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Page 1

Department of Civil Engineering

Thomas Hansen

Theory of Plasticity for Steel Structures
- Solutions for Fillet Welds, Plate Girders and Thin Plates

BYG • DTUP
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Report no R-146
ISSN 1601-2717
ISBN 87-7877-218-4

Page 2

Theory of Plasticity for Steel Structures

- Solutions for Fillet Welds, Plate Girders and Thin Plates























Thomas Hansen



Ph.D. Thesis

BYG DTU – Department of Civil Engineering
Technical University of Denmark

Birch & Krogboe A/S
Consultants and Planners

2006

Page 128

PART II

111

lateral stability occurred. These UNP-profiles may have influenced the load-carrying
capacity due to friction. Secondly, the applied loading system of four jacks turned out
to be unsuitable for representing a uniformly distributed load. At the start of the
uploading phase it appeared to function correctly, however before reaching the
maximum load, the jack nearest the fixed end loosened in both tests, so it was not
subjecting any load to the girders at all.
However, the correlation between theory and tests seems to be reasonable.

STRAIN MEASUREMENTS ON THE WEB
No strain rosettes were added to the web plate of the two girders. The photometric
equipment, Aramis, was used to measure the deformations as described in Section 5.2.
Due to the larger length of the test section (L = 3.0 m), Aramis only covered
approximately 70 % of the web plate on girder G8. On girder G7, only 30 % of the
web plate in the test section was covered, because of the special steel frames.
With the same explanation as in Section 5.2, the strains calculated by Aramis were of
no real use.
The aim of the two tests was to see whether a buckling pattern occurred with varying
direction throughout the girders. The deformation plot from Aramis for girder G8 in
Figure 5.37 shows that buckles with different angles with the girder axis indeed did
form more or less as expected. The figure shows a plot of the deformations just before
the maximum load is reached.



Figure 5.37: Deformation plot for girder G8

STRAIN MEASUREMENTS ON THE FLANGES AND STIFFENERS
On the two girder specimens, two pairs of strain gauges were applied to the top flange
as well as on the bottom flange. The gauges were placed 20 mm from the web plate
on one side of the web plate, as in the constant shear tests.
Each transverse web stiffener was equipped with a pair of strain gauges on one side of
the web plate. In the vertical direction, the gauges were placed in the middle of the
stiffeners. In the horizontal direction, the gauges were placed in the middle of the
calculated effective width of the stiffeners. The exact locations of all the strain gauges
are given in Appendix H.

The same notation as for the constant shear tests is used, i.e. H1, H2, V1, etc. where H
refers to gauges on the flanges, and V to gauges on the transverse web stiffeners.
Figure 5.38 shows the load-strain curves for girder G7, and Figure 5.39 shows the
load-strain curves for girder G8. Again, for each plate the strains are shown as the
mean value of the measured strains from each pair of gauges, in order to compensate
for the strains due to bending of the individual plates.

Page 129

D:\thh Documents\Afhandling\Part II - Plastic Tension Field Method\Figures - del 2\Figure 5.37b.eps


THE PLASTIC TENSION FIELD METHOD

112

−0.1 −0.05 0 0.05 0.1 0.15
0

10

20

30

40

50

60

Strain [%]

L
oa

d
[k

N
]

Mean (H1, H2)
Mean (H3, H4)
Mean (H5, H6)
Mean (H7, H8)

a.

−0.1 −0.05 0 0.05 0.1 0.15
0

10

20

30

40

50

60

Strain [%]

L
oa

d
[k

N
]

Mean (V1, V2)
Mean (V3, V4)
Mean (V5, V6)


b.

Figure 5.38: Load-strain curves from strain gauges on girder G7


−0.1 −0.05 0 0.05 0.1 0.15
0

10

20

30

40

50

60

Strain [%]

L
oa

d
[k

N
]

Mean (H1, H2)
Mean (H3, H4)
Mean (H5, H6)
Mean (H7, H8)

a.

−0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15
0

10

20

30

40

50

60

Strain [%]

L
oa

d
[k

N
]

Mean (V1, V2)
Mean (V3, V4)
Mean (V5, V6)
Mean (V7, V8)


b.

