Chen 2014

ORIGINAL ARTICLE

Experimental and finite element analysis research on I-beamunder web crippling

Yu Chen Xixiang Chen Chaoyang Wang

Received: 11 August 2014 / Accepted: 19 December 2014

RILEM 2014

Abstract To research web crippling property of

I-beam under concentrated load, 48 I-beam with

different boundary conditions, loading conditions,

bearing lengths and section heights were tested. The

experimental scheme, failure modes, concentrated

loadgeneral vertical deformation and equivalent strain

distribution curves were presented in the paper. The

effects of boundary condition, loading condition,

bearing length and section height on web crippling

ultimate capacity and ductility of I-beam were also

studied. Results of these tests show that as bearing

length increases, web crippling ultimate capacity of

I-beam increase significantly. When bearing length was

50 and 100 mm, web crippling ultimate capacity of

I-beam with web slenderness = 17.5 reached its peak;

when the bearing length was 150 mm, web crippling

ultimate capacity of I-beam with web slender-

ness = 22.5 reached its peak. The middle web entered

plasticity and formed plastic hinge zone in the ultimate

limit state. The web crippling ultimate capacity of

I-beam with bearing length = 50 mm in interior one

flange condition, interior two flanges condition, end one

flange and end two flanges condition decreased

progressively. Finite element analysis could simulate

experimental failure mode and web crippling ultimate

capacity. The simple calculation method of web

crippling ultimate capacity put forward in the paper

can accurately predict experimental value.

Keywords I-beam Web crippling Experimentalresearch Ultimate capacity Finite element analysis Simple calculation method

List of symbols

EOF End-one-flange

IOF Interior-one-flange

ETF End-two-flange

ITF Interior-two-flange

Rw,ul Experimental web crippling ultimate

capacity

Rw,ulc Web crippling ultimate capacity obtained

by using Chinese steel structures design

code (GB50013-2003)

Rw,ule Web crippling ultimate capacity obtained

by using European design of steel

structures (Eurocode 3)

Rw,ulFEA Web crippling ultimate capacity obtained

by using finite element analysis

Rw,ulre Web crippling ultimate capacity obtained

by using equations the paper put forward

Y. Chen

School of Urban Construction, Yangtze University,

Jingzhou 434023, China

Y. Chen C. WangCollege of Civil Engineering, Huaqiao University,

Xiamen 361021, China

X. Chen (&)College of Technology & Engineering, Yangtze

University, Jingzhou 434023, China

e-mail: [email protected]

Materials and Structures

DOI 10.1617/s11527-014-0508-z

fy Tensile yield stress

fu Ultimate tensile stress

m Poissons ratiod Elongation after fractureE Elastic modulus

MD Average deviation of yield stress

r Standard deviation of yield stressh Overall height of I-beam

b Flange height of I-beam

ht Web effective height of I-beam

t Web thickness of I-beams

r Internal radius of corner

a Bearing length

ht/t Web slenderness

ei Strain intensitye1 First principal straine2 Second principal straine3 Third principal strain

1 Introduction

I-beams nowadays are widely used in stadiums,

towers and bridges due to their high strength, easy

fabrication and fast construction. The web of I-beam

may buckle due to high localized bearing force.

Therefore, web crippling needs to be considered in

designing I-beams.

A considerable amount of research has been

carried out on cold-formed and aluminum tubular

sections under web crippling over many years by

numerous researchers, particularly to validate various

design rules for web crippling, and the majority was

based on experimental investigations. In order to

study the stability of the web in structural steel beams

under a concentrated load, a cooperative investigation

was undertaken by Lyse and Godfrey [1]. The test

program included the testing of six rolled beams, four

of which were cut from the same section and two

from another section. A series of tests on aluminum

square and rectangular hollow sections under web

crippling was presented by Zhou and Young [2, 3].

The web crippling strength in end-two-flange (ETF)

loading condition increased faster than those interior-

two-flange (ITF) loading condition as the bearing

length increased. The effect of the bearing length on

the web crippling strength in ETF loading condition

was more severe than those in ITF loading condition.

The new web crippling test data presented in this

paper could be used to develop design rules for

aluminum square and rectangular hollow sections. An

experimental study was conducted at the University

of Missouri-Rolla by Stephens and Laboube [4] to

establish the web crippling strength of both box and

I-beam in interior-one-flange (IOF) loading condition.

Ren et al. [5] accurately predicted the behavior and

ultimate strengths of cold-formed steel channels

subjected to pure bending as well as combined

bending and web crippling using the verified finite

element models against test results. Carden et al. [6]

investigated the critical web limit states in H-beams

experimentally. The web crippling strength was

greater than that for two independent, single web

C-sections. Genetic programming (GP) as a new tool

for the formulation of web crippling strength of cold-

formed steel decks for various loading cases was

presented by Cevik [7]. The results of the proposed

GP formulations were compared with results of

existing design codes and were found to be more

accurate for all loading cases. Nine specimens were

tested to collect data on V-core panels subjected to

end one-flange (EOF) loading by Okazaki et al. [8].

The modified equation was found to adequately

predict the measured web crippling strength of V-core

panels. Macdonald et al. [9] presented the results of

an investigation into web crippling behavior of cold-

formed thin-walled steel lipped channel beams in

IOF, ITF, EOF and ETF loading conditions as defined

by the American Iron and Steel Institute. An exper-

imental program was developed to obtain the load

deformation characteristics of beam members with

varying cross-sectional and loading parameters in the

three web crippling loading conditions. Eighty two

web crippling tests of cold-formed steel sections, with

20 tests on channel sections without web openings

and 62 tests on channel sections with web openings,

were conducted by Uzzaman et al. [10, 11]. The finite

element model was shown to be able to closely

predict the web crippling behavior of the channel

sections, both with and without circular web hole. It

was demonstrated that the main factors influencing

the web crippling strength were the ratio of the hole

depth to the flat depth of the web, and the ratio of the

length of bearing plates to the flat depth of the web. A

combination of experiments and non-linear finite

element analyses were used to investigate the effect

of offset web holes on the web crippling strength of


cold-formed steel channel sections in the ETF loading

condition by Uzzaman et al. [12]. Design recommen-

dations in the form of web crippling strength reduc-

tion factors are proposed. An experimental

investigation of web crippling in stainless steel cold

formed sections was presented by Bock et al. [13]. A

new equation was proposed to predict the ultimate

strength of stainless steel cold-formed members under

web crippling. Natario et al. [14] evaluated the web

crippling behavior of cold-formed steel beams by

using quasi-static analyses with explicit integration.

