tapered steel beams_1996

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Paper: Vellasco/Hobbs

Paper

Local web buckling in tapered composite beams

Professor P. C. G. da S. Vellasco

Polytechnic Institute, State Universityf Rio de Janeiro,Brazil

ProfessorR.E. Hobbs, BSc(Eng),PhD, CEng, FIStructE

Department of Civil Engineering, Imperial College of Science, Technology &Medicine

SynopsisRecent demand fo r very heavily serviced widespan ofi ce flo or shas led, as a atural development of the concept of haunched andtapered rames, to he use of composite floor s supported bytapered (varying webdep th) beams. One requirement is fo r a bet-ter understanding of the local buckling beh aviour of the relativelydeep slender web atchanges of slope in the lower flang e, in par-ticular at the slope change which occurs at the centre of a beamwhose depth increases linearly fro m each support.

The prima ry objective of the present experimental and num eri-cal study was to dentify the relative importance of several par a-meters that influence the phenomenon, such as angle of taper;web thickness, plastic neutral axis position, and others. For pra c-tical reasons, the experiments were executed at ha lfsc ale and themodels simulated the concrete slab of the composite beam by aheavy steel top flang e. A comparative study was made using anon-linear elasto-p lastic fini te elemen t program . A useful corre-lation was obtained between the results of this study and theexperiments. It is concluded that local buckling occurs only inrather slender webs at rather large changes in flang e slope andthat the behaviour is not very sensitive to neutral axis position.These conclusions make the task of identifying design checks fo rweb buckling relatively straightforward.

NotationD is thewebepthMP is the fully plastic moment of beam at deepest part of web

t is thewebhickness

Introduction

Composite flooring systems supported by tapered (varying web depth)beams are very attractive from an economic pointf view, combining wide

spans, rapid erection, and easy access to services between the shallow partsof the beam and the ceiling below (Fig).The potentialof this kind of struc-

tural section has been demonstratedby its use in several major projects in

the City of London and elsewhere. However, full exploitation has beeninhibited by the limited understanding of certain aspects of the behaviour

of such sections.

One of the most pressing needs s for a better understanding f the localbuckling behaviour of the relatively deep slender web at changes of slopein the lower flange, in particulart the slope change which occurst the cen-

tre of a beam whose depth increases linearly from each support. In the past,

with plate girders, this failure mechanism was less relevant than lateral-tor-

R

(extract) (supply)

Fig 1. Tapered beams: good integration of structure and services

Iig 2. Generationofweb buckling orce

sional buckling. With the substantial top flangef a composite section, at-

eral buckling is less likely, and local buckling more likely to govern thedesign.

The tapered beam sections are fabricated from platey welding and aresusceptible to imperfection effects and residual stresses. These phenome-

na may interact with the localized compressive stress field whichs gener-

ated in the web at any slope change in the flange to cause local web

buckling. The provisionof local stiffening is technically feasible, but veryexpensive. The beam itself is produced fully automatically, and the subse-

quent hand installation of stiffeners consumes manhours outf all propor-tion to the weight f steel involved.

One of the first investigations of the economics of long-span floors wasby Owens'. He demonstrated hat he apered and haunched solutions

achieved the bestesults, combining a good flexibility for services and a lowratio of steel to area of construction, for a span in the orderf 15m. In the

light of these figures a composite tapered beam was tested in 1986*. The

beam was initially produced without any web stiffeners. Under working

load a localised web buckle started to appear close to the changef slopein the bottom flange. It was then decided to weld a quarter depth stiffener

at that point and to continue the test. The results proved that the ultimatecapacity of the modified beam was nearly two timests working load, well

above the design factorof l .6. The localised buckle can be explainedy asimple equilibrium model (Fig2) . The vertical components of the tension

forces carried by the bottom flange induce a compression force in the webat the slope change to cause the buckling.

Raven3 and Raven&Glove? listed the advantages f composite taperedbeams. These included planninglexibility, fewer foundations, beam depth

similar to thatof rolled steel beam solutions, good integration f services,easier fit-out of floors and ceilings, and some other less significant factors.

