1

Study of Bridges with Composite Steel-Concrete Box Girder Decks

Manuel Maria Teixeira d’Aguiar Norton Brandão

Civil Engineering Department, Instituto Superior Técnico, Universidade de Lisboa, Portugal

Abstract

This dissertation studies the specific phenomena associated with the analysis and design of composite box girder decks, namely

under service conditions and during the incremental launching stages of construction.

Primarily, the phenomena of shear lag, stiffened plate buckling due to direct stresses, plate buckling due to shear, resistance to

Patch Loading and distortion of box girder decks’ cross section are identified and studied, and their analysis and design

methodologies defined in the Eurocodes are presented.

These methodologies are then applied through a design case of a bridge with a composite box girder deck with typical spans of

63 m. For this example the structural analysis, the verification of the deck’s slab, the global verification of the deck both in service

and during the deck’s launching are performed.

This study concludes that: a) the effects of shear lag and stiffened plate buckling due to direct stresses are decisive for the design of

the bottom flange of the deck, b) the effects of plate buckling due to shear and the local verifications for Patch Loading during the

incremental launching govern the web design, and finally that c) the effect of the deck cross section torsional distortion is

significantly reduced when diaphragms are used throughout the span.

Keywords: Bridge, Composite steel-concrete deck, Box girder deck, shear lag, Plate buckling, Patch Loading, Distortion, Incremental

launching.

1. Introduction

Bridges with composite steel-concrete box girder deck have been adopted in numerous cases. This type of solution has the benefit

of having great resistance relatively to its own weight, resulting from the optimization of steel and concrete properties. Often, the

most suitable construction process for this type of deck is the incremental launching method, usually being the steel structure

launched in the first place and then the slab concreted with the formwork directly supported on the steel structure.

The main goals of this dissertation are: (1) to study the specific aspects of composite steel-concrete box girder deck’s design,

namely the phenomena of shear lag, stiffened plate buckling due to direct stresses, web buckling due to shear, web resistance to

Patch Loading and evaluate the cross section distortion of a deck under eccentric loads; (2) to present the verification

methodologies of the composite steel-concrete deck according to European Eurocodes Standards (EC); and finally (3) to apply this

methodologies to a project example on a preliminary level.

2. Deck Description

The case study is a road bridge with a typical span of 63 m (Figure 1) and two symmetrical decks 10,5 m wide with a unidirectional

slope of 2,5%. The road profile over the deck is shown in Figure 2.

2

Figure 1 – Longitudinal view (m)

Figure 2 – Road dimensions (m)

The deck geometry was determined based on the expressions given by [1] and the structural solutions of cross sections at supports

and along the span are presented in Figure 3.

Support Span(section without diaphragm)

Figure 3 – Deck geometry (mm)

The materials used in the deck are:

- Concrete class C35/45;

- Structural steel grade S355 N (for thicknesses over 30 mm) and S355 J2 (otherwise);

- Reinforcement steel A500 NR.

3. Particular aspects of composite steel-concrete box girder decks

3.1 Shear lag

When flanges of a girder are wide relatively to its span, the hypothesis of conservation of plane sections, commonly used in

elementary bending theory of linear parts, can lead to considerable errors. Due to shear deformation, the direct stresses

distribution in a flange is no longer uniform and has a maximum value at the joint between the flange and the webs, decreasing

along its width (Figure 4). This phenomenon is known as shear lag and results in higher maximum direct stresses than those

obtained using the elementary bending theory [2 ; 3].

Shear lag causes deformations only in the flange plane and thus it’s a first order effect. Such effects should not be confused with

second order effects that occur in flanges due to plate buckling. Therefore, the shear lag effects affect both flanges under

compression and tension, where interaction between shear lag and plate buckling should be taken into account [3].

3

The main factor affecting shear lag in a flange is the ratio between its width (half width for internal flanges) and the span length

(length between girder points with zero bending moment). In long and narrow flanges, the shear lag effects can be considered

negligible but as this ratio increases, this phenomenon becomes more significant.