The failure mechanism emerged considerably more

clearly when the quasi-static analysis was adopted.

Wu and Bai [15] investigated the web crippling

behavior of pultruded GFRP sections under concen-

trated loading, employing four square hollow sections

of different sizes. A simple mechanism based design

equation was proposed to estimate the strength of

such pultruded GFRP sections subjected to web

crippling.

There is little research being carried out on the

behavior of I-beam under web crippling. Therefore,

the ultimate capacity, failure modes and ductility of

I-beam under web crippling need further investigation.

In this paper, the experimental work was conducted on

I-beam under web crippling. The effects of bearing

lengths, web slenderness, boundary and loading

conditions on the ultimate capacity and initial stiffness

of I-beam under web crippling were investigated.

Furthermore, using the calibrated finite element ana-

lysis, a parametric study was conducted to compre-

hensively investigate the effects of some important

geometric parameters on the ultimate capacity of

I-beam under web crippling. The new design simple

calculation method is proposed for I-beam under web

crippling at the end of the paper.

2 Experimental investigation

2.1 Specimens design

To research web crippling property of I-beam, 48

I-beams with different boundary condition, loading

condition, section height, and bearing length were

tested.

The bearing plates were fabricated with Q235 steel

whose nominal yield strength was 235 MPa having the

nominal thickness of 30 mm. All the bearing plates

were machined to specified dimensions whose the

length was 300 mm. The bearing plates were designed

to act across the full flange widths of the specimen

sections, so as to ensure the overall displacement

loading.

The test specimens under web crippling comprised

four different section sizes, having nominal heights

ranging from 100 to 160 mm. The measured ratio of

the height to the thickness (web slenderness) of the

webs was 15.0, 18.0, 17.5, 22.5, as shown in Fig. 1.

In the paper, the specimens were tested in four

loading conditions, namely, EOF, IOF, ETF and ITF.

In order to remove the influence of the boundary

condition, the distance from the edge of the bearing

plate to the end of the member was set to be at least 1.5

times the overall height of the web. Figure 2 shows

photos of web crippling tests in four boundary and

loading conditions.

In Table 1, the specimens were labeled so that the

height of sections, the boundary condition, the loading

condition and the width of the bearing plates, could be

identified from the label. Rw,ul is experimental value of

the web crippling ultimate capacity of I-beam spec-

imen in the test. Rw,ul is defined as the maximum load

reached during experiments. For example, the label

I100-ETF-N100 is explained as follows:

The notation I100 indicates the section height of

I-beam in mm (100 mm).

The next three letters indicate that the loading and

boundary condition ETF was used in the test.

Fig. 1 Definition of symbols of I-beam


N100 represents the width of bearing plate in mm

(100 mm).

2.2 Material properties

The I-beam specimens were fabricated by hot rolling

using the Chinese Q325 steel. Tensile coupon tests

were carried out to determine the material properties

of the I-beam specimens. The tensile coupons were

taken from the center face of the web plate in the

longitudinal direction of the untested specimens. The

nominal coupons were prepared and tested according

to Chinese metallic materials-tensile testing at ambi-

ent temperature (GB/T228-2002) [16], the coupons

were tested in an MTS displacement controlled the

testing machine using friction grips. The strain gauges

and a calibrated extensometer were used to measure

the longitudinal strain. A data acquisition system was

used to record the load and strain at regular intervals

during the material property tests. The material

properties obtained from the tensile coupon tests are

summarized in Table 2, including the tensile yield

stress (fy), the ultimate tensile stress (fu), Poissons

ratio (m), the elongation after fracture (d), the elasticmodulus (E), average deviation of yield stress (MD),

and standard deviation of yield stress (r).

2.3 Loading and test program

In all structural design, an accurate prediction of the

ultimate capacity of I-beam under web crippling is

required for an efficient and safe use. The local

transverse resistance of the web crippling specimens

was obtained according to European steel structures

design code [17], which can be used as the estimated

load.

The load classification was conducted according to

estimated ultimate capacities. Before the values of

preloading reached 10 % of the estimated ultimate

capacities, slow loading was made on bearing plate by

hydraulic jack. Before the values of formal load

reached 20 % of the estimated ultimate capacities,

continuous load was made, meanwhile monitoring the

loading process if the rosettes strain gauges enter

plasticity or displacement gauges increasing rapidly,

finally continuously slow load was applied until

Fig. 2 Photos of web crippling tests in four boundary and loading conditions


Table 1 Parameters and ultimate capacity of I-beam under web crippling

Boundary and

loading conditions

Specimens a (mm) b (mm) h (mm) L (mm) ht (mm) t (mm) ht/t r (mm) Rw,ul (kN)

