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Engineering Structures 30 (2008) 1659–1666

www.elsevier.com/locate/engstruct

Interactive shear buckling behavior of trapezoidally corrugated steel webs

Jongwon Yia, Heungbae Gilb, Kwangsoo Youmc, Hakeun Leed,∗

a Institute of Construction Technology, Hyundai Engineering & Construction, 102-4, Mabuk-Dong, Giheung-Gu, Yongin-Si, Gyounggi-Do, 446-716, South Koreab Structural Engineering Research Team, Expressway & Transportation Research Institute, 50-5, Sancheok-Ri, Dongtan-Myun, Whaseong-Si, Gyeonggi-Do,

445-812, South Koreac Technical Division, GS Engineering & Construction, 417-1, Duksung-Ri, Eedong-Myun, Chuin-Gu, Yongin-Si, Gyounggi-Do, 449-831, South Korea

d Department of Civil and Environmental Engineering, Korea University, 5-1, Anam-Dong, Sungbuk-Gu, Seoul, 136-701, South Korea

Received 4 February 2006; received in revised form 6 November 2007; accepted 8 November 2007

Available online 21 February 2008

Abstract

Trapezoidally corrugated steel plates have been used as the web of pre-stressed concrete box girder bridges to reduce dead load and increase

structural efficiency. Due to an applied shear stress, the trapezoidally corrugated web can fail by three different shear buckling modes: local,

global, and interactive shear buckling. Local buckling involves a single panel, whereas global buckling involves multiple panels, with buckles

extending over the entire depth of the web. The interactive buckling is rather complex and is an intermediate type of shear buckling between local

buckling and global buckling, which involves several panels. In this study, a series of finite element analyses was carried out to study the geometric

parameters affecting interactive shear buckling modes and strength. Based on the analysis results, the interactive shear buckling strength formula

is proposed. The proposed formula agreed well with the experimental data.c 2007 Elsevier Ltd. All rights reserved.

Keywords: Corrugated web; Shear buckling; Interactive buckling; Shear strength; Finite element method

1. Introduction

A trapezoidally corrugated steel plate is composed of aseries of plane and inclined sub-panels, as shown in Fig. 1.

The primary characteristics of the corrugated steel plates are

negligible bending capacity and adequate out-of-plane stiffness.

To take advantage of these characteristics, the corrugated steel

plates have been considered as an alternative to conventionalconcrete or steel girder webs. When used as the web, the

corrugated steel web carries the vertical shear, and the flanges

carry the moment due to the accordion effect. Pre-stressed

concrete box girder bridges with a corrugated steel webhave been pioneered in France and extensively constructed inJapan. The first pre-stressed concrete box girder bridge with a

corrugated web was recently constructed in South Korea.Research on the shear buckling behavior of corrugated plates

has been initiated by Easley and McFarland [1]. Since then,

numerous theoretical and experimental research on the buck-

ling characteristics and strength of corrugated steel webs have

∗ Corresponding author. Tel.: +82 2 3290 3315; fax: +82 2 928 5217. E-mail address: [email protected] (H. Lee).

been performed by Elgaaly et al. [2–4] and Abbas et al. [5] in

the United States and El-Metwally [6] and Sayed-Ahmed [7]

in Canada. Studies have also been conducted by Cafolla [8] in

Britain, Luo and Edlund [9] in Sweden, and Yoda et al. [10] and

Yamazaki [11] in Japan. The studies on geometric parameters

have been extensively carried out by Gil et al. [12,13] and Yi

et al. [14].

Despite significant research, however, the shear buckling

behavior of trapezoidally corrugated webs has not been clearly

explained. Depending upon the geometric characteristics of the

corrugated web, three different shear buckling modes, namely,local buckling, global buckling and interactive buckling are

possible. Local buckling represents the buckling of a sub-

panel, whereas global buckling is the buckling of the whole

web. Interactive buckling, which involves a few sub-panels,

occurs due to the interaction of local and global buckling.