Elementary

bending theory

Direct stresses distribution

due to shear lag

Figure 4 – Direct stresses distribution due to shear lag [2]

In the evaluation of the shear lag effects it is usual to replace the actual flange width by an effective width so that the application of

the elementary bending theory to the effective section leads to the maximum direct stresses value and to the girder displacements.

This effective width, 𝑏𝑒𝑓𝑓, is defined so that the total compression force resulting from the real direct stresses diagram in the gross

width, 𝑏, equals the total compression force resulting from a uniform direct stresses diagram of maximum value in the effective

width, that is:

𝑏𝑒𝑓𝑓 =∫ 𝜎𝑥 𝑑𝑦

𝑏

𝜎𝑚𝑎𝑥

The examples of Figure 5 present for a box girder deck the transformations of the real direct stresses diagrams (in gray) into the

equivalent uniform direct stresses diagrams.

effb

b

max,x

x

b

ieffb , ieffb , ieffb , ieffb , ieffb ,

max,x

x

x

y

z

x

y

z

Figure 5 – Flange effective width due to shear lag

3.2 Stiffened Plate Buckling

The stiffened plate in the bottom of the box girder is under great compression forces in the sections of negative bending moments

above internal supports. A common solution is to stiffen the bottom flange in the longitudinal direction. This type of solution

increases the plate moment of inertia, which improves its behaviour for buckling without increasing significantly its self weight.

However, stiffened plates have a complex behaviour due to the diferent buckling modes that can occur [2]:

- Global plate buckling of the stiffened plate;

- Buckling of longitudinally stiffened panel between transverse stiffeners;

- Local plate buckling between longitudinal stiffeners;

- Buckling of the stiffeners.

4

Since the interaction between two buckling modes can generate one unstable behaviour, it is usual to adopt geometrical

requirements for stiffeners in order to prevent buckling modes of stiffeners to be critical. Thus, in practice, the stiffened plate

buckling is commanded by the interaction between the global plate and column buckling modes, with or without local plate

buckling between longitudinal stiffeners [3].

Global Buckling of plates

Unstiffened slender plates under compression have post-critical resistance that can be taken into account in their design and have

the typical behaviour shown in Figure 6.

cr

max

Comportamento

pós-crítico

Comportamento

pré-crítico

Figure 6 – Typical behaviour of slender plates under compression [2]

In a plate with length 𝑎 and width 𝑏 compressed over its width, as the ratio 𝛼 = 𝑎𝑏⁄ decreases, its post-critical resistance

decreases as the plate stops exhibiting a plate type behavior (Figure 7a) and starts exhibiting a column type behaviour (Figure 7b),

which has no post-critical resistance.

Figure 7 – Plate type and column type behaviour for unstiffened plates under compression [2]

For unstiffened plates this phenomena occurs for α values below 1,0 but for longitudinally stiffened plates, column type behaviour

can manifest itself for values larger than 1,0 [2]. Thus, a plate, stiffened or unstiffened, can exhibit a global behaviour that is plate

type, column type or and interaction between the two types, so it is necessary evaluate both phenomena and their interaction.

Critical stress

Webs under shear are subjected to a state of pure shear stress until buckling occurs. If these shear stresses are converted into

principal stresses, they correspond to principal tensile stresses 𝜎1 and principal compressive stresses 𝜎2 of same value and with

45° inclination relative to the longitudinal axis of the web (Figure 9a). This state of stresses acts on the web until this reaches the

elastic critical stress given by Euler critical stress multiplied by the shear buckling coefficient 𝑘𝜏:

𝜏𝑐𝑟 = 𝑘𝜏

𝜋2𝐸

12(1 − 𝜈2)(

𝑡𝑤

ℎ𝑤)

2

3.3 Web Stability under Shear Forces

Webs contribution is mainly for shear resistance. Given the usual slenderness of such plates, this

resistance is generally determined taking into account its post-critical resistance (Figure 8) [4].

