Crack control of a steel and concrete composite plate girder with prefabricated slabs under hogging...

8/10/2019 Crack control of a steel and concrete composite plate girder with prefabricated slabs under hogging moments

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Engineering Structures 27 (2005) 16131624

www.elsevier.com/locate/engstruct

Crack control of a steel and concrete composite plate girder withprefabricated slabs under hogging moments

Hyung-Keun Ryua,,1, Sung-Pil Changa,2, Young-Jin Kimb, Byung-Suk Kimb

aSchool of Civil, Urban & Geosystem, Seoul National University, Republic of KoreabStructural System Research Group, Korea Institute of Construction Technology, Republic of Korea

Received 3 June 2004; received in revised form 25 May 2005; accepted 26 May 2005

Available online 15 July 2005

Abstract

In this research, an experimental test on a full-scale model of a steel and concrete composite plate girder with prefabricated slabs under

hogging moments was cautiously conducted and observed in order to study crack control. Details of prefabricated slab transverse joints were

determined from previous research. The test specimen was an overhanging simple support beam, in total 28 m long. Through the four-point

flexural test, the behaviour of the composite girder under hogging moments was observed. From the test results, crack development, crack

widths and strain of the composite section before and after cracking were observed. Initial cracking load and crack spacing were viewed

and the relations between crack spacing and transverse reinforcement spacing were studied. Moreover, the composite section behaviour of

the precast deck with loop joints was confirmed. Test results were analyzed by design equations in each code for crack control. The flexural

stiffness of the composite section after cracking is compared with that of the proposals in EUROCODE 4-2 and discussed.

2005 Elsevier Ltd. All rights reserved.

Keywords: Steel and concrete composite plate girder; Prefabricated slab; Loop joint; Hogging moment; Crack control; Crack width; Crack spacing; Flexural

stiffness of composite section; Eurocode 4-2

1. Introduction

Steel and concrete composite bridges are very attractive

solutions for short and medium span bridges. However, for

steel and concrete composite continuous bridges, when a

concrete slab is in tension and a lower flange of a steel

girder is in compression under hogging moments, there are

shortcomings in view of durability and strength. Especially,

concrete cracking affects the durability and service life

Corresponding address: Civil, Urban and Geo-system Engineering,Seoul National University, San 56-1 Shinlim Dong, Kwanak Gu, 71100Seoul, Republic of Korea. Tel.: +82 288 073 55; fax: +82 288 703 49.

E-mail addresses:[email protected] (H.-K. Ryu),[email protected] (S.-P. Chang), [email protected] (Y.-J. Kim),[email protected] (B.-S. Kim).

1 Also at: Korean Earthquake Engineering Research Center, SeoulNational University, San 56-1 Shinlim-Dong, Kwanak-Gu, Seoul 151-742,Republic of Korea.

2 Also at: Department of Civil Engineering, Seoul National University,San 56-1 Shinlim-Dong, Kwanak-Gu, Seoul 151-742, Republic of Korea.

0141-0296/$ - see front matter 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.engstruct.2005.05.015

of bridges. Therefore, crack control is an important issue

in steel and composite continuous bridges. There are two

approaches for dealing with concrete cracking in composite

bridges: one is to prevent cracking using prestressing

methods and the other is to allow the formation of cracks but

limit their widths to acceptable values. Prestressing methods,

however, are inconvenient and doubtful due to prestress

losses by the long-term behaviour of concrete. Therefore,

it is considered that the control of crack width without

prestressing is the more economical and interesting solution.Randl and Johnson [1] found that the first transverse

cracks that occur in lightly reinforced concrete slabs forming

tension flanges of composite beams were significantly wider

than is predicted by existing methods. They showed that a

reinforcement ratio of 0.9% is sufficient to ensure that bars

do not yield when the first crack forms, and it was suggested

that 0.9% is sufficient to control initial cracking in composite

main girders only when small-diameter bars are used. In the

study of Navarro and Lebet [2], the mechanical behaviour
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1614 H.-K. Ryu et al. / Engineering Structures 27 (2005) 16131624

