IJCERD-Civil-Engg- Influence of flange stiffness … OF FLANGE STIFFNESS ON ... a 3-D finite element...

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INFLUENCE OF FLANGE STIFFNESS ON

DUCTILITY BEHAVIOUR OF PLATE GIRDER

K. Baskar

Associate Professor Department of Civil Engineering, National Institute of Technology,

Tiruchirappalli 620 015, Tamilnadu, India

ABSTRACT

The ultimate strength of plate girders designed using tensional field theory is

assumed to depend upon critical buckling strength, post buckling strength of web

panel and yield strength of flanges. Though the load carrying mechanism

depends on the above three contributions, the post yield failure of the girder is

primarily governed by the flange stiffness. Experimental and analytical studies

on plate girders by various researchers show that the flange parameter influences

the post yield behaviour of girders significantly. In the present numerical study,

a 3-D finite element model developed using ANSYS was employed to analyze

plate girders in order to investigate further the influence of flange stiffness on the

behaviour of plate girders. It was observed from the results that the girders with

larger Mp/M ratio provide more ductile compared to the girders having lesser

Mp/M thus confirming the influence of flange parameter on ductility behaviour

of plate girders. Also, it was noted that the girders with larger d/t ratio provide

more ductility compared to the girders with smaller d/t ratios. The paper

presents the results obtained from the finite element analyses on girders having

different values of flange stiffness.

International Journal of Civil Structural

Environmental And Infrastructure

Engineering Research

Vol.1, Issue.1 (2011) 1-15

© TJPRC Pvt. Ltd.,

K. Baskar and Chitra Suresh

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Keywords: Plate girder, Flange, Buckling, Tension field, Stiffness, Post

buckling.

1. INTRODUCTION

Rockey and Skaloud (1968, 1972) showed that for plate girders having

proportions similar to those employed in civil engineering, the ultimate load

capacity is greatly influenced by the flexural rigidity of the flanges. They

showed that the collapse mode of the plate girders involve development of

plastic hinges in tension and compression flanges. Rockey and Skaloud

conducted ultimate load tests on three series of plate girders in each of which

only the size of the flanges, and therefore their flexural rigidity, was varied. The

position of the internal hinges was found to vary with flange stiffness, the value

‘c’, which defines the position of plastic hinge, increasing from near zero in the

case of flexible flanges to approximately 0.5b when the flanges are strong. It is

also proved experimentally that it is possible to increase the ultimate shear

strength of the web to the extent of 60% by simply increasing the flexural

rigidity of the flange.

Porter et al (1975) presented an equilibrium solution to calculate the

ultimate strength of plate girders. It is assumed that the web panels are simply

supported along its boundaries; this assumption obviously leads to lower limit.

Fujii (1968), Chern and Ostapenko (1969) and Komatsu (1971), on the other

hand assumed that the flanges provide a fully clamped condition and the vertical

stiffeners providing a simple edge support. The correct buckling solution lies

somewhere between these two extreme solutions. Porter et al, also assumed that

the effect of bending stresses on the shear buckling stress of the web and the

variation of over the web panel could be ignored.

Based on their experimental observation and equilibrium approach,

Porter et al (Ref) proposed the expression shown in Eqn. 1 to calculate the

ultimate shear carrying capacity of steel plate girders.

Influence Of Flange Stiffness On Ductility Behaviour Of Plate Girder

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c

pfMcbdt

ytdtcrsV

4)cot(

2sin ++−+= θθστ (1)

This expression has been shown as more effective and further reduced

to extreme cases such as girders with weak flanges, strong flanges and thick web.

In the case of weak flanges, the value of flange strength becomes very small and

it is neglected from the equation. When the flanges are very strong, it was

assumed that the distance of the plastic hinge, c, away from the end of the panel

increases and becomes equal to the panel width, b, the hinges formed at four

corners of the panel to form a ‘picture frame’ mechanism. The tension field was

assumed to act at an angle of 45o and the value of ‘c’ was considered as equal to

‘b’ to obtain the limiting value of shear capacity. In the case of a girder with

thick web, they assumed that the web may yield before it buckles so that no

tension field action would develop. The theory proposed by Porter et al has

been validated by checking with experimental results reported by a number of

researchers.

The development of tension field and collapse mechanism of shear

panels isolated from plate girders were studied using the finite element method

by Kuranishi et al (1988). Special attention was paid to the influence of the

rigidity of flanges and the boundary conditions of web panel. It was found that

no plastic hinge appeared in flanges ever in the ultimate state, and that a collapse

mechanism was formed when the yielded zones propagate completely in the

diagonal direction of the panel. Kuranishi et al (1988) considered four different

panel aspect ratios viz. 0.5, 0.75, 1.0 and 1.5 and three different web

slenderness ratios such as 152, 180 and 250 in their numerical study.

