the minimum length of the tie plates andmay be made larger depending on how the lacing 1--------------1----1spacing works out in thefinal details. Four 25-mm diameter anchor boit: are sho.un and Ihty engagea channel that is riveted to the end tie plates. It is well to hate some f.Wt'.\J of riveting in a detailof this khul so as to tie the end of the column into a single unit. 'The tit: IJlate is first checked forits adequacy in transmitting the shear since it [unctions to take the plaa of a lacing bar ill the endsegment. 'flu riret group is found to be more than adequate. 'The anchorage bars are assumedto be pretensioned 1o theirfull permissible stressoj I 260 kg/c1Il'J which is df.\irahle to ensure adequaterotational rigidity. In order to check the moment capacity, it is assumed that a rectangulnr stressblock is deieloped similar to ichat would be expected at ulumate load but here shoun at the allowableuorking bearing pressure on a concrete pier of 55 kg/on'!.. 'Jaking 1I10111(,.'l/) about the centre of thebearing plate, it is found thai the moment caparitv is more than double tlie actual cpplied moment.(It is obcious that the morecontentional assumption of triangular block ofpiessure would also providesatisfactory resistance.i The additional safety with respect to moment is desirable and shouldprot.ideadequate end fixity in accordance with design assumptions, The details fOT checking the thicknessof bearing plate shown as 3 em are also gil-en. There is approximately a JO-Oll oterhang beyondthe web ofthe main wide flange column members and this plate will distribute the load ill ItJS thanthepermissible I 890 kg/cml stress/or bendingin the bearingplate.

'fie Plate

q en,·

.~ 10 em

132·4ern- t

*6'62 t-'2,-

(j'61-l-t

,\.:: t)-

400Ul

7292 Ul.i

:3 969

7 204132,47 204 :·.3j·5

- O·jH l<3·5j tshear, .... (H~.

d~

Ih l19 j2

l ll!J 4'5'!.~ @ 13·:)% _.,~ @, 22·:)2.! (i1:: :I1. ~) 1

~lonlenl

~ 1'655:~ HO

Shear i)cr tit' plate

Shear per groupIll' rivets

Try sixteen 2U-111111 rivets:

..\vcragr vertical spacingHorizontal spacing

STIFFENER

CG Of THE: RIVETED GROUP

tOOcm

lOem

ANCHOR BOLTS --r;

toem

No need to compute R". Rivets UJ1d( ...~, n'~~c:d ill shear but needed to transfer load tobase plate.

* s., Sheet 10.

65

,12of12

100cm

Deal... "amp'e 10

Desl,n of "'rln.Plate and Anchora••

DIs;". 0/B,a"", PiauAssuming uniform load distribution:T~ 100 X 70 em bearing plate.

Bearing pressure on concrete :::s 55 kg/cm I

t I:: v'~(At _~)F. 4

(Sill 1....2 orIS : 800-1956) rr••

t =: ,y3X55 (101-0.) = 3 em 70cml1 890

elM", A.ru:/wragt I l'==========::::!l:::=:dllTry 25-mm anchor bolts. L

Net area = O'7'x~4

= 3·43, em' (assuming netarea = O'7 gross area)

Assuming bearing on concrete baseas 5~ kglcm I on rectangular stress blockof WIdth. say, a:

2xS'6t + 12:> ~. 70~~XIJ

a 37 cm

Applied moment 17·5 m·t (su Sheet 7)

Moment capacity 142.6 (JOO-37)2

4 500 cm·t> 1 750.....OK.

With the conventional triangular distribution

70 x.55 X a2'< 8·6+ 125 ~ 2XTooo

a ;,.: 74 em

Moment capacity 142·6 (25)

3565 cm·t> 1 750 em·t.....OK.

125 t

~-~~~--~------~~---~~----~----------~~~---~--~~-" It it conservative to assume B-O (s" sketch).t AIIume anchor bol~ prctensioned to 1 260 Ita/em' :

2)( 1·260)( ',43-8·6 t

66

SECTION VCONCLUDING REMARKS CONCERNING

COLUMN DESIGN

12. EFFICIENCY OF COMPRESSION MEMBERS

12.1 The design examples presented in this chapter have shown that forheavy loads and/or short lengths the centrally loaded column providesan effective stress carrying member. Because of the lesser stress that ispermitted, the column is usually not quite as efficient as the tension member,except in cases where large deductions must be made for net section of rivetor bolt holes.