Figure 8 – Post-critical behaviour of a plate under a state of pure shear stress [2]

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Figure 9 – a) State of pure shear stress and b) Tension field action [3]

Post-buckling behaviour

When the web reaches buckling, it loses the ability to resist to direct

stresses in the principal compressive stress 𝜎2 direction while in the

principal tensile stress 𝜎1 direct stresses can still increase. This leads

to the rotation of the stress field to achieve the equilibrium given the

difference between tensile and compressive stresses (Figure 9b).

The formation of this additional field, which is responsible for post-

buckling resistance, is only possible if the boundary elements, i.e. the

flanges and the transverse stiffeners, can anchor the axial forces that

are generated, represented in Figure 9b by 𝜎ℎ. When ultimate stress

is reached, a plastic hinge mechanism forms in the flanges (Figure

10).

3.4 Web Stability under Patch Loading

A girder can be under transverse loading, which is a load applied perpendicular to the flange in the plane of the web. Concentrated

transverse loading, or distributed in a small area, induce significant transverse stresses in the web and usually occur at supports or

in case of suspended loads. In such cases, the use of transverse stiffeners can be helpful for the web resistance. However, if there

are free and transient loads, as for crane runway girders or the reactions at supports during the incremental launching, transverse

stiffeners are no longer appropriate and the webs have to resist these loads by themselves. This concentrated transverse loading is

also known as Patch Loading [2 ; 3].

Failure modes

The failure of the web of a

girder under transverse forces

can occur in three distinct ways,

shown in Figure 11.

There is no clear distinction

between buckling and crippling

and it could be seen as a gradual change of the buckling shape. Usually, buckling occurs first and it is followed by crippling at loads

near the ultimate load. The failure mode that occurs depends mainly on the cross section geometry. Generally, a high ratio of 𝑡𝑓 𝑡𝑤⁄

imply buckling or crippling while a low ratio of 𝑡𝑓 𝑡𝑤⁄ lead to yielding [5].

Ultimate Resistance

The ultimate resistance of a girder under transverse forces is approximately proportional to the square of the web thickness 𝑡𝑤,

and is also influenced by the stiffeness of the flange, web yielding stress 𝑓𝑦𝑤 , loading width 𝑠𝑠 and the type of transverse load

application. Normally, three types of application are covered (Figure 12) [2 ; 5]:

- Load application through one flange, Figure 12a);

- Load application through both flanges, Figure 12b);

- Load application through one flange adjacent to an unstiffened end, Figure 12c).

Figure 10 – Plastic hinge flange mechanism [3]

Yielding Buckling Crippling

Figure 11 – Failure modes of girders under transverse forces [3]

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a) Load case 1 b) Load case 2 c) Load case 3

Figure 12 – Types of transverse load application [2]

3.5 Cross section distortion

The Load Model 1 established by EC1-2, which covers most of the effects of road traffic of trucks and automobiles, defines two

types of loads, the Uniform Distributed Load (UDL) and the Tandem System (TS). Both types of loads can be applied eccentrically in

relation to the vertical axis of the deck causing torsion and distortion of the cross section.

Box Girder Deck Behaviour under Eccentric Loads

The following presentation is based on the work of Pedro, J. [6]. Take into account a thin wall box girder deck with linear axis and

symmetrical with respect to the vertical axis of the cross section subjected to a vertical load 𝑝(𝑥) in the connection between the

upper flange and the web, represented in Figure 13a. This load can be decomposed in its symmetrical and anti-symmetrical loads.

(a) (b) (c)

2)(xp2)(xp 2)(xp2)(xp

)(xp

Figure 13 – Decomposition of 𝒑(𝒙) in its symmetrical and anti-simmetrical loads

The symmetrical load (Figure 13b), induces longitudinal bending. The anti-symmetrical load (Figure 13c) can be decomposed in two

systems:

- System of forces that correspond to a torsion moment, causing rotation of the cross section as a rigid body, Figure 14b;

- System of forces that tend to distort the cross section, Figure 14c.

The first system is referred to as pure torsion system and the second as torsional distortion system.

