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EUROSTEEL 2017, September 13–15, 2017, Copenhagen, Denmark
Flange buckling resistance of trapezoidal web girders
Experimental and numerical study
Bence Jáger*,a, Balázs Kövesdia, László Dunaia
a
Budapest University of Technology and Economics, Dept. of Structural Engineering, Hungary
jager.bence@epito.bme.hu, kovesdi.balazs@epito.bme.hu, ldunai@epito.bme.hu
ABSTRACT
Girders with trapezoidally corrugated web are widely used structural elements in the civil
engineering praxis due to their numerous advantages. However, there is a relatively small number
of previous investigations focusing on the determination of the flange buckling resistance of the
corrugated web girders. Previous experimental and numerical investigations confirmed that the
flange buckling resistance model provided by the EN1993-1-5 [2] predicts often unsafe results.
Therefore, the current paper collects all the previous proposals on the flange buckling resistance and
introduces an experimental research program investigating the flange buckling behaviour of
trapezoidally corrugated web girders. Based on the test results an advanced FE model is developed,
validated and presented. An intensive numerical parametric study is performed on this model to
investigate the buckling coefficient and the relationship between the relative slenderness and the
reduction factor for corrugated web girders. Based on the experimental and numerical results the
current paper introduces an enhanced design method for the determination of the flange buckling
resistance. This design method consists of proposal to determine the critical load amplifier of the
flange outstand and it also contains a new buckling curve which considers the specialties of the
structural behaviour coming from the corrugation profile.
Keywords: corrugated web, trapezoidal corrugation, bending moment resistance, flange buckling
1
INTRODUCTION
Research on steel girders with corrugated web was started in 1956 by NACA [1] for wings of
airplanes. After that the application of the corrugated web girder has been spread in the civil
engineering praxis as well, especially in the field of bridges. Numerous researchers investigate the
special structural behavior of this girder type, however, just a small number of research activities
were focusing on the flange buckling behavior and on the bending moment resistance of girders
with thin flanges. The current paper collects all the previous proposals for the determination of the
flange buckling resistance of corrugated web girders. In the international literature there are some
proposals available for flat web I-girders and for unstiffened plated elements which are also
discussed and their applicability for corrugated web girders are studied. Several papers deal with the
determination of the elastic buckling coefficient of flat web girders by considering the flange-toweb thickness ratio [7-8] what is usually neglected in the design codes. For trapezoidally corrugated
web girders the existing proposals [2, 4–6] gives different upper limits for the theoretically [3]
calculated buckling coefficient considering the buckling shape of the compressed flange subpanel
bounded by the inclined folds of the web. For the relationship between the relative slenderness and
reduction factor of outstand plated elements the EN1993-1-5 [2] recommends to use the same
Winter-curve based formula for trapezoidally corrugated web girders as for flat web girders.
Furthermore, additional formulas called reduced stress based effective equations were developed for
unstiffened outstand elements by Bambach and Rasmussen [9] in 2004 considering the stress
gradient in the flange. For trapezoidal web girders Koichi and Masahiro [6] proposed similar
equation for the effective width in 2006. These aforementioned formulas are collected in Section 2
and evaluated based on the numerical parametric study.
© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · ce/papers 1 (2017), No. 2 & 3
https://doi.org/10.1002/cepa.465
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In the frame of the current research program 16 laboratory tests are performed at the Budapest
University of Technology and Economics, Department of Structural Engineering in Hungary
investigating the flange buckling behavior of trapezoidally corrugated web girders. To investigate
the flange buckling resistance an advanced numerical model is developed and validated based on
the current experimental investigations. By using the current test results and the advanced numerical
model the magnitude of the equivalent geometric imperfection proposed by EN1993-1-5 [2] for
flange twisting is studied. The EN1993-1-5 [2] prescribes a rotational imperfection magnitude equal
to 1/50 for flange twisting. The applicability of this imperfection value is investigated and validated
in the current research program. On the validated numerical model parametric study is executed to
determine the buckling coefficient (kσ) of the large outstand part of the compressed flange. The
relationship between the relative slenderness ratio and the reduction factor for outstand compression
element is also investigated by geometrical and material nonlinear imperfect analysis (GMNIA).
Based on the numerical results an enhanced design equation is proposed for the determination of the
buckling coefficient (kσ) and the buckling curve (λ-ρ) for flange buckling of trapezoidally
corrugated web girders considering the corrugation profile and the quality of the web-to-flange
juncture. The layout of the tested girders, the applied dimensions and notations used in the current
paper are shown in Fig. 1.
Fig. 1. Used notations for girders with corrugated webs
2
LITERETURE REVIEW
2.1 Buckling coefficient (kσ)
It is commonly accepted by researchers [2, 3, 5-6, 10], that for trapezoidally corrugated web girders
the theoretically derived equation shown by Eq. (1) can be applied with adequate safety. However,
this design equation does not consider the rotational support effect of the trapezoidal web and the
non-uniform stress distribution in the flange, which may have significant effect on the flange
buckling resistance [1].
c
k  0.43   f
a



