Bending behavior of concrete-encased composite I-girder withcorrugated steel web

Jun He a,c, Yuqing Liu b,n, Airong Chen b, Dalei Wang b, Teruhiko Yoda c

a School of Civil Engineering and Architecture, Changsha University of Science & Technology, Hunan, Chinab Department of Bridge Engineering, Tongji University, Shanghai, Chinac Department of Civil and Environmental Engineering, Waseda University, Tokyo, Japan

a r t i c l e i n f o

Article history:Received 2 January 2012Accepted 2 August 2013Available online 17 October 2013

Keywords:Composite girderConcrete encasementCorrugated steel webFlexural loading testBending strength

a b s t r a c t

A partially encased composite I-girder with flat or corrugated web has been proposed to improve thestructural performance of continuous composite girder under hogging moment. The flexural behavior ofsuch structure under two points symmetric loading has been experimentally and analytically investi-gated. Static flexural loading tests showed that the partially encased girder improved bending strength incomparison to steel I-girder, as local bucking of steel flange was restricted by encased concrete. Especiallyfor the corrugated web girder, the ultimate bending strength was improved about 20%, and the ductilityalso increased about 3 times. In addition, the limitation of width-to-thickness ratios for steel andconcrete-encased composite I-girders with corrugated web were suggested to prevent premature failuredue to local buckling of compressive flange. Moreover, the analytical methods of flexural strength underservice and ultimate state for partially encased composite girder were proposed and verified withexperimental results. It was found that the analytical bending strengths agreed well with theexperimental ones at both service and ultimate state, which means the proposed analytical equationscan be applied in predicting flexural strength accurately for such encased composite girder with flat orcorrugated web.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Prestressed concrete girders with corrugated steel webs areone of the promising concrete–steel hybrid structures applied tohighway bridges, which include prestressed slabs, corrugated steelwebs and internal or external tendons. The way to substitutecorrugated steel webs for concrete webs of a box girder bridge willresult in no restraint among the upper or lower deck slab andwebs of the bridge, which will alleviate influences on the structuredue to concrete creep, drying shrinkage and temperature differ-ences. Prestressing can be efficiently introduced into the top andbottom concrete flanges due to the so-called “accordion effect” ofcorrugated webs. The strength, stability of structures and materialefficiency can be improved by concrete slab combined withcorrugated steel webs [1–3].

Flexural strength of steel girder with corrugated steel web isprovided by the flanges with almost no contribution from the web.Furthermore, there is no interaction between flexure and shearbehavior. Thus, the ultimate flexural strength of steel girder withcorrugated steel web can be based on the flange yield strength

[4–8]. The flexural capacity of composite girders with corrugatedsteel webs was also investigated and the same aspects defined forsteel girders were found to be applicable to composite girders [9].Lindner [10], Aschinger and Lindner [11] studied the elasticflexural behavior of corrugated web I-girders under in-plane loads.In their analyses, they assumed that the flanges carry only themoment and the web carries only the shear. Elgaaly et al. [6] didexperimental and analytical studies on bending strength of steelbeams with corrugated webs. Parametric analytical studies werealso conducted to examine the effect of the ratio between theflange and web thicknesses, the yield stresses, the corrugationconfiguration, the panel aspect ratio, and the stress-strain relation-ship to the ultimate bending moment capacity of steel beams withcorrugated webs. Chan et al. [12] and Khalid et al. [13] studied theeffect of web corrugation on the bending capacity of the beamusing finite element method. Beams with flat web, horizontallyand vertically corrugated web respectively were studied. Mo et al.[14] presented the experimental and analytical results of fourscaled prestressed concrete box-girder bridges with corrugatedsteel webs. It was found that both the thickness of end diaphragmsand the location of prestressing strands at both ends of thespecimens were insignificant when the specimens failed in themid-span due to concrete crushing. Huang et al. [15] perfor-med finite spring element analysis on the accordion effect of steel

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Thin-Walled Structures

0263-8231/$ - see front matter & 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.tws.2013.08.003

n Corresponding author. Tel.: þ86 21 65981675; fax: þ86 21 65983450.E-mail address: yql@tongji.edu.cn (Y. Liu).

Thin-Walled Structures 74 (2014) 70–84

beams with corrugated web. The accordion effect is a phenom-enon that, when prestressing is introduced to a member withcorrugated web, the web behaves like an accordion and foldseasily to the longitudinal direction. Song et al. [16] investigatedand analyzed the mechanical behavior of externally prestressedcomposite beams with corrugated steel webs by using a nonlinearprogram and model tests. Watanabe and Kubo [17] presentedexperimental and numerical analysis results of corrugated webgirders with four different trapezoidal corrugation configurations,including a flat web under pure bending. A predicting method ofthe ultimate strength considering local flange buckling was alsoproposed based on the parametric analysis of corrugated webgirders. He et al. [18] analyzed the mechanical behaviors ofcorrugated steel web box girders with different internal andexternal tendon parameters under flexural load, including thearrangement of the internal and external tendon, the tensile force,the position of the anchorage point and the distance of thediversion point.

In Japan, continuous and rigid frame bridges with the mainspan length from 50 m to 150 m account for about 80% of the totalnumber for composite bridges with corrugated steel webs. How-ever, at the intermediate supports of continuous or rigid framebridges, large bending moments and shear forces exist; theconcrete slab is in tension due to hogging bending moment anddoes not contribute to the bending strength. The lower flanges andlower parts of webs are in compression and are vulnerable to

lateral-torsional buckling. Thus, there are weak points with regardto durability and strength. Partially encased composite I-girderwith corrugated web has been proposed to improve the structuralperformance of continuous composite girder under hoggingmoment. Concrete is poured in the area surrounded by the upperflange, lower flange and web around the intermediate supportsespecially the section of large height. The encased concrete isexpected to prevent buckling of the web in compression and theconcrete itself also contributes to the bending and shear strength,as shown in Fig. 1.

At present, there are few reports about design codes andmethods for concrete-encased composite I-girder with corrugatedsteel web. The authors [19] tested seven steel and compositeI-girders with flat or corrugated web to investigate the shearperformance, the varying parameters such as the thickness of steelweb and shear connection degree between steel web and encasedconcrete were considered in the test. On the basis of experimentalresults, analytical and numerical models were established andverified to predict the shear strength of encased composite girderwith corrugated web [20].