(a) (b) (c)

itp

2)(xp2)(xpstp

atp atp

idp

sdp

adp adp

Figure 14 – Pure tensional system and torsional distortion system

Thus, when a box girder deck is under an eccentric load, the cross section moves in three ways:

- Vertical displacement due to longitudinal bending caused by symmetrical load, Figure 15a;

- Rigid body rotation caused by the pure torsion system, Figure 15b;

- Cross section deformation caused by torsional distortion system, Figure 15c.

(a) (b) (c)

Figure 15 – Movement of the cross section of a box girder deck under an eccentric load

7

The longitudinal bending induces direct stresses and shear stresses in the deck (Figure 16a and Figure 16b, respectively) and pure

torsion induces the shear stresses shown in Figure 16c.

f f

(a) (b)

T

(c)

Figure 16 – a) Direct normal and b) shear stresses induced by longitudinal bending, and c) Shear stresses induced by pure

torsion

The torsional distortion is more complex as a box girder deck, when under such load (Figure 14c), tends to move in the longitudinal

direction by individual bending of each plate and, at the same time, in the cross direction by deformation of the cross section

(Figure 17). Besides the displacement of the cross section in its plane, from torsional distortion also results an anti-symmetrical

longitudinal direct stresses distribution (Figure 18).

Longitudinal bending

of plates

Cross section deformation

d

Figure 17 – Movement of cross section caused by torsional distortion Figure 18 – Longitudinal direct stresses caused by

torsional distortion

If now one takes into account that the vertical load 𝑝(𝑥) is at a 𝑒 distance of the connection between the flange and web, it can

also be decomposed into the symmetrical and anti-symmetrical loads (Figure 19) and it also results in longitudinal bending, pure

torsion and torsional distortion.

)(xp )(xp

e

)(xm

2)(xm 2)(xm 2)(xm 2)(xm

)(xp

Figure 19 – Symmetrical and anti-symmetrical loads of a vertical load 𝒑(𝒙) eccentric in regard to the junction between the flange

and the web

4. Structural Analysis

The actions taken into account were the self weight, the other permanent loads, footway loads, traffic loads, linear temperature

difference and shrinkage. Creep is taken into account in the slab homogenization to steel.

For the Ultimate Limit States the verifications are done with the fundamental combination of actions according to EC0 and for the

Serviceability Limit States the verifications are done with the frequent combination of actions for the cross direction and with the

characteristic combination of actions for the longitudinal direction according to EC0 as well. The resulting shear and bending

moments for cross and longitudinal directions are presented in Table 1 and Table 2, respectively.

ULS SLS

Section 𝑉𝐸𝑑 (𝑘𝑁/𝑚) 𝑀𝐸𝑑(𝑘𝑁𝑚/𝑚) 𝑉𝑓𝑟𝑒𝑞. (𝑘𝑁/𝑚) 𝑀𝑓𝑟𝑒𝑞.(𝑘𝑁𝑚/𝑚)

Support 194,02 -247,98 98,96 -126,49

Span - 152,99 - 69,64

Table 1 – Shear and bending moments for cross direction

8

ULS SLS

Section 𝑉𝐸𝑑 (𝑘𝑁) 𝑀𝐸𝑑(𝑘𝑁𝑚) 𝑉𝑐ℎ𝑎𝑟𝑎𝑐𝑡. (𝑘𝑁) 𝑀𝑐ℎ𝑎𝑟𝑎𝑐𝑡.(𝑘𝑁𝑚)

Span 1 - 44464 - 30632

Support 1 9792 -98483 6961 -72689

Span 2 - 86023 - 59976

Support 2 10257 -112951 7295 -82754

Table 2 – Shear and bending moments for longitudinal direction

5. Verification of the Deck’s Slab

5.1 Ultimate Limit States

The deck’s slab design is done based on the shear and bending moments for cross direction in ULS. The reinforcement needed in

the slab to endure such forces is shown in Figure 20.