2
(1)
where cf is the larger flange outstand width, a=a1+2a4 is the estimated buckling wave length, where
a1 and a4 are the length of the parallel web fold and the length of the longitudinal projection of the
inclined web fold [2, 10], as shown in Fig. 1. Different researchers prescribe different limit values
for this theoretically considered buckling coefficient. The DASt-Richtlinie 015 [4] and the EN19931-5 [2] prescribe a maximum value of 0.6. Sayed-Ahmed [5] proposed a limit of 0.7 while Koichi
and Masahiro [6] proposed a value of 1.28. Johnson [7] proposed a new formula for the buckling
coefficient based on test results of unstiffened flat web girders in 1985. The provided buckling
coefficient takes the moderate rotational restraint of the web into account according to Eq. (2).
© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)
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k 
4
hw t w
 86.5  t w
 0.43  
 hw



0.5
(2)
where hw and tw are the web depth and thickness. Similar formula has been derived by Park et al. [8]
for flat web girders in 2016. The bending resistance of plated girders with longitudinal stiffeners
was numerically studied focusing on the supporting effect of the flange and web plates. Based on
the results of Park et al. a modified buckling coefficient was proposed in form of Eq. (3) where the
web-to-flange thickness ratio is also considered.
 cf tf 

k  3.0  
 hw t w 
0.6

cf t 
 0.43   25.5   w 

hw t f 

0.6
(3)
where tf is the compressed flange thickness, bf is the flange width and cf=bf/2.
2.2 Buckling curve (λ-ρ)
In the main part of the previously developed design proposals for unstiffened plated elements, the
relative slenderness may be calculated according to Eq. (4).
p 
cf /tf
f yf
28.4  k
235MPa
(4)
where fyf is the yield strength of the flange material. In the international literature different types of
design curves can be found regarding plate buckling. In the current EN1993-1-5 [2] the Wintercurve based formula is implemented in the form of Eq. (5) where the relative slenderness limit
(plateau length) is equal to 0.748 derived for buckling coefficient (kσ) equal to 0.43.
c f ,eff  p  0.188
(5)


 1.0
cf
 p2
For unstiffened plated elements new equation was developed by Bambach and Rasmussen [9] in
2004 in form of Eq. (6) for stress gradients between 0≤ѱ≤1. The equation was developed by curve
fitting based on test results.
c f ,eff 0.2  3  
(6)


 1.0
cf
 p0.75
Based on the experimental and numerical investigations of Koichi and Masahiro [6] a design
relationship was suggested in the form of Eq. (7) with no limitation in the theoretical buckling
coefficient kσ for plates being simply supported at the three edges (between 0.43 and 1.28 [3]).

