ANALYSIS OF BRIDGE DECK · Courbon’s Method Orthotropic Plate Theory Finite Difference Method...

ANALYSIS OF BRIDGE DECK

Ms. Kshitija S. Balwan 1, Mr. Vishal D. Sakhare2

1 Assistant Professor, Civil Engineering Department, DKTE’s Textile & Engineering Institute, Ichalkaranji

2 Assistant Professor, Civil Engineering Department, DKTE’s Textile & Engineering Institute, Ichalkaranji

ABSTRACT

The main objective of this study was to develop three-dimensional finite element modelling

(3D-FEM) of bridge deck. The accuracy of the results obtained from bridge deck analysis is

validated by comparing it with analytical solution. For analytical method the influence line

diagram method was used. In this work parameters considered as maximum bending moment

and maximum shear force which is future check with software result.

Key wards: Bridge deck, Influence line diagram, CSI Bridge software.

INTRODUCTION

Transportation needs to commensurate with infrastructural development demand of

shortest routes to cover distances. Such short routes require crossing of number of obstacles.

Bridge structures are the solutions for such problems.

Bridges are very special type of structures. They are characterized by their simplicity in

geometry and loading conditions. The bridges usually carried uniformly distributed dead load,

vehicular live load to its surface and transfers same to the support by flexure, shear and torsion.

Newly designed bridges are often skew. This is due to space constraints in congested urban

areas. It can be also needed due to geographical constraints such as mountainous terrains.

However, force flow in skew bridges is much more complicated than straight bridges.

Therefore, careful investigation and numerical analysis needs to be performed, in which a skew

bridge can be modelled in several ways [7].

Bridges are essential and vital elements of any road network. Bridges form vital links in

the communication system and with man’s increasing mobility, it calls for the solution of a

multitude of engineering problems. Hence bridges with complex features such as heavy skew,

edge stiffening, deep haunches over support etc. are being analysed, designed and constructed

[8].

REVIEW OF LITERATURE

1. Literature Review-Bridge Deck

Bridge decks are developing today as fast as they have at any time since the beginning

of the industrial revolution. Methods of analysis of bridge decks have been developed and in

the last thirty years progress has been particularly significant. Hand methods of load

distribution and more recently the application of digital computers have enabled engineers to

analyse decks with complex cross sections and complicated skew, curved and continuous

spans.

This design method demands a considerable amount of theoretical and experimental research

to improve and test their reliability. However, several have now been developed to such usable

JASC: Journal of Applied Science and Computations

Volume V, Issue XII, December/2018

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form that with an understanding of physical behaviour designers can analyse complex decks

without recourse to complicated mathematical theory [8]. The structural forms of bridge decks are usually divided into following five types:

Beam decks

Grid decks

Slab decks

Beam-and-slab decks

Cellular decks

2. Methods of Bridge Deck Analysis

Introduction

Extensive research into behaviour of bridge decks under loading had been carried out over the

past five decades and a number of methods of bridge deck analysis were evolved from time to

time. Prior to the general use of the computer-aided analysis, hand computation methods and

charts based on some approximations and idealizations, provided convenient methods of load

distribution. These were reasonably accurate for design purposes. However, with the advent of

digital computers, many computer-aided methods have been developed and are in use although

some of these methods are highly numerical and expensive [2].

Methods of Analysis

Different techniques commonly in use for the analysis of bridge decks of various types and

configurations are

Courbon’s Method

Orthotropic Plate Theory

Finite Difference Method

Method of Harmonic Analysis

Grillage Analogy

Folded Plate Analysis

Finite Element Method

Finite Strip Method

Computer aided analysis.

Each of the above techniques is more suited to a particular type or types of bridge decks

depending upon the closeness of the actual structure with the assumptions of the method. The

applicability of the methods to various types of bridges is illustrated in table. It may be evident

that one particular type of bridge deck can be analyzed by more than one method and in such

cases, the choice rests with the designer depending upon the facility, time available, economy

and of course his familiarity with the method.

3. Literature on Box Girder

General Remarks

Bridges systems form an important part of much of the modern highways across the

world. In recent years, the use of the reinforced box girder is very much increased. This increase

is primarily due to the box girder’s pleasing aesthetic appearance, its structural efficiency and

its favourable economic position as contractors have become familiar with its construction.

A box girder bridge consists of a top and bottom slab connected by vertical webs to

form a cellular structure. An analytical solution of the true response of a box girder bridge



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under load is complicated by the usual factors common to other reinforced concrete structural

systems. It is a highly indeterminate structure and is generally made of two materials, concrete

and steel [6].

Evolution of Box Girder

The spanning of bridges started with simple slabs. As the spans increased, the design depth of

the slab also increased. It is known that the material near the centre of gravity contributes very

little for flexure and hence could be removed. This leads to the beam-and-slab type systems.

The reinforcement in the bottom bulb of the beam provided capacity for tensile forces and the

top slab concrete, the capacity to resist the compression. They formed a couple to resist flexure

(bending moment).

As the width of the deck is increased, more number of longitudinal beams are required

leading to a reduction of stiffness in the transverse direction and relatively high transverse

curvature. The webs of the beams get opened out spreading radially from the top slab. Under

high transverse bending (curvature), they cannot maintain their relative position. To keep the

webs in their original position, the bottom bulb of the webs is required to be tied together. This

leads to the evolution of box girder. For longer spans and wider decks, box girders are found

to suitable cross section. Long span wide decks and eccentric loading on the cross section suffer

high curvature both in longitudinal and transverse direction causing heavy distortion of the

cross section. Hence such bridge decks require high torsional rigidity to keep the effect of

distortion of the deck to be a minimum [6].