EOF I100-EOF-N50 50 67.42 99.82 400 75.00 5.08 14.76 6.88 122.3

I100-EOF-N100 100 67.54 99.80 400 75.06 5.00 15.01 6.60 201.6

I100-EOF-N150 150 67.70 99.80 400 75.10 5.04 14.90 6.64 179.7

I120-EOF-N50 50 73.10 119.20 400 91.72 5.10 17.98 7.60 141.6

I120-EOF-N100 100 73.00 119.52 400 91.58 5.20 17.61 7.64 197.8

I120-EOF-N150 150 72.32 119.40 400 91.60 5.18 17.68 7.64 170.0

I140-EOF-N50 50 78.60 140.06 400 113.10 6.40 17.67 7.42 156.8

I140-EOF-N100 100 79.54 140.00 400 113.12 6.54 17.30 7.88 193.5

I140-EOF-N150 150 78.62 140.02 400 113.08 6.48 17.45 7.60 256.0

I160-EOF-N50 50 89.10 161.50 400 135.10 5.90 22.90 7.90 113.3

I160-EOF-N100 100 89.30 162.00 400 135.10 5.98 22.59 7.88 166.8

I160-EOF-N150 150 89.22 161.36 400 135.06 5.92 22.81 7.72 343.4

IOF I100-IOF-N50 50 67.50 99.82 600 75.04 5.06 14.83 6.88 188.3

I100-IOF-N100 100 67.54 99.84 600 75.04 5.04 14.89 6.76 224.7

I100-IOF-N150 150 67.62 99.80 600 75.12 5.04 14.90 6.66 311.9

I120-IOF-N50 50 73.12 119.28 600 91.68 5.18 17.70 7.62 214.1

I120-IOF-N100 100 73.20 119.52 600 91.54 5.20 17.60 7.64 217.3

I120-IOF-N150 150 72.30 119.82 600 91.62 5.20 17.62 7.70 353.0

I140-IOF-N50 50 78.60 140.08 400 113.10 6.44 17.56 7.52 300.5

I140-IOF-N100 100 79.32 140.10 400 113.12 6.52 17.35 7.88 366.5

I140-IOF-N150 150 78.80 140.04 400 113.20 6.46 17.52 7.60 431.1

I160-IOF-N50 50 89.14 161.50 400 135.10 5.92 22.82 7.92 242.8

I160-IOF-N100 100 89.32 161.48 400 135.18 5.98 22.61 7.88 284.6

I160-IOF-N150 150 89.22 161.36 400 135.06 5.94 22.74 7.78 458.6

ETF I100-ETF-N50 50 67.62 99.90 400 75.08 5.08 14.78 6.88 76.0

I100-ETF-N100 100 67.51 99.80 400 75.06 5.02 14.95 6.60 117.6

I100-ETF-N150 150 67.68 99.82 400 75.14 5.02 14.97 6.66 200.9

I120-ETF-N50 50 73.00 119.32 600 91.72 5.10 17.98 7.60 127.0

I120-ETF-N100 100 73.26 119.52 600 91.58 5.16 17.75 7.68 146.5

I120-ETF-N150 150 72.32 119.40 600 91.68 5.18 17.70 7.64 193.5

I140-ETF-N50 50 78.60 140.08 400 113.10 6.48 17.45 7.46 137.3

I140-ETF-N100 100 78.90 140.02 400 113.16 6.54 17.30 7.88 209.2

I140-ETF-N150 150 78.62 140.02 400 113.08 6.46 17.50 7.60 263.1

I160-ETF-N50 50 89.12 161.50 400 135.08 5.88 22.97 7.86 81.7

I160-ETF-N100 100 89.28 162.00 400 135.10 5.94 22.74 7.88 114.9

I160-ETF-N150 150 89.20 161.80 400 135.06 5.96 22.66 7.78 314.8

ITF I100-ITF-N50 50 67.48 99.82 400 75.08 5.00 15.02 6.70 168.8

I100-ITF-N100 100 67.54 99.80 400 75.06 5.00 15.01 6.60 171.7

I100-ITF-N150 150 67.68 99.80 400 75.12 5.06 14.85 6.64 230.1

I120-ITF-N50 50 73.10 119.22 600 91.72 5.10 17.98 7.66 157.0

I120-ITF-N100 100 73.30 119.52 600 91.58 5.12 17.89 7.84 214.5

I120-ITF-N150 150 72.32 119.86 600 91.64 5.14 17.83 7.64 266.7

I140-ITF-N50 50 78.60 140.06 400 113.10 6.42 17.62 7.42 270.7

I140-ITF-N100 100 79.44 140.04 400 113.12 6.50 17.40 7.88 212.0


failure. In the actual control, the upper limit of graded

load is continuously adjusted according to the dis-

placement gauges feedback. At the appearance of

obviously large displacement or drop load, the tests

were stopped.

Two displacement gauges D1 and D2 were located

at the surface of the bearing plates on the top flange of

the I-beam in order to record the vertical displacement

during the test, as shown in Fig. 3a. Five rosette strain

gauge (T15), which enabled strain values to be

measured simultaneously, were distributed at the same

interval on the web of I-beam, as shown in Fig. 3b.

3 Test results

3.1 Failure modes

All types of failure modes in four loading conditions,

namely, EOF, IOF, ETF and ITF were observed from

the tests, as shown in Fig. 4ad, respectively. In both

EOF and ETF conditions, the compressive top flange

buckled, the bottom flange did not buckle, web

crippled into S type out-of-plane, and the corner

kept right angle. In IOF condition, the top flange

buckled, the bottom flange did not buckle, and the

upper part of web under the bearing plate slightly

buckled. In ITF condition, both the top and bottom

flange buckled, while the upper part of web right under

the bearing plate slightly buckled. Generally, com-

pressive top flange buckled first, then web crippled,

and finally bottom flange buckled. The effects of

bearing lengths and section heights on failure modes

of I-beam under web crippling were little.