This paper focuses on the experimental and analytical studies onbending behavior of steel and composite girder with corrugated web.Four steel and composite I-girders with corrugated or flat web weretested under bending moment to investigate the flexural strength andfailure mechanism, such as load-displacement relation, failure modeand strain distribution. On the basis of experimental failure modes andstrain distribution, analytical methods to estimate bending strengthwere proposed, and the analytical equations were validated throughcomparisons with experimental results. The overall investigation canserve as a basis for bending strength calculation and design of partiallyencased composite I-girder with corrugated web.

2. Experimental program

2.1. Test specimens

Four steel or composite I-girders with the height of 0.44 m andlength of 3.94 m were fabricated and tested to investigate thebending performance. The web was 400 mm high and 10 mmthick, and the flange was 300 mm wide and 20 mm thick.

Two series of specimens were classified: one was the steel I-girders (Series BS), the other was the concrete-encased composite I-girders (Series BC). In comparison to the I-girders with corrugatedweb, specimens with flat web (BS-0, BC-0) were provided in eachFig. 1. Concrete-encased composite girder with corrugated web.

BS-0 BS-1

BC-0 BC-1

BS-0 BS-1

BC-1BC-0

BC-0 BC-1Plan view

Section viewElevation view

Corrugated profile

P/2 P/2

P/2 P/2

Fig. 2. Test specimens/mm.

J. He et al. / Thin-Walled Structures 74 (2014) 70–84 71

series. The details of the parameters for the test specimens areshown in Fig. 2. In which, the unit wavelength of corrugated web is560 mm, the width of both horizontal and inclined plate is 150 mm,the projected width of inclined plate is 130 mm. Shear studs withdiameter of 16 mm and height of 80 mm were welded on one sideof steel web to connect with concrete encasement.

The reinforcing bars with the diameter of 8 mm were arrangedvertically and horizontally, both ends of all the reinforcing barswere welded on the flanges or stiffeners to keep their positions, asshown in Fig. 2 and Fig. 3(a). The steel girder was placed flat andconcrete was then poured to the one side of the model. The endand intermediate stiffeners welded to the I-girder make concreting

works easy and also increase confinement of the concrete encase-ment, the fabricate process of test specimens are shown in Fig. 3.

2.2. Material properties

Mix proportion of concrete with a design compressive strengthof 50 N/mm2 is shown in Table 1. The material properties includ-ing compressive strengths, tensile strengths and Young's modulusof three cubes at 28 days after the casting of the concrete are givenin Table 2. The characteristic tensile strengths are used in predic-tion of the cracking resistance of the specimens. The mean tensileproperties of samples cut from the web, the flange and thereinforcement of the girders are summarized in Table 3. The steelI-girders of these four models were fabricated from the samegrade of steel plate. From the material test results of steel samples,it was found that the yield strength of the steel flange and webwas about 384 and 380 MPa, respectively. The specified yieldstrength of the deformed reinforcing bars is 342 MPa.

2.3. Loading and measurements

The static tests on the performance of concrete-encased com-posite I-girders under bending load were carried out in StructureLaboratory. The specimens were simply supported by two rollerswith span of 3640 mm long, and loaded at two points with spacingof 710 mm by distributive girder. The shear span from thesupporting to loading point is 1465 mm, and the ratio of shearspan to height is 3.33, which may result in bending failure for testspecimen. A concentrated load was applied on the distributivegirder using servo loading system with loading capacity of10,000 kN, and the loading equipment is shown in Fig. 4.

Generally, the preloading should be taken into account to checkthe good contact between the support and loading equipment, thereliability of all the test equipment and the workability of all themeasurement instruments. The loading was divided into twolevels by force control and displacement control respectively, inwhich the specimens were firstly loaded to yield state of steel

Table 2Material properties of concrete.

Nominal strength (MPa) Axial compressive strength (MPa) Splitting tensile strength (MPa) Young's modulus (MPa)

Sample value Representative value Sample value Representative value Sample value Representative value

50 54.5 54.5 3.78 3.78 47900 4940051.9 3.62 5030057.1 3.95 49900

Table 1Mix proportion of concrete.

Strength (N/mm2) Aggregate size (mm) Slump (mm) W/C (%) Air (%) Unit content (Kg/m3)

Water Cement Sand Aggregate Fly ash

50 5-25 180730 49 4.571.5 159 325 725 1010 100

Fig. 3. Fabricate process of test specimen. (a) Steel structures with reinforcing barsand (b) Concrete casting.

Table 3Material properties of steel.

Component (mm) Yield strength (MPa) Tensile strength (MPa) Elongation (%) Young's modulus (MPa)

Flange and stiffener (20) 384 460 40 1.99�105

Web (10) 380 475 33 2.02�105

Rebar (Φ 8) 342 556 34 1.96�105

J. He et al. / Thin-Walled Structures 74 (2014) 70–8472

flange by force control with the load speed of 2 kN/s, thenmonotonically increased the displacement at an increment of0.0067 mm/s up to the failure of the girders for the second levelby displacement control.

Displacement transducers LVDTs (Linear Variable DifferentialTransformer) were used to measure the vertical deflection at themid-span of the girder. LVDTs were also installed to measure thelateral displacements at the middle of steel web in center span.In addition, LVDTs were located at the supported bottom flange invertical direction and at both upper/lower flange of middle sectionin lateral direction for the girder to ascertain the uneven settle-ment and to check lateral torsional twist of the flexural girderespecially partial concrete-encased composite girder.

At critical sections, such as the middle span of pure bendingmoment zone, the strains were measured using 50 mm electricalgauges for the concrete and 5 mm electrical gauges for the steelgirder and reinforcement. Besides the measurement of displace-ment and strain for specimens during loading process, crackinginitiation and propagation (crack length and width) on the surfaceof concrete were observed. All the information obtained from thetransducers, gauges, and load cells were automatically recorded bya data acquisition system at regular intervals during the tests.

