Investigation on shear buckling of steel welded I-
section beams with reinforced web openings
Jian Wang1 | Zheng Li2 | Mathias Euler1
1 Introduction
Plate girders with I-section frequently require large web
openings to accommodate ducts and pipes in buildings and
bridges. However, Part 1-5 of Eurocode 3 [1] has not pro-
vided appropriate design rules for the shear resistance of
plate girders having large web openings (maximum di-
mension 30 % of the section depth) with or without re-
inforcement up to now.
There have been a large number of investigations in the
last decades from which only the investigations in Cardiff
are addressed here. In the 1980’s, Narayanan et al. [2-4]
investigated girders with slender webs subjected to shear
loading and containing rectangular cutouts with or without
reinforcement in a larger number of studies. The equilib-
rium solution for predicting the ultimate load of unperfo-
rated plate girders (Cardiff model) had been extended for
perforated webs, with the difference that the load is as-
sumed to be carried by the membrane stress developed in
two tension bands in perforated webs, one band above and
the other below the cutout [2].
Furthermore, a procedure for designing the reinforcement
for circular and rectangular web openings has been sug-
gested based on a theoretical model [3]. In general, hori-
zontal reinforcements above and below the cutout are con-
sidered as shown in Figure 1a. Furthermore, Narayanan et
al. [4] determined the elastic buckling loads of plates sub-
jected to shear loads containing circular and rectangular
openings with or without reinforcement through linear
elastic finite element analyses (FEA). It could be shown
that the critical load equivalent to an unperforated plate
can be achieved by an appropriate reinforcement of the
opening. Sabir & Chow [5] extended the linear elastic in-
vestigations on plates with reinforced square holes by
means of FEA for uniform uniaxial and biaxial loading.
Figure 1 Types of square web opening reinforcement: a) horizontal,
b) vertical, c) all around
The results of the aforementioned and other experimental
investigations were summarized by several international
design guides such as the German DASt-Richtlinie 015 [6]
and AISC Steel Design Guide on steel and composite
beams with web openings [7]. Both guidelines were firstly
published in 1990.
In the recent past, several authors investigated web open-
ings by means of nonlinear finite element models and per-
formed extensive parametric studies on the influence of
the size, the type (see Figure 1), the number and the lo-
cation of the web openings and the wall thickness of the
opening reinforcement, see for example Prakash et al. [8],
Shaker & Shahat [9,10], Wafi & Al-Thabhawee [11], Durif,
Al-Dafafea et al. [12,13].
ORIGINAL ARTICLE
Abstract
Plate girders with I-section frequently require large web openings to accommodate
ducts and pipes in buildings and bridges. It is known that the critical load equivalent
to an unperforated plate can be achieved by an appropriate reinforcement of the
web opening. The majority of the investigations on thin-walled webs with web open-
ing under shear loading has been focused on web slendernesses ranging between
200 to 360. Three tests on plate girders with a web slenderness of 416 are presented
that contain web openings. The effect of an all-around reinforcement (hollow sec-
tion) of the web opening is studied in three-point bending tests. The tests are cal-
culated with finite elements accounting for imperfections that had been measured
before testing. A parametric study is performed to evaluate different types of rein-
forcements for high web slendernesses.
Keywords
Shear buckling, Reinforced web openings, Steel plate girder, 3D Laser Scanning
Correspondence
Jian Wang M.Sc.
Brandenburg University
of Technology
Chair of Steel and Timber
Structures
Konrad-Wachsmann-Allee 2
03046 Cottbus
Email: Jian.Wang@b-tu.de
1
Brandenburg University of
Technology, Cottbus, Germany
2
Technical University of Berlin,
Berlin, Germany
Proceedings
in civil engineering
Proceedings
in civil engineering
https://doi.org/10.1002/cepa.2361 wileyonlinelibrary.com/journal/cepa
ce/papers 6 (2023), No. 3-4
© 2023 The Authors. Published by Ernst & Sohn GmbH.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and
reproduction in any medium, provided the original work is properly cited
1754
The majority of the investigations on thin-walled webs with
web opening has been focused on web slendernesses
ranging between 200 to 360 [14]. In this paper, three
tests on plate girders with a very high web slenderness
(height-to-thickness ratio) of 416 are presented that con-
tained web openings. The effect of a reinforcement accord-
ing to Figure 1c is studied. The tests are calculated with
finite elements accounting for imperfections. A parametric
study is performed to evaluate different types of reinforce-
ments for very high web slendernesses.