3.2 Comparison of ultimate capacity under web

crippling with different bearing lengths

Table 3 shows the ultimate capacity of I-beam under

web crippling with different bearing lengths. The

effect of bearing plate length on the ultimate capacity

Table 1 continued

Boundary and

loading conditions

Specimens a (mm) b (mm) h (mm) L (mm) ht (mm) t (mm) ht/t r (mm) Rw,ul (kN)

I140-ITF-N150 150 78.62 140.04 400 113.08 6.48 17.45 7.64 337.3

I160-ITF-N50 50 89.12 161.50 400 135.04 5.94 22.73 7.96 176.1

I160-ITF-N100 100 89.30 161.38 400 135.10 5.98 22.59 7.88 241.2

I160-ITF-N150 150 89.28 161.36 400 135.06 5.92 22.81 7.72 414.5

Table 2 Result of materialcharacteristic test

Members fy (MPa) fu (MPa) m d (%) E (GPa) MD r

I100 9 68 9 5.0 275 390 0.31 38 209 14 2

I120 9 74 9 5.0 284 396 0.29 36 206 13 1

I140 9 80 9 6.5 293 385 0.28 37 208 17 2

I160 9 88 9 6.0 285 405 0.30 34 210 11 3

D1 D2D1 D2

Displacement transducers

Hydraulic jackHydraulic jack

(ETF and ITF) (EOF and IOF)

(a) Displacement transducers

Rosette strain gauge

Hydraulic jackHydraulic jack

(ETF and ITF) (EOF and IOF)

(b) Rosette strain gaugesFig. 3 Arrangement of displacement and rosette strain gauges


of I-beam under web crippling was different in the

different loading conditions.

Increasing bearing length ranged from 50 to 100 and

150, the ultimate capacity of I-beam under web

crippling increased by 44 and 83 % in EOF loading

condition compared with 41 and 148 % in ETF loading

condition. Meanwhile, increasing bearing length ran-

ged from 50 to 100 mm, the ultimate capacity of I-beam

under web crippling increased by about 15 % in both

IOF and ITF loading conditions; increasing bearing

length ranged from 50 to 150 mm, the ultimate capacity

of I-beam under web crippling increased by about 65 %

Fig. 4 Failure modes in testand FEA


in both IOF and ITF loading conditions, respectively. It

is shown that the effect of the bearing length on the web

crippling ultimate capacity of I-beam in end-flange

loading condition was more obvious than those of

I-beam in interior-flange loading condition.


crippling with different web slenderness

The comparison of the ultimate capacity of I-beam

under web crippling with different web slenderness is

Table 3 Comparison of ultimate capacity of I-beam under web crippling with different bearing lengths

Boundary and

loading conditions

Specimens Rw,ul(N = 50,

kN)

Rw,ul(N = 100,

kN)

Rw,ul(N = 150,

kN)

Rw,ul (N = 100)/

Rw,ul (N = 50)

Rw,ul (N = 150)/

Rw,ul (N = 50)

EOF I100-EOF-

N(50,100,150)

122.30 201.60 179.70 1.65 1.47

I120-EOF-

N(50,100,150)

141.60 197.80 170.00 1.40 1.20

I140-EOF-

N(50,100,150)

156.80 193.50 256.00 1.23 1.63

I160-EOF-

N(50,100,150)

113.30 166.80 343.40 1.47 3.03

Mean 1.44 1.83

COV 0.120 0.446

IOF I100-IOF-

N(50,100,150)

188.30 224.70 311.90 1.19 1.66

I120-IOF-

N(50,100,150)

214.10 217.30 353.00 1.01 1.65

I140-IOF-

N(50,100,150)

300.50 366.50 431.10 1.22 1.43

I160-IOF-

N(50,100,150)

242.80 284.60 458.60 1.17 1.89

Mean 1.15 1.66

COV 0.080 0.112

ETF I100-ETF-

N(50,100,150)

76.00 117.60 200.90 1.55 2.64

I120-ETF-

N(50,100,150)

127.00 146.50 193.50 1.15 1.52

I140-ETF-

N(50,100,150)

137.30 209.20 263.10 1.52 1.92

I160-ETF-

N(50,100,150)

81.70 114.90 314.80 1.41 3.85

Mean 1.41 2.48

COV 0.128 0.412

ITF I100-ITF-

N(50,100,150)

168.80 171.70 230.10 1.02 1.36

I120-ITF-

N(50,100,150)

157.00 214.50 266.70 1.37 1.70

I140-ITF-

N(50,100,150)

270.70 212.00 337.30 0.78 1.25

I160-ITF-

N(50,100,150)

176.10 241.20 414.50 1.37 2.35

Mean 1.13 1.67

COV 0.253 0.299


shown in Fig. 5. The web slenderness values of I-beam

ranged from 15.0 to 22.5.

When the bearing length was 50 and 100 mm,

ultimate capacity of I-beam with the web slender-

ness = 17.5 reached its peak; when the bearing

lengths was 150 mm, the ultimate capacity of

I-beam with the web slenderness = 22.5 was the

largest value, the ultimate capacity of I-beam with

the web slenderness = 17.5 was the second largest

value.

100

150

200

250

300

350

15.0(I100) 17.5(I140) 18.0(I120) 22.5(I160)

R w,ul/k

Nht /t

N50 N100 N150

150

200

250

300

350

400

450

500

15.0(I100) 17.5(I140) 18.0(I120) 22.5(I160)

R w,ul/k

N

ht /t

N50 N100 N150

(a) EOF (b) IOF

50

100

150

200

250

300

350

15.0(I100) 17.5(I140) 18.0(I120) 22.5(I160)

R w,ul/k

N

ht /t

N50 N100 N150

100

150

200

250

300

350

400

450

15.0(I100) 17.5(I140) 18.0(I120) 22.5(I160)

R w,ul/k

N

ht /t

N50 N100 N150

(c) ETF (d) ITF

Fig. 5 Comparison ofcapacity of I-beam under

web crippling with different

web slenderness

0

50

100

150

200

250

300

350

400

0 1 2 3 4 5

N/k

N

/mm

I100-EOF-N150(15.0)I140-EOF-N150(17.5)I120-EOF-N150(18.0)I160-EOF-N150(22.5)

Top flange buckle

Web cripple

050

100150200250300350400450500

0 1 2 3 4 5

N/k

N

/mm

I100-IOF-N150(15.0)I140-IOF-N150(17.5)I120-IOF-N150(18.0)I160-IOF-N150(22.5)