3. Experimental results and discussion

3.1. Load–displacement relationship

The relationships between load and vertical displacement atmid-span of each specimen until the ultimate state are shown inFig. 5. The load was the concentrated load applied on thedistributive girder by servo loading system. And out-of-planedeformation for web was measured by lateral displacement gaugeon the middle section, the load-deformation relationship curvesare described in Fig. 6.

As for steel I-girders with corrugated or flat web (BS-0,-1), thevertical displacement increased almost linearly with the appliedload in the elastic stage, but the relation became non-linear afterthe compressive flange yielded, and the applied load decreasedafter the maximum point. However, after the yielding of compres-sive flange, flat web can still resist bending moment until failurewhile the compressive flange in corrugated web girder buckledrapidly without the bending resistance contribution of corrugatedweb due to its accordion effects. At ultimate load, compressiveflange of steel I-girders buckled, followed by the web deformedoutwards so that the web and the flange remained perpendicular.And out-of-plane deformation became obviously after maximumload (more than 5 mm for BS-0, about 3 mm for BS-1). Moreover,it was found that out-of-plane deformation of web for BS-1

increased linearly with applied load due to its asymmetric sectionand accordion effect of corrugated web.

For the concrete-encased specimens (BC-0,-1), the verticaldeflection increased almost linearly with applied load before thesteel flange yield, and then the composite girders entered intononlinear state. The lateral deformation of the web increased withapplied load, especially after steel flange yielding, lateral torsion ofthe girder appeared due to asymmetric section for partialconcrete-encased girders. The partial encased composite specimenwith corrugated steel web BC-1 improved the bending strengthand ductility compared to steel specimen BS-1. However, themaximum load of specimen BC-0 was about 10% higher than thatof the specimen BS-0, and they almost generated the same verticaldisplacement at maximum load which means they have the sameductile behavior under bending moment.

3.2. Loading capacity and failure modes

Steel flanges undertake most of the bending load for I-girderswith corrugated or flat web. The failure modes of the specimens BSseries are shown in Fig. 7. For specimen BS-0, the upper flangebuckled between the two loading points with the far side up andthe near side down. The web was also deformed outwards so thatthe web and the flange remained perpendicular. This deforma-tion shows a typical torsional buckling shape of the plate girders.For specimen BS-1, the compressive flange with large outstandbuckled between the two inclined plates of corrugated web, and

0

500

1000

1500

2000

2500

0 20 40 60 80 100 120 140

BS-0 BC-0 BS-1 BC-1Lo

ad /

kN

Displacement /mm

0.5 P 0.5 P

D

Fig. 5. Load-deflection curves at middle span.

0

500

1000

1500

2000

2500

-10 -5 0 5 10 15 20 25 30

BS-0 BC-0 BS-1 BC-1

Load

/ kN

Displacement /mm

0.5 P 0.5 P

D

Fig. 6. Load-lateral deformation curves at middle span.

Fig. 4. Test setup/mm.

J. He et al. / Thin-Walled Structures 74 (2014) 70–84 73

out-of-plane deformation for web increased dramatically aftermaximum load.

The failure modes of the specimens BC series are shown inFig. 8. The upper flange on one side deformed outwards due to therestriction of concrete encasement and the other side deforminwards. The buckled length of BC series was slightly shorter thanthat of BS series. This buckled length nearly equals the spacing ofthe reinforcing bars. The concrete crushed at the ultimate load andthe applied load sharply decreased after ultimate load. After thetest, the concrete was removed to see the inside of the specimen.The concrete crushed only on the surface and the concrete insidewas undamaged. The web deformed outwards but the buckledshape of BC series was much shallower than that of BS series. Thereinforcing bars only buckled in the compressive part but unda-maged at the other parts.

Table 4 lists the load carrying capacity of the test specimensunder initial cracking, steel flange yielding and ultimate staterespectively. It was found that the loading capacity was improvedfor steel web encased with concrete, especially for corrugated web

girder. The ultimate load increased about 10% and 20% for flatand corrugated web girder respectively by the concrete encase-ment. In addition, the ductility of concrete-encased girder withcorrugated web increased about 3.58 times in comparison to that ofsteel girder with corrugated web. However, as the steel I-girderwith flat web at ultimate state, the cross section became full plasticsection including web, high strength and sufficient deformation

Fig. 7. Failure modes of specimens BS series. (a) BS-0 and (b) BS-1.

Fig. 8. Failure modes of specimens BC series. (a) BC-0 and (b) BC-1.

Table 4Loading capacity of test specimens.

Specimen Initial cracking Yield of flange Ultimate state

Load(kN)

deflection(mm)

Load(kN)

deflection(mm)

Load(kN)

deflection(mm)

BS-0 – – 1221 14.1 2056 86.3BS-1 – – 1156 12.7 1634 24.3BC-0 135 1.4 1157 12.4 2240 95.5BC-1 125 1.2 1010 11.2 1974 87.1

J. He et al. / Thin-Walled Structures 74 (2014) 70–8474

capacity may be attained, thus the concrete encasement had only alittle influence on the loading capacity and ductility.

Fig. 9 shows the process of crack initiation and development ofconcrete-encased web for specimens BC-0 and BC-1. An initialcracking occurred along vertical direction at middle section ofBC-0 while at junction between inclined and longitudinal fold forBC-1 below loading of 200 kN. With increasing of load, the crackspropagated from the bottom tensile flange to the top compressivearea, leading to the neutral axial moving upward. Under ultimatestate, cracks distributed uniformly with the spacing of verticalreinforcements for BC-0, but the cracks concentrated at both sidesnear loading points for BC-1 as these parts were the weak areawith minimum concrete thickness. The crack width of concretedeveloped proportional to applied load before yielding of flange,after that width of the main cracks increased rapidly, as shown inFig. 10.

3.3. Load-strain Curves

Flexural normal strains on the middle section under purebending were measured to investigate the strain distribution. Steeland concrete strains were obtained by the one-axis strain gaugesattached on the steel and concrete surface respectively.

Figs. 11 and 12 show the load–strain relationship on the steelweb and flanges respectively. For all the specimens, the normalstrains on the web and flange increased proportionally with theapplied load in the elastic range. The upper flange was compressedwhile the bottom flange subjected to tension, and the strain at theweb center was nearly zero in elastic stage, indicating that theneutral axis was at the web center.