2 Experimental investigations
2.1 Test specimens
Three test specimens with a web slenderness of 416 were
fabricated as shown in Figure 2. Specimen #1 contained a
square web opening in one of its two subpanels without
reinforcement and served as reference for the other two
specimens whose square web openings were reinforced.
Table 1 summarizes the dimensions of the test specimens.
The length of all test specimens measured 2368 mm al-
lowing a span of 2360 mm for the tests. The dimensions
of the flanges and stiffeners were chosen in such a way
that web failure under shear stresses was induced. Due to
the very high web slenderness, the effect of the bending
moments on the web could be neglected.
Figure 2 Geometry of the test specimens
Table 1 Dimensions of the test specimens
No Web
depth
Web opening Web opening
reinforcement
hw [mm] number B [mm] t [mm] b [mm]
1 416 1 200
2 416 1 200 8 140
3 416 2 200 8 140
The outer dimensions B of the square web openings in Fig-
ure 2a are constant and measured 200 mm for all speci-
mens. Thus, the web opening dimensions corresponded to
almost half of the web depth. The diagonal length of the
openings is 282 mm, which roughly corresponds with the
width of the tension band of the unperforated web under
shear loading according to DASt-Richtlinie 015 [6].
The web openings were automatically cut into the sub-
panel by plasma cutting. There is only one opening in one
subpanel for specimens #1 and #2, thus the other sub-
panel is unperforated. Both subpanels of specimen #3 had
a web opening.
The web openings of specimens #2 and #3 were rein-
forced by a hollow section profile serving as stiffener and
connected to the web by double filet welds. The depth b of
the web opening reinforcement was 140 mm for speci-
mens #2 and #3. Thus, the ratio b/B amounted to 0.70
for these specimens. The thickness of the stiffeners was
8 mm, so that the reinforcement had a sufficiently large
plastic bending moment capacity to avoid plastic failure of
the reinforcement during the tests.
All web openings were located in the middle of the sub-
panels. Nevertheless, the position of the web opening
seems to have hardly any influence on the shear re-
sistance according to Wang et al. [15].
2.2 Material properties
The test specimens were made of structural steel having
different steel grades. For the numerical analysis of the
test specimens, the material properties of the steels were
determined from tensile tests with flat samples. Since the
thickness of the web measured only 1 mm, flat samples
according to DIN 50125 [16] were chosen. Three samples
were tested for each component in longitudinal and trans-
verse direction of the plate.
Based on the tensile tests, Young’s modulus was approxi-
mately 200 GPa for the flanges and stiffeners and about
165 GPa for the webs. The true stress-strain relationships
were determined according to Annex C to Part 1-5 of Eu-
rocode 3 [1] from the engineering stress-strain curve of
the tensile tests. Table 2 shows the true stress-strain re-
lationships of the specimens. The yield strength was
180 MPa for the webs, 380 MPa for stiffeners and 320 MPa
for the flanges.
Table 2 True stress-strain relationships for test specimens
Plastic strain [-] 0.00 0.05 0.10 0.15 0.20
Stress
[MPa]
Flange 320 355 415 455 485
Stiffener 380 480 520 550 580
Web 180 280 310 360 380
2.3 Imperfection measurement
The geometric imperfections of all test specimens were
captured by 3D laser scanning. The local imperfections of
the webs were measured. The resulting point clouds were
processed in Matlab. Figure 4 shows the out-of plane im-
perfections of the specimen #2’s web in comparison to the
perfectly flat web. The maximum amplitude amounted to
about 3 mm.
