Steel Designer''''s Manual Part 7 pps

The design of a beam taking into account lateral – torsional buckling consistsessentially of assessing the maximum moment that can safely be carried from aknowledge of the section’s mate

likeli-In cases where the web is found to be incapable of resisting the required level ofload, additional strength may be provided through the use of stiffeners The design

of load-carrying stiffeners (to resist web buckling) and bearing stiffeners is covered

in both BS 5950 and BS 5400 However, web stiffeners may be required to resistshear buckling, to provide torsional support at bearings or for other reasons; a fulltreatment of their design is provided in Chapter 17

16.3.6 Lateral – torsional buckling

Beams for which none of the conditions listed in Table 16.6 are met (explanation

of these requirements is delayed until section 16.3.7 so that the basic ideas andparameters governing lateral – torsional buckling may be presented first) are liable

to have their load-carrying capacity governed by the type of failure illustrated inFig 16.4 Lateral – torsional instability is normally associated with beams subject to

Fig 16.3 (continued)

The design of a beam taking into account lateral – torsional buckling consistsessentially of assessing the maximum moment that can safely be carried from aknowledge of the section’s material and geometrical properties, the support condi-tions provided and the arrangement of the applied loading Codes of practice, such

as BS 5400: Part 3, BS 5950: Parts 1 and 5, include detailed guidance on the subject.Essentially the basic steps required to check a trial section (using BS 5950: Part Ifor a UB as an example) are:

(1) assess the beam’s effective length LEfrom a knowledge of the support tions provided (clause 4.3.5)

condi-(2) determine beam slenderness lLTusing the geometrical parameters u (tabulated

in Reference 2), LE/ry, v (Table 19 of BS 5950: Part 1) using values of x

(tabu-lated in Reference 2)

(3) obtain corresponding bending strength pb(Table 16)

(4) calculate buckling resistance moment Mb = pb ¥ the appropriate section

Table 16.6 Types of beam not susceptible to lateral – torsional buckling

loading produces bending about the minor axis beam provided with closely spaced or continuous lateral restraint closed section

Fig 16.4 Lateral – torsional buckling

The central feature in the above process is the determination of a measure of the

beam’s lateral – torsional buckling strength (pb) in terms of a parameter (lLT) whichrepresents those factors which control this strength Modifications to the basicprocess permit the method to be used for unequal flanged sections including tees,fabricated Is for which the section properties must be calculated, sections contain-ing slender plate elements, members with properties that vary along their length,closed sections and flats Various techniques for allowing for the form of the appliedloading are also possible; some care is required in their use

The relationship between pband lLTof BS 5950: Part 1 (and between sli/sycand

lLT÷(syc/355) in BS 5400: Part 3) assumes the beam between lateral restraints to be

subject to uniform moment Other patterns, such as a linear moment gradient ing from a maximum at one end or the parabolic distribution produced by a uniformload, are generally less severe in terms of their effect on lateral stability; a givenbeam is likely to be able to withstand a larger peak moment before becoming lat-erally unstable One means of allowing for this in design is to adjust the beam’s slen-

reduc-derness by a factor n, the value of which has been selected so as to ensure that the resulting value of pbcorrectly reflects the enhanced strength due to the non-uniformmoment loading An alternative approach consists of basing lLTon the geometricaland support conditions alone but making allowance for the beneficial effects of non-

uniform moment by comparing the resulting value of Mbwith a suitably adjustedvalue of design moment is taken as a factor m times the maximum moment within the beam Mmax; m = 1.0 for uniform moment and m < 1.0 for non-uniform moment Provided that suitably chosen values of m and n are used, both methods

can be made to yield identical results; the difference arises simply in the way in

which the correction is made, whether on the slenderness axis of the pbversus lLT

relationship for the n-factor method or on the strength axis for the m-factor method Figure 16.5 illustrates both concepts, although for the purpose of the figure the m- factor method has been shown as an enhancement of pbby 1/m rather than a reduc- tion in the requirement of checking Mbagainst = mMmax BS 5950: Part 1 uses the

m-factor method for all cases, while BS 5400: Part 3 includes only the n-factor

method

When the m-factor method is used the buckling check is conducted in terms of

a moment less than the maximum moment in the beam segment Mmax; then a

separate check that the capacity of the beam cross-section Mc is at least equal to

Mmax must also be made In cases where is taken as Mmax, then the buckling

check will be more severe than (or in the ease of a stocky beam for which Mb= Mc,identical to) the cross-section capacity check

Allowance for non-uniform moment loading on cantilevers is normally treatedsomewhat differently For example, the set of effective length factors given in Table

14 of Reference 1 includes allowances for the variation from the arrangement used

as the basis for the strength – slenderness relationship due to both the lateral supportconditions and the form of the applied loading When a cantilever is subdivided byone or more intermediate lateral restraints positioned between its root and tip, thensegments other than the tip segment should be treated as ordinary beam segmentswhen assessing lateral – torsional buckling strength Similarly a cantilever subject to

M M

M

M M

effective design point using n—factor method

(Pb' nXLT)

LI

an end moment such as horizontal wind load acting on a façade, should be regarded

as an ordinary beam since it does not have the benefit of non-uniform momentloading

For more complex arrangements that cannot reasonably be approximated by one

of the standard cases covered by correction factors, codes normally permit the direct

use of the elastic critical moment ME Values of MEmay conveniently be obtainedfrom summaries of research data.6For example, BS 5950: Part 1 permits lLTto becalculated from