Shanmugam and Baskar (2003), vice-verse, have carried out experimental and

numerical investigation on steel-concrete composite plate girders. Two bare

steel plate girders and ten steel-concrete composite plate girders with two

different d/t ratios of web plate and varying Mp/M ratio of flanges were

considered in the investigation. It was noticed from these experimental and


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numerical studies that the stiffness of the flanges greatly influences the post yield

behaviour of the plate girders. Further numerical investigation is made in this

present study using four different bare steel plate girders with d/t ratios of 250,

150, 125 and 94 which are named as SPG1, SPG2, SPG3 and SPG4,

respectively. A constant panel aspect ratio 1.5 is considered for all the girders.

The previously tested girders (Baskar & Shanmugam, 2003), SPG1 and

SPG2 are considered as reference girders and the numerical investigation is

made by varying the flange stiffness over the girders. SPG3 and SPG4 are

subjected to only numerical study and the results obtained from the studies are

presented herein.

2. DETAILS OF THE PLATE GIRDER

The girders were designed using tension field theory in accordance with

BS5950: Part 1: 1990. When d/t ratio is less than 63ε (ε = (275/ρy)0.5), the

girder has to be considered as a beam in which no tension field effect can be

considered; when the ratio exceeds the above value the effect of tension field

action can be included and designed as plate girder. In normal practice plate

girders are designed with a d/t ratio ranging from 120 to 160 and BS5950: Part1

allows up to a maximum value of 250. It is also noted (Evans and Moussef,

1988) that the contribution from the post buckling reserve strength of the web

plate increases with increasing d/t ratio. In view of the above factors,

Shanmugam and Baskar (2003) considered two different d/t ratios viz. 250 and

150 in order to study the behaviour of plate girders. From a practical

consideration of welding and availability of minimum thickness of plates, a 3mm

thick plate was chosen for the web for girders with a d/t ratio of 250 (SPG1), and

a 5mm thick plate for girders with a d/t ratio 150 (SPG2). The panel aspect ratio

of the web was restricted to 1.5 in all girders. SPG3 and SPG4 are provided

with a web thickness of 6mm and 8mm, respectively, such that their d/t ratios are

125 and 94. The d/t ratios of all the four girders are more than 63ε and

therefore, the tension field theory can be applied.


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Proportioning the flange dimension is critical in the case of girders

subjected to tension field action. The shear carrying capacity is calculated from

the three different contributions such as critical buckling strength of web, post

buckling reserve strength of web panel and the yielding of flanges. At the

beginning, the flange sections are designed by beam theory; but such a

calculation provides a minimum flange dimension which leads to the ultimate

load in perfect cases and lateral torsional mode of failure in some other cases.

Therefore, the SPG1 and SPG2 were designed with larger Mp/M ratio where Mp

is the plastic moment capacity of section provided and M is the bending moment

due to the load which is calculated from the ultimate shear capacity of the girder.

The minimum flange thickness required from the beam theory is shown in Table

1. In view of controlling the experimental behaviour of SPG1 and SPG2, the

flange dimensions were taken as 200mm x 20mm and 260mmx20mm,

respectively. These dimensions were decided based on a parametric study

through FE analyses. The details of the considered girders are shown in Fig.1

and Table-1.

3. FINITE ELEMENT ANALYSIS

In view of carrying out a parametric study with various flange stiffness,

a three dimensional finite element (FE) model of a plate girder was developed

using the multi-physics finite element software ANSYS (Version-11). Girder

SPG1 was employed in developing the finite element model. The web, flanges

and stiffener plates were modelled with 8-noded shell element with six degrees

of freedom at each node which is referred as SHELL281 in ANSYS element

library. SHELL281 is identified as well-suited for linear, large rotation, and/or

large strain nonlinear applications and for analyzing thin to moderately-thick

shell structures. The element also provides special features such as stress

stiffening, large deflection and large strain capabilities.

The elastic and inelastic properties of the girder materials were

provided to represent the entire behaviour. In the elastic region the material was


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treated as linear isotropic and in the plastic region the von-Mises yield criterion

invoked with Multi-linear Isotropic Hardening. The first mode shape from

buckling analysis was considered as the initial imperfection in the web panel.