The previous research [14] shows that the buckling failure of

the corrugated web is mainly governed by interactive shear

buckling. However, the causes of interactive shear buckling

have not been clearly defined, with much of the research

conservatively underestimating the shear buckling strength.

0141-0296/$ - see front matter c

2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.engstruct.2007.11.009

http://www.elsevier.com/locate/engstruct

mailto:[email protected]

http://dx.doi.org/10.1016/j.engstruct.2007.11.009

http://dx.doi.org/10.1016/j.engstruct.2007.11.009

mailto:[email protected]

http://www.elsevier.com/locate/engstruct

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1660 J. Yi et al. / Engineering Structures 30 (2008) 1659–1666

Nomenclature

a flat panel width

b horizontal projection of the inclined panel width

c inclined panel width

d corrugation depth

h web heightθ corrugation angle

τ E cr, L elastic local shear buckling stress

E Young’s modulus of elasticity

ν Poisson’s ratio

t web thickness

k local shear buckling coefficient

τ E cr,G elastic global shear buckling stress

β global shear buckling coefficient

D x longitudinal bending stiffness per unit length of

the corrugated web

D y transverse bending stiffness per unit length of the

corrugated web I x moment of inertia about the axis along web height

I y moment of inertia about the neutral axis along

web height

τ cr, I critical interactive shear buckling stress

τ cr, L critical local shear buckling stress

τ cr,G critical global shear buckling stress

τ y shear yielding stress

η length reduction factor = (a + b)/(a + c)

τ f e shear buckling stress from numerical analysis

results

τ cr critical shear buckling stress

λs shear buckling parameter

τ E cr, I elastic interactive shear buckling stress

τ ex shear buckling stress from test results

C L coefficient unrelated with geometric parameters

for simplified local shear buckling stress

C G coefficient unrelated with geometric parameters

for simplified global shear buckling stress

C I = C G /C L

Fig. 1. Trapezoidally corrugated web.

In this paper, the interactive buckling behavior of corrugated

steel webs was investigated. Geometric parameters, which

affect the buckling mode, were first derived from local and

global buckling formulas. To study the effects of derived

Fig. 2. Local shear buckling mode.

parameters on interactive buckling modes, an elastic bifurcation

buckling analysis and a nonlinear analysis considering

geometric and material nonlinearities were performed using

three-dimensional finite element models of corrugated webs.

The analysis results were also used to propose an interactive

buckling strength formula. The proposed formula was verifiedusing the experimental data from the literature.

2. Shear buckling behavior of corrugated webs

2.1. Shear buckling mode

Local buckling occurs when a flat sub-plate between vertical

edges has a large width to thickness ratio as shown in Fig. 2.

The buckling strength equation is taken from the classical plate

buckling theory [15] as follows:

τ E

cr, L = k ×π 2 E

12(1 − ν2) t

a2

, (1)

where E = Young’s modulus of elasticity, ν = Poisson’s ratio,

a = the maximum width of a flat or inclined fold, t = the web

thickness, and k = the buckling coefficient defined according to

the boundary conditions and aspect ratio of the sub-panel.

In the case of dense corrugations, global buckling, as shown

in Fig. 3, becomes the dominant failure mode. The buckling

stress, calculated from the orthotropic-plate buckling theory,

was provided by Easley [1,16]. He derived a set of formulae

for the buckling loads from research on the general buckling

behavior of light-gage corrugated webs, and the buckling stress

is defined as:

τ E cr,G = 36β

D1/4 y D

3/4 x

t h2, (2)

where D x and D y are the longitudinal and the transverse

bending stiffness per unit length of the corrugated web,

respectively, and β is the global buckling coefficient. D y and

D x are calculated from E I y ( I y = moment of inertia about the

neutral axis along web height) and E I x ( I x =moment of inertia

about the axis along web height), respectively. The coefficient,

β, changes from 1.0 to 1.9 according to the boundary conditions

between the web and flanges.In theory, local buckling involves a single flat panel, whereas

global buckling involves multiple panels, with buckles that may

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J. Yi et al. / Engineering Structures 30 (2008) 1659–1666 1661

Table 1

Interactive shear buckling strengths

Researcher Interactive shear buckling strength Remarks

Bergfelt [18]

1τ cr, I

=

1

τ E cr, L

+

1

τ E cr,G

The material inelasticity and yielding are not considered.