of steelconcrete composite bridges under non-monotonic

service loading was presented. In their study, it could

be observed that the reinforcement ratio and longitudinal

bar diameter do not significantly influence the crack

widths. Since the crack spacing is equal to the transverse

reinforcement spacing, crack widths are not influenced by

a decrease of the transmission length induced by reducingthe longitudinal reinforcement bar diameter. Therefore,

reducing the longitudinal reinforcement bar diameter is not

an effective method for diminishing crack widths.

Ramm and Elz [3] mentioned that local weakening of

the tensile capacity of a concrete slab can lead to an early

occurrence of cracks and can cause decreased need of

minimum reinforcement. In the case of composite beams,

such local weakening can be caused by shear connectors

or transverse reinforcement. This can lead not only to an

earlier development of cracks, but also can influence the

crack spacing. Thus, the development of cracking in slabs

as part of composite beams is decisively influenced by the

transverse reinforcement.

A precast concrete deck could be very attractive because

the system can ensure the quality of concrete decks, improve

working environments for the workers, and reduce man

hours outdoors and traffic disruption. A shorter construction

time could be an important factor in choosing precast deck

bridges. A precast deck bridge has two types of connection:

shear connection between steel girder and precast deck,

and transverse joint between precast panels. Shim and

Chang [4]suggested a design basis for longitudinal prestress

of continuous composite bridges with full-depth precast

decks having female-to-female joints through experimental

and analytical studies.Recently, Ryu et al. [5]carried out experimental works on

the mechanical behaviour of precast concrete elements with

loop joints. From the observation of crack distribution, crack

widths, ductility and ultimate strength considering variable

diameters of reinforcements and joint widths of cast-in-place

parts, they suggested details of precast elements with loop

joints.

However, in order to apply precast decks to continuous

composite bridges, the tensile behaviour of precast decks

or transverse joints between slabs in hogging moment

regions should be confirmed in view of serviceability and

durability. Particularly, stiffness of the composite sectionduring cracking should be evaluated precisely, because it is

very important to estimate crack widths, deflection and stress

ranges applied to structural members under service loads. In

this paper, an experimental test on a full-scale model of a

steel and concrete composite plate girder with prefabricated

slabs under hogging moments was cautiously conducted

and observed in order to study crack control. Details of

prefabricated slab transverse joints were determined from

previous research [5]. The test specimen was an overhanging

simple support beam, in total 28 m long. Through the four-

point flexural test, the behaviour of the composite girder

under hogging moments was observed. The test results

showed crack development, crack widths and strain of the

composite section before and after cracking. Initial cracking

load and crack spacing were observed and the relations

between crack spacing and transverse reinforcement spacing

were studied. Moreover, the composite section behaviour

of the precast deck with loop joints was confirmed. Test

results were analyzed by design equations in each code forcrack control. The flexural stiffness of the composite section

after cracking is compared with that of the proposals in

EUROCODE 4-2 and discussed.

2. Static test

2.1. Test specimen

The testing was carried out with the four-point flexural

bending test. The span of the overhanging cantilever part

is 11 m on either side. The length of mid-span simply

supported is 6 m.Fig. 1illustrates the composite plate girdersection and elevation. This specimen is an effective one-

girder full-scale model of a bridge designed by current

Korean highway standard specifications. The bridge is

a first rate three span continuous composite plate girder

and four lane highway bridge (Fig. 2) having a width of

12.145 m.

In the test specimen, the precast deck panel was 260 mm

thick and had three shear pockets for stud shear connectors

(Fig. 1(b)). Details of transverse loop joints in precast

decks were determined from previous research [5]. The

longitudinal reinforcement ratio was 2.0%, which is a

limitation for bridge slabs under hogging moments in

Korean Highway Standard Specification [6]. 22 mm studshear connectors were welded at 680 mm spacing for a full

shear connection.