ø10//150

ø10//150 ø10//150

ø10//150 ø16//150 (C/ 10500) +

ø16//150 (C/ 4000)

ø16//150 (C/ 10500) +

ø16//150 (C/ 4000)

ø16//150 (C/ 10500)

ø12//150 (C/ 10500) +

ø12//150 (C/ 4000)

ø12//150 (C/ 10500)

Figure 20 – Reinforcement in the slab

5.2 Serviceability Limit States

In SLS the crack widths do not exceed the 0,3 mm limit imposed by EC2-1-1:

𝑤𝑘𝑠𝑢𝑝𝑝𝑜𝑟𝑡

= 0,14 𝑚𝑚 𝑤𝑘𝑠𝑝𝑎𝑛

= 0,15 𝑚𝑚

6. Global Verification of the Deck

6.1 Ultimate Limit States

The verification for ULS of bending moment, it is necessary to evaluate the reduction caused by the effects of shear lag and

stiffened plate buckling. The reduction factors are shown in Table 3.

Section Span 1 Support 1 Span 2 Support 2

𝛽𝑘 0,998 0,967 0,999 0,978

𝜌𝑐 1,0 0,905 1,0 0,905

Table 3 – Reduction factors for shear lag and stiffened plate buckling for ULS

Then, the resistant bending moments were calculated and compared to the bending moments calculated above. The verification is

shown in the following Table 4.

Section 𝑀𝐸𝑑 (𝑘𝑁𝑚) 𝑀𝑅𝑑 (𝑘𝑁𝑚) safety factor

Span 1 44464 146582 3,30

Support 1 -98483 -128236 1,30

Span 2 86023 146718 1,71

Support 2 -112951 -129473 1,15

Table 4 – Verification for ULS of bending moment

It was observed that the webs with 40 mm of thickness do not exhibit buckling. Therefore, this thickness was updated to 25 mm. It

was obtained, then, a reduction factor of 𝜒𝑤 = 0,790 and the correspondent ULS shear verification is shown in Table 5.

Section 𝑉𝐸𝑑 (𝑘𝑁) 𝑉𝑅𝑑 (𝑘𝑁) safety factor

Support 1 9792 13250 1,35

Support 2 10257 13250 1,29

Table 5 – Verification for ULS of shear

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6.2 Serviceability Limit States

The verification for SLS is done comparing the stresses in service with the yield stress. The stresses in service are calculated taking

into account the bending moment, shear, torsion and distortion of the cross section.

It must be said that stresses due to distortion were calculated based on the method proposed by [6] and taking into account

diaphragms along the span spaced by 5,25 m. The stress reduction is approximately 80% comparatively to a span with no

diaphragms.

The stresses from bending moment are significantly reduced by the shear lag which factors for SLS are shown in Table 6. The final

stresses for the critical point in each section are presented in Table 7.

Section 𝛽

Span 1 0,973

Support 1 0,671

Span 2 0,985

Support 2 0,723

Table 6 – Reduction factors for shear lag for SLS

Section Point 𝜎𝑓0

(𝑀𝑃𝑎)

𝜎𝑓1 (𝑀𝑃𝑎)

𝜎𝑑2 (𝑀𝑃𝑎)

𝜏𝑉0 (𝑀𝑃𝑎)

𝜏𝑉1 (𝑀𝑃𝑎)

𝜏𝑇2 (𝑀𝑃𝑎)

𝜎𝑐𝑜𝑚𝑝. (𝑀𝑃𝑎)

𝑓𝑦 (𝑀𝑃𝑎)

s. f.

Span 1 D 31,3 34,5 2,9 0,0 0,0 2,7 107,3 335 4,86

Support 1 A 200,4 40,1 1,0 10,8 7,4 2,8 259,2 335 1,37

Span 2 D 79,7 53,1 3,9 0,0 0,0 2,7 191,5 335 2,45

Support 2 A 238,2 45,0 0,9 11,6 7,5 2,8 301,0 335 1,17

Table 7 – Verification for SLS

7. Verification during the Deck’s Launching

The steel structure of the deck was launched using a nose at the front so the stresses during launching wouldn’t surpass the yield

stress. The maximum bending moment and stress occurs when the deck is reaching a support on an internal span. The stresses

during launching are shown in Figure 21 as well as the yield stress limit.