(16.3)

As an example of the use of this approach Fig 16.6 shows how significantly higherload-carrying capacities may be obtained for a cantilever with a tip load applied toits bottom flange, a case not specifically covered by BS 5950: Part 1

16.3.7 Fully restrained beams

The design of beams is considerably simplified if lateral – torsional buckling effects

do not have to be considered explicitly – a situation which will occur if one or more

of the conditions of Table 16.6 are met

In these cases the beam’s buckling resistance moment Mb may be taken as its

lLT =÷(p2E p/ y)÷(Mp/ME)

Fig 16.5 Design modifications using m-factor or n-factor methods

princi-sections of the same area The limits on l below which buckling will not affect Mb

of Table 38 of BS 5950: Part 1, are sufficiently high (l = 340, 225 and 170 for D/B ratios of 2, 3 and 4, and py= 275 N/mm2) that only in very rare cases will lateral –torsional buckling be a design consideration

Situations in which the form of construction employed automatically providessome degree of lateral restraint or for which a bracing system is to be used toenhance a beam’s strength require careful consideration The fundamental require-ment of any form of restraint if it is to be capable of increasing the strength of themain member is that it limits the buckling type deformations An appreciation ofexactly how the main member would buckle if unbraced is a prerequisite for theprovision of an effective system Since lateral – torsional buckling involves bothlateral deflection and twist, as shown in Fig 16.4, either or both deformations may

be addressed Clauses 4.3.2 and 4.3.3 of BS 5950: Part 1 set out the principles erning the action of bracing designed to provide either lateral restraint or torsionalrestraint In common with most approaches to bracing design these clauses assume

Fig 16.6 Lateral – torsional buckling of a tip-loaded cantilever

8 Noticeably absent from the code clauses is a quantitative definition of ‘adequatestiffness’, although it has subsequently been suggested that a bracing system that is

25 times stiffer than the braced beam would meet this requirement Examination

of Reference 7 shows that while such a check does cover the majority of cases, it isstill possible to provide arrangements in which even much stiffer bracing cannot

Fig 16.7 Effect of type of cross-section on theoretical elastic critical moment

16.4 Lateral bracing

For design to BS 5950: Part 1, unless the engineer is prepared to supplement the coderules with some degree of working from first principles, only restraints capable ofacting as rigid supports are acceptable Despite the absence of a specific stiffnessrequirement, adherence to the strength requirement together with an awareness thatadequate stiffness is also necessary, avoiding obviously very flexible yet strongarrangements, should lead to satisfactory designs Doubtful cases will merit exami-nation in a more fundamental way.7,8Where properly designed restraint systems areused the limits on lLTfor Mb= Mc(or more correctly pb= py) are given in Table 16.7.For beams in plastically-designed structures it is vital that premature failure due

to plastic lateral – torsional buckling does not impair the formation of the full plasticcollapse mechanism and the attainment of the plastic collapse load Clause 5.3.3

provides a basic limit on L/ryto ensure satisfactory behaviour; it is not necessarilycompatible with the elastic design rules of section 4 of the code since acceptablebehaviour can include the provision of adequate rotation capacity at moments

The first effect may be included in Equation (16.4) by adding the correction term

Table 16.7 Maximum values of l LT for

which pb=pyfor rolled sections

compression boom

of Brown,9the basis of which is the original work on plastic instability of Horne.10This is covered explicitly in clause 5.3.3 A method of allowing for both effects whenthe beam segment being checked is either elastic or partially plastic is given inAppendix G of BS 5950: Part 1; alternatively the effect of intermittent tension flange

restraint alone may be allowed for by replacing Lm with an enhanced value Ls

obtained from clause 5.3.4 of BS 5950: Part 1

In both cases the presence of a change in cross-section, for example, as produced

by the type of haunch usually used in portal frame construction, may be allowedfor When the restraint is such that lateral deflection of the beam’s compressionflange is prevented at intervals, then Equation (16.4) applies between the points

of effective lateral restraint A discussion of the application of this and otherapproaches for checking the stability of both rafters and columns in portal framesdesigned according to the principles of either elastic or plastic theory is given insection 18.7

16.5 Bracing action in bridges – U-frame design

The main longitudinal beams in several forms of bridge construction will, by virtue

of the structural arrangement employed, receive a significant measure of restraint

against lateral – torsional buckling by a device commonly referred to as U-frame

action Figure 16.8 illustrates the original concept based on the half-through girderform of construction (See Chapter 4 for a discussion of different bridge types.) In

a simply-supported span, the top (compression) flanges of the main girders, althoughlaterally unbraced in the sense that no bracing may be attached directly to them,cannot buckle freely in the manner of Fig 16.4 since their lower flanges arerestrained by the deck Buckling must therefore involve some distortion of thegirder web into the mode given in Fig 16.8 (assuming that the end frames preventlateral movement of the top flange) An approximate way of dealing with this is

to regard each longitudinal girder as a truss in which the tension chord is fully

Bracing action in bridges – U-frame design 449

U—frame

unit load

unit load

(b)

laterally restrained and the web members, by virtue of their lateral bending ness, inhibit lateral movement of the top chord It is then only a small step to regardthis top chord as a strut provided with a series of intermediate elastic springrestraints against buckling in the horizontal plane The stiffness of each support cor-responds to the stiffness of the U-frame comprising the two vertical web stiffenersand the cross-girder and deck shown in Fig 16.9

stiff-The elastic critical load for the top chord is

(16.5)

in which LEis the effective length of the strut

If the strut receives continuous support of stiffness (1/d LR) per unit length, in

which LRis the distance between U-frame restraints, and buckles in a single wave, this load will be given by

where K is a parameter that takes account of the stiffness of the end U-frames For effectively rigid frames, K = 2.22, which is the same as p/÷2.