They also called attention to the web buckling problem, stating that atiff-

ener would be necessary t the change of slope in some cases to avoid pre-

mature failure.A major study on tapered and haunched beams was producedy Home

e t aZ5S6.t comprised a theoretical study of the stability of tapered andhaunched beams and some experimental work to calibrate the formulaerc-

posed for design. It covered the lateral torsional buckling performance ofthis type of structure in detail and suggested some ideas to deal with poin

such as the effectivenessf lateral supports, achievementf plastic momentcapacity, and several others. One of the main conclusions of the experiment

was that, if it was intended to develop the plastic moment capacity of atapered beam, it was necessary to provide a web stiffenert slope changesin the flange.

Finally, Lawson&Rackham' developed a design method or haunchedcomposite beams based on the plastic capacity of the beam section. Theysuggested that the tapered composite beam was economic for spans betwe

The Structural EngineedVolume 74/No 3/6 February 1996 41




Al l dimensions in mm

Fig 3. Test rig dimensions

13 and 20m.A web stiffener at the point where the flange slope alters was

thought to be necessary only when the change in slope exceeded”=1/10.

With hindsight, this appears to bean oversimplification because a number

of other parameters are equally important. Lawson & Rackham gave no

explanation for their criterion.

The primary objective of the present study was to consider the relativeimportance of several parameters that influence the web buckling phenom-

enon, suchas angle of taper,web thickness,flange area,and others.Experiments were thus designed to investigate the influencef these para-

meters. The experimental results were compared with data obtained usinga non-linear elasto-plastic finite element program, wherea simulation of a

panel of a tapered beam was developed and validated against the experi-ments. This work was extended as a parametric study to cover practical

ranges of the important variables.

Experimentalwork

The main objective of the experiments was to determine whether verticalstiffeners were really necessary in the web at the point where the bottom

flange changes direction. The first series of tests was designed to study the

influence of web depth-to-thickness ratio on the loadcarrying capacityf thebeams. For practical reasons, the experiments were executed at half-scalewith a maximum web depth of 650mm, and the models simulated the on-

crete slab of the composite beamy a heavy steel top flange. Three unstiff-

ened tapered models were tested with different web thicknesses, i.e. 7, 5 ,and 3mm. The plastic neutral axes of these beams were in or close to the

top flange, to simulate the likely condition in composite beam.Once these results were to hand, a second test series was conducted in

which the plastic neutral axis was lowered progressively, including the con-

struction case where the steel beam has to carry the freshly cast slab.sec-

ondary purposeof this series was to exploresignificant difference betweenclassical patch loading and the concentrated load induced by the slope

change in the lower flange, i.e. that patch loads normally act on the com-

pression flange and induce biaxial compression in the adjacent web whilethe slope change creates vertical compression in part of the web which s

under horizontal tension. This difference significantly increases the buck-ling load of the web and makes the slope change less ritical than conven-

tional patch loading for the same input force.

Materials and methodsThe experiments had the supportof Ward Brothers Sherburn Ltd. Initially,

specimens of about one-quarter ull size had been envisaged, buthis scalewould have given specimens too small and (importantly) too thin for Ward’s

automated processes and standard plate thicknesses. As a result, beams ofapproximately half full-size were used.

As noted earlier, it was decided to model the concrete slab of the com-

posite beams by using a heavy steel top flange (sized to give the same plas-tic neutral axis position) to the fabricated beam. The properties of theconcrete deck, and of its interaction with the steel section, were notf great

interest, and a great deal of time and expense was saved by this decision.An additionaladvantage was thegreatercontrol of model propertiesachieved by employing a homogeneous top flange. The only drawback to

the use of the steel top flange was the reduced lateral-torsional restraintwhich it gave for the same axial stiffness. It was relatively easy to provideexternal lateral restraintso overcome this problem: details are given below.