100

50

0

50

100

150

200

250

300

350

400

0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 360 375 390 405

Position 0

Position 1

Position 2

Position 3

Position 4

Position 5

Position 6

Position 7

Position 8

Position 9

Position 10

Nosefy

[MPa]

kNm5,239max

[m]

Figure 21 – Direct stresses in the upper flange during launching

For the local verification for Patch Loading it is necessary to know the maximum reaction that occurs on supports during lauching.

This value is 𝐹𝐸𝑑 = 2558 𝑘𝑁 in each web. The resistant force to Patch Loading for a support section (where the maximum reaction

occurs) is given by 𝐹𝑅𝑑 = 12078 𝑘𝑁. And therefore the Patch Loading verification is given by:

𝜂2 =2558

12078= 0,21 ≤ 1,0

However, it is necessary to perform a verification that takes into account the interaction between the global effect of bending

moment and the local effect of the web due to Patch Loading:

10

𝜂1 =𝑀𝐸𝑑

𝑓𝑦𝑓𝑤𝑒𝑙

𝛾𝑀0

=52313

73030= 0,71 and 𝜂∗ = 𝜂2 + 0,8𝜂1 = 0,21 + 0,8 × 0,71 = 0,78 < 1,4

8. Conclusions

This work resulted in a series of conclusions that are summarized below:

The shear lag effect has great influence in the design of the compressed plate, particularly in the evaluation of

in service stresses. In ULS, the reduction of effective area of the plate is very low and doesn’t need to be taken

in account in structural analysis , which is the most common case in the design of this type of deck;

Stiffened plate buckling due to direct stresses has great influence in the evaluation of the resistance of the

box bottom in ULS and, like the shear lag effect, it was not taken in account in structural analysis;

Web buckling due to shear has influence in the design for ULS. The Patch Loading effect also has great

influence in web design when the incremental launching method is adopted;

At first the web thickness was chosen to be 40 mm at support sections and 20 mm at span sections. After the

design for web buckling and Patch Loading effect, it was observed that the web thickness was oversized at

support sections and undersized at span sections. Tough less significantly, web thickness also influences the

SLS verifications. Choosing the most appropriate web thickness is of great importance in steel and composite

steel-concrete bridges for there is a great amount of steel in such plates. Therefore, the proposed values for

the new web thickness are 25 mm for support sections and 22 mm for span sections;

The cross section distortion due to eccentric loads such as the road loads established by EC1-2 causes an

increase of direct stresses that must be taken into account in the design of this type of decks, namely when

calculating the in service stresses. When diaphragms are placed along the span, these stresses are significantly

reduced;

During incremental launching of the steel structure it was necessary to use, as usual, a front nose to ensure

that the critical steel fibers did not reach the yield stress limit.

References

[1] SÉTRA – Steel-Concrete Composite Bridges Sustainable Design Guide – Ministère de l’Écologie, de l’Énergie, du Développement durable et de la Mer, May 2010.

[2] Silva, L. S. & Gervásio, H. – Manual de Dimensionamento de Estruturas Metálicas: Métodos Avançados – CMM, Fevereiro de 2007.

[3] Beg, D., Kuhlmann, U., Davaine, L. & Braun, B. – Design of Plated Structures – ECCS, 2010.

[4] Virtuoso, F. – Dimensionamento de Estruturas: Vigas de Alma Cheia – IST, Maio de 2009.

[5] Gozzi, J. – Patch Loading Resistance of Plated Girders: Ultimate and serviceability limit state – Luleå University of Technology. Luleå , Suécia, Junho de 2007.

[6] Pedro, J. – Distorção em tabuleiros de pontes em caixão – IST, Fevereiro de 1995.

[7] Eurocódigo 0 – Bases para o projecto de estruturas – EN 1990. CEN. Bruxelas, 2008.

[8] Eurocódigo 2 – Projecto de estruturas de betão – Parte 1-1: Regras gerais e regras para edifícios – EN 1992-1-1. CEN. Bruxelas, 2004.