c f ,eff
cf
 0 .7 


 
p


0.64
 1 .0
(7)
The DASt-Richtlinie 015 [4] proposes effective width for the compressed flange of flat and
corrugated web girders according to Eqs. (8a)-(8b).
b f ,eff  25.8  t f 
240
 b f for flat web girders
f yf
(8a)
b f ,eff  30.7  t f 
240
 b f for trapezoidally corrugated web girders
f yf
(8b)
where bf,eff is the effective width of the compressed flange. In addition Johnson and Cafolla [11]
verified that the average flange outstand (bf/2) can be used for the calculation of the relative
slenderness ratio of corrugated web girders, if Eq. (9) satisfies. This formula characterizes how
large is the enclosing effect of the web from the whole flange width. In case of flat web girders R is
equal to zero.
a  a 4   a3
(9)
R 1
 0.14
a1  2a 4   bcf
© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)
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3
NUMERICAL MODEL DEVELOPMENT AND VALIDATION
3.1 Applied analysis method
Advanced numerical model is developed by the authors in ANSYS 15.0 [12] finite element
program. The model is based on a full shell model using eight-node-thin (SHELL281) shell
elements. Two analysis types are applied in the current study, geometrical nonlinear buckling
analysis (GNBA) for the determination of the critical load amplifier and geometrical and material
nonlinear imperfect analysis (GMNIA) for the determination of the ultimate resistances. The
applied numerical model can handle the application of equivalent geometric imperfections using the
first eigenmode shape. Figure 2 presents the developed geometrical model with the boundary and
loading conditions. The numerical model is simply supported and the compressed flange is
constrained against lateral displacement to eliminate lateral torsional buckling. The bending
moments are applied in the flanges through force pairs at both ends. Convergence study shows that
4 elements along the fold lengths could be acceptable in average in the numerical model. A linear
elastic-hardening plastic material model with von Mises yield criterion is used in the numerical
model. The material model behaves linear elastic up to the yield stress (fy) by obeying Hook’s law
with Young’s modulus equal to 210000 MPa. The yield plateau is modelled up to 1% strains with a
small increase in the stresses. By exceeding the yield strength, the material model has an isotropic
hardening behavior with a reduced modulus until it reaches the ultimate strength (fu). From this
point the material is assumed to behave perfectly plastic. In the validation procedure of the FE
model the measured yield and ultimate strengths are implemented for all the tested girders,
however, in the numerical parametric study the nominal yield and ultimate strengths are applied
relevant for S355 steel grade.
Fig. 2. Geometric model with boundary and loading conditions
3.2 Model validation
For the model validation a recently performed experimental research program is applied. 16 large
scale simply supported specimens are tested under four-point-bending to investigate the local flange
buckling phenomenon and to determine the bending resistance of the investigated girders. Ten
different girder geometries having four different trapezoidal profiles (denoted by TP) are
investigated as shown in Table 1. The geometrical properties of the tested girders are summarized
in Tables 1-2; the applied notations are given in Fig. 1.
Table 1.
No.
TP1
TP2
TP3
TP4
Geometry of the investigated corrugation profiles
α [°]
45
45
30
30
a1 [mm]
97
145
88
134
a2 [mm]
97
145
88
134
a3 [mm]
69
103
44
67
a4 [mm]
69
103
76
116
© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)
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The nominal web depth of all the tested girders is 500 mm. The widths of the parallel and inclined
folds of the web are varied between 88 – 145 mm using different corrugation angles equal to 30°and
45°. The applied steel material is S355. The measured geometrical and material properties of the
test specimens are summarized in Table 2 (column #2 - #8). The first column of Table 2 refers to
the specimen numbers, which contains the applied corrugation profile (e.g. TP1 in 1TP1-1
specimen) denoted according to Table 1. For the specimen types 1-6 always two test series are
executed on the same geometry to be able to evaluate the reliability of the test results. The
schematic drawing of the applied test arrangement is presented in Fig. 3. The damaged part of the
specimens is localized to an internal removable panel subjected by pure bending moment with a
length of 1050 mm. The span of the tested girders is 8 m, which has two external girder parts with a
length of 3475 mm for each and an internal panel with a length of 1050 mm. The internal part of the
girder is only changed between the tests to improve the productivity of the tests. The joints between
the outer and inner parts are bolted connections, which are significantly over-designed to represent
fixed and moment transmitting connection with full rigidity. The test specimens are simply
supported at both ends; vertical stiffeners are placed at the support locations. The specimens are