Since flangeslope changes inducing web compression normally occurt

the centre of the beam, the loading chosen was a pure moment with zeroshear, a choice simply achieved in the lab by a four-point loading system.The test rig consisted of a simply supported beam 11.46m long subjected

to two symmetrically disposed concentrated loads (Fig 3). The beam wasformed from three distinct parts: the central ‘specimen’ and two ‘loading

42

arms’. The loading arms were reused in all of the tests, and their purposewas simply to receive the load from the hydraulic jacks and transmit it e

tively as a pure moment to the specimen which was changed everyest.

Each loading arm was. lm long with an effective lever arm between the

roller support and theack centreline of 2.15m. The otal depth of the load-ing arms was 500mm, the top and bottom flanges were 25mm thick and

300mm wide, and the web was 12mm thick. The specimens (Fig 4) were

5.26m long, of which the central 3m formed tapered test panel with min-imum and maximum heightsf 500and 650mm, respectively. These dimen-

sions correspond to taper angleof 1:10or=5”, he maximum accepted yWard’s machinery. The top and bottom flanges were 25 and 12mm thick,

respectively, and 300mm wide. The outer ends of the specimens had tomatch the loading arms, and were thus 500mm deep with 300mm25mm

flanges and a 12mm web thickness. o avoid any risk f failure in the load-ing arms, they were constructed in grade 50 steel, while the specimens

were fabricated in grade 43 steel.

The moment was transmitted from the loading arms to the specimensymeans of full moment friction-grip connections using 20 preloaded M20

bolts in the web and 16 preloaded M24 bolts in each flange. In each flangeconnection, an outside cover plate00X 650 X 20mm and two inside coverplates 120 X 650 X 20mm were used. As noted previously, four lateral

restraint frames were used to provide the necessary support to the top flato prevent a lateral buckling failure. They were located 500mm inboard f

the two jacks and 500mm in from the centres of the connections, respec-tively. The restraint was provided y guide rollers carried on the top flangeof the beam acting on running surfaces mounted on robust portals bolted to

the strong floorof the laboratory.

To monitor the behaviour of the beam during the test, transducers andstrain gauges were used. The value of the load in the jacks was obtained

through a pressure transducer located at the return tube to the loading cab-inet and was frequently checked against the pressure indicatedy the con-

trol cabinet itself. A jig carrying 36 displacement transducers was built to

monitor the lateral deflectionsf the web at its critical central area. Verticaldisplacement transducers were positioned on the top flange at the ends and

centre of the tapered beam section. o measure the values f the strains andhence stresses present in the beam, linear and rosette strain-gauges were

employed. Linear strain gauges were used in the flanges andt points near

the edges of the tapered panels. Rosettes were utilised at the centre of the

tapered web.Further details of the test equipment may be found elsewhere8.

Phase l tests

Table 1 summarises the first test series. The fully plastic moment and plas-tic neutral axis positions are based on yield stresses derived from coupon

tests. Unfortunately, because coupons wereot supplied with the beams, thecoupons had to be cut from the beams themselves after they had beenest-

ed, and the resultant yield values are almost certainly higher than wouldhave been obtained with virgin material. They are obviously well above the

grade 43 minima, although this is hardly unusual, particularly for plate asthin as 3mm. The calculated plastic neutral axes lay within the top flangefor the two thicker webs while the axis for the 3mm beam lay 74mm into

the web.

I L-d50mm

1130mm 3000mm 1130mm

1 1

Fig 4 . Specimen geometry

The Structural Engineer/Volume 74/No 3/6 February 1996




TABLE I -First test series

Beam no.

Web thickness (mm)

D/ t ratioNeutral axis position (mm)

Nominal plastic moment (kNm)

l

7

9321.2

1169

2

5

13024.2

1012

3

3217

99.2839.4

~ ~

Beam I (7mm web)

The beam sustained the load in the elastic rangep to a value correspond-

ing to 30%of its nominal plastic capacity at thecentral section. After that,

some plasticity began todevelop and the beam also tended to come into con-

tact with the lateral support frames. The failuremode (Fig 5 ) corresponded

to the formation of plastic hinges at the edge of the tapered panel where the

web had the minimum depth. The plastic moment recorded in the test was

equal to 84% of the nominal plastic capacity (based on thesuspect coupon

tests) at these points.