When the normal strain of the upper flange reached to about2000 με, the upper flange started to buckle and the strains on theright and left sides of the upper flange (S17, S19 in Fig. 12) behaved

Flat web Encased ConcretCorrugatedweb

Encased Concret

BC-1

BC-1

BC-1

BC-0

BC-0

BC-0

Flat web Encased Concret Corrugatedweb

Encased Concret

Concret crush

Flat web Encased Concret

Concret crush

Corrugatedweb

Encased Concret

Fig. 9. Process of crack initiation and development/mm (red solid lines represent cracks, blue dot lines are the reinforcing bars). (a) Initial cracking, (b) Yield of flange and(c) Ultimate load.

J. He et al. / Thin-Walled Structures 74 (2014) 70–84 75

differently for BS-0. For the specimen BS-1 with corrugated web,the strain gauges S19 and S21 on top flange are not symmetrical tothe web; the value of them are different during all the loadingstage, especially after the yielding of the compression flange.Furthermore, the larger outstand buckled quickly after yielding.

When one side of the web encased with concrete, normalstrains on the flanges were different for the side with or withoutconcrete encasement. Moreover, the bottom of flange was firstlyinto plastic region after steel yielding, then the compressive flangebegun to buckle at ultimate load. The encased-concrete in theupper part contributed to the bending moment and raised theneutral axis upwards, leading to higher flexure resistance incompassion to steel I-girders.

Fig. 13 illustrates the load–strain relationship on the surface ofencased-concrete and horizontal reinforcements at middle span. Forthe specimen BC-0, the concrete strain at the upper part (C4 in Fig. 13)increased with the applied load and finally reached to about 2000 με.

When the concrete crushed, strains of reinforcements and concrete incompression were almost in the same level during all loading stage.And the concrete strain at the bottom part (C7) reached to crack strain(80 με) when the applied load less than 200 kN, strain on thereinforcement (R7) at the same position increased dramatically asthe cracked concrete did not resist any tensile force. It was also foundfrom the measured data that the horizontal reinforcing bars at thelower part were in tension and contributed to the bending strength.The measured stains of specimen BC-1 showed the similar tendencyin comparison to that of specimen BC-0; the difference is thatconcrete strain of BC-1 at upper part did not reach crush strain underultimate load. Because concrete crushed only at weak area withminimum concrete thickness, and the middle section with maximumconcrete thickness did not damage at maximum loading, as shown inFig. 8.

3.4. Strain distributions

Fig. 14 shows the normal strains distribution on the middlesection along the height of steel girder under the different loadingstages. For specimen BS-0, the normal stains on the web almost keeplinearly with the height, which indicates that plane section assump-tion can be applied, and the natural axis is located at the center of thegirder. However, the strains on the corrugated web are very smalleven after the yielding of flange. Due to the “accordion effect” ofcorrugated web, flexural strength of specimen BS-1 is provided bythe flanges with almost no contribution from the web. The strains onboth end of outstands for compressive flange behave differently afteryielding which means local buckling begins to occur; while thestrains on the end of outstands for tensile flange are almost the samelevel even after the flange yielding.

For the concrete-encased specimen BC-0, plane section assump-tion of strain distribution along height also can be adopted. Forspecimen BC-1, as corrugated steel web is connected with concreteby shear studs, the two components deformed compatibly, thestrains on corrugated web in compression part has the same levelas concrete part. The strains on the end of outstand of tensile flange

0 500 1000 1500 2000 25000

1

2

3

4

Cra

ck w

idth

/ m

m

Load / kN

BC-0 BC-1

Fig. 10. Relation of main-crack width and applied load.

0

500

1000

1500

2000

2500

-3000 -2000 -1000 0 1000 2000 3000

BS-0

Strain (uε)

Strain (uε) Strain (uε)

Strain (uε)-3000 -2000 -1000 0 1000 2000 3000

-3000 -2000 -1000 0 1000 2000 3000-3000 -2000 -1000 0 1000 2000 3000

Load

(kN

)

s4 s5 s6 s7

S4

S5

S6

S7

0

500

1000

1500

2000

2500

BS-1

Load

(kN

)

s4 s5 s6

S4

S5

S6

0

500

1000

1500

2000

2500

BC-0Load

(kN

)

s4 s5 s6 s7

S4

S5

S6

S7

0

500

1000

1500

2000

2500

BC-1

Load

(kN

)

s4 s5 s6 s7

S4

S5

S6

S7

Fig. 11. Relation of load and strain on the steel web.

J. He et al. / Thin-Walled Structures 74 (2014) 70–8476

behave differently when one side of the web encased with concretefor BC-0 and BC-1.

The flexural strain distribution along the height of concrete isshown in Fig. 15. It can be seen that the compressive strainsdistribute linearly along the height form the natural axis to upperflange. The concrete at bottom part is in tension, generally aftercracking, this part is ignored taking into account the contribution tobending moment resistance.

4. Analytical study

4.1. Analytical method to calculate bending strength

4.1.1. Bending strength of steel girders with flat webThe load-carrying capacity of plate girders under pure bending

mainly depends on the ultimate strength of compression flangesand in particular on their resistance to torsional buckling, local

0

500

1000

1500

2000

2500

-6000 -4000 -2000 0 2000 4000 6000

Strain (uε)-6000 -4000 -2000 0 2000 4000 6000

Strain (uε)

Load

/ K

NLo

ad /

KN

BS-0

Top flange S17 S18 S19

Bottom flange S20 S21 S22C-C

0

500

1000

1500

2000

2500Top flange

S19 S20 S21

Bottom flange S22 S23 S24

BS-1

Load

/ K

N

C-C

0

500

1000

1500

2000

2500

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

Top flange S17 S18 S19

Bottom flange S20 S21 S22

Strain (uε)-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

Strain (uε)

BC-0

C-C0

500

1000

1500

2000

2500

Top flange S17 S18 S19

Bottom flange S20 S21 S22

BC-1

Load

/ K

NC-C

Fig. 12. Relation of load and strain on the steel flanges.