For unstiffened girders a similar approach is possible with the effective U-framenow comprising a unit length of girder web plus the cross-member In all cases theassessment of U-frame stiffness via the d parameter is based on summing the deflec-tions due to bending of the horizontal and vertical components, including any flex-ibility of the upright to cross-frame connections Clauses 9.6.4.1.3 and 9.6.4.2.2 dealrespectively with the cases where actual vertical members are either present orabsent

Because the U-frames are required to resist the buckling deformations, they willattract forces which may be estimated as the product of the additional deformation,

as a proportion of the initial lateral deformation of the top chord, and the U-framestiffness as

(16.11)

in which the assumed initial bow over an effective length of flange (LE) has been

taken as LE/667, and 1/(1 - sfc/sci) is the amplification, which depends in a non-linearfashion on the level of stress sfcin the flange

For a frame spacing LRand a flange critical stress corresponding to a force level

of p2EIc/LR2, the maximum possible value of FR given in clause 9.12.2 of BS 5400:Part 3 is

(16.12)

Additional forces in the web stiffeners are produced by rotation q of the ends ofthe cross beam due to vertical loading on the cross beam Clause 9.12.2.3 of BS 5400:Part 3 evaluates the additional force as:

ˆ

-ÊË

Bracing action in bridges – U-frame design 451

Fig 16.10 Buckling mode for half-through construction with flexible end frames

In this expression, q is the difference in rotation between that at the U-frame andthe mean of the rotations at the adjacent frames on either side The division in theexpression represents the combined flexibility of the frame (conservatively taken as1.5d ) and of the compression flange in lateral bending

16.6 Design for restricted depth

Frequently beam design will be constrained by a need to keep the beam depth to aminimum This restriction is easy to understand in the context of floor beams in amulti-storey building for which savings in overall floor depth will be multipliedseveral times over, thereby permitting the inclusion of extra floors within the sameoverall building height or effecting savings on expensive cladding materials byreducing building height for the same number of floors Within the floor zone ofbuildings with large volumes of cabling, ducting and other heavy services, only afraction of the depth is available for structural purposes

Such restrictions lead to a number of possible solutions which appear to run trary to the basic principles of beam design However, structural designers shouldremember that the main framing of a typical multi-storey commercial building typically represents less than 10% of the building cost and that factors such as theefficient incorporation of the services and enabling site work to proceed rapidly and easily are likely to be of greater overall economic significance than trimmingsteel weight

con-An obvious solution is the use of universal columns as beams While not as turally efficient for carrying loads in simple vertical bending as UB sections, as illus-trated by the example of Table 16.8, their design is straightforward Problems of web

struc-bearing and buckling at supports are less likely due to the reduced web d/t ratios.

Lateral–torsional buckling considerations are less likely to control the design of erally unbraced lengths because the wider flanges will provide greater lateral

lat-stiffness (L/ryvalues are likely to be low) Wider flanges are also advantageous forsupporting floor units, particularly the metal decking used frequently as part

of a composite floor system

Difficulties can occur, because of the reduced depth, with deflections, althoughdead load deflections may be taken out by precambering the beams This will notassist in limiting deflections in service due to imposed loading, although compositeaction will provide a much stiffer composite section Excessive deflection of the floorbeams under the weight of wet concrete can significantly increase slab depths atmid-span, leading to a substantially higher dead load None of these problems needcause undue difficulty provided they are recognized and the proper checks made at

a sufficiently early stage in the design

Another possible source of difficulty arises in making connections betweenshallow beams and columns or between primary and secondary beams The reduced

c

R 3 c

=

+

ÊË

ˆ

¯q

d

1

1 5 /12

71 kN/m

6m

web depth can lead to problems in physically accommodating sufficient bolts tocarry the necessary end shears Welding cleats to beams removes some of the dimen-sional tolerances that assist with erection on site as well as interfering with thesmooth flow of work in a fabricator’s shop that is equipped with a dedicated sawand drill line for beams Extending the connection beyond the beam depth by usingseating cleats is one solution, although a requirement to contain the connectionwithin the beam depth may prevent their use

Beam depths may also be reduced by using moment-resisting beam-to-columnconnections which provide end fixity to the beams; a fixed end beam carrying acentral point load will develop 50% of the peak moment and only 20% of the centraldeflection of a similar simply-supported beam Full end fixity is unlikely to be a real-istic proposition in normal frames but the replacement of the notionally pinnedbeam-to-column connection provided by an arrangement such as web cleats, with asubstantial end plate that functions more or less as a rigid connection, permits thedevelopment of some degree of continuity between beams and columns Thesearrangements will need more careful treatment when analysing the pattern of inter-nal moments and forces in the frame since the principles of simple construction will

no longer apply

An effect similar to the use of UC sections may be achieved if the flanges of a

UB of a size that is incapable of carrying the required moment are reinforced bywelding plates over part of its length Additional moment capacity can be providedwhere it is needed as illustrated in Fig 16.11; the resulting non-uniform section isstiffer and deflects less Plating of the flanges will not improve the beam’s shearcapacity since this is essentially provided by the web and the possibility of shear