The test was stopped when the central vertical deflection reached approx-imately 450mm, even though the load-deflection curve was still rising (Fig

6). The web had very ittle lateral displacement, and no vertical or any other

kind of buckling could be seen. It remainedtraight, but had yielded to veryconsiderable degree. The maximum lateral deflection measured in the web

was about 6mm. These very small lateral displacements can be seen inFig 7, where the deflections at one of the lateral transducers are plotted

against the applied moment.

The maximum vertical compressive force available to cause verticalbuckling of the web is generated when the bottom flange yields complete-

ly. The strain gauges located on the bottom flange achieved the yield strain

very early in the test, proving that the flange was fully plastified well beforethe end of the experiment. Almost all the strain gauges at the edges of the

tapered panel also reached the yield strain, showing that these sections of

the beam were almost fully plastified, corresponding to the formation of the

plastic hinges.

Beam2

(5mm web)The beam remained elastic up to 46% of the nominal plastic moment,M,,

at the central section. Very large vertical deflections followed from about 0.6

MP t the central section, showing the decrease of stiffness imposed by the

growth of plasticity in the web of the beam. The plastic moment recorded

in the test was equal to91.6% of the nominal plastic capacity at the edges

of the tapered panel. The failure mode was again the appearance of plastic

hinges at the edges of the tapered web. The 5mm web also remained straight

Fig 5. Failure of beam I (t. =7mm)

100

901

3

2

80 -

- eam 1. Beam 2

Beam 3--

80 -70 -

I I I I I I I I I I0 50 100 150 20050 300 350005000

Vertical disp lacement (mm)

Fig 6.Load against vertical eflection for beams 1-3

100

904

c-

_-----

0 I l I I I I I I I

0 1 2 3 4 5 6 7 8 9

Lateral dis placement (mm)

Fig 7. Load against web lateral displacementor beams 1-3

and showed no igns of a buckle. In the final moments of the test, it was pos-sible tohear and see the mill-scale falling from theweb and flanges of the

tapered beam, confirming the existenceof large strains in the girder.

A load against vertical deflection curve for the beam is also plotted inFig 6. The maximum lateral deflection of the web was found to be about

5mm, which could again be considered small. The vertical compressive

force that appears in the web to ause vertical buckling also reached its max-imum possible value well before this test was finished.

Beam 3 (3mm web)

From the very early stages of the test, it was noted that-the web did not stay

straight,bucklingadjacent o heslopechange n he lower flange.Nevertheless, the beam remained elastic up to a value corresponding to 35%

of its nominalplastic capacity at the central section. The vertical buckle con-tinued to grow, changing the shape of the web significantly. The web

response was very sensitive to every load increase, displacing more and

more in the lateraldirection. When the load reached 59% ofMP,he beamalmost completely lost its capacity toustain further load. The vertical dis-

placements also increased significantly, ogether with a continuous progress

of the buckling. Around 69% of MP t the deepest oint, the tapered girderreached its failurepoint. At this stage, the flangestarted to act aswo sep-

arate plates, with no effective connection between them. The web com-

pletely buckled, and the load dropped as the lever armbetween top andbottom flanges fell.

A general view of the failure is shown in Fig 8, and a detailed view in

Fig 9. In the vertical direction, the buckle ormed three half-waves, whilelongitudinally one half-wave was present. In this test only one ‘hinge’

formed, at the entral section, ratherhan the two hinges at the edges of the

tapered panel noted in the first two beams.The load against central vertical deflection plot for theeam is shown in

Fig 6 . The maximum vertical displacement of the girder was 240mm. The

very large displacements recorded by the lateral ransducers can be seen in

Fig 7. The alue of the force hat caused the buckling can be estimated with

The Structural EngineerIVolume 741No 316ebruary 1996 43




Fig 8. Failure of beam 3 (t. =3mm)

the aid of theinear strain-gaugespositioned in the tension flange, at the cen-

tre of the girder. Strain gauges positioned on the inner part of the flange

reached the yield stress at about 0.4 M,. he external auges never reachedthe yield stress, which implies that the vertical force did not attain its max-

imum possible value in this test.