also supported laterally at the locations of the load introduction points to prevent the lateral
torsional buckling failure mode.
Fig. 3. Applied load and support conditions
Figure 4 shows a typical flange buckling failure mode observed in the tests and a typical first
eigenmode shape related to specimen 5TP2-1. The first eigenmode shape has a specific importance
in the numerical model validation, since in the GMNI analysis the first eigenmode shape is applied
as equivalent geometric imperfection with an imperfection rotation magnitude equal to 1/50
proposed by the EN1993-1-5 [2].
a)
b)
Fig. 4. a) Typical flange buckling failure (5TP2-1); b) Typical first eigenmode shape (5TP2-1)
The measured load carrying capacities (2·Ftest), the calculated bending moment resistances (Mtest)
and the relevant material properties are also summarized in columns #9 and #10 of the Table 2. The
self-weight of the specimens is also considered in the moment resistance calculation process as
uniformly distributed load having the intensity of 2.5 kN/m for the outer girders and 1.37-1.62
kN/m for the internal panels. The self-weight results in ~18 kNm bending moment calculated in the
cross-sections of the bolted connection. The column #11 represents the computed FEM based
© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)
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bending moment resistances. The ratios of the FEM based and test based resistances are included in
column #12. The comparison shows that the application of 1/50 as imperfection magnitude for
flange buckling in the first eigenmode shape results in a conservative solution for girders having
thicker flanges (12-14 mm) and/or thin web plates (3-4 mm). But all the results are on the safe side
with a minimum and maximum differences equal to 2% and 15%, therefore, the application of an
imperfection magnitude of 1/50 is proposed for girders with trapezoidally corrugated web
calculating the flange buckling resistance under bending.
Table 2.
Number
1TP1-1
1TP1-2
2TP1-1
2TP1-2
3TP1-1
3TP1-2
4TP2-1
4TP2-2
5TP2-1
5TP2-2
6TP2-1
6TP2-2
7TP1
8TP2
9TP3
10TP4
4
tf
[mm]
7.92
7.92
7.9
7.88
14.59
14.52
7.73
7.82
7.82
7.69
14.57
14.62
12.2
12.27
12.16
12.2
bf
[mm]
250
249
250
250
250
250
249
250
250
248
250
250
250
246
247
250
Measured properties, capacities and FEM based resistances
tw
[mm]
2.88
2.93
5.97
5.97
3.01
2.84
2.99
2.93
5.97
5.95
2.99
2.96
3.84
4.05
4.04
3.89
fyf
[MPa]
455
450
452
447
387
382
465
488
455
495
382
396
364
365
365
361
fyw
[MPa]
410
364
406
383
363
418
376
366
390
392
373
364
474
450
457
457
fuf
[MPa]
548
541
548
541
516
516
561
595
557
590
518
515
496
499
500
488
fuw
[MPa]
555
511
530
507
514
566
510
511
508
516
503
510
584
584
584
560
2.Ftest
[kN]
200.4
175.5
202.1
199.5
417.1
415.3
148.7
156.2
172.0
174.5
411.6
415.8
327.8
306.2
326.2
318.5
Mtest
[kNm]
366.0
322.7
369.1
364.8
742.9
739.9
276.1
289.2
316.9
321.3
733.4
740.7
587.7
550.1
585.0
571.5
Mnum
[kNm]
319.6
312.8
360.4
357.3
681.5
670.0
244.0
253.4
310.6
313.4
624.9
646.1
521.2
478.7
541.9
515.2
Mnum/
Mtest
0.87
0.97
0.98
0.98
0.92
0.91
0.88
0.88
0.98
0.98
0.85
0.87
0.89
0.87
0.93
0.90
NUMERICAL PARAMETRIC STUDY
4.1 Investigated parameter domain
A numerical parametric study is performed using the validated numerical model. Two analysis
types are applied; first bifurcation analysis (GNBA) in order to determine the critical load amplifier
and a nonlinear analysis (GMNIA) to investigate the ultimate bending moment resistance of the
trapezoidally corrugated web girders. The parameter domain is chosen in order to cover the average
geometries used in the praxis and even the most extreme layouts as well. In the numerical analysis
the following parameter domains are analysed:
 a1/a2: 0.33 – 0.67 – 1.0 – 1.5 – 2.0 – 3.0,
 α:
10⁰ – 20⁰ – 30⁰ – 40⁰ – 45⁰– 60⁰– 80⁰,
 R:
0.043 – 0.47,
bf/a3: 1.0 – 15.6,
 cf/tf:
8 – 26,
tf/tw: 1 – 6,
 hw/tw: 100 – 800,
fy:
355 MPa.
In the frame of the parametric study more than thousand different geometries are investigated.
4.2 Evaluation of EN1993-1-5 proposal
Figure 5 shows all the results of the GNB and GMNI analysis in comparison with the standard
resistances. In Fig. 5a the vertical axis represents the ratio of the standard based (Eq. (1)) and the
FEM based buckling coefficients derived according to Eq. (10). Ratio equal to 1 means that the
hand calculated and the numerically computed values are identical. All the results are plotted in the
function of the flange width-to-thickness ratio (cf/tf/ԑ) regarding the larger flange outstand. The
results show that for class 4 flanges the current design method approximates the buckling
coefficient with a large scatter and there is a large amount of numerical results on the unsafe side. In
Fig. 5b all the GMNIA results are summarized. The diagram also contains the design curve of the
© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)
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EN1993-1-5 [2] given by Eq. (5). The required reduction factor related to the effective width of the
larger flange outstand is determined according to Eq. (11), while the buckling coefficient and the
relative slenderness are determined according to Eq. (1) and Eq. (4).
2
 cr , num 12  1   2   t f 
 