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Figure 3 Measured out-of plane imperfection, web of specimen #2
2.4 Experimental test setup
The specimens were tested under three-point bending as
shown in Figure 4. The vertical force was applied by a hy-
draulic cylinder, denoted as ‘2’ in Figure 4, and concentri-
cally introduced as line load on the specimen through the
transverse stiffener (‘3’) at midspan.
Figure 4 Experimental setup of specimen #3 (1 – supports, 2 – hy-
draulic cylinder, 3 – transverse stiffener at loading section)
The test set-up was statically determinate since angle pro-
file at the supports, denoted as ‘1’ in Figure 4, prevented
horizontal support actions. Transducers were arranged on
top and bottom flanges of one subfield and measured the
vertical displacements u
z
(deflection) of the top and bot-
tom flanges at midspan. Additionally, six transducers were
attached to the web to record the lateral displacements of
the test specimen. Furthermore, four strain gauges were
attached to the outer faces of the web opening stiffener’s
corners of each specimen to examine the strain state of
the stiffeners since these regions are subject to stress con-
centrations.
The loading of the specimens was initially force-controlled
with a loading speed of 5 kN/s and then displacement-con-
trolled with a loading speed of 2 mm/min and a sampling
rate of 10 Hz.
Each specimen was first loaded up to 20% of the estimated
load-bearing capacity, that was assumed to be 10 kN, in
order to check the test set-up and the measuring system.
Then, the load was increased until web buckling occurred.
The test was terminated when the load dropped signifi-
cantly.
2.5 Test results
Figure 5 indicates the failure mode of all tested specimens
after testing. Test specimens #1 and #3 began to buckle
in vicinity of one corner of the web opening induced by
shear stresses. In contrast, the unperforated subpanel of
specimen #2 buckled.
Figure 5 Failure modes in tests: a) specimen #1, b) specimen #2,
c) specimen #3
At the post-critical stage, a classical tension band devel-
oped in the unperforated subpanel of specimen #2 with
corresponding plastic hinges in the flanges. The structural
behaviour of specimen #2 can obviously explained with
classical tension band theory of Höglund [17] for unperfo-
rated webs under shear loading.
In contrast, two tension bands formed in the subpanels
with web openings of specimen #1 and #3; one above and
the other below the web opening. Plastic hinges in the
flanges are also recognisable for these specimens.
For specimen #1, the subpanel with web opening had a
lower shear resistance due to the missing reinforcement
than the unperforated subpanel. Therefore, it failed, and
the unperforated subpanel stayed elastic, Figure 5a. In
contrast, the unperforated subpanel of specimen #2 be-
came decisive since the reinforcement of the web opening
in the other subpanel was strong enough to compensate
the loss of shear resistance due to web opening, Figure 5b.
The symmetrical specimen #3 showed a similar failure
mode in both subpanels, Figure 5c.
The load-displacement curves are displayed in Figure 6.
The vertical displacement at midspan is considered. The
curve initially runs almost linearly elastic until about 70%
of ultimate load of specimens #1, #2 and about 85% of
ultimate load of specimens #3. When approaching the
elastic critical load, the slope of the curve decreases in a
nonlinear way until the curve runs almost horizontally.
[mm]
1756
The development of a significant post-buckling strength
before final collapse for specimen #1 is assumed to be
caused by the two tension bands. The plastic deformation
was finally limited due to the formation of cracks starting
from the sharp corners (high stress concentration) of the
unreinforced web opening, see Figure 5a.
Figure 6 Load-displacement curves of tested specimens from tests and
FEA (maximum amplitude of imperfection = 3 mm, see Sec. 2.3)
The plastic plateau at ultimate load for specimen #2 and
#3 is caused by tension bands in connection with strain
hardening and the Vierendeel failure mechanism (plastic
hinges) in the flanges.