Top flange buckle

Upper part of web cripple

(a) EOF (b) IOF

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7 8

N/k

N

/mm

I100-ETF-N150(15.0)I140-ETF-N150(17.5)I120-ETF-N150(18.0)I160-ETF-N150(22.5)

Top flange buckle

Web cripple

050

100150200250300350400450

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

N/k

N

/mm

I100-ITF-N150(15.0)I140-ITF-N150(17.5)I120-ITF-N150(18.0)I160-ITF-N150(22.5)Top flange buckle

Upper part of web cripple

Bottom flange buckle

(c) ETF (d) ITF

Fig. 6 Loaddisplacementof I-beam under web

crippling with different web

slenderness


The loaddisplacement of I-beam under web crip-

pling with different web slenderness is shown in

Fig. 6. X-axis represents the global vertical displace-

ment of specimens (d), Y-axis represents the verticalload at loading end (N). The global vertical displace-

ment of specimens was calculated as average of D1

and D2 displacement values. The important points on

the loaddisplacement curves corresponding to the

attainment of specific phenomena including top flange

buckled, bottom flange buckled and web crippled were

marked in Fig. 6. The measured web slenderness

values of the specimens ranged from 15.0 to 22.5.

Ductility ratio (du/dy) is defined as ratio of displace-ment at ultimate load (du) to displacement at yield load(dy) of all specimens based on the design criteriarecommended by Kurobane et al. [18]. The greater

ductility ratio (du/dy), the better ductility of specimens.The greater web slenderness, the smaller initial

stiffness and the better ductility. Rw,ul can be defined

as the peak load of loaddisplacement curve.


crippling in different boundary and loading

conditions

The comparison of the ultimate capacity of I-beam

under web crippling in different boundary and loading

conditions is shown in Fig. 7. When the bearing length

was 50 mm, the values of the web crippling ultimate

capacity in interior-flange loading condition were

larger than those in end-flange loading condition. The

values of the web crippling ultimate capacity of

I-beam with bearing length = 50 mm in one flange

loading condition were larger than those in two flange

loading conditions. As the bearing length increased,

the trend got unobvious.

When the web slenderness was 22.5, the values of

the web crippling ultimate capacity of I-beam in

interior-flange loading condition were larger than

those in end-flange loading condition. Similarly, the

values of the web crippling ultimate capacity of

I-beam with the web slenderness = 22.5 in one flange

loading condition were larger than those in two flange

loading conditions. As the web slenderness decreased,

the trend got unobvious.

Loaddisplacement of I-beam under web crippling

in different loading conditions is shown in Fig. 8.

Value of X-axis is the average of D1 and D2

displacement values. It is shown that the specimens

in the interior-flange loading conditions had high

ultimate capacity and good ductility. The initial

stiffness of the specimens labeled I160 in interior

loading condition was higher than those of I160 in end

loading condition. The initial stiffness of the other

specimens in interior and end loading conditions was

basically the same.

3.5 Loadequivalent strain on web curves

Equivalent strain distribution in the web region was

derived from the readings of three-element rosettes

strain gauges. The failure mechanism of the joints

were studied from equivalent strain distribution. The

equivalent strain at the measuring points of rosettes

strain gauges corresponding to different load levels

covering the elastic and plastic range of typical

specimens are plotted in Fig. 9, in which the horizon-

tal axis represents the measuring points of strain

gauges (as shown in Fig. 3b), the vertical axis

represents the equivalent strain (ei), and the dash linerepresents the boundary equivalent strain correspond-

ing to the yield strength.

50

100

150

200

250

300

350

15.0(I100) 17.5(I140) 18.0(I120) 22.5(I160)

N/kN

ht/t

EOF IOFETF ITF

100

150

200

250

300

350

400

15.0(I100) 17.5(I140) 18.0(I120) 22.5(I160)

N/kN

ht/t

EOF IOFETF ITF

150

200

250

300

350

400

450

500

15.0(I100) 17.5(I140) 18.0(I120) 22.5(I160)

N/kN

ht/t

EOF IOFETF ITF

(a) N50 (b) N100 (c) N150Fig. 7 Comparison of capacity of I-beam under web crippling in different boundary and loading conditions


050

100

150

200

250

300

350

0 1 2 3 4 5N/kN

/mm

I100-EOF-N150I100-ETF-N150I100-IOF-N150I100-ITF-N150

0

50

100

150

200

250

300

350

400

0 1 2 3 4 5

N/kN

/mm


(a) I100-N150 (b) I120-N150

050

100150200250300350400450500

0 1 2 3 4 5

N/kN

/mm


050

100150200250300350400450500

0 1 2 3 4 5

N/kN

/mm


(c) I140-N150 (d) I160-N150

Fig. 8 Loaddisplacementof I-beam under web

crippling in different

loading conditions

y=13570

1000

2000

3000

4000

5000

6000

7000

8000

T1 T2 T3 T4 T5

i/

Ti

100kN 200kN250kN 300kN343kN

y=1357

0

1000

2000

3000

4000

5000

6000

7000

T1 T2 T3 T4 T5

i/

Ti

200kN 300kN350kN 400kN458kN

(a) I160-EOF-N150 (b) I160-IOF-N150

y=1357

0

2000

4000

6000

8000

10000

12000

14000

16000

T1 T2 T3 T4 T5

i/

Ti

200kN 250kN285kN 300kN314kN

y=13570

100020003000400050006000700080009000

T1 T2 T3 T4 T5

i/

Ti

200kN 300kN350kN 400kN414kN

(c) I160-ETF-N150 (d) I160-ITF-N150

Fig. 9 Equivalent straindistribution curves


ei 12

p 1m

e1e2 2 e2e3 2 e3e1 2q

12

p 1m

exey 2 eyez

2 ezex 232

c2xyc2yzc2zx

r

:

1In elastic range volume is supposed fixed,

cyz 0; czx 0; v 0:5: 2The equivalent strain (ei) could be calculated as

follows [19, 20]:

ei

2p

3

e1 e2 2 e2 e3 2 e3 e1 2q

; 3

where e1, e2 and e3 are the first, second and thirdprincipal strains, respectively, which were obtained

from three-element rosettes strain gauges along the

joint intersection region.