El-Metwally [6]

1τ cr, I

2 =

1τ E

cr, L

2

+ 1

τ E cr,G

2

+ 1

τ y

2

Sayed-Ahmed [19]

1τ cr, I

3 =

1

τ E cr, L

3

+

1

τ E cr,G

3

+

1τ y

3

Abbas [5]

1τ cr, I

2 =

1τ cr, L

2 +

1τ cr,G

2

The yielding of material can be considered using inelastic buckling strength.

Hiroshi [20]

1τ cr, I

4 =

1τ cr, L

4 +

1τ cr,G

4

Design manual [21] Corrugated web is designed to have no local and global buckling as well as interactive buckling failure.

Fig. 3. Global shear buckling mode.

Fig. 4. Interactive shear buckling mode.

extend diagonally over the entire depth of the web. However,

test specimens with characteristics of both local and global

buckling modes had been observed [17]. These shear buckling

modes termed as interactive buckling are explained as a result

of the interaction between local and global buckling, as shown

in Fig. 4, but have never been clarified in the literature.The buckled shapes of the interactive buckling mode are not

as definitive as those of the local or global buckling mode but

vary depending on the geometry of the corrugated web [14].

To predict interactive buckling strength, different formulae

have been proposed as shown in Table 1. These formulae are

basically based on Eq. (3), which represents the interaction

among local buckling, global buckling and yield strength.

1

(τ cr, I )n= 1

(τ cr, L )n+ 1

(τ cr,G )n+ 1

(τ y )n, (3)

where τ cr, I = the interactive buckling strength, τ cr, L = the

local buckling strength, τ cr,G = the global buckling strength,

and τ y = the shear yield strength. Table 1 also shows

that interactive buckling is typically considered as either the

interaction between local and global buckling [18] or the

interaction between buckling and yielding [6,19]. However,

in this paper, the interactive shear buckling is defined as the

interaction between elastic local and global buckling withoutconsideration for shear yielding and inelastic buckling.

2.2. Geometric parameters affecting the interactive shear

buckling mode

To predict interactive shear buckling behavior, parameters

affecting interactive shear buckling need to be defined. The

geometric parameters of a corrugated web are a, d , t , h, c

and θ as shown in Fig. 1. Within these parameters, d , c and

θ are coupled. For corrugated webs used in bridge structures,

the width of the flat panel (a) is almost equal to the width of the

inclined panel (c). Sayed-Ahmed [19] also suggested that theideal ratio for a/c is 1.0. At this ratio, the critical stress is close

to the yield stress of the steel for a wider range of a. Assuming

a to be equal to c, the geometric parameters are reduced to only

five: a, d , t , h and θ .

Assuming that all the sides of the panels are simply

supported, the local buckling strength defined in Eq. (1) can

be rewritten as follows:

τ E cr, L =

5.34+ 4

a

h

2

π 2 E

12

1 − ν2 t

a

2

. (4)

Since a/ h for a typical corrugated web is very small, 0.1–0.2,

(a/ h)2

can be neglected in Eq. (4). Then the theoretical local

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shear buckling strength becomes:

τ E cr, L =

5.34π 2 E

12

1 − ν2 t

a

2

. (5)

The global buckling strength given in Eq. (2) can also be

expressed as follows:

τ E cr,G = 36β E

112

1 − υ21/4

(d /t )2 + 1

6η

3/4 t

h

2

, (6)

where η = a+ba+c

. The corrugation angle of bridges, θ , is

typically about 25◦–35◦, and when a is equal to c, the variable

η can be considered constant because the changes in η are less

than 5%. When d /t is larger than 8.66, the theoretical global

shear buckling strength can be simplified with less than 1%

difference as given below:

τ E cr,G = C G

d

t 1.5 t

h2

, (7)

where C G is a constant and is defined as C G = 5.045β E

(1−υ2)1/4

(η)3/4.