The ultimate load of 22 kN for specimen #1 was approxi-
mately doubled for specimen #2 (43 kN) and specimen #3
(48 kN). Interestingly, specimen #3 with reinforced web
openings reached a slightly higher ultimate load than
specimen #2 that failed in the unperforated subpanel. Ob-
viously, the reinforcement of the web openings of speci-
men #3 over-compensated the loss of shear resistance
due to the web openings. While the specimens with rein-
forced web openings showed a comparable initial stiffness,
specimen #1 behaved softer in the elastic range.
3 Finite element calculations and analytical con-
sideration
3.1 Finite element calculations
The specimens are numerically investigated by a finite el-
ement analysis (FEA) using the software package Abaqus
[18]. The tested specimens are simulated with their geo-
metric dimensions according to Figure 2 and Table 1. The
material properties of the FE model are based on the ma-
terial characterization according to Table 2. To mesh the
generated numerical geometry, four-node shell elements
(S4R) are used. The minimum element size of 10 mm was
identified through a sensitivity study.
The boundary conditions of the FE model are shown in Fig-
ure 7. In slight deviation from the tests, one support was
horizontally restrained. The analysis method GMNIA ac-
cording to Part 1-5 of Eurocode 3 is performed. The web
is generated as perfectly flat. Equivalent imperfections
based on equivalent deformations affine to the first
Eigenmode shape are considered in the FEA. Therefore, a
linear buckling analysis (LBA) is performed first. Figure 8
shows the first Eigenmode shape of all specimens obtained
from a LBA.
Figure 7 Finite element model of specimen #3 with boundary condi-
tions and load application
Figure 8 First Eigenmode from LBA: a) unperforated web, b) speci-
mens #1, c) specimen #2, d) specimen #3
According to Part 1-5 of Eurocode 3, the maximum defor-
mation of the first Eigenmode is scaled to be h
w
/200 which
gives a maximum amplitude of about 2 mm. This value is
lower than the measurements presented in Section 2.3. It
has to be mentioned that this maximum value is only pro-
posed by Part 1-5 for flat webs without openings. There
are no proposals for webs with openings. Residual stresses
are not considered. Any imperfection of the web opening
reinforcement is neglected.
Figure 6 shows the experimental and numerical load-dis-
placement curves for the specimens. The curves show a
good fit between the FEA and the test results in the elastic
deformation range between 0 mm and 3 mm. When ap-
proaching the elastic critical load, the outcome of the FEA
slightly deviate from the test results. After reaching the
elastic critical load, all numerical simulations show a typi-
cal plastic plateau.
1757
It can be seen that the imperfections of the considered
specimens with a very high web slenderness do not seem
to have a great effect on the ultimate load level according
to Figure 6. Presumably, the development of tension
bands is the reason for this observation.
Figure 9 compares the numerically calculated load-dis-
placement curves for the tested specimens with a refer-
ence specimen with unperforated web. As expected, there
is almost no difference between specimen #2 and refer-
ence specimen, see explanation above. As already men-
tioned, reinforcement of the web opening seem to over-
compensate the loss of shear resistance due to the web
opening, significantly.
Figures 10 and 11 show the calculated von Mises stresses
and the deformations of specimens at elastic critical load
level and at the post-buckling stage. The post-buckling be-
haviour that is predicted by FEA corresponds well with the
test results that are shown in Figure 5.
Figure 9 Load-displacement of the specimens and the unperforated
web (as reference, highlighted in green) from FEA
Figure 10 Critical load level, von Mises stresses in N/mm²:
a) specimen #1, b) specimen #2, c) specimen #3
Figure 11 Post-buckling stage, von Mises stresses in N/mm² corre-
sponding with u
z
= 20 mm: a) unperforated web, b) specimen #1, c)
specimen #2, d) specimen #3
3.2 Analytical consideration
In the following, the rough approximation is investigated
that assumes that the reduction of shear resistance of the
unperforated web depends on the ratio B/h
w
according to
Equation (1) if the web opening is not reinforced.