(10)
k  , num 
c 
E  2
 f 
 req 
N u ,num  c f ,eff , 2  t f  f yf
(11)
c f  t f  f yf
where Nu,num is the ultimate normal force in the compressed flange obtained by the GMNI analysis
and cf,eff,2 is the effective width of the small flange outstand according to Eq. (1) and Eqs. (4)-(5). It
can be seen that several points are on the unsafe side. There is a contradiction in the calculation of
the relative slenderness limit of 0.748 suggested by the standard since it is based on the buckling
coefficient equal to 0.43 applicable only for flat web girders. These results prove that the standard’s
buckling curve needs revision and development for girders with corrugated web.
a)
b)
Fig. 5. a) GNBA results; b) GMNIA results
4.3 Investigation of the buckling coefficient (kσ)
The test results prove that the web-to-flange juncture including the enclosing effect of trapezoidal
web panel has significant effect on the load carrying capacity. Previous investigations pointed out
that the buckling coefficient could be smaller or larger than 0.43 depending on the web-to-flange
juncture and on the corrugation profile. To consider these effects, the buckling coefficient formula
developed for plates (Eq. (1)) should be further improved based on the results of the numerical
simulations. The development is performed according to the concept that the first term of the
buckling coefficient (0.43) should consider the stress gradient and all the boundary conditions of the
fictitious plate subjected by compression. The second term should consider the width-to-length ratio
of the sub-plate bounded by the inclined folds. It means that only the first term should be modified
by considering the previous proposals and numerical and experimental investigations. This concept
is convenient and compatible with the previous proposals developed for flat web girders. By
considering the experimental and numerical results and the proposal of Park et al. [8] (Eq. (3)) the
equation given by Eq. (12) is developed by the authors to determine the buckling coefficient.

t
k   0.43   2.5  w

tf





0.6  R
cf

 
 a1  2  a 4
2

  1.3 .