Vertical stiffeners were welded in supports, loading

points and among those to prevent shear buckling failure

and crippling of the web before flexural failure (Fig. 1(c)).

Also, to prevent lateral torsional buckling of the overhanging

beam, lateral bracings were installed at each end of the

overhanging beam to allow vertical deflection but lateral

displacement and rotation.

2.2. Fabrication procedure

First, the prefabricated slabs were placed on a steel

plate girder. Then, shear pockets were filled with mortar

for achieving composite action. Transverse reinforcements

were arranged in loop joints and then filled with

expansive concrete to connect precast decks longitudinally.

A composite plate girder was completed as shown inFig. 3.

2.3. Loading and measurements

The test specimen was an overhanging simply supported

beam using roller supports (Fig. 4). A concentrated load was

applied at each edge of the beam (Fig. 1(c)). A closed-loop


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H.-K. Ryu et al. / Engineering Structures 27 (2005) 16131624 1615

(a) Composite girder section.

(b) Precast panel.

(c) Elevation.

Fig. 1. Test specimen.


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Fig. 2. Model bridge section.

Fig. 3. Completed composite plate girder.

electro-hydraulictesting system was used as shown inFig. 3.

Static tests to investigate elastic and inelastic behaviour of

the specimen were carried out.

Displacements of the composite plate girder were mea-

sured at both ends and each mid-part of the overhang-

ing girder with an LVDT (Linear Variable Differential

Transformer). An LVDT was also installed to measure the

relative displacements (slips) between the steel girder and

the concrete slab as presented in (Fig. 5(a)). Several strain

gauges were installed on the composite sections to observe

Fig. 4. Support condition.

composite section behaviour. After cracking, crack widths

were measured with Omega gauges.

2.4. Material properties

The material properties of the steel sections and of

concrete and mortar are listed in Tables 1 and 2,respectively.

As mentioned in previous research [4], the compressive

strength of the filling material should be higher than that

of the precast concrete to obtain the same elastic modulus


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(a) Deflection and slip.

(b) Sectional strain.

Fig. 5. Instrumentation.

and to ensure the quality of the mortar in actual construction

sites. It is very important to control the quality of the fillingmaterial as specified in a design guideline of a precast deck

bridge. In this experiment, the compressive strength of the

mortar was higher than the required strength.

Table 1

Material properties of steel

Yield strength Tensile strength (in spec.)

(MPa) (MPa)

Flange & web 320 500650

Stiffeners, diaphragm 240 410520

Reinforcements 400 520

Table 2

Compressive strength of concrete and mortar (MPa)

Strength (MPa) Note

Precast concretea 36 28 days

Transverse jointb 57 Loading time

Shear connectionb 43 Loading time

a Average value of all the precast concrete panels.b Average value of material test specimens.

In the Table 2, the strength of the prefabricated slab

specimen was 28 days strength. However, the real strength

of precast elements was expected to be higher than 28 days

strength, because the loading time was over 28 days.For shear connection, shear pockets were filled with non-

shrink mortar and transverse slab joints were filled with

expansive concrete expecting chemical prestressing to be

locally introduced at joints.

3. Test results and analysis

3.1. Elastic behaviour

In the test specimen, it was intended that shear

connections were installed to achieve full shear connections.

The ultimate strength of a stud shear connector was

determined from Eq.(1)developed by Kim et al. [7].

Pd= (0.36Ash + 18.71) (1)

= 1 0.0086(bh 20)

Pd: ultimate strength of shear connection,

Ash: stud area of shear connection(mm2),

bh: thickness of bedding layer.

To achieve full shear connection, the degree of shear

connection, , which is defined as the strength of the shear

connection in a shear span, as a proportion of the strength

required for full shear connections, should be higher than

unity.


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Fig. 6. Loadslip curve.

Fig. 7. 3-D finite element model.