As a group, the phase 1 tests showed that an unstiffened web wouldbuckle only if it was less than 5mm thick (Dlt>130) even with the steep

taper used.

Phase 2 tests: influence of the lastic neutral axis position

As noted earlier, the most important difference between a classical patchload situation and the vertical buckling problem is thenature of the biaxial

stress distribution in the web. The vertical buckling of tapered composite

beams is, in thereat majority of cases, associated with compressive stress-

es in the vertical direction and tension stresses in theongitudinal direction,

because of the very localised character of the phenomena, together with thetypical position of the plastic eutral axis of a composite beam. With a low

enough plastic neutral axis, the longitudinal component might change to

compression and the response be closer to theatch case.

To cover cases where the neutral axis might be lower in the web, the sec-ond series of tests was planned. A 5mm web was used in all the new tests

because it had not buckled in the first series.f any disadvantageous change

in behaviour should occur due tohe neutral axis effect, itwas expected thatthe 5mm web would demonstrate it. To alter the neutral axis position, the

Fig 9.Detail of web failure, beam 3

TABLE 2 - econd test series

Beam no.

Web thickness (mm)

Top flange thickness (mm)Bottom flange thickness (mm)

Neutral axis position (mm)

Plastic moment (m m)

4

5

20

12171.3

918.2

5

5

15

12

298.4

848.0

6

5

15

25

625.7

1082

flange,dimensions were varied (Table 2). In particular, the sixth beam’s

proportions were chosen to simulate a case where unpropped constructionwas used and the beam had only the bare steel to sustain the construction

loads.

With top flange thicknesses of 15mm, beams 5 and 6 lay within the semi-compact class of BS5950. The flange could, in principle,chieve the yield

stress at the xtreme compression fibre but not be fully plastified. However,

in view of he experience cquired in theother tests, this was not expectedto affect the experiment, because the maximum tension flange force that

might cause vertical buckling was expected to be achieved with relatively

low values of the applied moment.

The values of the yield and ultimate stresses for the plates used in he fab-rication of beams 4, 5 and 6 were determined in a series of coupon tests

using virgin material. While the average yield and ultimate stress results

were still well above the specification for grade 43 steel, the yield values

were certainly not as high as those found for the first est series on ‘recy-

cled’ coupons.

The plastic neutral axis positions, measured from the top of the com-pressive steel flange, and the plastic moments at the central point for the sec-

ond series of beams, calculated using the measured steel properties, are also

given in Table 2. he sixth beam had he web fully in compression with the

plastic neutral axis 0.7mm inside the bottom flange.

Beam 4

The tapered panel remained elastic up to 50%of M, t the central section.

After that, the beam tended to displace towards the lateral supports and plas-

ticity began to spread over the web. The plastic moment recorded in the testwas equal to 95.7% of the plastic capacity at theminimum depth or 89% of

the plastic capacity at the maximum depth. The failuremode yet again cor-

responded to plastic hinge formation at the edges of the tapered section. The

test was stopped when the central vertical deflection of the beam reached360mm (Fig 10).

The maximum lateral displacements in the web were very small and

were due to he twist induced by the tendency to lateral-torsional buckling

(Fig 11). Indeed, a slight buckle of the top flange was observed at theplas-

tic hinge location and close to he web stiffener.The achievement of the maximum possible compressive forcewas again

indicated by the linear strain-gauges located on the bottom flange. Theyreached the yield stress at load levels between 42 and 55% of the central

’0°190-

- 0-00-c*e.. . .Y

30

20

- eam4

--- eam 5

Beam 6

l0i1

90-

80

- eam4

--- eam 5

Beam 6

0 50 100 150 200 2500050 400

44

Vertical displacement mm )

Fig 10.Load against vertical deflection fo r beams 4-6

The Structural EngineerIVolume 74/No 316 February 1996




lo o T-h

l

..*.*-.....

I I I ll I I I

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

Lateral displacement (mm)

Fig 11. Load against web lateral displacementfor beams 4-6

plastic moment capacity. All of the linear gauges placed on the web and

flanges at the edge of the panel reached the yield stress.