(12)
The derived equation is verified by the numerical results. The comparison is plotted in Fig. 6 where
the dark points represent the results regarding the current proposal. It can be seen that safe side
solutions are provided with significantly smaller coefficient of variation than the standard’s
proposal shown in Fig. 5a.
© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)
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Fig. 6. Verification of the current proposal for the buckling coefficient (Eq. (12))
4.4 Investigation of the buckling curve (λ-ρ)
The numerical results proved that the original plate buckling curve is not suitable for corrugated
web girders, it needs improvement. As a first step the theoretical limit value of the relative
slenderness is determined by substituting cf/tf/ԑ=14 into Eq. (4) using the larger flange outstand.
This limit value is derived and applied for the slenderness limit value in the form of Eq. (13) which
represents the plateau length of the buckling curve. This limit value is equal to 0.751 for flat web
girders if kσ is equal to 0.43. In case of corrugated web girders, the corrugation profile results in
changes in the buckling coefficient which should be also considered in the buckling curve plateau
length.
0.493
(13)
 p , lim 
k
If Eq. (13) is implemented into the proposed equation of the buckling curve of [6, 9], Eq. (14) is
obtained. It can be observed that the reduction factor depends on the relative slenderness, on the
buckling coefficient and on the index β, what should be calibrated based on the numerical results.

c f ,eff
cf


  p ,lim 
   0.493

  
 k 
 p 
  p



t
  14    f


cf




  1.0


(14)
Fig. 7. GMNIA results with the current proposal using β=1.0
Figure 7 presents the comparison of the FEM based reduction factors using Eq. (12) for the
buckling coefficient determination and the surface represented by Eq. (14) using β=1.0. It can be
seen that the FEM based results are in the close region of the design proposal, however, some points
© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)
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are found to be too conservative. Therefore, a systematic parametric study is executed to determine
the index β depending on the geometry of the corrugation profile. It is to be noted that the enclosing
effect of trapezoidal web (R – Eq. (9)) cannot describe the supporting effect of the web alone since
any α can belong to any R and vice versa. The parametric study reveals that the index β depends on
three parameters such as the enclosing effect of the web (R), the corrugation angle of the inclined
fold (α) and the flange-to-web thickness ratio (tf/tw) which clearly defines a specific profile for a
given flange width. Figure 8a presents the effect of the flange-to-web thickness ratio for a geometry
having fold lengths equal by a1=a2=200 mm in the function of increasing α (and R) represented by
the upper and lower horizontal axes, respectively. It is shown that the larger is the tf/tw ratio, the
larger is the index β and smaller is the resistance to flange buckling. In addition, it can be seen that
the curves have a reverse parabola character which peak value is obtained by α=45⁰ representing
the most unfavourable layout from flange buckling point of view. By increasing the corrugation
angle from α=45⁰ the supporting effect of the web increases. By decreasing the corrugation angle
from α=45⁰ the web contribution to the longitudinal load bearing increases. In the “accordion
effect” based flange buckling resistance model the web is completely neglected from the bending
moment resistance, however, through the index β it can be indirectly considered. In the case of α=0⁰
– representing flat web girder – the whole web panel practically takes part in the longitudinal load
carrying and therefore the value of β can be decreased.
a)
b)
Fig. 8. a) tendency and effect of tf/tw (a1=a2=200mm)on β; b) β – R relationship (tf/tw=4.8)
Figure 8b presents the computed β values in the function of R having flange-to-web thickness ratio
equal by 4.8. The black solid polygon represents the same polygon found in Fig. 8a. It can be seen
that the index β linearly depends on the R if the corrugation angle is constant. However, the slope of
the coloured lines must depend on the corrugation angle. Therefore, the slopes are calculated for
each investigated corrugation angle and the relationship is determined by curve fitting. As a result, a
closed formula with lower limit of 0.5 and upper limit of 1.0 is developed for the approximation of
the index β in the form of Eqs. (15a)-(15b) considering the flange-to-web thickness ratio.