12.2 When small loads are to be carried over long distances, such as is thecase in secondary bracing, the column becomes an inefficient memberbecause of the very low stress that is permitted. When the permittedcolumn stress for the minimum practicable llr falls below 600 kg/cml , it isprobable that the use of cross bracing, designed to carry the load in tensiononly, may be more economical than the use of a single diagonal that shallcarry the load either in tension or compression. Thus column action iseliminated. There are many illustrations to be found in actual structuresof such use of cross bracing. One such example is shown in Fig. 2 wherelight cross bracing is used for end wind load and crane braking, both in theplane of the roof and plane of the walls.

Figure 2 also shows crane runway girders carried by welded bracketsatta~hed to tapered columns ~ an alternate to stepped columns used in theprevious Design Example 10. The use of such brackets may introducemore of a fatigue problem and will also cause greater eccentric momentthan the use of the stepped columns,

67

• HANDBOOK 'OR STRUCTURAL ItNOIHEEItJ: STF.EL. COLUMN! :'NO STRl""

68

SECTION V : CONCLUDING REMAkKS CONCERNING COLUMN DESIOi~

TABLE I ALLOWABLE AVERAGE STRESSES FOR AXIAL COMPRESSION

(Clause 2.2)

lfr Fo l/r Jr.rr: .A ,.,

kK/eml tons/in.' kg/em! ton~/in.'(I) (2) (3) (I) (2) (3)

I 1233 7·83 45 I 187 7·542 I 233 7·83 46 11M 7·523 1233 7·83 47 I 18:1 7·514 1 232 7·82 48 1180 7·49

:J 1232 7·82 49 1 178 7·486 1232 7·82 50 I 175 7·467 1232 7·82 51 I 172 7·44-8 1232 7·82 52 1 169 7·42

9 1232 7-82 53 I 165 7·4010 1232 7·82 54 1 162 7·3811 1230 ;,81 55 1 159 7·3612 1230 7·81 56 1 156 7·34

13 1230 7·81 57 1 153 7·3214- 1 228 7-80 58 I 150 7-3015 1228 7·80 59 1 145 7-2716 1228 7-80 60 1140 7-24

17 1 '227 7·79 61 I 137 7-2218 1 227 7-79 62 I 134 7-2019 1225 7·78 63 I 129 7·1720 1 225 7·78 64 1 124 7·14-

21 I 224 7-77 65 I 120 7-1122 1224 l-77 66 1 115 7-0823 1 222 7·76 67 1 110 7·0524- 1221 7·75 68 I lOb "-02

25 1221 7·75 69 1101 6·9926 1219 7·74 70 1096 6-9627 1 217 7·73 71 I 090 6·9228 1217 7·73 72 1085 6·89

29 12J6 7·72 73 1079 6·8530 1214 7·71 74 1072 6-8131 1 213 7-70 75 1 068 6·7832 1211 7-69 76 1061 6·74

33 1210 7-68 77 1 055 6·7034 1208 7·67 78 1050 6·6735 1206 7-66 79 1044 6-6336 1205 7·65 80 1038 6·59

37 1203 7·64 81 1032 6·5538 1202 7-63 82 I 025 6·5139 1200 7·62 83 1 017 6·4640 1 198 7·61 84- 1009 6·41

41 I 195 7·59 85 1003 6·3742 1 194- 7·58 86 996 6-3243 1 192 7·57 87 989 6·2844 1 189 7·55 88 981 6·23

(COfIIiItwd )

69

III IlAJlfDBOOX FOR ITaUaruRAL ItNOINUU: IftEL COLUMNS AND ITJltrl'l

TABLE I ALLOWABLE AVERAGE 8TRESIES POR AXIAL COMPRESSION-Cmttcl

1/, F. 1/, F.A A

kg/emlto(~;n.• kg/eml tonl/in.-

(1) (2) (1 ) (2) (3)89 973 6·ui 135 592 ',7690 965 6·13 136 586 3·7291 958 6·08 137 578 3·6792 950 6·03 138 572 36393 942 5·98 139 565 3·5994- 934 5·93 140 559 3·5595 926 5-88 141 553 ',5196 917 5·82 142 546 3·4797 909 5·77 143 540 3·4398 899 5·71 144- 534- 3·3999 891 5·66 145 528 5·35100 884 5·61 146 521 3·31