Previous studies [14] have shown that interactive shear

buckling is affected by the ratio of the elastic local and global

buckling strengths. The ratio can be arranged as follows:

τ E cr,G

τ E cr, L

= C I

a

h

2

d

t

1.5

, (8)

where

C I = C G

C L= 36β E

1

[12(1−υ2)]1/4

1

(6η)3/4

5.34 π 2 E 12(1−υ2)

= 0.6813β

2

1 − υ2

η

3/4

.

The coefficient, C I , has only one geometric parameter, η,

which is almost constant as shown earlier. Therefore, it can

be concluded that the interactive shear buckling strength is

affected only by the geometric parameters a/ h and d /t . In

the following chapter, the effects of the relationship between

interactive shear buckling and the two geometric parameters,

a/ h and d /t , is studied through finite element analysis.

3. Finite element analysis

Bifurcation buckling analysis, using the finite element

method, was first performed to determine the elastic shear

buckling strength of the corrugated web and to investigate

the geometric parameters affecting interactive shear buckling

modes and strength. Next, a nonlinear finite element analysis,

which considered both the geometric and the material

nonlinearities, was carried out to verify the proposed theoretical

buckling formulae.

Fig. 5. Shear buckling analysis model.

Table 2

Boundary conditions of the analytical model

AB BC CD DA

Translation X (1) R F R F

Y (2) R R R RZ (3) F F F R

Rotation X (1) F F F F

Y (2) F R F F

Z (3) F R F F

F: Free, R: Restrained.

3.1. Finite element analysis modeling

Previous analytical studies typically used the girder with

flanges and stiffeners to examine the buckling behavior of

corrugated web plates [2,5,10,12]. However, the effects of the

flange and stiffeners on the shear behavior of a corrugated web

could not be completely ignored in these models. It was alsodifficult to confirm the shear behavior of a pure corrugated web.

In this study, a corrugated web plate was only modeled.

The analytical model shown in Fig. 5 was built using the

general-purpose finite element program, ABAQUS [22]. In

the construction of the model, the following conditions were

considered.

– Modeling under shear load (boundary and loading condi-

tions).– Number of elements per panel.– Influence of the overall dimension (h and L).– State of pure shear.

S8R5 reduced integration thin shell elements were used to

model the corrugated plate. The flange and stiffeners were

modeled as simply support boundary conditions as given in

Table 2. In order to minimize the computational effort without

sacrificing the accuracy of the results, the model used four

elements per panel, and the number of corrugation cycles

determined for the ratio, L/ h, was kept greater than two. Load

was applied at the BC edge in three directions, as in Fig. 5.

The pure shear state of the web panel under the defined loading

and boundary conditions were checked by static analysis of the

model.

To verify the analytical model, shear buckling analyses

of a flat plate were first conducted under the boundary and

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Table 3

Geometric parameters of constructed bridges: a/ h and d /t

Bridge a (mm) d (mm) b (mm) t (mm) h (mm) a/ h d /t

Shinkai 250 150 200 9 1183 0.211 16.667

Matsnoki 300 150 260 10 2210 0.136 15

Hondani 330 200 270 9 3315 0.0995 22.222

Cognac 353 150 319 8 1771 0.199 18.75Maupre 284 150 241 8 2650 0.107 18.75

Dole 430 220 370 10 2546 0.169 22

Ilsun 330 200 330 18 2292 0.144 11.111

loading conditions as mentioned above. The analytical results

corresponded well with the shear buckling stress calculated

from the classical plate buckling theory [15]. Young’s modulus

of 210,000 MPa and a Poisson’s ratio of 0.3 were used

throughout the analysis.

3.2. Elastic analysis

A parametric study was conducted using finite elementbuckling analysis to determine the effects of the geometric

parameters, a/ h and d /t , on buckling strength. According to

the literature survey shown in Table 3, a/ h and d /t for actual

bridges are limited: a/ h and d /t vary from 0.1 to 0.2 and

from 10 to 25, respectively. In this study, a/ h and d /t were

conservatively assumed to be in the range of 0.1–0.3 and 5–30,

respectively, while other geometric characteristics held fixed as

follows: θ = 30◦, a = 300 mm and d = 150 mm. As a result,

the web height was varied from 1000 to 3000 mm, and t from

5 to 30 mm. A total of 315 models were constructed. About

two-thirds of those models were designed to have higher global

buckling strength than local buckling strength and the rest of

them had lower global buckling strength than local bucklingstrength.