Non-linear behaviour of material and geometric non-linearity due to large

deformations were considered in the analyses. The load was applied in steps

with smaller increment to simulate the monotonic ramp loading of the

experiment. The load vs deformation pattern was analyzed under all the critical

load steps.

4. RESULTS AND DISCUSSION

The girder was initially analyzed without considering the web

imperfection and noticed that the webs reached to a yielding mode of failure

rather than reaching the buckling mode as expected in tension field theory.

Further analysis was made with assumed initial imperfection in the web panels

and noticed the expected tension field action in the web panels. Modelling the

initial imperfection plays a major role in achieving the post yield behaviour of

the girder. Out of various available methods, the mode shape superposition was

employed to simulate the web imperfection. A buckling analysis was carried out

at the first stage and the deformed shape from the first mode of buckling analysis

was imported as the imperfection of web panels. In the second stage, the non-

linear analysis was carried out.

The mid-span deflections under various load steps were monitored and

retrieved from the FE analysis. A graph was plotted between load and the mid-

span deflection and was compared with the experimental prediction. The FE

model was able to predict the ultimate failure load and the behaviour of girder to

an acceptable accuracy. The same modelling technique was adapted to model

the previously tested girder SPG2 and the numerically predicted results were

compared with experimental results as shown in Fig.2. From these comparisons

of experimental vs numerical results of previously tested girders, SPG1 and


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SPG2, it is concluded that the FE model can predict the ultimate load and its

behaviour to an acceptable accuracy and thus the FE model was validated.

Further to the validation of model, the parametric study was carried out.

The flange thickness alone varied keeping the other parameters constant. The

girders were investigated from the minimum flange thickness which is required

from the beam theory to a maximum limit of 30mm. The minimum thickness

shown in Table 1 may be sufficient if the girder webs also designed by beam

theory. Since, the present girder webs are designed using tension field theory,

the web start buckles and further leads to lateral torsional buckling mode of

failure under lower flange thicknesses. The FE model predicted a premature

failure of girders without reaching the ultimate load. Therefore, further increase

in flange thickness was considered.

The girder SPG1 with a flange thickness of 10mm reached the desired

load of 420kN and showed reduction in load carrying capacity after reaching the

ultimate load. It is proved that the minimum thickness of flanges could reach the

ultimate load but no ductility would be obtained.

Further increase in flange thickness increased the ultimate to certain

extent and the ductility to a greater extent. The uniform increase in the load-

deflection profiles can be clearly seen from Fig-3. It is observed that the yield

load as well as the ultimate load increases with the flange stiffness. It can also

be noted that the increase in flange stiffness widens the curve and becomes more

flatten with considerable increase in the deflection range. It reveals that the

ductility factor increases i.e. it undergoes large deformations without decrease in

the load. The ductility factor and ultimate load of the plate girders with various

flange thicknesses were calculated and listed below in Table 2.

Similar behavior was observed in Girder SPG2. The minimum flange

thickness required for SPG2 is 10mm as shown in Table-1. Referring to the Fig-


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4, though the 10mm thickness flange reached the required ultimate load, it loses

its load carrying capacity immediately after the yield load which indicate the

lower thickness flange is not able to provide any ductile behavior. The same

behavior is observed in SPG2 up to a flange thickness of 18mm. A lateral

torsional buckling mode of failure was observed for the flange thicknesses varies

from 10mm to 18mm. On the other hand the ductility behavior is observed only

when the flanges are provided such that the Mp/M ratio more than 2.5. The

ductility factor increases with increase in Mp/M ratio and shows a direct

proportion. This can be noticed from Table-3

Results obtained from SPG3 and SPG4 indicated a different behavior

from SPG1 and SPG2. The girders SPG3 and SPG4 are not reached the

expected ultimate loads which were calculated through the tension field theory.

A sudden decrease in load capacity is noticed after the yield load. No ductile

behavior was observed for SPG3 and SPG4. These can be revealed from Fig-5

and Fig-6. No increase in ultimate load also noticed for smaller d/t girders.

From the Table-2 it can be seen that the ultimate load capacity increases

even up to 41.5% with the increase in flange stiffness for the girder SPG1 with a

d/t ratio of 250. But Table -3 to Table -5 indicate that the increase in ultimate

load w.r.t. flange thickness is decreasing with decreasing d/t ratios.

5. CONCLUSION

From the present study the following conclusions are drawn.

• The ductility factor is less for the girders with Mp/M ratio less than 2.5, and

it increases drastically with increase in Mp/M ratio more than 2.5. This

observation is made only for girders with d/t ratios equal to or greater than

150. For girders with d/t ratio 125 and 94, no ductility behaviour is

observed.

