ijcerd-civil-engg- influence of flange stiffness … of flange stiffness on ... a 3-d finite element...
TRANSCRIPT
1
6
.
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
2
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
3
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
K. Baskar and Chitra Suresh
4
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.
Influence Of Flange Stiffness On Ductility Behaviour Of Plate Girder
5
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
K. Baskar and Chitra Suresh
6
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
Influence Of Flange Stiffness On Ductility Behaviour Of Plate Girder
7
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-
K. Baskar and Chitra Suresh
8
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
Influence Of Flange Stiffness On Ductility Behaviour Of Plate Girder
9
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.
K. Baskar and Chitra Suresh
10
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
Influence Of Flange Stiffness On Ductility Behaviour Of Plate Girder
11
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
K. Baskar and Chitra Suresh
12
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
Influence Of Flange Stiffness On Ductility Behaviour Of Plate Girder
13
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 )
K. Baskar and Chitra Suresh
14
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
Influence Of Flange Stiffness On Ductility Behaviour Of Plate Girder
15
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
K. Baskar and Chitra Suresh
16
Figure 10: Load-deflection Behaviour of SPG4 with Various Flange Thickness