𝐹
𝐹
,
∙1
(1)
where 𝐹
,
is ultimate load in case of an unperforated web,
B
is
the height of the web opening, and ℎ
is the web
depth. Further investigations are needed to specify the ap-
plication range of Equation (1). The ultimate load of the
unperforated web has been determined in the test of spec-
imen #2: 𝐹
,
= 43 kN. Thus, one obtains with B = 200 mm
for the height of the web opening:
𝐹 𝐹, ∙1
= 22,3 kN (2)
This value corresponds well with the test result of speci-
men #1, see Figure 5a.
3.3 Types of reinforcement
A parametric study is performed with the generate FE
model to numerically investigate the influence of different
reinforcement types. The types that are described by Fig-
ure 1 are considered. One-sided and two-sided reinforce-
ments are taken into account. Following anchorage
lengths of vertical and horizontal reinforcements are in-
vestigated: 0, 25, 100 mm. Figure 12 summarizes the out-
come of the parametric study. The results indicated that
there is a little difference between one-sided and two-
sided reinforcement of the web opening. The improvement
of the shear resistance significantly depends on the an-
chorage length. As long as an appropriate anchorage
length is ensured, all types of reinforcement allow an in-
crease of the shear resistance by about 50% or more for
the considered cases.
1758
Figure 12 Shear resistance depending on the type of reinforcement
(specimen #1 with a web opening without reinforcement as reference
100%), varying anchorage length for vertical and horizontal reinforce-
ment: 0, 25 and 100 mm.
Vertical reinforcements with an anchorage length of
100 mm and all-around reinforcements give the greatest
increase of about 70%.
At the first glance it is surprising that the vertical rein-
forcement performs better than the horizontal reinforce-
ment of the web opening as this outcome seems to con-
trast the findings of previous investigations in [7, 12]. A
closer look on the vertical reinforcement in case of an an-
chorage length of 100 mm reveals that in this case the
length of vertical reinforcement reaches the full web depth
and thus nearly acts as a transverse stiffener, see Figure
13b. The reinforcement subdivides the subpanel so that
the web opening region is separated. The influence of the
web opening on the buckling behaviour of the subpanel is
thus nearly eliminated.
It is remarkable that the all-around reinforcement (closed
stiffener) performs best for the considered cases. For web
slendernesses ranging between 200 and 360, the horizon-
tal reinforcement is considered as the best stiffening solu-
tion. It is worth investigating in future if this observation
is caused by the very high web slenderness of the consid-
ered girders.
Figure 13 Post-buckling stage, von Mises stresses in N/mm² corre-
sponding with u
z
= 20 mm: a) horizontal reinforcement with 100 mm
anchorage, b) vertical reinforcement with 100 mm anchorage, c) all-
around reinforcement
4 Conclusions
Experimental and numerical investigations on the behav-
iour of plate girders with thin-walled webs having a very
high web slenderness of 416 and containing large web
opening with or without reinforcement have been pre-
sented. Following conclusions can be drawn from these in-
vestigations:
1. The investigated specimens showed out-of-plane im-
perfections that were greater than h
w
/200. Neverthe-
less, the effect of the imperfections seems to be lim-
ited due to the development of a significant post-
critical strength before final collapse. This seems to be
valid for cases with and without web opening rein-
forcement.
2. The reduction of shear resistance due to a large web
opening can be restored by an appropriate reinforce-
ment of the web openings. All-around reinforcements
give the greatest increase for the considered cases.
3. The influence of a one- or two-sided application of the
reinforcement seems to be negligible based on the FEA
results.
4. The approximation of the shear resistance for web
openings without reinforcement by Equation (1)
seems to be reliable. Further investigations are
needed to specify the application range of Equation
(1).
Acknowledgements
The authors take this opportunity to express their pro-
found gratitude to all supporters of their research. Special
thanks to BTU Graduate Research School (Conference
Travel Grant) who kindly supported this conference con-
tribution.
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