• Girders with larger d/t ratio (i.e for 250 and 150) are sensitive to the flange

stiffness. These types of girders provide more ductile behaviour for the


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increasing flange thickness. Also, showed up to 41% increase in ultimate

load for the increased flange thickness.

• For girders with smaller d/t ratios, not much difference is observed between

Mp and M.

• Consideration of small increase in flange thickness provides better ductility

behaviour and therefore well suited for seismic regions.

REFERENCES

1. Baskar. K and Shanmugam. N. E.(2003). Steel–concrete composite plate

girders subject to combined shear and bending. Journal of Constructional

Steel Research, Volume 59, Issue 4, pp 531-557.

2. Chern, C. and Ostapenko, A. (1969). Ultimate Strength of Plate Girders

under Shear. Lehigh Univ, Dept Civ. Eng. Fritz Eng Laboratory Report

328.7.

3. Evans, H.R. and Moussef, S. (1988) Design Aid for Plate Girders.

Proceedings of the Institution of Civil Engineers, V.85, Pt. 2, pp.89 – 104.

1988.

4. Fujii, T. (1968), On an Improved theory for Dr. Basler’s theory. Proc. 8th

Congress, IABSE, New York, Sep.pp.477-487.

5. Komatsu, S. (1971). Ultimate Strength of Stiffened Plate Girders Subjected

to Shear. Proc., Colloquium on Design of Plate and Box Girders for

Ultimate Strength. IABSE, London, pp.49-65.

6. Kuranishi, S. et al. (1988). On the Tension Field Action and Collapse

Mechanism of a Panel under Shear. Structural Eng. /Earthquake Eng.,

Japan Society of Civil Engineers, V.5, N.1, pp.183-193.

7. Porter, D.M., Rockey, K.C. and Evans, H.R. (1975). Collapse Behaviour of

Plate Girders Loaded in Shear. Struct Eng, Volume 53, Issue 8, pp.313-

325.


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8. Rockey, K.C and Skaloud, M. (1972). The Ultimate Load Behaviour of

Plate Girders Loaded in Shear. The Structural Engineer, 50(1), pp.29-48.

9. Rockey, K.C. and Skaloud, M. (1968). Influence of Flange Stiffness upon

the Load Carrying Capacity of Webs in Shear. Final Report, Proc. 8th

Congress, IABSE, New York, pp.429-439.

10. Shanmugam, N E and Baskar, K. (2003) “Steel-concrete Composite Plate

Girders Subject to Shear Loading.” Journal of Structural Engineering,

ASCE, Volume 129, Issue 9, pp. 1230-1242.

Table 1: Dimensions of the Plate Girders Considered

l. No Girder

d/t ratio

Thickness of web provided, mm

Min. Flange size required, mm

Actual flange size of tested girders, mm

bf tf bf tf

1 SPG1 250 3 200 6.71 200 20

2 SPG2 150 5 260 9.99 260 20

3 SPG3 125 6 260 13.35 - -

4 SPG4 94 8 260 21.72 - -

Table 2: Ductility Factor and Increase in Ultimate Load of SPG1

Sl.N

o

Fla

ng

e th

ickn

ess,

m

m

Mp/

M r

atio

Def

lect

ion

at M

y

Def

lctio

n a

t M

ult

Du

ctili

ty f

acto

r

Ulti

mat

e lo

ad,

kN

% in

crea

se in

u

ltim

ate

load

w.r

.t fir

st g

ird

er

1 10 .57 5 - - 422.77 0.00 2 14 2.20 5 - - 440.47 4.20

3 16 2.51 5 - - 453.31 7.20

4 18 2.83 5 45 9.0 467.57 10.6

5 20 3.14 5 81 16.2 483.68 14.4

6 22 3.46 5 11 22.2 502.28 18.8

7 24 3.77 5 >126 >25.2 523.36 23.8

8 26 4.08 5 >126 >25.2 546.86 29.4


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9 28 4.40 5 >126 >25.2 572.28 35.4