Beam 5

Beam 5 sustained the load in the elastic range up to a value correspondingto 35% of its plastic capacity at the central section. After that, plasticity

began to play a substantial role in the load-response behaviour. Around70%ofMP,he upper flange began to buckle at the edge of the tapered panel. The

buckling happened very quickly, and at this point the beam completely lost

its capacity to sustain he applied moment. The beam failed at approximately

73%ofMP t the central section, dueo a combination of a plastic hinge and

top flange buckling (see Fig 12).The load against vertical deflection curvefor the test is shown in Fig 10,with a maximum of around230mm. he cen-

tral portion of the web remained virtually undeformed during the test.

The maximum possible vertical force on the'web as again reached. The

flange strain-gauges reached the yield stress between 40%and 50%of MP,

well before the failure. Ail the linear gauges at the point where the buck-

ling of the top flange occurred reached the yield stress. The maximum

stresses were located in the bottom part of the web, although they were lesssignificant than those present in the previous beams. This is again related

to the sudden failure relatively early in the load history.

Beam 6

This beam remained elastic up to 38% of the plastic capacity of the central

section. After that point, the material and geometric non-linearities began

to affect the loadcarrying capacity of the beam and the displacements grewsignificantly (Fig IO). The maximum moment recorded in the test corre-

sponded to 69%of the plastic capacity. The failure was again due to the

buckling of the top flange at the edge of the tapered panel. The web was thenmuch affected by the buckling of the flange.

Some of the linear strain-gauges had reached only between 60% and

70%of the yield stress when the test ended, showing that the maximum pos-sible vertical force had not been reached. This did not matter because this

1

Fig 12 . Beam 5: buckling of topflange

case, which had the plastic neutral axis in the bottom flange, was conceived

in order to est the beam at construction load levels. These oad levels wereclearly exceeded before the test as finished, and the objectiveof proving

that no harm would occur to the central part of the girder was achieved. Theresults from the linear gauges at the edge of the tapered panel showed the

beginning of plastic hinge formation that was suddenly stopped by the

buckling of the top flange.As a group, the phase 2 tests confirmed that the 5mm (O h=130)web

would not buckle even with a plastic neutral axis in the bottom flange.

Finite element modellingThe experimental work had provided a great deal of information about thebuckling problem, but if the eventual objective of developing design rules

to avoid web buckling in unstiffened or, if need be, stiffened webs was to

be achieved, a numerical procedure for parametric studies was necessary.

Accordingly, a simulationof the tapered beam was developed using a non-linear large deflection elasto-plastic finite element program, FINAS 9.10,

which is particularly useful for plate and shell problems. This simulation

was first validated against the experimental results. It was then used to gen-

erate new results, initially to extend the experimental work by predicting the

thickness between 5mm and 3mm where buckling would first occur, and

then to produce a full blown parametric study" which made it possible to

formulate simple design rules l*.

It was not trivial matter to develop the finite element simulation. On one

hand, a number of computer system changes delayed progress, and other

computing constraints meant that the mesh wasperhaps rather coarser than

was ideal. On the other hand, the mechanics of the tapered panel itself

meant that a number of spurious modes such aslasticity at shallow sections

4RI Node disposiiion l49

94

89

33

25

17

9

' II 1.3 0.65

t

Fig 13.Finite element meshfor web

The Structural EngineerIVolume 74/No 16 February 1996 45




of the simulation or points where loads were applied had to be eliminatedby local changes to the yield stress r incorporation of stiffeners. The finalmesh, of 112 shell elements, is shown in Fig 13. Because of symmetry, it

was possible to consider one-half of the tapered panel, plus an adjacent

‘loading arm’ which had rather different proportions from those used in thelab but a very similar purpose, i.e. to introduce a uniform moment into the

central panel. The flanges,ot shown in the figure, were also modelled usingshell elements. Lateral (but not torsional) buckling of the compression

flange was prevented by the use of out-of-plane constraints at the top edge

of the web.The first set of runs for the web panels of phase 1 used a nominal yield

stress of 265MPa andan imperfection pattern in the formf a half sine wave

in the longitudinal and vertical directionsf maximum amplitudeDl250 orabout 2.5mm. In a subsequent stage, some check calculations were made

with the experimentally measured imperfections and thetrue’ (i.e. non-vir-gin coupon) yield stresses. An exhaustive discussion of the results of the

simulations has been given elsewhere* and will not be repeated here. Insteada few salient features will be discussed.