101 874 5·55 147 515 3·27102 865 5·49 148 509 3·23lOS 855 5·43 149 504- 3·20104 847 5·38 150 499 3·17105 838 5·32 151 491 3·12106 830 5·27 152 485 3·08107 821 5·21 153 479 3·04-108 813 5·16 154- 472 3·00109 803 5·10 155 466 2·96110 795 5·05 156 461 2·93III 786 4·99 157 455 2·89112 776 4-93 158 449 2·85113 769 4·88 159 444- 2·82114 759 4·82 160 438 2·78115 751 4·77 161 433 2·75116 742 4·71 162 427 2·71117 734 4·66 163 422 2·68118 726 4·61 164 416 2·64JI9 ·717 4·55 165 411 2·61120 709 4·50 166 406 2·58121 701 4·45 167 402 2·55122 693 4·40 168 397 ~'52123 585 4·35 169 392 2·49124 676 4·29 170 387 2·46125 668 4·24 171 381 2·42126 660 4·19 172 376 2·39127 652 4·14- 173 972 2·36128 644- 4·09 174 367 2·33129 636 4·()f 175 362 2·30ISO 630 4·00 176 357 2·27191 622 3·95 177 953 2·24-132 614 3·90 178 348 2·21133 608 3·86 179 345 2·19134 600 3·81 180 340 2·16

70

taCTION Y : CONCLUDING uMAau OONCEIlHINO COLtJKN DUIOflt

TA8L& D APPROXIMATE IlADD OF GYRATION

(Clausu 2.3 41Id 2.4)

., ...-b--.. t--b --..~l r a()oU' d

,.. '1 '•• 0-42 d 3[1 r. -0-4141• x.J. ';=0.2.9 b d r =0-.2 b 0. 1ry=O-Ub

I--b.....J L ...1 y

~$r- b --.t

I,,..1 'X=0-42d 1fx-003• d41

rx :o·.-odm ..JL..1 ry=0-21 b 1 ry=Oo22b

fe-b --t

1:~ r="o25d Il r =003941 1 r :0-40 dd ~ d x

d •u 1ry =0'21 b 1 ry. 0 -21 ~

b-G! r =o-iselm IT r :0-4041 HIr••~lldt "'

d x1 rv 1: 0-24 b

., .......b---t ~b~""lffi1 r. -o-Id [ ]1 f••Oo,.d rx .0-42 d"-X -- ,..-«1...1 r. -0-3 b

I-b 1 r: ++b)/lo1 fy =0-40 b ... ...J 'y =0-a5 b

t--b~ liII r.·oo"

d1[1 r. -OoJOd

dJ'. -0-a9 cI

---.J- r -0-2' b j J r -0-60b r. -o·as It'1 _. Y Y

71

APPENDIX A(See Foreword)

INDIAN STANDARDS ON PRODUCTION, DESIGN AND USEOF STEEL IN STRUCTURES

lSI Las so far issued the following Indian Standards in the field ot­production, design and utilization of steel and welding :

IS : 800-1956 CODE OF PRACTICE FOR Us..: OF STRUCTURAL ST":"~L IN

GENERAL BUILDING CONSTRUCTION

IS : 801-1958 CODE OF PRACTICE FOR USE OF COLU FORMED LIGHT

GAUGE STEEL STRUCTURAL MEMBERS IN GENERAL BUILDING CONS­

TRUCTION

IS : 804-1958 SI)ECIFI(;ATION FOR RECTANGULAR PRESSED STEEL 'rANKS

IS : 806-1~57 COllE OF PRACTICE FOR USE OF ST":EL TUBES IN GENERAl.

BUILDING CONSTRUCTION

lS : 808-1957 SPECIFICATION FOR ROLLED STEEl. BEAM, (~HANN":L ANn

ANGLE SECTIONS

IS : 812-1957 GLOSSARY OF 'fERMS RELATING TO WELDING AND UU1TINO

OF METALS

JS : 813-1961 SCIIEME OF SYMBOLS Ji'OR WELDING (Amended)