10 30 4.71 5 >126 >25.2 598.40 41.5

Table 3: Ductility Factor and Increase in Ultimate Load of SPG2 S

l.No

Fla

ng

e th

ickn

ess,

m

m

Mp/

M r

atio

Def

lect

ion

at M

y

Def

lect

ion

at

M ult

Du

ctili

ty f

acto

r

Ulti

mat

e lo

ad,k

N

% in

crea

se in

u

ltim

ate

load

w.r

.t fir

st g

ird

er

1 10 1.13 5 - - 754.66 0.00

2 14 1.58 5 - - 766.09 1.51

3 16 1.80 5 - - 767.47 1.69

4 18 2.03 5 - - 780.68 3.41

5 20 2.25 5 34 6.8 788.79 4.45

6 22 2.48 5 59 11.8 806.31 6.67

7 24 2.70 5 88 17.6 825.04 8.99

8 26 2.93 5 >88 >17.6 846.39 11.58

9 28 3.15 5 >88 >17.6 871.38 14.53

10 30 3.38 5 >88 >17.6 900.32 17.86

Table 4: Ductility Factor and Increase in Ultimate Load of SPG3

Sl.N

o

Fla

ng

ethic

knes

s,

mm

Mp/

M r

atio

Def

lect

ion

at M

y

Def

lect

ion

at

Mul

t

Du

ctili

tyfa

cto

r

Ulti

mat

e lo

ad,

kN

% in

crea

se in

u

ltim

ate

load

w

.r.t

first

gir

der

1 4 1.13 4 - - 1006.79 0.00 2 6 1.29 4 - - 1009.35 0.25 3 8 1.45 4 - - 1023.26 1.63 4 0 1.61 4 - - 1027.43 2.04 5 2 1.77 4 - - 1034.76 2.75 6 4 1.93 4 - - 1041.09 3.37


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7 6 2.10 4 - - 1046.72 3.91 8 28 2.26 4 - - 1052.79 4.49 9 30 2.42 4 - - 1070.40 6.16

Table 5: Ductility Factor and Increase in Ultimate Load of SPG4 S

l.No

Fla

ng

e th

ickn

ess,

m

m

Mp/

M r

atio

Def

lect

ion

at M

y

Def

lect

ion

at

M ult

Du

ctili

ty f

acto

r

Ulti

mat

e lo

ad,

kN

% in

crea

se in

u

ltim

ate

load

w.r

.t fir

st g

ird

er

1 24 1.10 5 - - 1591.42 0.00

2 26 1.19 5 - - 1603.20 0.74

3 28 1.28 5 - - 1614.16 1.42

4 30 1.37 5 - - 1622.90 1.97

Fig. 1 Variation of Shear Strength with Web Slenderness


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0

50

100

150

200

250

300

350

400

450

0 0.05 0.1 0.15 0.2 0.25

Strain

Str

ess

[N/m

m2 ]

Fig. 2: Details of Plate Girder

Fig. 3 Typical Stress-Strain Curve for Steel

Fig. 4: Load vs Deflection Behaviour of Girders SPG1 to SPG4 (Ansys vs Experimental results)

0

200

400

600

800

1000

1200

1400

1600

1800

0 20 40 60 80 100

Load, kN

D eflection , m m

SPG 1 (Ex p t) SPG 1 (An sy s ) SPG 2 (Ex p t)

SPG 2 (An sy s ) SPG 3 (An sy s ) SPG 4 (An s y s )


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Fig.5. Typical View of the Girder SPG1 at Ultimate Load [Shanmugam, N.E. and Baskar, K., 2003]

Fig.6. Deformed Shape of the Girder SPG1 Predicted through FE Model

Figure 7: Load-deflection Behaviour of SPG1 with Various Flange Thickness

0

100

200

300

400

500

600

0 20 40 60 80 100

Deflection, mm

Load,

kN

30mm

28mm

26mm

24mm

22mm

20mm

18mm

16mm

14mm

10mm

0

100

200

300

400

500

600

700

800

900

1000

0 20 40 60 80 100Deflection, mm

Load,

kN

30mm

28mm

26mm

24mm

22mm

20mm

18mm

16mm

14mm

10mm


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Figure 8: Load-deflection Behaviour of SPG2 with Various Flange

Thickness

Figure 9: Load-deflection Behaviour of SPG3 with Various Flange

Thickness

0

200

400

600

800

1000

1200

0 20 40 60 80 100Deflection, mm

Load,

kN

30mm

28mm

26mm

24mm

22mm

20mm

18mm

16mm

14mm

10mm

0

250

500

750

1000

1250

1500

1750

2000

0 20 40 60 80 100Deflection, mm

Lo

ad,

kN

30mm

28mm

26mm

24mm

22mm

20mm

18mm

16mm

14mm

10mm


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Figure 10: Load-deflection Behaviour of SPG4 with Various Flange Thickness

IJCERD-Civil-Engg- Influence of flange stiffness … OF FLANGE STIFFNESS ON ... a 3-D finite element...

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