(1) The finite element calculations generally overestimated the experimen-

tal peak loads by up to 20%. This suggests that the FE model withts coarsemesh was overstiff and that the residual stresses present in the tests and

ignored in the FE model were significant. As well, constraints to the panel

edges prevented plastic hinges forming rightt the edges, forcing the hingesinwards and the peak load up. In the lab, peak loads were often not reachedas deflection limits determined the endf some of the experiments. The FE

results were insensitive to the yield stress and deflection imperfectionVal-

ues used.(2) On a more positive note, theFE model produced very similar buckling

patterns in the beams that did buckle. A good match was seen to the post-buckled shapeof the 3mm web, and even to the flange failures of the phase

experiments.(3) Accordingly, enough confidence was felt to extend the phase 1 experi-ments numerically by analysing beams with 3.5, 4 and 4.5mm webs to

complement the experimental and numerical data for 3 , 5 and 7mm webs.

The boundary between buckling failure and panel edge plastification wasfound to be the 4mm webDlt =162) where features f both modes appeared

in the FE results.

(4) The FE modelling confirmed the phase 2 experimental results, in thatweb buckling was not induced in a 5mm web (Dlt =130) by dropping theplastic neutral axis. Instead, the calculations predicted the flange failures

found in the lab.

Conclusions

The phase 1 experiments demonstrated that a tapered web panel with 1 10

slopes will buckle f Dlt =215 but not buckle f Dlt =130. Numerical stud-

ies showed that the switch between buckling and plastification occurs atabout Dlt =l6 0 for these rather large slopes. These results suggest that, inthe absenceof shear, the web buckling problems not as serious as was orig-

inally thought, occurring in rather slender webs in response to rather large

slope changes.The phase 2 experiments demonstrated that dropping the plastic neutral

axis down the web did not seriouslyrode the stability of the D/t =l3 0 webin the absence of coexisting shear, although some unlooked-for conse-

quences were found on the top flange stability in the laboratory model.Taken together, these conclusions suggested that it would be possible to

avoid the use f stiffeners in most practical beams. This view was confirmedin the subsequent parametric study” and made the formulation of designchecks ’* rather simpler than was expected t the start of the project. Giventhe highcost of fitted stiffeners, the expedientf slightly increasing the webthickness to avoid buckling seems to be the most satisfactory approach in

limiting cases.

Acknowledgements

The experimental programme was funded by the Science & EngineeringResearch Council, and specimens, advice and support provided by WardBrothers Sherburn. The Brazilian National Science Foundation, CNPq, pro-vided a studentship which made t possible to do the work.We are grateful

to these three bodies and to the laboratory stafff Imperial Collegefor theirsterling work.

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Home, M.R., Shakir-Khalil, H., and Akhtar, S.: ‘Tests on tapered andhaunched beams,’Proc. ICE, Part 2,67, 1979, pp845450

Lawson, R.M., Rackham, J.W.: ‘Designf haunched composite beams

in buildings,’ Steel Construction nstitute, SCI Publication 060, 1989

Vellasco, P.C.G. da S . : ‘Local web buckling n apered composite

beams’, PhD thesis, Imperial College, London, 1992Bates, D.N.: ‘Non-linear inite element analysis of curved beams and

shells’, PhD thesis, Imperial College, London, 1986Trueb, U.: ‘Stability problems of elasto-plastic plates and shells by

finite elements’, PhD thesis, Imperial College, London, 1983

Vellasco, P.C.G. da S . , Hobbs, R.E:. ‘Local web buckling in taperedcomposite beams - a parametric study’ (in preparation)

Vellasco, P.C.G. da . ,Hobbs, R.E.: ‘A design model for the local webbuckling of tapered beams’ (submitted for publication).

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