Figure 5.39: Load-strain curves from strain gauges on girder G8

Øskan and Bak (2006) made an analysis of the measured strains in the flanges and the
transverse web stiffeners. They calculated the stresses corresponding to the measured
strains and compared the results with the stresses predicted by the lower-bound
solution, cf. Section 2.1. They found a relatively good agreement with the stresses in
the flange and the transverse web stiffeners, determined by the strain gauges closest to
the supported end of the girder, but they found less good agreement with
measurements from the gauges on the flanges and stiffeners closest to the free end of
the girders.

Page 256

APPENDIX J

239



Experiments by Kalyanaraman et al. (1977).

Test series Beams.


be / b No. b / t
[in]

k
[ ]

E
[ksi]

fy
[ksi]


[ ]

cr
[ksi] Test Theory

Theory
/ Test

B-1 60.5 0.961 29457 51.0 2.517 6.99 0.419 0.262 0.625
B-2 53.1 0.920 29908 53.8 2.252 8.82 0.466 0.290 0.623
B-3 44.5 0.832 29556 53.8 1.899 11.21 0.500 0.339 0.679
B-4 36.9 0.791 29559 51.0 1.533 15.52 0.514 0.411 0.800
B-5 29.8 0.798 28984 51.3 1.254 23.54 0.555 0.490 0.883
B-6 23.7 0.584 29477 51.3 0.989 27.70 0.595 0.599 1.006
UP-9 26.0 0.747 29567 42.0 0.980 29.53 0.739 0.603 0.816
UP-10 32.1 0.666 29546 36.0 1.120 17.26 0.622 0.539 0.867
UP-11 38.0 0.804 29430 36.0 1.329 14.81 0.609 0.466 0.765
UP-12 42.8 0.560 29352 36.0 1.499 8.11 0.500 0.419 0.839
Average: 0.790



Experiments by Winter (1947).

Test series I-beams.


be / b No. b / t
[ ]

fy
[psi]


[psi]


[ ] Test Theory

Theory
/ Test

I-S-2 9.3 35400 34600 0.317 0.977 1.000 1.023
I-S-3 10.1 49400 35800 0.407 0.725 1.000 1.380
I-B-3 10.1 37300 30200 0.353 0.810 1.000 1.235
I-B-4 17.5 36800 40300 0.608 1.095 0.873 0.797
I-S-6 18.5 35400 31800 0.631 0.898 0.850 0.946
I-S-7 19.0 34500 26100 0.639 0.757 0.842 1.112
I-S-8 19.1 49400 38800 0.769 0.785 0.732 0.932
I-B-5 20.3 37300 29400 0.710 0.788 0.778 0.987
I-B-6 20.8 34000 29200 0.695 0.859 0.791 0.921
I-B-7 21.6 32600 28800 0.707 0.883 0.781 0.884
I-S-9 21.6 34000 25500 0.722 0.750 0.769 1.025
I-B-8 25.2 38700 30000 0.898 0.775 0.647 0.835
I-S-10 27.1 34500 22900 0.912 0.664 0.639 0.963
I-S-11 27.8 34000 23900 0.929 0.703 0.630 0.896
I-S-12 27.8 34500 29200 0.936 0.846 0.626 0.740
I-S-13 28.3 49400 29200 1.140 0.591 0.532 0.899
I-B-9 28.9 29200 26200 0.895 0.897 0.649 0.724
I-B-10 29.9 32600 24600 0.978 0.755 0.604 0.800
I-B-11 30.6 34900 25700 1.036 0.736 0.576 0.782
I-B-12 31.2 37300 28300 1.092 0.759 0.551 0.727
I-B-14 33.1 34000 23000 1.106 0.676 0.545 0.806
Average: 0.925

Page 257

Department of Civil Engineering

Thomas Hansen

Theory of Plasticity for Steel Structures
- Solutions for Fillet Welds, Plate Girders and Thin Plates

BYG • DTUP
H

D


T
H

E
S

I
S

T
h
o
m

a
s H

a
n
se

n
T
h
e
o
ry

o
f P

la
sticity

fo
r S

te
e
l S

tru
ctu

re
s –

S
o
lu

tio
n
s fo

r F
ille

t W
e
ld

s, P
la

te
G

ird
e
rs a

n
d
T

h
in

P
la

te
s

2
0
0
6

Report no R-146
ISSN 1601-2717
ISBN 87-7877-218-4

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