=Psh

Pcp 1. (2)

Psh can be calculated using Eq. (1) over the shear spans,

and Pcp is the horizontal force of the concrete slabs or steel

girders at the full sectional plastic moment.

In the test specimen, the degree of shear connection wasestimated to be higher than unity according to Eq. (2), and

then in the test, maximum slips were measured at 0.06 mm

until 80% of maximum load (Fig. 6). It is considered that the

experimental slips monitored during the tests were scattered

due to the very low values measured. From this result, it

is considered that the shear connection would not reach

the ultimate load state [7], thus the test specimen could

be assumed as the full composite section until the ultimate

state.

To be compared with the test results, elastic analyses

were carried out with a 3-D finite element model (Fig. 7)

by the commercial finite element code, ABAQUS v6.3. Theconcrete slab and the steel girder were modeled with 8-node

shell elements. The slab and the plate girder were connected

by beam elements to describe the shear connection. The

number of finite element in which the test specimen was

divided was 3024 in total. From the analysis, the flexural

stiffness of the composite section could be evaluated, and

variation of the flexural stiffness with increasing load in the

test could be compared with results of the finite element

analysis.

During the static test in the elastic range of loading,

the flexural stiffness of the composite girder showed linear

elastic behaviour. Deflection of the end of the girder from

Fig. 8. Loaddisplacement curve in the elastic range.

the analysis was compared with the test results (Fig. 8). It is

worth noting that, in the elastic range, the stiffness of the slab

in hogging moment regions can be included in the flexural

stiffness of the composite section. In the serviceability limitstate, an uncracked section could be assumed for the flexural

stiffness of composite sections.

3.2. Cracking

Crack distribution on the deck of the uniform negative

moment regions was observed as presented inFig. 9. In the

test specimen, in total 14 precast panels were used; panels

7 and 8 are prefabricated slabs in a middle position of the

composite girder under uniform hogging bending as shown

in Fig. 9. The initial cracks were detected by the naked

eye at the edge of transverse joints (Fig. 10). It is consid-ered that the cracks occurred because the age of concrete

material in precast panels and joints of cast-in-place parts

were different. Due to the different casting ages, construc-

tion joint surfaces were made and the surfaces have weak

points of cracking. Thus, before casting in the transverse

joints, the surfaces should be cleaned, and it is necessary to

consider effective methods for increasing bonding between

precast panels and joints; for example, surfaces can be made

rough using a water jet to increase bonding. The cracking

load of the test specimen was observed as 340 kN, which is

lower than the design value of 405 kN. The value was ob-

tained from the following equation given in EUROCODE4-2 [8].

Ns = Ns,cr= Act fctm1

1 + hc2z0

(1 + s n0) (3)

wheres = As/ActAct is the area of the tensile zone immediately prior to

cracking of the cross section (for simplicity the area of the

concrete section within the effective width should be used),

As is the area of reinforcement steel within the effective

width,

fctmis the mean tensile strength of concrete,

hc is the depth of the concrete slab,


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Fig. 9. Crack distribution under uniform hogging moments (units: kN).

z0 is the vertical distance between the centroids of the

uncracked unreinforced concrete flange and the uncracked

unreinforced composite section.

As in Eq. (3), the shrinkage effect was not considered.

Therefore, it is considered that the cracking load can be eval-

uated by reducing the tensile strength of concrete consider-

ing the shrinkage effects, particularly in cast-in-place (CIP)

parts (transverse joints). In the case of continuous compositebridges with CIP slabs, it is considered that initial shrinkage

effects can be more important for estimating the cracking

load, crack width and flexural stiffness.

It is noted that the spacing of the initial transverse crack

was significantly wide because the crack occurred mainly in

the transverse joints and edges of shear pockets. After the

initial cracking, cracks developed on deck surfaces which

are shown inFig. 9.