The analytical and theoretical strengths are compared in

Fig. 6. The horizontal axis represents the ratio of elastic global

buckling stress to elastic local buckling stress, τ E cr,G /τ E

cr, L , in

a logarithmic scale. For each d /t , a/ h varied from 0.10 to

0.30 at the increment of 0.01 all the way. Fig. 6 shows that the

interactive shear buckling strength is affected by the ratio of the

local to global buckling strength. When the ratio approaches

1.0, the strength is lower than both the local buckling and

global buckling strength. The geometric parameters, a/ h and

d /t , also have a significant effect on both shear buckling mode

and strength. However, as mentioned above, the relationshipbetween the buckling strength and the geometric parameters

cannot be easily expressed using a simple formula. The lines

named ‘1st order’ and ‘2nd order’ in Fig. 6 represent the 1st

(n = 1) and 2nd (n = 2) order interactive shear buckling

strength calculated using Eq. (9). Fig. 6 shows that the 1st-order

interactive shear buckling strength formula can safely estimate

the elastic shear buckling strength for a corrugated web.1

τ E cr, I

n

=

1

τ E cr, L

n

+

1

τ E cr,G

n

. (9)

Fig. 7 shows the relationship between the ratio of analytical

buckling stress to 1st-order interactive buckling strength and

Fig. 6. Comparison of the analytical results to the theoretical elastic buckling

strength.

Fig. 7. Comparison of the analytical results to the 1st-order interactive buckling

stress.

geometric parameters, a/ h and d /t . Analytical buckling

stresses of some models are lower than the 1st-order interactive

buckling strength. This appears to be caused by the fact that

some of the analytical models cannot satisfy required geometric

stiffness as corrugated plates. Cafolla [8] suggested that a

reasonable lower bound for D x / D y is 50.0 while Easley [16]

suggested that D x / D y > 200.0. D x / D y > 200.0 is roughly

equivalent to d /t > 10.0. However, Fig. 7 suggests that the

limiting conditions should be defined not only for d /t , but also

for a/ h, which is not considered in the calculation of D x / D y .In addition to the requirement of d /t > 10.0, the corrugated

plates need to satisfy the following geometric condition: a/ h <

0.2.

3.3. Nonlinear analysis

The influence of geometric parameters, a/ h and d /t , on

interactive buckling was studied through linear elastic buckling

analysis. A nonlinear analysis considering geometric and

material nonlinearities was carried out to study the effect

of geometric parameters on inelastic buckling. The boundary

and loading conditions were the same as those used in the

elastic analysis. The loading increment was less than 1% of

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Fig. 8. Material property for the nonlinear analysis.

Table 4

Geometric properties of the nonlinear analysis models

No. a/ h d /t τ f e /τ cr

(Elastic

analysis

results)

τ E cr, L

(Theory)

τ E cr,G

(Theory)

τ

E

cr,Gτ E

cr, L

y-1

0.11 6.0 1.532

3577.66 707.09 0.198

i -1 724.48 140.20 0.194

e-1 377.89 72.95 0.193

y-2

0.15 8.0 0.738

2225.71 1241.97 0.558

i -2 272.65 148.32 0.544

e-2 144.21 78.32 0.543

y-3

0.29 25.0 0.947

780.84 9249.49 11.846

i -3 135.56 1459.80 10.768

e-3 86.76 928.80 10.705

y-4

0.18 15.0 0.713

762.88 1558.99 2.044

i -4 154.48 306.91 1.987

e-4 68.66 135.90 1.979

y-5

0.22 7.0 0.442

918.52 870.83 0.948

i -5 146.96 138.33 0.941

e-5 82.67 77.76 0.941

y-6

0.11 17.5 0.667

572.43 559.08 0.977

i -6 143.11 135.95 0.950

e-6 80.50 76.18 0.946

the ultimate load. The tri-linear elastic–plastic stress–strain

relationship shown in Fig. 8 was used in the nonlinear analysis.A total of 18 analytical models described in Table 4 were

developed by combining six different a/ h and d /t ratios.