IS : 814-1957 SPECIFICATION FOR COVERED ELECTRODES POR METAL ARC

WELDING OF MILD STF..EL

IS : 815-1956 CLASSIFICATION AND CODINO ot COVERED ELECTRODES

FOR METAL ARC WELDING OF MILD STEEL AND Low ALLOY HIGH­

"rENSILE STEELS

IS : H16-1956 CODE OF PRACTICE FOR USE OF METAl.. ARc WELVINO FOR

GENERAL CONSTRUCTION IN MILD STEEL

IS : 817-1957 CODE OF PRACTICE FOR T~AINING AND TESTING OF METAL

ARC WELDERS

JS : 818-1957 CODE OF PRACTICE FOR SAFETY AND HEALTH REQ,UIREMENTS

IN ELECTRIC AND GAS WELDING AND CUTTING OPERATIONS

IS : 819-1957 CODE OF PRACTICE FOR RF~ISTANCE SPOT WELDING FOR

LIGHT Assl.MBLIES IN MILD STEEL

IS : 1173-1957 SPECIFICATION FOR ROLLED STEEL SECTIONS, TEE BARS

IS : 1179-1957 SPECIFICATION FOR EQ,UIPMENT FOR EVE AND FACE PROTEC­

TION DURING WELDING

72

APP&NDIX A

IS: 818-1968 CoDK OP PRAanCB FOR SAnTY AND nEALTH aaQ.ulUIGrrnIN ELECTRIC AND GAl WELDING AND Ct.rIIlNG OPERATIONS (Firstr~ision )

IS: 819-1957 CODB OF PRACTICE FOR RESISTANCE SPOT WaLDli~O PORLIGHT ASSEMBLIBS IN MILD STEEL

IS: 1173-1967 SP&CII!ICATION FOR HOT ROLLED AND SILT STEEL, TaBBARS ( First revision )

IS: J179-1967 SPECIFICATION POR EQ,UIPMENT FOR EYE AND FACE PRO­TECTION DURING WELDING ( First "vision)

IS: 1181-1967 QUALIFYINO TESTS POR METAL ARC WELDERS (ENGAOEDIN WELDINO STRUCTURES OTHER THAN PIPES) (First revision)

IS: 1182-1967 RECOMW.NDED PRACTICE FOR RADIOGRAPHIC EXAMINA­TION . OF FUSION WELDED BUTT JOINTS IN SnEL PLATES (First"l'ision)

IS: 1252-1958 SPECIFICATION FOR ROLLED STEEL SECTIONS, BULB ANOLa

IS: 1261-1959· CODE OP PRACTICB FOR SEAM WELDING IN MILD STEBL

IS: 1278-1972 SPECIPICATION FOR FILLER RODI AND WIRES FOR GAa~

WE,LDINO ( Second rt"ilion )IS: 1323-1966 CODE 0.. PRACTICE fOR OXy-ACETYLENE WELDING FOR

STRUCTURAL WORK IN MILD STEltL ( Revised)IS: 1395-1971 SPECIFICATION FOR. MOLYBDENUM AND CHROMIUM-MOLY­

BDltNUM-VANADIUM Low ALLOY STEEL ELECTRODES FOR METAL ARCWELDING (Second ,nision )

IS: 1442-1964 SPECIPICATION POR COVERED ELECTRODES FOR THE METALARC WELDING 0' HIGH TaNllLE STRUCTURAL STEEL ( Revised)

73

ApPENDIX B(Se, Foreword)

COMPOSmON OF STRUCT1JRAL ENGINEElUNG SECTIONALCOMMnTEE, SMDC 7

The lSI Structural Engineering Sectional Committee, SMDC 7, whichwas responsible for processing this Handbook, consists of the following:

Ch.ir11UJ1IDnlaCfoR, STANDARDS (CIviL)

llIpr,smtingRailway Board (Ministry of Railways1

Public Works Department, ~adra..

Hindustan COnstruction Co. Lrd., Bombay~ew St.andard Engineering (;0. Ltd., Bombay)nspecrion Wing, Directorate General of Supplies

& Disposals (Ministry of Works, Housing atSupply)

Central Watt'r & Power Commission ("'at~r Wing),~~W Delhi

~finistry of Transport & 'Communications (Roads. Wing) ,

Braithwaite, Burn at jessop Construction Co. Ltd.,Calcutta ,

Committee on Plan Project, PJannir.g Commission,New Delhi'

Brid~ & Roof Co. (India) ua., l:alcuttaPublic Works Department, Calcutta

. Engin~r-in-Chief'. Branch, Army Headquarters(.4ItInuJII) ,

K. R. Irani & Co., BombayInstitution of Engin~n (India), CalcuttaRichardson & (:ruddas Ltd., Bombay

SHal ~1. P. N"OARSHF.TH

SHRI C. ~1. SHAHANI

SHRI SARl'P SINOH

SHal P. L. DM (.4.lln"4~)

SHill Y. K. Mt.·RTHY

MmtbnsSHill P. BALAKRISHNAN

SHRJ D. I. PAUL (~)

SHRJ B. N. BANNERJ£ESHRJ RACHVDAS BAt:LCOL G. BENJAMIN

SHal R. s. ~fEHANDRU

SH" J. G. BoDHESHill b. S. DUAl~IR. F. j. FONSECA

~IR. W. FERNANDES (Allmaall)JOINT DIRECfOR STASDAIlOS (8 & S) Railway Board (~Iini~try of Railway..)