Design for restricted depth 453

Table 16.8 Comparison of use of UB and UC for simple beam

is L/360 and service load is 47 kN m

Irqd= 2.23 (47 ¥ 3) 6 2 = 11 319 cm 4

for base section

M for compound section

development of this idea is the use of tapered sections fabricated from plate.11To

be economic, tapered sections are likely to contain plate elements that lie outsidethe limits for compact sections

Because of the interest in developing longer spans for floors and the need toimprove the performance of floor beams, a number of ingenious arrangements havedeveloped in recent years.12Since these all utilize the benefits of composite actionwith the floor slab, they are considered in Chapter 21

16.7 Cold-formed sections as beams

In situations where a relatively lightly loaded beam is required such as a purlin orsheeting rail spanning between main frames supporting the cladding in a portalframe, it is common practice to use a cold-formed section produced cold from flatsteel sheet, typically between about 1 mm and 6 mm in thickness, in a wide range ofshapes of the type shown in Fig 16.12 A particular feature is that normally eachsection is formed from a single flat bent into the required shape; thus most avail-able sections are not doubly symmetric but channels, zeds and other singly sym-metric shapes The forming process does, however, readily permit the use of quitecomplex cross-sections, incorporating longitudinal stiffening ribs and lips at theedges of flanges Since the original coils are usually galvanized, the members do notnormally require further protective treatment

The structural design of cold-formed sections is covered by BS 5950: Part 5, whichpermits three approaches:

(1) design by calculation using the procedures of the code, section 5, for members

In practice option (2) is the most frequently used, with all the major suppliers viding design literature, the basis of which is usually extensive testing of theirproduct range, design being often reduced to the selection of a suitable section for

pro-a given sppro-an, lopro-ading pro-and support pro-arrpro-angement using the tpro-ables provided

Most cold-formed section types are the result of considerable development work

Fig 16.12 Typical cold-formed section beam shapes

near optimum performance, a typical example being the ranges of purlins produced

by the leading UK suppliers Because of the combination of the thin material andthe comparative freedom provided by the forming process, this means that most sec-tions will contain plate elements having high width-to-thickness ratios Local buck-ling effects, due either to overall bending because the profile is non-compact, or tothe introduction of localized loads, are of greater importance than is usually the casefor design using hot-rolled sections BS 5950: Part 5 therefore gives rather moreattention to the treatment of slender cross-sections than does BS 5950: Part 1 Inaddition, manufacturers’ design data normally exploit the post-buckling strengthobserved in their development tests

The approach used to deal with sections containing slender elements in BS 5950:Part 5 is the well accepted effective width technique This is based on the observa-tion that plates, unlike struts, are able to withstand loads significantly in excess oftheir initial elastic buckling load, provided some measure of support is available to

at least one of their longitudinal edges Buckling then leads to a redistribution ofstress, with the regions adjacent to the supported longitudinal edges attractinghigher stresses and the other parts of the plate becoming progressively less effec-tive, as shown in Fig 16.13 A simple design representation of the condition of Fig 16.13 consists of replacing the actual post-buckling stress distribution with theapproximation shown in Fig 16.14 The structural properties of the member

Fig 16.13 Loss of plating effectiveness at progressively higher compressive stress

Fig 16.14 Effective width design approximation

be/2 be/2

(strength and stiffness) are then calculated for this effective cross-section as trated in Fig 16.15 Tabulated information in BS 5950: Part 5 for steel of yieldstrength 280 N/mm2makes the application of this approach simpler in the sense thateffective widths may readily be determined, although cross-sectional propertieshave still to be calculated The use of manufacturer’s literature removes this require-ment For beams, Part 5 also covers the design of reinforcing lips on the usual basis

illus-of ensuring that the free edge illus-of a flange supported by a single web behaves as ifboth edges were supported; web crushing under local loads, lateral–torsional buck-ling and the approximate determination of deflections take into account any loss ofplating effectiveness

For zed purlins or sheeting rails section 9 of BS 5950: Part 5 provides a set ofsimple empirically based design rules Although easy to use, these are likely to lead

to heavier members for a given loading, span and support arrangement than either

of the other permitted procedures A particular difference of this material is its use

of unfactored loads, with the design conditions being expressed directly in memberproperty requirements

16.8 Beams with web openings

One solution to the problem of accommodating services within a restricted floordepth is to run the services through openings in the floor beams Since the size ofhole necessary in the beam web will then typically represent a significant propor-tion of the clear web depth, it may be expected that it will have an effect on struc-tural performance The easiest way of visualizing this is to draw an analogy between

a beam with large rectangular web cut-outs and a Vierendeel girder Figure 16.16shows how the presence of the web hole enables the beam to deform locally in asimilar manner to the shear type deformation of a Vierendeel panel These defor-mations, superimposed on the overall bending effects, lead to increased deflectionand additional web stresses

A particular type of web hole is the castellation formed when a UB is cut, turnedand rewelded as illustrated in Fig 16.17 For the normal UK module geometry thisleads to a 50% increase in section depth with a regular series of hexagonal holes

Fig 16.15 Effective cross-section

of plates welded between the two halves of the original beam Some aspects of thedesign of castellated beams are covered by the provisions of BS 5950: Part 1, whilemore detailed guidance is available in a Constrado publication.13

Based on research conducted in the USA, a comparatively simple elastic methodfor the design of beams with web holes, including a fully worked example, is avail-able.14This uses the concept of an analysis for girder stresses and deflections thatneglects the effects of the holes, coupled with checking against suitably modifiedlimiting values The full list of design checks considered in Reference 14 is:

(1) web shear due to overall bending acting on the reduced web area

(2) web shear due to local Vierendeel bending at the hole

(3) primary bending stresses (little effect since overall bending is resisted pally by the girder flanges)

princi-(4) local bending due to Vierendeel action

(5) local buckling of the tee formed by the compression flange and the web ing the web hole

adjoin-(6) local buckling of the stem of the compression tee due to secondary bending(7) web crippling under concentrated loads or reactions near a web hole; as a simple

guide, Reference 14 suggests that for loads which act at least (d/2) from the edge

of a hole this effect may be neglected

(8) shear buckling of the web between holes; as a simple guide, Reference 14 gests that for a clear distance between holes that exceeds the hole length thiseffect may be neglected

sug-(9) vertical deflections; as a rough guide, secondary effects in castellated beams may

be expected to add about 30% to the deflections calculated for a plain web beam

of the same depth (1.5D) Beams with circular holes of diameter (D/2) may be

expected to behave similarly, while beams with comparable rectangular holesmay be expected to deflect rather more

As an alternative to the use of elastic methods, significant progress has been made

in recent years in devising limit state approaches based on ultimate strength conditions A CIRIA/SCI design guide15dealing with the topic principally from thepoint of composite beams is now available If some of the steps in the 24-point designcheck of Reference 15 are omitted, the method may be applied to non-compositebeams, including composite beams under construction Much of the basis for Ref-erence 15 may be traced back to the work of Redwood and Choo,16and the fol-lowing treatment of bare steel beams is taken from Reference 16

The governing condition for a stocky web in the vicinity of a hole is taken asexcessive plastic deformation near the opening corners and in the web above andbelow the opening as illustrated in Fig 16.18 A conservative estimate of webstrength may then be obtained from a moment–shear interaction diagram of the

type shown as Fig 16.19 Values of M0and V1in terms of the plastic moment ity and plastic shear capacity of the unperforated web are given in Reference 14 for

capac-both plain and reinforced holes; M1may also be determined in this way Solution of

References to Chapter 16

1 British Standards Institution (2000) Part 1: Code of practice for design in simple and continuous construction: hot rolled sections BS 5950, BSI, London.

Fig 16.18 Hole-induced failure

Fig 16.19 Moment–shear interaction for a stocky web in the vicinity of a hole

2 The Steel Construction Institute (SCI) (2001) Steelwork Design Guide to BS 5950: Part 1: 2000, Vol 1, Section Properties, Member Capacities, 6th edn SCI,

Ascot, Berks

3 Johnson R.P & Buckby R.J (1979) Composite Structures of Steel and Concrete, Vol 2: Bridges with a Commentary on BS 5400: Part 5, 1st edn Granada, London.

(2nd edn, 1986)

4 Woodcock S.T & Kitipornchai S (1987) Survey of deflection limits for portal

frames in Australia J Construct Steel Research, 7, No 6, 399–418.

5 Nethercot D.A., Salter P & Malik A (1989) Design of Members Subject to Bending and Torsion The Steel Construction Institute, Ascot, Berks (SCI Pub-

lication 057)

6 Dux P.F & Kitipornchai S (1986) Elastic buckling strength of braced beams

Steel Construction, (AISC), 20, No 1, May.

7 Trahair N.S & Nethercot D.A (1984) Bracing requirements in thin-walled

struc-tures In Developments in Thin-Walled Structures – 2 (Ed by J Rhodes & A.C.

Walker), pp 93–130 Elsevier Applied Science Publishers, Barking, Essex

8 Nethercot D.A & Lawson R.M (1992) Lateral stability of steel beams and columns – common cases of restraint SCI Publication 093 The Steel Construc-

tion Institute, Ascot, Berks

9 Brown B.A (1988) The requirements for restraints in plastic design to BS 5950

Steel Construction Today, 2, No 6, Dec., 184–6.

10 Horne M.R (1964) Safe loads on I-section columns in structures designed by

plastic theory Proc Instn Civ Engrs, 29, Sept., 137–50.

11 Raven G.K (1987) The benefits of tapered beams in the design development of

modern commercial buildings Steel Construction Today, 1, No 1, Feb., 17–25.

12 Owens G.W (1987) Structural forms for long span commercial building and

associated research needs In Steel Structures, Advances, Design and tion (Ed by R Narayanan), pp 306–319 Elsevier Applied Science Publishers,

Construc-Barking, Essex

13 Knowles P.R (1985) Design of Castellated Beams for use with BS 5950 and BS

449 Constrado.

14 Constrado (1977) Holes in Beam Webs: Allowable Stress Design Constrado.

15 Lawson R.M (1987) Design for Openings in the Webs of Composite Beams.

CIRIA Special Publication S1 and SCI Publication 068 CIRIA/Steel struction Institute

Con-16 Redwood R.G & Choo S.H (1987) Design tools for steel beams with web

open-ings In: Composite Steel Structures, Advances, Design and Construction (Ed by

R Narayanan), pp 75–83 Elsevier Applied Science Publishers, Barking, Essex

A series of worked examples follows which are relevant to Chapter 16

7.2 in

The

Steel Construction

Institute

Silwood Park, Ascot, Berks SL5 7QN

Checked by

BEAM EXAMPLE 1 LATERALLY RESTRAINED UNIVERSAL BEAM

DAN

BS 5950: Part 1 GWO

16 1

Problem

Select a suitable UB section to function as a simply supported beam

carrying a 140 mm thick solid concrete slab together with an

spaced at 3.6 m intervals The slab may be assumed capable of

pro-viding continuous lateral restraint to the beam’s top flange.