0

500

1000

1500

2000

2500

-2000 -1500 -1000 -500 0 500 1000

BC-0

Strain (uε) Strain (uε)

Strain (uε)Strain (uε)

Load

(kN

)

Concrete c4 c5 c6 c7

C4

C5

C6

C7 Initial crack

0

500

1000

1500

2000

2500

-3000 -2000 -1000 0 1000 2000 3000

Rebars R4 R5 R6 R7

BC-0

Load

(kN

)

R4

R5

R6

R7

0

500

1000

1500

2000

2500

-1000 -800 -600 -400 -200 0 200 400

BC-1

Load

(kN

)

Concrete c4 c5 c6 c7

Initial crack

0

500

1000

1500

2000

2500

-1000-800 -600 -400 -200 0 200 400 600 800 1000

Rebars R4 R5 R6 R7

BC-1

Load

(kN

)

Fig. 13. Relation of load and strain on the concrete and reinforcements.

J. He et al. / Thin-Walled Structures 74 (2014) 70–84 77

buckling of plates with three edges supported and one edgefree, lateral buckling, and also vertical buckling in the plane ofthe web plate. The torsional and vertical buckling of compressionflanges can be avoided by limiting the width-to-thickness ratios of

outstanding flange and web plates respectively, and the lateralbuckling can be prevented to restrict the effective buckling lengthof the compression flange. This part only focuses on the localbuckling of compression flange. In order to prevent premature

-150-100

-500

50100150

-3000 -2000 -1000 0 1000 2000 3000

BS-0

Flan

ge w

idth

(x)/

mm

0

100

200

300

400

-3000 -2000 -1000 0 1000 2000 3000

BS-0

Hei

nght

(y) /

mm

500kN1000kN Yielding 1500kN

x

y

-150-100-50

050

100150

-3000 -2000 -1000 0 1000 2000 3000

BS-0

Flan

ge w

idth

(x) /

mm

-150-100-50

050

100150

-3000 -2000 -1000 0 1000 2000 3000

BS-1

Flan

ge w

idth

(x)/

mm

0

100

200

300

400

-3000 -2000 -1000 0 1000 2000 3000

BS-1

Hei

nght

(y) /

mm

500kN1000kN Yielding 1500kN

x

y

-150-100-50

050

100150

-3000 -2000 -1000 0 1000 2000 3000

BS-1

Flan

ge w

idth

(x) /

mm

-150-100-50

050

100150

BC-0

Flan

ge w

idth

(x) /

mm

0

100

200

300

400

500

-3000 -2000 -1000 0 1000 2000 3000

BC-0

Hei

ght (

y) /

mm

Steel 2000kN 1500kN Yielding 1000kN 500kN Cracking

x

y

-150-100-50

050

100150

-3000 -2000 -1000 0 1000 2000 3000

BC-0

Flan

ge w

idth

(x) /

mm

-150-100-50

050

100150

-3000 -2000 -1000 0 1000 2000 3000-3000 -2000 -1000 0 1000 2000 3000

BC-1

Flan

ge w

idth

(x) /

mm

0

100

200

300

400

500

-3000 -2000 -1000 0 1000 2000 3000

BC-1

Hei

ght(y

) /m

m

Steel 1800kN 1500kN 1000kN Yielding 500kN Cracking

x

y

-150-100-50

050

100150

-3000 -2000 -1000 0 1000 2000 3000

BC-1

Flan

ge w

idth

(x) /

mm

Strain (uε) Strain (uε)

Strain (uε)

Strain (uε)

Strain (uε)Strain (uε)

Strain (uε)

Strain (uε)

Fig. 14. Normal strains distribution on steel girder along the height. (a) BS-0, (b) BS-1, (c) BC-0 and (d) BC-1.

J. He et al. / Thin-Walled Structures 74 (2014) 70–8478

failure due to local buckling, design codes have prescribed limita-tions on the width-thickness ratio of the cross-section.

CAN/CSA-S16.1-02 specifications [21] classify I-sections into4 classes according to the following flange outstand-to-thicknessand the web-to thickness ratios:

Class 1 :bf l2tf l

r 145ffiffiffiffiffiFy

p hw

twr1100ffiffiffiffiffi

Fyp

Class 2 :bf l2tf l

r 170ffiffiffiffiffiFy

p hw

twr1700ffiffiffiffiffi

Fyp

Class 3 :bf l2tf l

r 200ffiffiffiffiffiFy

p hw

twr1900ffiffiffiffiffi

Fyp ð1Þ

where bfl/2 is the flange outstand. Classes 1 and 2 compactsections develop the fully plastic moment with higher rotationcapacity of Class 1 section. For I-sections with slender flanges orwebs, local buckling may take place to the flange or the web beforethe fully plastic moment is developed. If local buckling occurs afterdeveloping the yield moment, then the section is classified as aClass 3 non-compact section. On the other hand, if the sectioncannot even develop the yield moment then it is classified as aClass 4 slender section. According to the AISC-LRFD [22], theselimits are defined by

Compact section:

bf l2tf l

r0:38

ffiffiffiffiffiEFy

shwtw

r3:76

ffiffiffiffiffiEFy

s

Non-compact section:

bf l2tf l

r0:83

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiE

Fy�69

shwtw

r5:70

ffiffiffiffiffiEFy

sð2Þ

Both Class 1 and Class 2 sections of CAN/CSAS16.1-02 specifica-tions are considered as one class according to the AISC-LRFD(compact section). On the other hand, the limit on Class 3 sectionaccording CAN/CSA-S16.1-02 is more restricted. For non-compactsections, the AISC-LRFD uses Fy-69 in determining the yieldmoment to account for a residual stress of 69 MPa in case ofhot-rolled steel sections (for welded sections the 69 MPa isreplaced by 114 MPa).

After section classification is determined, the bending strengthcan be calculated as fully plastic moment or yield moment.Generally, at least yield moment is expected to be obtained beforelocal buckling of compression flange to make full use of the steelmaterial.

4.1.2. Bending strength of steel girders with corrugated websThe flexural strength of steel girder with corrugated web is

provided by the flanges with almost no contribution from the web,and there is no interaction between flexure and shear behavior.Local buckling of the compression flange of I-girder with corru-gated web affects its bending strength. Generally, local buckling ofthe compression flange of an I-section mainly depends on theflange outstand-to-thickness ratio. Limits are placed on this ratio,so the critical stress initiating local flange buckling will not be lessthan the yield stress.