DEpUTY DIRECTOR STANDARDS (8 at S) (Allt,""u)SHill S. C. MPl,;1t Central Public Works Department, New DelhiKHltI C. P. ~f~JK ~alional Buildings. Organization (~lini!lr)" of

~L' works, Housing & Supply)SURI SHRlltRlsnNA (Allmallll)

SHal L. R. ~IAawAul

SHR. P. S. ~IEHTA

SHRI B. ='l. ~fOZl'Mf)AR

SHRI T. S. \'£DAGIRl \AIImuJIt) ,SHRJ D. S. THAKUR Bombay Municipal Corporation, Bombay

SHIU A. R. \:AINOANXAR (AltmttJil)~fAJ R. P. E. V,uIFDAR . Bombar Port Trust, BombaySHRI V, \·I.NlJOOPAUN Centra Water &. Power Commission (Power Winl),

New Delhi5H" S. S. MURTHY (AllmuJlI)

SHaIB. Sr~HNA~ACHAa,Depury Director (S & ~)

Director, lSI (Ex-ojJicio Mtmbn)

Surtl4rySHRJ H. S. KRISHNAMURTHY

Auistant Director (S It M), lSI

74

BUREAU OF INDIAN STANDARDS

Helldquarters:Manak Bhavan, 9 Bahadur Shah Zatar Marg, NEW DELHI 110002Telephones: 323 0131,323 3375,323 9402Fax: 91 11 3234062,91 11 3239399,91 11 3239382

32376 17

3378662

603843

235 23 15

8329295

Telegrams: Manaksanstha(Common to all Offices)

Telephone

a-n0032

Central Laboratory:

Plot No. 20/9, Site IV, Sahibabad Industrial Area, Sahibabad 201010

Regional Offices:

Central: Manak Shavan, 9 Sahadur Shah Zatar Marg, NEW DELHI 110002

*Eastern: 1/14 CIT Scheme VII M, v.I.P.Road, Maniktola, CALCUTIA 700054

Northern: SCO 335-336, Sector 34-A, CHANDIGARH 160022

Southern: C.I.T. Campus, IV Cross Road, CHENNAI 600113

t Western: Manakalaya, E9, Behind Marol Telephone Exchange, Andheri (East),MUMBAI 400093

Branch Offices:

'Pushpak', Nurmohamed Shaikh Marg, Khanpur, AHMEDABAD 380001

i Peenya Industrial Area, 1st Stage, Bangalore-Tumkur Road,BANGALORE 560058

Gangotri Complex, 5th Floor, Bhadbhada Road, T.T. Nagar, BHOPAL 462003

Plot No. 62-63, Unit VI, Ganga Nagar, BHUBANESHWAR 751001

Kalaikathir Buildings, 670 Avinashi Road, COIMBATORE 641037

Plot No. 43, Sector 16 A, Mathura Road, FARIDABAD 121001

Savitri Complex, 116 G.T. Road, GHAZIABAD 201001

53/5 Ward No. 29, A.G. Barua Road, 5th By-lane, GUWAHATI 781003

5-8-56C, L.N. Gupta Marg, Nampally Station Aoad, HYDERABAD 500001

E-52, Chitaranjan Marg, C-Scheme, JAIPUR 302001

117/418 B, Sarvodaya Nagar, KANPUR 208005

Seth Bhawan, 2nd Floor, Behind Leela Cinema, Naval Kishore Road,LUCKNOW 226001

NIT Building, Second FlOOr, Gokulpat Market, NAGPUR 440010

Patliputra Industrial Estate, PATNA 800013

Institution of Engineers (India) Building 1332 Shivaji Nagar, PUNE 411005

T.C. No. 14/1421, University P.O. Palayam, THIRUVANANTHAPURAM 695034

5501348

8394955

554021

403627

21 01 41

8·288801

8-711996

54 11 37

20 1083

372925

21 68 76

238923

52 51 71

262305

323635

621 17

·Sale& Office is at 5 Chowringhee Approach, P.O. Princep Street,CALCUTIA 7tJOO72

t Sales Office is at Novelty Chambers, Grant Road, MUMBAI 400007

i Sales Office is at IF' Block, Unity Building, Narashimaraja Square,BANGALORE 560002

27 1085

309 65 28

2223971

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