The first two combinations of a/ h and d /t were designed

to be governed by local buckling while the third and forth

combinations were governed by global buckling. The models

from the remaining two combinations had lower interactive

buckling stress than either local or global buckling stress. The

models also had different ratios of buckling stress to yield

stress. The elastic buckling stresses of ‘ y’ series models were

much higher than the material yielding stress. The ‘i’ series

models had elastic buckling stresses similar to the material yield

stress. The elastic buckling stresses of the ‘e’ series models

were about 50% of the material yield stress.

The buckling stresses from nonlinear analyses were

compared to the theoretical interactive buckling strengths in

Fig. 9. Comparison of the nonlinear analytical results to the interactive

buckling strengths.

Fig. 9. The horizontal axis represents the shear buckling

parameter, λs , which is calculated using the buckling stress of the governing buckling mode. The analysis results were not in

good agreement with the theoretical strength. This is because

the available formulae for interactive shear buckling strengths

are not derived to theoretically explain the interactive shear

buckling phenomena, but are derived to simply provide smaller

failure loads than predicted by local and global buckling modes.

The models in the yielding zone in Fig. 9 are the ‘ y’ series

models, which were designed to fail by material yielding,

and the buckling stress of those models was conservatively

predicted from existing formula. The buckling stress formulae

suggested by Hiroshi et al. [20] and Abbas et al. [5] were

too conservative in their predictions. For the ‘i’ series models,there were only small differences between critical buckling

stresses calculated by the different formulae, but the prediction

of the shear buckling strength was less accurate. For the

models whose buckling stress is less influenced by interactive

buckling, shear buckling strength was predicted conservatively,

irrespective of buckling formulae. The predictions for the

strength of the models governed by the global buckling mode

were too conservative, while the strength of the models with

a large strength reduction due to interactive shear buckling

was overestimated. This tendency became more obvious in the

elastic region. These results indicate that the existing formulae

for interactive shear buckling cannot clearly describe interactive

shear buckling phenomena nor predict the shear strength.

Results from the nonlinear finite elements analysis results,

along with theoretical buckling stresses, are plotted as a

function of the shear buckling parameter, λs , in Fig. 10.

The parameter λs and the theoretical buckling stresses were

calculated using the elastic 1st-order interactive shear buckling

strength, τ E cr, I , defined in Eq. (10).

τ E cr, I =

τ E cr, L

× τ E cr,G

τ E cr, L + τ E

cr,G

. (10)

The shear buckling parameters calculated using the elastic

interactive buckling stress of Eq. (10) are greater than ones

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Fig. 10. Results of nonlinear analyses.

calculated using either the elastic local or global buckling stress

because interactive buckling stress is smaller than local orglobal buckling stress. As shown in Fig. 10, this leads to a better

estimation of the shear buckling strength of the corrugated web.

The buckling stress of the only one model was lower than the

theoretical buckling strength in the elastic range, but this model

could not satisfy the geometric requirements of a/ h < 0.2 and

d /t > 10.0.

4. Comparison with published experimental data

Many shear buckling tests of trapezoidally corrugated webs

have been conducted. Abbas et al. [5] summarized the results

of numerous tests carried out in Europe and the United States.

Yamazaki [11] and Gil et al. [13] reported the results of sixtests conducted in Japan and nine tests conducted in Korea,

respectively. Both tests were carried out using large-scale test

specimens.The evaluation of shear buckling tests conducted in the

United State and Europe showed that the available local

and global buckling formulae could overestimate the shear

capacity for corrugated webs. But, most of these shear bucklingtests were conducted on relatively small-scale specimens with

dimension and plate thickness significantly smaller than what

would be used in bridge construction. The results of relatively

large-scale tests using a 4 mm (or 8 mm) thick web [ 5] showed

that the buckling stress is greater than the shear yielding stress.