Due to restraint from slab there is no possibility of lateral-torsional

buckling, so design beam for:

Loading

Total load for ultimate limit state

= 3 3 2

D L = (2 4 ¥9 81 ¥0 14 )

Worked examples 463

The

Steel Construction

Institute

Silwood Park, Ascot, Berks SL5 7QN

Checked by

BEAM EXAMPLE 1 LATERALLY RESTRAINED UNIVERSAL BEAM

DAN

BS 5950: Part 1 GWO

16 2

Limit on b/T for plastic section = 9 > 5.06

Limit on d/t for shear = 63 > 44.7

\ Section is plastic

= 396 ¥ 10 6 N mm

= 396kN m > 369kN m OK Vertical shear capacity

\ P v = 0.6 ¥ 275 ¥ 9.1 ¥ 457.2 = 686 ¥ 10 3 N

= 686kN > 205kN OK

Steel Construction

Institute

Silwood Park, Ascot, Berks SL5 7QN

Checked by

BEAM EXAMPLE 1 LATERALLY RESTRAINED UNIVERSAL BEAM

DAN

BS 5950: Part 1 GWO

16 3

mm span /

Worked examples 465

The

Steel Construction

Institute

Silwood Park, Ascot, Berks SL5 7QN

Checked by

BEAM EXAMPLE 2 LATERALLY UNRESTRAINED UNIVERSAL BEAM

DAN

BS 5950: Part 1 GWO

16 1

Problem

For the same loading and support conditions of example 1 select a

suitable UB assuming that the member must be designed as laterally

unrestrained.

It is not now possible to arrange the calculations in such a way that

a direct choice is possible; a guess and check approach must be

Steel Construction

Institute

Silwood Park, Ascot, Berks SL5 7QN

Checked by

BEAM EXAMPLE 2 LATERALLY UNRESTRAINED UNIVERSAL BEAM

DAN

BS 5950: Part 1 GWO

16 2

Vol 1

L E = 7.2 m suggests as possible sections:

Silwood Park, Ascot, Berks SL5 7QN

Checked by

BEAM EXAMPLE 3 UNIVERSAL BEAM SUPPORTING POINT LOADS

DAN

BS 5950: Part 1 GWO

16 1

Problem

Select a suitable UB section in S275 steel to carry the pair of point

loads at the third points transferred by crossbeams as shown in the

accompanying sketch Design to BS 5950: Part 1.

The crossbeams may reasonably be assumed to provide full lateral

and torsional restraint at B and C; assume further that ends A and

D are similarly restrained Thus the actual level of transfer of load

at B and C (relative to the main beam’s centroid) will have no effect,

the lateral-torsional buckling aspects of the design being one of

con-sidering the 3 segments AB, BC and CD separately.

From statics the BMD and SFD are

BMD

SFD

Steel Construction

Institute

Silwood Park, Ascot, Berks SL5 7QN

Checked by

BEAM EXAMPLE 3 UNIVERSAL BEAM SUPPORTING POINT LOADS

DAN

BS 5950: Part 1 GWO

16 2

Vol 1 AB

Satisfactory by inspection OK

A 457 ¥ 191 ¥ 82 UB provides sufficient resistance to

lateral-torsional buckling for each segment and thus for the beam as a

whole.

Worked examples 469

The

Steel Construction

Institute

Silwood Park, Ascot, Berks SL5 7QN

Checked by

BEAM EXAMPLE 3 UNIVERSAL BEAM SUPPORTING POINT LOADS

DAN

BS 5950: Part 1 GWO

16 3

Check shear capacity; maximum shear at L is 135 kN

P v = 752 kN > 135 kN OK

Check bearing and buckling capacity of web at the supports –

Design Guide

adequate.

For initial check on serviceability deflections assume as equivalent

UDL and factor down all loads by 1.5 to obtain

Beam is clearly satisfactory for deflection since these (approximate)

calculations have used the full load and not just the imposed load.

. . /

/

d

as the basis for design in some codes of practice.

For a given bending moment the required flange areas can be reduced by ing the distance between them Thus for an economical design it is advantageous toincrease the distance between flanges To keep the self-weight of the girder to aminimum the web thickness should be reduced as the depth increases, but this leads

increas-to web buckling considerations being more significant in plate girders than in rolledbeams

Plate girders are sometimes used in buildings and are often used in small tomedium span bridges They are designed in accordance with the provisions con-tained in BS 5950: Part 1: 20001 and BS 5400: Part 32 respectively This chapterexplains current practice in designing plate girders for buildings and bridges; refer-ences to the relevant clauses in the codes are made

17.2 Advantages and disadvantages

The development of highly automated workshops in recent years has reduced thefabrication costs of plate girders very considerably; box girders and trusses still have

to be fabricated manually, with consequently high fabrication costs Optimum use

of material is made, compared with rolled sections, as the girder is fabricated fromplates and the designer has greater freedom to vary the section to correspond withchanges in the applied forces Thus variable depth plate girders have been increas-ingly designed in recent years Plate girders are aesthetically more pleasing than