a
 1 
  5    R   4
  5    R  
 tg ( ) 
 a3
  0.45  0.06 


 where 0.5    1.0

tf
(16a)
(16b)
tw
The statistical evaluation of the current design and FEM based resistances are determined and
evaluated regarding β equal to 1.0 (as a lower bound solution) and according to Eq. (15). It is shown
that by using β=1.0 (Fig. 7) the average ratio is obtained to 7.3% on the safe side with coefficient of
variation equal to 0.058. The maximum deviations on the safe and unsafe sides are obtained to
27.4% and 3.0%, respectively. By applying Eq. (15) for the determination of the index β the results
fit better the numerical calculations with an average ratio equal to 0.97 on the safe side and with a
coefficient of variation equal to 0.027. The maximum deviations on the safe and unsafe sides are
obtained to 13.4% and 3.0%, respectively.
© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)
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SUMMARY
In the current research program experimental and numerical investigation is executed on the flange
buckling resistance of girders with trapezoidally corrugated webs. Numerical model is developed
and validated based on the executed test results. It is shown that by using the flange buckling
eigenmode as equivalent geometric imperfection in the nonlinear analysis the proposal of the
EN1993-1-5 [2] for the imperfection magnitude is applicable with adequate safety. By evaluating
the numerical results, the following conclusions are drawn:
(i) The results of the GNB analysis show that the proposal of the EN1993-1-5 [2] is not
suitable for girders with trapezoidally corrugated webs since it does not consider the
web-to-flange juncture.
(ii) New proposal is developed for the buckling coefficient considering the effect of the
web-to-flange juncture in form of Eq. (12) with the theoretical upper limit of 1.3. The
proposal considers the previous proposals in the field of flat and corrugated web girders
and the evaluation of the current numerical results as well.
(iii) Nonlinear analysis revealed that the proposal of the EN1993-1-5 [2] for the reduction
factor is not applicable for girders with trapezoidally corrugated webs. Therefore, a new
formulation is developed in form of Eq. (14). According to the FEM based resistances
the index β of the buckling curve is derived and calibrated in form of Eq. (15).
ACKNOWLEDGMENT
The presented research program is part of the “BridgeBeam” R&D project No. GINOP-2.1.1-152015-00659; the financial support is gratefully acknowledged. Through the first author the paper
was also supported by the ÚNKP-16-3-I. New National Excellence Program of the Ministry of
Human Capacities and by the second author’s János Bolyai Research Scholarship of the Hungarian
Academy of Sciences; all the financial supports are gratefully acknowledged.
REFERENCES
[1] NACA Technical note 3801. “Experimental investigation of the strength of multiweb beams with
corrugated webs”. Washington, 1956
[2] EN 1993-1-5:2005, Eurocode 3: Design of steel structures, Part 1-5: Plated structural elements
[3] Timoshenko S.P., Gere J.M. “Theory of elastic stability”. 2nd Edition, McGraw-Hill Publishing Co.,
New York, 1961
[4] DASt-Richtlinie 015. “Trager mit schlanken Stegen”. Stahlbau-Verlagsgesellshaft, Köln, 1990
[5] Sayed-Ahmed E.Y. “Design aspects of steel I-girders with corrugated steel webs”. Electronic Journal of
Structural Engineering 7, pp. 27-40, 2007
[6] Koichi W., Masahiro K. “In-plane bending capacity of steel girders with corrugated web plates”.
Journal of Structural Engineering (JSCE) 62, No. 2, pp. 323-336, 2006
[7] Johnson DL. “An investigation into the interaction of flanges and webs in wide
flange shapes”. Proc. SSRC Annual Technical Session, Structural Stability Research
Council, pp. 395–405, 1985
[8] Park Y.M., Lee K.-J., Choi B.H., Cho K.I. “Modified slenderness limits for bending resistance of
longitudinally stiffened plate girders”. Journal of Constructional Steel Research 122, pp. 354-366, 2016
[9] Bambach M.R., Rasmussen K.J. “Effective widths of unstiffened elements with stress gradient”.
Journal of Structural Engineering 130, No. 10, pp. 1611-1619, 2004
[10] Johansson B., Maquoi R., Sedlacek G., Müller C., Beg D. “Commentary and worked examples to
EN1993-1-5: Plated Structural Elements”, pp. 152-167, 2007
[11] Johnson R.P., Cafolla J. “Local flange buckling in plate girders with corrugated webs”. Proceedings of
the Institution of Civil Engineers, Structures and Buildings 122, No. 2, pp. 148–156, 1997
[12] ANSYS® v15.0, Canonsburg, Pennsylvania, USA.
[13] EN 1993-1-1:2005, Eurocode 3: Design of steel structures, Part 1-1: General rules and rules for
buildings.
© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin ∙ CE/papers (2017)
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