Measuring points first entered plasticity were

determined by different loading conditions. All mea-

suring points on web of I-beam enter plasticity in the

ultimate limit state. Strain intensity of T3 located at

the centerline of web was the minimum of equivalent

strain.

4 Comparison of web crippling ultimate capacity

The experimental web crippling ultimate capacity and

the calculated value of specification in EOF, IOF, ETF

and ITF loading condition are given in Table 4,

respectively. The specification values are calculated

using the measured I-beam geometry size and the

measured yield strength. Rw,ulc and Rw,ule are the web

crippling ultimate capacity of I-beam obtained by

using Chinese steel structures design code (GB50017-

2003) [21] and European design of steel structures

(Eurocode 3) [17], respectively. Rw,ulre is the web

crippling ultimate capacity of I-beam obtained by

using the following design equation the paper put

forward. Up to the authors knowledge, the European

standard is applied to cold formed steel elements or

profiled sheet. There is no design rule for the hot rolled

specimens under web crippling. A comparison

between calculation value obtained by using Eurocode

3 and experimental result was made to check whether

design equation of Eurocode 3 is applicable for hot

rolled specimens or not.

The design strengths of web crippling ultimate

capacity of cross-sections with a single unstiffened

web can be calculated using the design equations as

follows:

Rw;ule k1k2 5:92 ht=t132

1 0:01 at

h i

t2fy

EOF Eurocode 3 17;4

Rw;ule k4k5 14:7 ht=t49:5

1 0:0007 at

h i

t2fy

IOF Eurocode 3 17;5

Rw;ule k1k2 6:66 ht=t64

1 0:01 at

h i

t2fy

ETF Eurocode 3 17;6

Rw;ule k4k5 21:0 ht=t16:3

1 0:0013 at

h i

t2fy

ITF Eurocode 3 17;7

Rw;ulc t a 5hy

fy Chinese code 21; 8

hy h ht =2; 9where fy is the yield stress of I-beam, t is the web

thickness, a is the bearing length, ht is web height, k1and k4 are the same parameters that account for the

influence of yield stress, and k2 and k5 are the influence

function for internal radius of the corners and web

thickness.

The mean values of Rw,ulc/Rw,ul ratio are 1.46, 0.90,

1.74 and 1.14 with the corresponding COV of 0.188,

0.128, 0.227 and 0.171 in EOF, IOF, ETF and ITF

loading and boundary conditions, respectively. The

calculated result obtained by using Chinese steel

structures design code (Rw,ulc) was far larger than the

experimental web crippling ultimate capacity (Rw,ul),

because that the ultimate capacity reduction caused by

out-of-plane buckling of the thin web and effects of

loading and boundary conditions on web crippling

ultimate capacity were not considered in Chinese steel

structures design code. The mean values of Rw,ule/Rw,ulratio are 0.28, 0.46, 0.37 and 0.73 with the correspond-

ing COV of 0.275, 0.176, 0.370 and 0.253 for EOF,

IOF, ETF and ITF loading and boundary conditions,

respectively. The calculated result obtained by using


Table 4 Comparison of capacity of I-beam under web crippling between test, equation and code