Initial choice of cross-section for plate girders in buildings 471

There are only a very few limitations in the use of plate girders Compared withtrusses they are heavier, more difficult to transport and have larger wind resistance.The provision of openings for services is also more difficult The low torsional stiff-ness of plate girders makes them difficult to use in bridges having small plan radius.Plate girders can sometimes pose problems during erection because of concern forthe stability of compression flanges

17.3 Initial choice of cross-section for plate girders in buildings

17.3.1 Span-to-depth ratios

Advances in fabrication methods allow the economic manufacture of plate girders

of constant or variable depth Traditionally, constant-depth girders were morecommon in buildings; however, this may change as designers become more inclined

to modify the steel structure to accommodate services.3 Recommended depth ratios are given in Table 17.1

span-to-17.3.2 Recommended plate thickness and proportions

In general the slenderness of the cross-sections of plate girders used in buildingsshould not exceed the limits specified for class 3 semi-compact cross-sections (clause

Fig 17.1 Elevation and cross-section of a typical plate girder

472 Plate girders

3.5 of the Code), even though more slender cross-sections are permitted The choice

of plate thickness is related to buckling If the plates are too thin they may requirestiffening to restore adequate stiffness and strength, and the extra workmanshiprequired is expensive

In view of the above the maximum depth-to-thickness ratio (d/t) of the webs of

plate girders in buildings is usually limited to

where pywis the design strength of the web plate The outstand width-to-thickness

ratio of the compression flange (b/T) is usually limited to

where pyfis the design strength of the compression flange

Changes in flange size along the girder are not usually worthwhile in buildings.For non-composite girders the flange width is usually within the range 0.3–0.5 timesthe depth of the section (0.4 is most common) For simply-supported compositegirders these guidelines can still be employed for preliminary sizing of compressionflanges The width of tension flanges can be increased by 30%

17.3.3 Stiffeners

Horizontal web stiffeners are not usually required for plate girders used in ings Vertical web stiffeners may be provided to enhance the resistance to shear nearthe supports Intermediate stiffening at locations far away from supports will, ingeneral, be unnecessary due to reduced shear

build-The provision of vertical or transverse web stiffeners increases both the critical

shear strength qcr (initial buckling strength) and the shear buckling strength qw

(post-buckling strength) of web panels The critical shear strength is increased by

a reduction in the web panel aspect ratio a/d (width/depth) Shear buckling strength

Table 17.1 Recommended span-to-depth ratios for plate girders used in buildings

for simply-supported non-composite girders, with concrete decking

concrete decking (NB continuous composite girders are rare in buildings)

stresses, which develop during the post-buckling phase, are resisted by the ary members (vertical stiffeners and flanges).

bound-Transverse stiffeners are usually spaced such that the web panel aspect ratio isbetween 1.0 and 2.0, since there is little increase in strength for larger panel aspectratios For end panels designed without utilizing tension field action the aspect ratio

is reduced to 0.6–1.0 Sometimes double stiffeners are employed as bearing

stiffen-ers at the end supports, to form what is known as an end post The overhang of the

girder beyond the support is generally limited to a maximum of one eighth of thedepth of the girder

17.4 Design of plate girders used in buildings to

BS 5950: Part 1: 2000

17.4.1 General

Any cross-section of a plate girder will normally be subjected to a combination of

shear force and bending moment, present in varying proportions BS 5950: Part 1:

20001specifies that the design of plate girders should satisfy the relevant provisionsgiven in clauses 4.2 (members subject to bending) and 4.3 (lateral-torsional buck-ling) together with the additional provisions in 4.4 (plate girders) The additionalprovisions in clause 4.4 of the Code are related primarily to the susceptibility ofslender web panels to local buckling

17.4.2 Dimensions of webs and flanges

Minimum web thickness requirements (clause 4.4.3 of the Code) are based on viceability considerations, such as adequate stiffness to prevent unsightly bucklesdeveloping during erection and in service, and also to avoid the compression flangebuckling into the web

ser-The buckling resistance of slender webs can be increased by the provision of webstiffeners In general the webs of plate girders used in buildings are either unstiff-ened or have transverse stiffeners only (see Fig 17.1)

The following minimum web thickness values are prescribed to avoid bility problems

ˆ

¯

250250

1 2

t≥ d250

Design of plate girders used in buildings to BS 5950: Part 1: 2000 473

The following minimum web thickness values are prescribed to avoid the sion flange buckling into the web.

compres-(3) Unstiffened webs

(4) Transversely stiffened webs

Local buckling of the compression flange may also occur if the flange plate is of

slender proportions In general there is seldom good reason for the b/T ratio of the

compression flanges of plate girders used in buildings to exceed the class 3

semi-compact limit (clause 3.5 of the Code) b/T £ 13 e.