The flange outstands for girder with flat web was approxi-mately to be bfl/2. For corrugated web girder at a section where theweb is parallel to the axis of the girder, there is a large outstand onone side and a small outstand on the other (Fig. 16).

Thus, which flange outstand (the large flange outstand bc max,the small flange outstand bc min or the average flange outstand bav,as shown in Fig. 16) should be used to classify the cross section

0

100

200

300

400

500

-1500 -1000 -500 0 500 1000 1500

C4

C5

C6

C7

BC-0

Strain (uε)

-1500 -1000 -500 0 500 1000 1500

Strain (uε)

Hei

ght (

mm

)Concrete

2000kN 1500kN Yielding 1000kN 500kN Cracking

0

100

200

300

400

500

BC-1

Hei

ght (

mm

)

Concrete 1800kN 1500kN 1000kN Yielding 500kN Cracking

C4

C5

C6

C7

Fig. 15. Normal strains distribution on concrete along the height.

bavbcmaxbcmin

bf

tw

tf

hw A D

B C

E

F G

H

bcav

bcmax

b d

a

hr bf

bc

b+d

bcmin

σx

Fig. 16. Outstands of compressive flange.

J. He et al. / Thin-Walled Structures 74 (2014) 70–84 79

class of corrugated web girders (Eqs. (1) and (2))?

bc max ¼ ðbf þhrÞ=2; bc min ¼ ðbf�hrÞ=2 ð3Þ

Based on a previous investigation [7], it was argued that theaverage flange outstand bav may only be used as bf/2 if a ratio R isless than 0.14 where R is the ratio between area EFGH and areaABCD defined in Fig. 16. For R is greater than 0.14, which is morepractical, it is recommended to be conservative using the largeflange outstand bc max. Thus, a considerable uncertainty still existsregarding the correct value which should be used for the flangeoutstand of corrugated web girders.

Corrugated web provides a support condition for the flangeoutstand which lies somewhere between a fixed support (k¼1.277)and a simple support (k¼0.425). The buckling coefficient kf forcorrugated steel web girder is assumed to be

kf ¼ 0:425þ 1α2

r1:28 α¼ bþdbc max

ð4Þ

where b, d and bc max are shown in Fig. 16.Local buckling behavior of the compression flange for corrugated

web girders was numerically investigated by Sayed-Ahmed [8]. Thegirders were simply supported and subjected to constant momentsthrough the span. The span of all the analyzed girders was 11.52 m.The corrugated web panel width (a¼b) adopted in the analysis was200 mm. Web thicknesses of 2 mm and 4 mm were considered inthe analysis which corresponds to web height-to-thickness ratioshw/tw of 120 and 240; and panel width to web thickness ratios b/tw

of 50 and 100 respectively. The width of flange bf was 300 mm. Theflange width-to-thickness ratio bf/2tf was varied between 7.5 and37.5 based on the average flange outstand bav. The critical com-pressive force Ncr acting on the upper flange at which local flangebuckling occurred was numerically determined based on eigenvalueanalysis. This force was normalized with respect to the yieldstrength of the flange Ny where Ny¼bfl� tfl� Fy and plotted versusthe large flange outstand-to-thickness ratios in Fig. 17. The non-compact section limit according to the AISC-LRFD was also plotted.It reveals that the calculated value of buckling coefficient kf by Eq.(4) which is adopted by the AISC-LRFD specifications for plane webgirders are equally applicable to corrugated web girders when thelarge outstand is used.

Therefore, local buckling of the compression flange of corru-gated web girders can be avoided by the limitation of outstand-to-thickness ratio. The bending strength of corrugated web girderscan be predicted as follows:

Myfe ¼ FyfWef f ; Wef f ¼ Ize=dce ð5Þ

where Fyf is the yielding stress of flange; Weff, Ize are the effectivesection coefficient and second order inertial moment without thecontribution of corrugated web, dce is the distance from theneutral axis to flange.

4.1.3. Stability of concrete-encased composite girderLimitations concerned with buckling problems in concrete-

encased composite girders have to do with the width-to-thicknessratio of a steel plate element and the slenderness ratio of amember. These limitations are assigned to prevent local bucklingand overall buckling of members, so as to ensure sufficientductility.

Previous experimental studies [23,24] concluded that sufficientductility can be expected in the composite member, if the coveringconcrete was confined by steel hoops so that it did not come off.However, according to the arrangement and/or shape of the steelhoops, the covering concrete may come off. Hence, it is necessaryto choose a suitable width-to-thickness ratio so as to ensuresufficient plastic deformation capacity in the member.

Even if the covering concrete does come off, there is still anessential difference between the composite member and a baresteel member about the local buckling mode of the flange, asshown in Fig. 18. The buckled flange of the bare steel member hassuccessively located simple supported conditions. On the otherhand, the buckled flange of the composite member, has succes-sively located fixed support conditions, because the inner concreteprevents the flange from deforming inward.

5 10 15 20 25 30 35 40 450.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Ncr

/Ny

bcmax / tf

b/tw=100 kf=1.277 kf=0.765 (Eq.4) kf=0.425 b/tw=50

AISC Non-compact

Fig. 17. Local buckling of corrugated web girders' flanges and buckling coefficients.

Fig. 18. Deformation shape of local buckling in flange. (a) Steel girder and (b) Concrete-encased composite girder.

J. He et al. / Thin-Walled Structures 74 (2014) 70–8480

The critical stress to local buckling of a plate element, scr, canbe expressed as follows:

scr ¼ π2kE12ð1�υ2Þ

tb

� �2

ð6Þ

where k¼0.425 for a simple support condition, and k¼1.277 fora fixed support condition. The limit width-to-thickness ratio isgiven as

bt¼ π

6

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3kE

Fyð1�υ2Þ

sð7Þ

The limit width-to-thickness ratio for the steel element in thecomposite member can be relaxed up to

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1:277=0:425

p¼ 1:73

times the limit ratio for the corresponding bare steel element,as specified in the design standard for steel structures. In reality,

one does not encounter either a perfectly simple support conditionin a buckled flange of a steel member, or a perfectly fixed supportcondition in a buckled flange of a composite member. Therefore,the limit width to thickness ratio for a steel plate element ina composite member would in practice be relaxed to about1.5 times the limit ratio specified in the design standard for steelstructures.