Boundary and

loading conditions

Specimens Rw,ul (kN) Rw,ulc (kN) Rw,ulc/

Rw,ul

Rw,ule (kN) Rw,ule/

Rw,ul

Rw,ulre (kN) Rw,ulre/

Rw,ul

EOF I100-EOF-N50 122.3 156.53 1.28 35.87 0.29 82.00 0.67

I100-EOF-N100 201.6 222.54 1.10 37.95 0.19 123.80 0.61

I100-EOF-N150 179.7 293.49 1.63 41.70 0.23 169.15 0.94

I120-EOF-N50 141.6 171.93 1.21 36.64 0.26 84.82 0.60min

I120-EOF-N100 197.8 250.83 1.27 41.39 0.21 134.07 0.68

I120-EOF-N150 170.0 322.91 1.90max 44.41 0.26 179.97 1.06max

I140-EOF-N50 156.8 220.15 1.40 57.65 0.37 122.72 0.78

I140-EOF-N100 193.5 320.39 1.66 64.41 0.33 187.59 0.97

I140-EOF-N150 256.0 412.67 1.61 67.53 0.26 245.37 0.96

I160-EOF-N50 113.3 195.05 1.72 48.23 0.43max 104.88 0.93

I160-EOF-N100 166.8 285.04 1.71 53.33 0.32 160.68 0.96

I160-EOF-N150 343.4 364.01 1.06min 56.11 0.16min 211.56 0.62

Mean 1.46 0.28 0.81

COV 0.188 0.275 0.210

IOF I100-IOF-N50 188.3 155.78 0.83 97.28 0.52 148.29 0.79

I100-IOF-N100 224.7 224.53 1.00 102.80 0.46 212.58 0.95

I100-IOF-N150 311.9 293.42 0.94 109.06 0.35 277.78 0.89

I120-IOF-N50 214.1 175.06 0.82 103.75 0.48 158.23 0.74min

I120-IOF-N100 217.3 250.98 1.16max 111.14 0.51 228.44 1.05max

I120-IOF-N150 353.0 325.63 0.92 117.73 0.33min 297.65 0.84

I140-IOF-N50 300.5 221.62 0.74min 161.93 0.54 230.86 0.77

I140-IOF-N100 366.5 319.89 0.87 174.38 0.48 325.16 0.89

I140-IOF-N150 431.1 410.92 0.95 179.67 0.42 409.49 0.95

I160-IOF-N50 242.8 195.72 0.81 133.81 0.55max 194.73 0.80

I160-IOF-N100 284.6 282.49 0.99 144.04 0.51 277.29 0.97

I160-IOF-N150 458.6 365.24 0.80 149.69 0.33min 353.40 0.77

Mean 0.90 0.46 0.87

COV 0.128 0.176 0.113

ETF I100-ETF-N50 76.0 156.53 2.06 39.70 0.52 67.49 0.89

I100-ETF-N100 117.6 223.43 1.90 42.31 0.36 96.60 0.82

I100-ETF-N150 200.9 292.25 1.45 45.82 0.23 126.96 0.63

I120-ETF-N50 127.0 172.36 1.36 40.42 0.32 69.48 0.55

I120-ETF-N100 146.5 248.90 1.70 45.00 0.31 102.77 0.70

I120-ETF-N150 193.5 322.62 1.67 49.00 0.25 135.43 0.70

I140-ETF-N50 137.3 223.00 1.62 65.18 0.47 104.68 0.76

I140-ETF-N100 209.2 320.30 1.53 71.09 0.34 148.15 0.71

I140-ETF-N150 263.1 411.40 1.56 74.10 0.28 186.80 0.71

I160-ETF-N50 81.7 194.48 2.38 52.54 0.64max 85.82 1.05

I160-ETF-N100 114.9 283.14 2.46max 57.77 0.50 123.67 1.08max

I160-ETF-N150 314.8 368.34 1.17min 62.32 0.20min 160.81 0.51min

Mean 1.74 0.37 0.76

COV 0.227 0.370 0.232


European steel structures design code was very con-

servative. The experimental web crippling ultimate

capacity was relatively close to calculated result in ITF

condition. The mean values and COV of Rw,ule/Rw,ul in

ITF condition were 0.73 and 0.251, respectively.

5 Finite element analysis

5.1 General

The finite element program ABAQUS version 6.11

[22] was used to simulate I-beam under web crippling.

Three main components have been carefully consid-

ered in the FEM. These components are the bearing

plates, I-beam, and the interfaces between the bearing

plates and I-beam. In the FEM, the measured cross-

section dimensions and material properties obtained

from the tests were used. The model was based on the

centerline dimensions of the cross-sections. Both

material and geometric nonlinearities have been taken

into account in the finite element models. The bilinear

material model based on the elastic modulus and post-

yield tangential modulus of steel obtained from the

tensile coupon tests was developed for the material

modelling, while the Von-Mises yield criterion was

applied. Arc-length method was adopted as the

incremental and iterative solution method in the finite

element analysis.

5.2 Element type and mesh

The bearing plates were modeled using analytical rigid

plates and the I-beams were modeled using the C3D8I

solid elements. The C3D8I element is an eight-node

doubly curved thin or thick shell element with reduced

integration, hourglass control, and finite membrane

strains. It is mentioned in the ABAQUS manual that the

element is suitable for complex buckling behavior. The

C3D8I element has six degrees of freedom per node and

provides accurate solutions to most applications. The

finite element mesh used in the model was investigated by

varying the size of the elements in the cross-section to

provide both accurate results and less computational time.

The finite element mesh sizes ranging from 3 9 3 mm

(length by width) to 8 9 8 mm were used for the flanges

and webs depending on the size of the sections.

5.3 Boundary conditions and interfaces

Following the test procedures, the top bearing plate

was restrained against all degrees of freedom, except

for the translational degree of freedom in the loading

direction. The interfaces between the bearing plates

and the I-beam were modeled using the contact pair.

The steel bearing plates were the master elements,

while the I-beam specimen was the slave element of

the interface elements in the FEM. The contact pair

allowed the surfaces to separate under the influence of

Table 4 continued

Boundary and

loading conditions

Specimens Rw,ul (kN) Rw,ulc (kN) Rw,ulc/

Rw,ul

Rw,ule (kN) Rw,ule/

Rw,ul

Rw,ulre (kN) Rw,ulre/

Rw,ul

ITF I100-ITF-N50 168.8 153.79 0.91 125.48 0.74 120.56 0.71

I100-ITF-N100 171.7 222.54 1.30 127.10 0.74 136.29 0.79

I100-ITF-N150 230.1 294.58 1.28 131.82 0.57 155.20 0.67

I120-ITF-N50 157.0 172.00 1.10 132.36 0.84 127.95 0.81

I120-ITF-N100 214.5 246.98 1.15 135.10 0.63 145.41 0.68

I120-ITF-N150 266.7 321.95 1.21 137.85 0.52 162.98 0.61

I140-ITF-N50 270.7 220.84 0.82min 214.08 0.79 203.91 0.75

I140-ITF-N100 212.0 318.62 1.50max 221.75 1.05max 230.52 1.09max

I140-ITF-N150 337.3 412.76 1.22 222.53 0.66 250.74 0.74

I160-ITF-N50 176.1 196.63 1.12 177.04 1.01 168.34 0.96

I160-ITF-N100 241.2 282.40 1.17 181.43 0.75 189.57 0.79

I160-ITF-N150 414.5 364.01 0.88 179.64 0.43min 204.83 0.49min

Mean 1.14 0.73 0.76

COV 0.171 0.251 0.202


a tensile force. However, the two contact surfaces are

not allowed to penetrate each other.

5.4 Method of loading

The loading method used in the FEA was identical to

that used in the tests. The displacement control method

was used for the analysis of the I-beam section under

web crippling. Transverse compressive load was

applied to the specimen by specifying a displacement

to the reference point of the analytical rigid plate that

modeled the bearing plate. Generally, a displacement

of 5 mm was specified in the elastic stage. As the

loading increased, displacement may be reduced to

increase the convergence of the solution.

5.5 Material modeling

The measured stressstrain curves of the tensile

specimens were used in the FEA. The material

behavior provided by ABAQUS allows the multi-

linear stressstrain curve to be used. The first part of

the multi-linear curve represents the elastic part up to

the proportional limit stress with measured Youngs

modulus as well as Poissons ratio of 0.30. Since the

analysis of post-buckling involves large in-elastic

strains, the nominal (engineering) static stressstrain

curve was converted to a true stress and logarithmic

plastic strain curve. The equations for true stress and

plastic true strain were specified in ABAQUS.