17.4.3 Moment resistance

17.4.3.1 Web not susceptible to shear buckling

Determination of the moment resistance Mc of laterally restrained plate girdersdepends upon whether or not the web is susceptible to shear buckling If the web

depth to thickness ratio d/t £ 62 e the web should be assumed not to be susceptible

to shear buckling, and the moment resistance of the section should be determined

in accordance with clause 4.2.5 of the Code

17.4.3.2 Web susceptible to shear buckling

If the web depth to thickness ratio d/t > 62 e it should be assumed susceptible to shear buckling The moment resistance of the section Mc should be determinedtaking account of the interaction of shear and moment, using the following methods.(1) Low shear

Provided that the applied shear force Fv£ 0.6 Vw, where Vwis the simple shear ling resistance from clause 4.4.5.2 of the Code (see section 17.4.4.2 (1)), the momentresistance should be determined from clause 4.2.5 of the Code For class 1 plasticand class 2 compact cross-sections:

where pyis the design strength of the steel and S is the plastic modulus For class 3

(2) High shear flanges-only method

If Fv> 0.6 Vwbut the web is designed for shear only, provided that the flanges are

not class 4, a conservative value Mffor the moment resistance may be obtained byassuming that the moment is resisted by the flanges only Hence:

Mf= pyfSf

where Sfis the plastic modulus of the flanges only

(3) High shear general method

If Fv> 0.6 Vwand the applied moment does not exceed the low shear value given

by (1), the web should be designed using Annex H.3 of the Code for the appliedshear combined with any additional moment beyond the flanges-only moment

resistance Mfgiven by (2)

17.4.4 Shear resistance

17.4.4.1 Web not susceptible to shear buckling

If the web depth to thickness ratio d/t £ 62 e it is not susceptible to shear buckling and the shear resistance Pvshould be determined in accordance with clause 4.2.3 ofthe Code, i.e

Pv= 0.6 pywAv= 0.6 pywtd

where Av= td is the shear area.

17.4.4.2 Web susceptible to shear buckling

If d/t > 62 e the shear buckling resistance of the web should be determined in

accord-ance with clause 4.4.5 of the Code

Design of plate girders used in buildings to BS 5950: Part 1: 2000 475

Both methods are based on the post-critical shear buckling strength of the web qw,and result in significantly greater values of shear resistance than the elastic critical

method of BS 5950: Part 1: 1985 The relationship between qw and qcr, the elastic

critical shear strength, is illustrated in Fig 17.2 The more exact method incorporates

a flange related component of shear resistance and is comparable with the methodbased on tension field theory in BS 5950: Part 1: 1985 The critical shear buckling

resistance Vcr, based on qcr, is retained only as a reference value and for the design

of particular types of end panel

The two methods for determining the shear buckling resistance are as follows.(1) Simplified method

The shear buckling resistance Vbof a web, with or without intermediate transverse

stiffeners, may be taken as the simple shear buckling resistance Vwgiven by:

Vw= dtqw

where qw is the shear buckling strength of the web Values of qw are tabulated inTable 21 of the Code for web panel aspect ratios from 0.4 to infinity The equations

on which qwis based are specified in Annex H.1 of the Code

(2) More exact method

Alternatively the shear buckling resistance Vbof a web panel between two

trans-Fig 17.2 Relationship between shear buckling strength qwand critical shear strength qcr

stressed, i.e the mean longitudinal stress in the smaller flange due to moment or

axial force ffis equal to the flange strength pyf, then:

Vb= Vw= dtqw

If the flanges are not fully stressed ( ff< pyf):

Vb= Vw+ Vf but Vb£ Pv= 0.6 pywtd

in which Vfis the flange-dependent shear buckling resistance given by

Mpfis the plastic moment resistance of the smaller flange about its own equal area

axis, perpendicular to the plane of the web Mpwis the plastic moment resistance ofthe web about its equal area axis perpendicular to the plane of the web, determined

using pyw For a rectangular flange and a web of uniform thickness:

(3) Critical shear buckling resistance

The critical shear buckling resistance Vcrof the web of an I-section is given by

Vcr= dtqcr

where qcr is the critical shear buckling strength determined in accordance withclause 4.4.5.4 of the Code as follows (see also Annex H.2 of the Code)

17.4.4.3 Panels with openings

Web openings frequently have to be provided in girders used in building tion for service ducts etc When any dimension of such an opening exceeds 10% ofthe minimum dimensions of the panel in which it is located, reference should bemade to clause 4.15 of the Code Panels with openings should not be used as anchorpanels, and the adjacent panels should be designed as end panels

construc-Guidance on the design of plate girders with openings is provided in erence 5

17.4.5 Resistance of a web to combined effects

If the moment resistance of a plate girder is determined using the high shear generalmethod (see section 17.4.3.2 (3)) the resistance of the web to combined effectsshould be checked in accordance with Annex H.3 of the Code

The interaction between bending and shear in plate girders is illustrated in Fig.17.3 The broken line represents the high shear flanges only method (see section17.4.3.2 (2)) while the full line represents the low shear and high shear generalmethods

Fig 17.3 Interaction between shear and moment resistance of plate girder webs

17.4.6 End panels and end anchorage

17.4.6.1 General

End anchorage need not be provided if either the shear resistance Pv(see section

17.4.4.1) not the shear buckling resistance Vw(see section 17.4.4.2 (1)) is the

gov-erning design criterion, indicated by Pv£ Vw, or the applied shear force Fvis less

than the critical shear buckling resistance Vcr(see section 17.4.4.2 (3)) For all othersituations some form of end anchorage is required to resist the post-critical mem-brane stresses (tension field) which develop in a buckled web

Three alternatives for providing end anchorage are recommended in Annex H.4

-—- —

(c)

Design of plate girders used in buildings to BS 5950: Part 1: 2000 479

panels (see Fig 17.4) End anchorage should be provided for a longitudinal anchor

force Hqrepresenting the longitudinal component of the tension field, at the ends

of webs without intermediate stiffeners and at the end panels of webs with mediate transverse stiffeners

inter-If the web is fully loaded in shear (Fv≥ Vw):

If the web is not fully loaded in shear:

V P

v cr

w cr

cr v

-ÊË

ˆ

-ÊË