4.1.4. Bending strength of concrete-encased composite girderIt is important to establish an analytical method to calculate the

bending strength of partially encased girders in designing actualbridges. Based on experimental results of the partially encasedcomposite girders, some assumptions are proposed for analyticalmodel to predict bending moment

tcmintcav

tcmaxA

A

C

C B

BA - AC - C B - B

tcmin

h

ts ts ts

tcmax tcav

Strains Stress & Force

fs≥Fy

Strains Stress & Force

Cc Ctf

s,web

Ts,web

CCst

TbfTst

Cc Ctf

TbfTst

Cs,web

Ts,web

Cst

C - C

h

C - C

tcmin

HorizontalReinforcing

Flange

tsWeb

VerticalReinforcing

Concrete

ds'

dstdw

,i

C - C

h

C - C

tcmin

HorizontalReinforcing

Flange

tsWeb

VerticalReinforcing

Concrete

ds'

dstdw

,i

�tf

�tf

�s′

�s′

�w,i

�w,i

�st

�st

�bf

�bf

Fig. 19. Section analysis of concrete encased composite girder with corrugated web. (a) Cross section, (b) Under service load and (c) Ultimate state.

J. He et al. / Thin-Walled Structures 74 (2014) 70–84 81

1) The stress of steel flange attain to yielding strength at ultimatestate.

2) Encased concrete is fully connected to steel web by shear studs,and compressive strains of composite web reduce lineally alongthe height from upper flange to the neutral axis.

3) The contribution of cracked concrete in tension to flexurestrength is ignored when the tensile strength up to crackresistance strength.

An analytical method has been proposed to calculate thebending strength of concrete-encased girder using a multiplelayers model. Each layer consists of either the steel plate, thereinforcing bar or the concrete. Fig. 19 shows the strains andstresses of the concrete-encased composite girder with corrugatedweb under the service load and at ultimate state respectively. Themost unfavorable section C–C with minimum thickness of encasedconcrete was chosen as the analytical object for predicting bend-ing moment resistance.

The assumed stress-strain curve of steel is shown in Fig. 20. Thestress-strain relation of steel is assumed to be a bilinear curveincluding the strain hardening effect on the both tension andcompression side. The relations of stress and strain are given by

ss ¼ Esεsrsy εsrεy

ss ¼ syþðsu�syÞεs�εyεu�εy

rsu εyoεsrεuð8a;bÞ

where εs, ss are the strain and stress of steel, Es is the Young'smodulus of steel, sy and su are the yield and ultimate strength ofsteel, respectively.

The non-linear model is adopted for the relationship betweenthe stress (fc) and strain (εc) of concrete in compression (as shownin Fig. 21), which is assumed to be a parabolic curve for the strainunder εc and constant afterwards [25], as follows:

f c ¼ f ′c 2 εcε′c

� �� εc

ε′c

� �2� �

εcrε′c

f c ¼ f ′c ε′coεcrεcu

ð9a;bÞ

where fc and εc are the compressive stress and strain of concrete,f′c and ε′c the compressive strength of concrete and the corre-sponding strain. The ultimate concrete strain εcu is set at 0.004,considering the confined effect of the concrete encasement.

On the tensile side, linear model is adopted for the relationshipbetween the stress (ft) and strain (εt), and after crack resistancestrength (ftr), tensile stress reduced lineally to 0 at ultimate strain (εtu)considering the soften of concrete in tension (as shown in Fig. 21),

which are given by

f t ¼ Ecεtr f tr εtrεtr

f t ¼ f tr 1� εt�εtrεtu�εtr

� �εtroεtrεtu

f tr ¼ 0:23f ′2=3c

ð10a;b; cÞ

Generally, cracked concrete parts are assumed to be no con-tribution to resist bending moment. Thus, after tensile stressreaches crack resistance strength, the tensile force of concrete isnot considered for simplification.

Then, the sectional force by the concrete in compression can beobtained by integrating the stress of each layer, which is given byZ c

0f cbdy¼ α1f ckβ1cd ð11Þ

where b is the width of the composite section, α1 and β1 are thecoefficients of concrete stress block, and c is the distance from topfiber of composite section to the neutral axis. By substitutingEqs. (9) and (11), α1 β1 is expressed as

α1β1 ¼εtfε′c

�13

εtfε′c

� �2

ð12Þ

where εtf is the strain on top fiber of composite section.Also, by definition, the centroid of the concrete stress block (y)

should be

y¼R c0 f cbydyR c0 f cbdy

¼ c�0:5β1c ð13Þ

Moreover, using the relation between Eqs. (10)–(13), thecoefficient of concrete stress block (β1) is obtained by

β1 ¼4�εt=ε′c6�2εt=ε′c

ð14Þ

As shown in Fig. 19, once all the stresses at each layer on thesection are determined, the sectional force can be calculated bymultiplying the corresponding sectional area, which should satisfythe equilibrium condition as follows:

∑Fx ¼ CcþCtf þCs;webþCstþTs;webþTstþTbf ð15ÞThen, the bending moment of the concrete-encased composite

girder (Mn) is calculated by

Mn ¼ ∑N

i ¼ 1Ciðdi�cÞþ ∑

N

i ¼ 1Tiðdi�cÞ ð16Þ

Also, the curvature (φ) is obtained by:

ϕ¼ εtc¼ εbh�c

ð17Þ

These proposed analysis models will be verified and discussedin the in the next Section 4.2.

4.2. Comparison of analytical and experimental bending strength

On the basis of experimental specimens and material proper-ties of steel and composite I-girders, the width-to-thickness ratioof flange outstand for each specimen is listed in Table 5, thelimitations of specifications according to CSA 2002 and AISC 2003are also provided to determine the cross section classification. Itcan be seen that cross sections of all specimens were considered ascompact section which can develop fully plastic moment withhigher rotation capacity. However, the bending strength of BS-1was resisted only by top and bottom flanges without the con-tribution of corrugated web, therefore, after the yielding of flange,fully plastic moment was quickly obtained, followed by thebucking of compressive flange without enough rotation capacityin comparison to BS-0.