As in previous research [2,3], it could be observed

that the crack spacing was very similar to the transverse

reinforcement spacing. Local weakening of the tensile

capacity of the concrete slab which was caused by shear

connectors or transverse reinforcements can lead to the

occurrence of cracks and can influence the crack spacing.

Thus, it can be said that the development of cracking in

slabs as part of composite girders is decisively influenced

by transverse reinforcements.

In the crack development of the slabs, the crack spacing

was observed, and then minimum, maximum and average

crack spacings were recorded as shown in Table 3. FromTable 3,it is seen that the average crack spacing was similar

to the average spacing of the transverse reinforcements.

3.3. Flexural stiffness during cracking

Fig. 11shows loaddisplacement curve of each ends of

the overhanging beam of the present test. Before cracking,

the stiffness of the composite section was similar to that of

the uncracked composite section. However, after cracking,

the cracks were propagated and distributed, and the stiffness

of the composite section became similar to that of the

cracked composite section in Fig. 11with increasing load.


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Table 3

Cracking load (kN) and crack spacing (mm)

Cracking load Cracking load Ratio Minimum crack Maximum crack Average crack Average tr-re-bar

(cal.) (test) (test/cal.) spacing spacing spacing spacinga

405 340 0.84 77 280 165 173

a tr-re-bar means transverse reinforcement.

Fig. 10. Initial cracking at the joints.

Fig. 11. Loaddisplacement curve.

The loaddeflection curve named uncracked was evaluated

from the 3-D elastic finite element analysis (Fig. 7).

As shown in Fig. 11, the stiffness of the composite section

after cracking became similar to that of the cracked section

gradually, but the stiffness did not directly become equal

to that of the cracked section as soon as a crack occurred.Thus, the tension stiffening effect between cracks should be

considered to evaluate the more exact flexural stiffness of

the composite section under hogging moments. At 1200 kN,

the deflection of the test specimen was larger than the

calculated deflection of the cracked section. It is considered

that local buckling or yielding due to residual stress reduces

the stiffness of the composite section as well as cracking.

In the crack formation of composite beams, there are

three stages before yielding of the composite section. First,

a stage before cracking an uncracked section, second,

after cracking and development of cracks, and last, a

crack stabilizing stage which continues before yielding. To

Fig. 12. The stiffness of a composite plate girder.

divide the first and second stages, the initial cracking load

should be considered, which can be evaluated from Eq. (3).

Also, the moment at the beginning of the stabilized crack

formation should be evaluated to define the level of crack

stabilizing. The bending moment, Mcr,ts, at the beginning of

the stabilized crack formation can be calculated using thefollowing equation,

Mcr,ts = [Ns,crNs,ts]I2

Asz2(4)

where Ns,ts is the additional normal force of the concrete

section due to tension stiffening. I2 is the second moment

of area of the composite section neglecting concrete. z2is the distance between the centroidal axis of the cracked

composite section with the second moment of area I2 and

the center of area of the reinforcement.

The normal force of the concrete slab is determined in

the stages of cracking mentioned above. During cracking


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and before stabilizing, the axial force is maintained to

be constant even with increasing external moments. But

after stabilizing moments, the axial force increased with

increasing external moments linearly.

After initial cracking, the internal normal force of the

concrete section can be defined by the following equation.

Ns = Ns0 +Ns,ts. (5)

The additional normal force Ns,ts of the concrete section

due to tension stiffening for bridges without prestressing by

tendons is given by

Ns,ts = 0.4fctmAs

sst(6)

st = A I2/AaIa , where A is the area of the composite

section neglecting concrete in tension, and Aa and Ia are

the corresponding properties of the structural steel section.

Therefore, the effective stiffness of the composite section

after cracking can be defined in all load levels, continuously.

The effective stiffness EaI2,ts depends on the bending

moment M acting on the composite section. The bending

moment M, calculated with the uncracked stiffness, may be

used. The stiffness EaI2,tsmay be calculated from

EaI2,ts =EaIa

1 Ns aM

(7)

where EaIa is the stiffness of the structural steel section,

Mis the bending moment for the relevant load combination

and Ns is the tension force in the slab. a is the distance

between the neutral axes of the structural steel section and

the uncracked concrete section.