Abbas et al. suggested that the cause of the discrepancy betweenthe theoretical and experimental results is initial imperfection,

and proposed that Eq. (11) be used as the nominal design

shear capacity of the corrugated plate until further research

results become available. However, Eq. (11) tends to estimate

the shear yielding stress and inelastic buckling stress too

conservatively.

τ n =

τ cr, L × τ cr,G

2

τ 2cr, L+ τ 2

cr,G

. (11)

A plot of the normalized shear stress capacity, τ ex /τ y , versus

the shear buckling parameter, λs is given in Fig. 11 for the

Fig. 11. Results of tests conducted in Japan and Korea.

large-scale test results conducted in Japan and Korea. The shear

buckling parameters for ‘6 tests (Yamazaki, I )’ and ‘9 tests

(Gil et al., I )’ were calculated by Eq. (1) or Eq. (2) depending

on the governing shear buckling mode, and the shear bucklingparameters for ‘6 tests (Yamazaki, II )’ and ‘9 tests (Gil et al.

II )’ were calculated by Eq. (10). Fig. 11 shows that the shear

buckling stress from Eq. (10) can safely estimate the buckling

stress for corrugated webs.

To account for the effects of inelasticity, residual stress,

and initial deformations, Eq. (12) was proposed in the Design

Manual [21]. The inelastic buckling stress given in Eq. (13) was

also suggested by Elgaaly et al. [2] when the elastic local and

global buckling stresses are greater than 80% of the shear yield

stress. As shown in Fig. 11, Eq. (12) provides a lower bound for

these test results.

τ cr

τ y=

1 λs < 0.6

1 − 0.614(λs − 0.6) 0.6 < λs

√ 2

1/λ2s

√ 2 < λs

(12)

τ I N cr =

0.8τ y τ E

cr . (13)

Buckling stresses of two specimens shown in Fig. 11 were

lower than the theoretical buckling stresses though the shear

buckling parameter was calculated by Eq. (10). Local buckling

stresses of the specimens were theoretically lower than global

buckling stresses, yet the specimens were reported to be failed

by a global buckling mode [13]. The ratios d /t and a/ hwere almost 10.0 and greater than 0.3, respectively. These

test specimens could not satisfy the geometric requirement of

a/ h < 0.2 and d /t > 10.0.

5. Summary and conclusion

In this paper, the shear capacity of a trapezoidally corrugated

web was studied numerically by using elastic buckling analysis

and nonlinear analysis considering material and geometric

nonlinearities. The influence of the geometric parameter on

interactive shear buckling was first investigated, and the

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analytical results were compared to the strength from existing

theoretical interactive shear buckling formulae. The strength

suggested from the analysis was also compared to experimental

data.

The elastic buckling analysis results showed that the

interactive shear buckling mode and strength was not influenced

by material inelasticity or yielding, but rather by the geometryof the corrugated plate. The geometric parameters which affect

the interactive shear buckling were determined as a/ h and

d /t . a/ h < 0.2 and d /t > 10.0 were proposed as the

limit conditions for the corrugated webs. It was recommended

that Eq. (10) be used for the conservative estimation of the

elastic interactive shear buckling stress. It was also showed

that the existing interactive shear buckling formulae could not

accurately predict the behavior and strength of interactive shear

buckling.

The shear buckling stresses calculated by Eq. (10) were

compared with the published test results to examine the validity

of the proposed shear buckling stress. The proposed shear

buckling stresses were shown to conservatively estimate theshear buckling stress of trapezoidally corrugated webs. The

comparison also showed that Eq. (12) can be effectively used

to predict the inelastic shear buckling stresses.

Acknowledgments

This work was supported by a grant (05 construction core

C14) from the Construction Core Technology Program by

the Ministry of Construction & Transportation of the Korean

government. The authors wish to express their gratitude for the

financial support. The opinions, findings, and conclusions of the

paper are the authors and do not necessarily reflect the views of

the sponsors.

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