5.6 Verification of FEM

In the verification of the FEM, a total of 48 I-beam

specimens under web crippling were analyzed. A

comparison between the experimental results and the

finite element results was carried out. The main

objective of this comparison is to verify and check the

accuracy of the FEM. The comparison of the ultimate

capacities of all specimens obtained from the test

results (Rw,ul) and finite element analysis results

(Rw,ulFEA) is shown in Table 5. The mean values of

the Rw,ulFEA/Rw,ul ratio were 0.91 with the correspond-

ing COV of 0.052. The minimum error was -9 %, the

maximum error was 9 %. The failure modes, load

displacement curves and equivalent strain-point of

measurement curves obtained from the test and finite

element analysis were also compared in Figs. 4 and 10

for typical specimens, respectively. It is shown from

the comparison that the finite element analysis results

generally agreed well with the test results.

6 Proposed design equations

Based on material strength failure of compressive

local web, the calculated results obtained by using

Chinese steel structures design code were larger than

the experimental value. Because the small effect of

bearing length on the web crippling strength in

European steel structures design code, the calculated

obtained by using European steel structures design

code were generally quite conservative.

The calculation equations of web crippling ultimate

capacity in four boundary and loading condition

according to European steel structures design code

were very complicated and very conservative com-

paring with experimental results, so the effect of the

bearing length was improved in accurate calculation

Eqs. 1013 of I-beam web crippling ultimate capacity

this paper put forward by using curve fitting method.

The design values can be reduced appropriately

according to importance of structure. The design

ultimate capacity (Rw,ulre) of the I-beam under web

crippling calculated using Eqs. 1013, respectively,

were compared with the ultimate capacity obtained

from the test, as shown in Table 5. The calculation

equation could accurately predict experimental value.

The mean values of ratio between the calculation

values obtain by using Eqs. 1013 (Rw,ulre) and

experimental values (Rw,ul) were 0.81, 0.87, 0.76 and

0.76 with the corresponding COV of 0.210, 0.113,

0.232 and 0.202 for EOF, IOF, ETF and ITF in

Table 4, respectively.

The web crippling ultimate capacity of I-beam in

four boundary and loading condition are calculated

using Eqs. 1013 as follows:

Table 5 Comparison of design strengths of equations andFEA results with test results

A total of 48 specimens Comparison

Rw,ulFEA/Rw,ul Rw,ulre/Rw,ul

Max 1.09 1.09

Min 0.81 0.49

Mean 0.91 0.80

COV 0.052 0.189


Rw;ulre 0:9 6 ht=t130

1 0:12 at

h i

t2fy EOF;

10


1 0:08 at

h i

t2fy IOF;

11


1 0:085 at

h i

t2fy ETF;

12


1 0:015 at

h i

t2fy ITF;

13where fy is the yield stress of I-beam, t is the web

thickness, a is the bearing length, and ht is web height.

7 Conclusions

An experimental investigation was conducted in this

study on the behavior of I-beam under web crippling.

The ultimate capacity, failure modes, local deforma-

tions and strain distributions of all specimens were

reported. In addition, the corresponding finite element

analysis was also performed and the validated FE

model was used for the parametric study to evaluate

the effects of main geometric parameters on the

behavior of I-beam under web crippling Based on the

experimental and numerical investigations, the fol-

lowing conclusions can be drawn:

(1) The ultimate capacity and initial stiffness of all

specimens under web crippling significantly

increased with the increase of bearing lengths.

(2) The greater web slenderness of I-beam, the

smaller initial stiffness and the better ductility.

(3) The web crippling ultimate capacity of I-beam

with web slenderness = 22.5 in interior-flange

loading condition were larger than those in end-

flange loading condition. Similarly, the web

crippling ultimate capacity in one flange load-

ing condition were larger than those in two

flange loading condition.

(4) A FEA that incorporated the geometric and

material non-linear has been developed and

verified against the experimental results. The

FEM accurately predicted the behavior of

I-beam under web crippling.

(5) The proposed simple calculation method of web

crippling ultimate capacity was verified to be

accurate and reliable for I-beam under web

crippling.

Acknowledgments This research work was supported by theNational Natural Science Foundation of China (Nos. 51278209

and 51478047) and the Research Grant for Young and Middle-

aged Academic Staff of Huaqiao University (No. ZQN-PY110).

The authors are also thankful to Fuan Steel Structure Engineering

Co., Ltd., for the fabrication of test specimens. The tests were

conducted in Fujian Key Laboratory on Structural Engineering

and Disaster Reduction at Huaqiao University. The support

provided by the laboratory staff is gratefully acknowledged.

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0 1 2 3 4 5N

/kN

/mm

I100 -EOF-N150(Test)I100 -ETF-N150(Test)I100 -IOF-N150(Test)I100 -ITF-N150(Test)I100 -EOF-N150(FEA)I100 -ETF-N150(FEA)I100 -IOF-N150(FEA)I100 -ITF-N150(FEA)

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200kN(Test)200kN(FEA)400kN(Test)400kN(FEA)

(a) load-displacement curves (b) equivalent strain-point of measurement curves (I160-ITF-N150)

Fig. 10 Comparisonbetween FEA and test

results for typical specimens


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Experimental and finite element analysis research on I-beam under web cripplingAbstractIntroductionExperimental investigationSpecimens designMaterial propertiesLoading and test program

Test resultsFailure modesComparison of ultimate capacity under web crippling with different bearing lengthsComparison of ultimate capacity under web crippling with different web slendernessComparison of ultimate capacity under web crippling in different boundary and loading conditionsLoad--equivalent strain on web curves

Comparison of web crippling ultimate capacityFinite element analysisGeneralElement type and meshBoundary conditions and interfacesMethod of loadingMaterial modelingVerification of FEM

Proposed design equationsConclusionsAcknowledgmentsReferences

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Chen 2014