From the above equations, the flexural stiffness of thecomposite section for the test specimen could be estimated

as shown in Fig. 12. Initial cracking and stabilizing moments

were evaluated and the effective stiffness was calculated

with external moments. After the initial cracking moment,

the stiffness which gradually decreased due to cracking can

be observed as in this figure.

From the curve in Fig. 12, the momentcurvature

relationship of the composite plate girder can be calculated.

Then this result could be compared with the test results

for the momentcurvature of the test specimen. From the

experimental results, momentcurvature relationships of the

composite sections were evaluated as shown inFig. 13.In the figures, sections AE refer to those shown in

Fig. 5(b). Among the curves, the curve for section A

in Fig. 13(a) is overestimated by the EC4-2 curve at a

high moment level compared with the other curves. It is

considered that because the section A is the nearest to

the supports, the stiffness was reduced by yielding and

local buckling as well as cracking with increasing external

moments. Except for section A, the curves of the composite

sections in the test specimen were very consistent with the

EC4-2 curve. It is also confirmed that the precast decks with

loop joints are continuous because the curve for section E

inFig. 13(e) also showed good consistency of the effective

stiffness in the EC4-2. In section E, there are transverse

joints of the slabs.

Under uniform hogging moments, the momentcurvature

curve of all composite sections was very consistent with

the moment curvature curve defined in Eurocode 4-2. From

these results, it is concluded that the momentcurvature

curve relation or effective flexural stiffness of the compositegirder section considering tension stiffening effects in

Eurocode 4-2 can be also applied to composite plate girders

with loop joint prefabricated slabs.

3.4. Crack widths

Fig. 15shows the relation between external moments and

reinforcement strain. LP1 and LP2 were attached in lon-

gitudinal top reinforcement in joint parts (Fig. 14). Also,

RE1RE3 were installed in top reinforcement as shown in

Fig. 14. InFig. 15,it can be seen that strain of the reinforce-

ment in loop joints measured by LP1 and LP2 is less than

that of the reinforcement in decks (RE1RE3) because, in

the joints, reinforcements are overlapped to connect longitu-

dinally. In all reinforcements, the strain did not yield.

Momentcrack width curves are presented inFig. 16. It

is considered that the curve could show the limitation of

service load for crack control in composite girders with loop

joint prefabricated slabs.

According to the Korean Highway Standard Specifica-

tion [6]for the design of plate girder bridges such as Fig. 2,

the design moment for the test specimen is 6050 kN m,

which includes dynamic effects by truck loads. In this mo-

ment, the measured maximum crack width was shown as

0.14 mm in CR3 (Fig. 16). This value does not violate thelimitation of crack width for serviceability of the general

condition.

Also, to estimate the maximum crack width of the slab,

test results were compared with values of design equations

for crack control in each code.

Steel strain and crack width curves could be obtained

from the measurements as in Fig. 14. There are variable

design equations for crack width in each code. In this

research, experimental results were compared with design

values in equations such as the GergelyLutz equation, the

equation in CEB-FIP 78 [9]and in Eurocode 2(90) [10]. The

GergelyLutz equation is recommended in ACI-318-99 [11]and in AASHTO-LRFD specifications (1998) [12].

wmax = 1.08cfs3

dcA 105 (8)

where c is the ratio of the distances to the neutral axis

from the extreme tension fiber and from the centroid

of the reinforcement. fs is the stress calculated in the

reinforcement at service loads. dc is the thickness of the

concrete cover measured from the extreme tension fiber to

the center of the bar or wire located closest to it. A is the

effective tension area of concrete surrounding the flexural

tension reinforcement and having the same centroid as that

reinforcement, divided by the number of bars or wires.


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(a) Section A. (b) Section B.