αEs

σy

σy

σu

εy

εy

Compression

TensionStress, σs

εu

Strain, εsEs

Eq. (8)

Fig. 20. Stress–strain relationship of steel.

J. He et al. / Thin-Walled Structures 74 (2014) 70–8482

According to section classification, bending strength can becalculated as fully plastic moment for steel-I girder with flatweb and as yield moment for steel-I girder with corrugatedweb. And the bending strength of concrete-encased composite

girder is predicted by the proposed multiple layers model.Table 6 shows the comparison of experimental and calculatedbending moment of each specimen. The yield and ultimatestrength of the steel plates, the compressive strength of the

ε’c εcu

fc'

Com

pres

sive

stre

ss ,

f c

Compressive strain, εc

Ec

Eq. (9)

εtu

(ftr , εtr )

Tens

ile s

tress

, f t

Tensile strain, εt

Es

Eq. (10)

Fig. 21. Stress–strain relationship of concrete.

0

500

1000

1500

2000

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Curvature (1/m)0.00 0.01 0.02 0.03 0.04 0.05 0.06

Curvature (1/m)

Ben

ding

Mom

ent (

kN.m

)

BC-0 Test Calculation

0

500

1000

1500

2000

Ben

ding

Mom

ent (

kN.m

)

BC-1 Test Calculation

Fig. 22. Moment-curvature of concrete-encased composite girders.

Table 5Width-to-thickness ratio and its limitations for compressive flange outstand.

Specimen Size Material properties Width-to-thickness

bfo/mm tfo/mm Fy/MPa E/GPa bfo/tfo CSA Section class AISC Section class

BS-0 145 20 384 199 7.25 o 145ffiffiffiffiffiFy

p Class 1o0:38

ffiffiffiffiffiEFy

sCompact

BS-1 182.5 20 384 199 9.13o

ffiffiffiffiffiffiffiffiffiffiffiffiffikf

0:425

r145ffiffiffiffiffiFy

p Class 1o0:38

ffiffiffiffiffiffiffiffiffiffiffiffiffikf

0:425

r ffiffiffiffiffiEFy

sCompact

BC-0 145 20 384 199 7.25 o1:5145ffiffiffiffiffiFy

p Class 1o1:5� 0:38

ffiffiffiffiffiEFy

sCompact

BC-1 182.5 20 384 199 9.13 o1:5145ffiffiffiffiffiFy

p Class 1o1:5� 0:38

ffiffiffiffiffiEFy

sCompact

Note: bfo and tfo are the width and thickness of flange outstand, E and Fy are the young's modulus and yielding strength of flange outstand, kf is the buckling coefficient forcorrugated steel web girder (Eq. (4)).

Table 6Comparison of experimental and calculated bending moment.

Specimen Yielding moment (kNm) Ultimate moment (kNm)

Test MTy Calculation MCy MCy/MTy Test MTu Calculation MCu MCu/MTu

BS-0 894 884 0.99 1506 1454 0.96BS-1 847 829 0.98 1197 1140 0.95BC-0 847 806 0.95 1642 1524 0.93BC-1 740 728 0.98 1446 1392 0.96

J. He et al. / Thin-Walled Structures 74 (2014) 70–84 83

concrete obtained by sample tests, as described in Section 2.2,are used in the calculations. The mean ratio of predictedyielding and ultimate strength to experimental ones for steeland composite I-girders are 0.97 and 0.95 respectively, while thestandard deviations are 0.017 and 0.016 respectively. The agree-ment of experimental and calculated results indicates thatbending strength can be predicted by the above proposedequations.

Figure 22 shows relation between bending moment andcurvature of BC-0 and BC-1, both from calculated and testedresults. The proposed model accurately evaluates the flexuralbehavior from the initial curvature to the yielding of flange. Butthe ultimate moments of the test results exceed the calculatedvalues, which is due to the confined effect of the concreteencasement. Within the scope of the undertaken tests, thesecomparisons show that the proposed analytical method is appro-priate in predicting flexural strength of steel and concrete-encasedcomposite I-girders with flat or corrugated web. For designpurposes, the model conservatively ignores the additional bene-ficial effects of concrete confinement and further delay to localbuckling in concrete-encased composite girders. Moreover, thewidth-thickness ratio of flanges and webs, the aspect ratio ofwebs, the spacing and size of reinforcing bars would affect theflexural strength of partially encased composite girders. Furtherstudies will be required to clarify these effects.

5. Conclusion

Partially encased composite I-girder with flat or corrugatedweb has been proposed to improve the structural performance ofcontinuous girder under hogging moment. The bending behaviorof such structure under two points symmetric loading has beenexperimentally and analytically investigated. The following con-clusions may be drawn from the present study:

(1) Flexural experiments show that the partially encased com-posite girder has higher bending strength in comparison tosteel girder, since local bucking of compressive flange isrestricted by encased concrete, especially for the corru-gated web girder, the ultimate bending strength isimproved about 20%, while the ductility also increasesabout 3 times.

(2) The flexural normal strains on the whole corrugated web arevery small even after the yielding of flange. Due to the“accordion effect” of corrugated web, flexural strength ofcorrugated web steel girder (specimen BS-1) is provided bythe flanges with almost no contribution from the web. Afterconcrete is encased and fully connected with steel web byshear studs, the compression part of corrugated web resistspart of bending moment.

(3) The limitation of width-to-thickness ratios for steel andconcrete-encased composite I-girders with corrugated webare suggested to prevent premature failure due to localbuckling of compressive flange under bending moment.

(4) Bending strength prediction methods for concrete-encasedcomposite girder with flat or corrugated web are proposedand verified by experimental results. The calculated bendingstrengths for steel and composite girders under service loadand at ultimate state agree well with the experimental results,which means proposed analytical equations can be applied topredict flexural strength accurately for such encased compo-site girder with flat or corrugated web.

Acknowledgments

This research is sponsored by the National Nature ScienceFoundation of China under Grant no. 51308070, and the LiaoningProvince Transportation Construction Technology Program. Thesesupports are gratefully acknowledged. This paper was writtenwhen the first author visited the Department of Civil and Envir-onmental Engineering of Waseda University in Japan. The assis-tance is also gratefully appreciated.

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