(c) Section C. (d) Section D.

(e) Section E.

Fig. 13. Momentcurvature curve.

As shown in Fig. 17, the crack width curve of the

test results is similar to that of CEB-FIP 78 and EC 2.

However, the crack width of the test result is somewhat

larger than that of GergelyLutz equation. It is considered

that crack widths of the composite girder with prefabricated

slabs were more enlarged in weak surfaces of construction

joints. Moreover, crack spacing is decisively influenced by

transverse reinforcement spacing. Therefore, it is necessary

to consider the existence of construction joints and the

influence of transverse reinforcement spacing on the crack

spacing in the calculation of crack widths. Also, it is

considered that a safety factor or an enlargement factor for

estimation of maximum crack width of a plate girder bridge

with prefabricated slabs with loop joints is needed.

4. Conclusions

From the experimental study, it is concluded that:

1. Initial crack spacing of the slab in the composite girder

with prefabricated slabs can be wider than those of

general RC beam structures.

2. Initial cracking can occur earlier than calculation because

there are construction joint surfaces between a precast


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Fig. 14. Position of omega gauges and strain gauges.

Fig. 15. Momentsteel strain curve.

Fig. 16. Momentcrack width curve.

panel and a transverse joint that is a cast-in-place part

in slabs; thus the construction joint surfaces should be

cautiously maintained and cleaned before casting.

3. It is considered that crack spacing is mainly dependent on

the transverse reinforcement spacing.

4. The momentcurvature relationship or the flexural

stiffness defined in Eurocode 4-2 can be applied well to

Fig. 17. Steel stress versus crack width.

the composite plate girder with loop joint prefabricated

slabs.5. It is considered that crack widths of the composite

girder with prefabricated slabs were more enlarged in

weak surfaces of construction joints. Moreover, the

crack spacing is decisively influenced by transverse

reinforcement spacing. Therefore, it is necessary to

consider the existence of construction joints and the

influence of transverse reinforcement spacing on the

crack spacing in the calculation of crack width.

Acknowledgement

This study is a part of projects Bridge 200. The authors

would like to thank the Korea Institute of Construction

Technology.

References

[1] Randl E, Johnson RP. Widths of initial cracks in concrete tension

flanges of composite beams. In: IABSE proceedings P-54/82. 1982.

p. 6980.


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[2] Navarro MG, Lebet JP. Concrete cracking in composite bridges: tests,

models and design proposals. Structural Engineering International

2001;18490.

[3] Ramm W, Elz S. Behaviour and cracking of slabs as part of composite

beams in regions with negative bending moments. In: Composite

construction in steel and concrete III, proceedings of an engineering

foundation conference, ASCE. 1996. p. 871886.

[4] Shim CS, Chang SP. Cracking of continuous composite beams with

precast decks. Journal of Constructional Steel Research 2003;59:

20114.

[5] Ryu HK, Chang SP, Kim YJ, Joo BC. Experimental works on precast

concrete beams with loop joints, In: EASEC-9 (The ninth East Asia-

Pasific conference on structural engineering and construction). 2003.

Paper No. 075.

[6] Korea Highway Standard Specification. Korea Ministry of Construc-

tion and Transportation, 2000.

[7] Kim JH, Shim CS, Matsui S, Chang SP. The effect of bedding layer

on the strength of shear connection in full depth precast deck. Third

Quarter Engineering Journal, AISC 2002;39(3).

[8] EUROCODE 4. Design of composite steel and concrete structures,

part 2. Composite bridges. DD ENV 1994-2. BSI.

[9] Ghali A, Favre R. Concrete structures (stresses and deformation).

Chapman and Hall; 1994.

[10] EUROCODE 2. Design of concrete structures. DD ENV 1992-1-1.

BSI.

[11] Building code requirements for structural concrete and commentary

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[12] AASHTO. LRFD Bridge Design Specifications.SI units, 2nd ed.1998.

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