METHODOLOGY A proposed research work comprises a study of response of bridge deck for analytical

analysis and software analysis in terms of bending moment and support reaction. The model

will be developed using software.

For achieving the objectives of the study will be conducted in following phases -

• Preparation of model of bridge deck by using relevant software.

• Analyse it in that software and find the responses in terms of bending moment and

support reaction.

• Validate it by comparing it with the analytical solution in term of bending moment,

support reaction.

INPUT PARAMETERS

The bridge under study is a simply supported single cell reinforced concrete box girder. It is a

single-lane National Highway bridge without footpath. It is having a reinforced concrete deck

slab 250 mm in depth. The span of the bridge is 30.00 m in the direction of the traffic. The

effective span of the bridge is 30.00 m. The carriageway width is 8.5 m and the overall width

of the deck is 9.5 m. The overall depth of the box section is 2.5 m. Grade of concrete used is

M40. [4]



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Cross Section of Box Girder (Model in CSI Bridge)

a) Analysis of deck by Analytical Method

Running Section and Calculation of Sectional Properties:

Running cross section of deck Various Elements of Box Girders

Element Area (m²)

1 0.345

2 0.75

3 1.475

4 1.95

5 0.75

6 0.345

Total area of section = 5.67

Loading Calculations

Due to dead load (DL):

Density of reinforced concrete = 25 kN/m³.



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Total area of support section = 5.67m²

Therefore, self-weight of support section = 5.67 x 25 =141.75 kN/m.

Analysis of Box Girder Right Bridge Deck

Validation of model for dead load

Since the length of the bridge deck is exceeding its width by a considerable amount, the

above box bridge deck can be analysed as beams to determine the distribution of longitudinal

bending moments. Single cell box girder is considered in this example. Both the webs of the

box girder are being analysed.

Due to dead load (DL):

Dead Load Distribution on Bridge Deck

�� = �� = (w x l)/2

= (141.75 x 30)/2

= 2126.25 kN

�� = (w x l²)/8

= (141.75 x 30²)/8

= 16000 kNm

Due to live load (LL):

a) Calculation of maximum bending moment First of all compute the center of gravity of loads from first point load 78.45 kN [3]

Fixing the CG of loads



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Centre of Gravity

=

�117.67 × 3.96� + �117.67 × 5.48� + �166.71 × 7.61� + �166.71 × 8.98� +

�166.71 × 12.03� + �166.71 × 13.4�

78.45 + �117.67 × 2� + �166.71 × 4�

Centre of Gravity =#$$%.&%

&#'.$# = 8.28 m

Now place the loads as shown in fig.

Live Load Distribution on Bridge Deck for max. Bending moment

Draw the influence line diagram as shown fig.

ILD for maximum bending moment

Bending moment =

(78.45X3.5)+(117.67X5.57)+(117.67X6.36)+(166.71X7.48)+(166.71X6.82)+(166.71X5.37)+(166.71

X4.71) = 5747 kN m

b) Calculation of maximum shear force at support

Shear force is minimum when 1st point load (78.45 kN) is at start of span and shear force is

maximum when end point load (166.71 kN) is at end of span.



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Live Load Distribution on Bridge Deck for Shear Force at A

Influence line diagram for max. Shear at A

�� = (78.45X1)+(117.67X0.87)+(117.67X0.8)+(166.71X0.75)+(166.71X0.7)+

(166.71X0.6)+(166.71X0.55)

= 709.57 kN

Live Load Distribution on Bridge Deck for Shear Force at B



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Influence line diagram for max. shear at B

)* =

(166.71X1)+(166.71X0.9)+(166.71X0.85)+(166.71X0.75)+(117.67X0.7)+(117.67X0.65)+(78.45X0.5

5)

= 785 kN

b) Analysis of deck by Software Method

Modelling of the Structure:

For the analysis, the girder is being modelled as shown in figure 4.1. The bridge deck

is simply supported at the ends. Before modeling the structure, it is important to define the

units system that is going to be used. The unit system used will be the following:

Length: meter (m)

Force: Kilo-Newton (kN)

The bridge deck is located in the X-Z plane. The direction of traffic flow is along the X

direction. The gravity loads act along the Y direction. Hence the shear forces and bending

moments are given by Fy and Mz respectively. Torsion moments are given by Mx.

Material Properties

Material Properties Used for deck Model

Material type – concrete (M40)

Weight per unit Volume – 24.99 kN/m³

Modules of elasticity (E) – 31622777 N/m²

Poisson’s ratio (µ) – 0.2



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Model Loading

For moving load condition I.R.C. class 70 R loading consists of a tracked a wheeled vehicle

of total load of 1000 KN. wheel specifications are as shown in Fig as per IRC-6-2000 [3]

Model loading

Full bridge deck model



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Shear force diagram for dead load case

Bending moment diagram for dead load case



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Shear force diagram for live load case

Bending moment diagram for live load case



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Response to Loads Causing Maximum Bending Moments:

The results of the CSI BRIDGE analysis for DL

Mmax = 16027 kN-m.

Results for LL analysis

Mmax = 5764 kN-m.

Response to Loads Causing Shear Force

The results of the CSI BRIDGE analysis for DL are as follows:

RA = RB = 2137 kN

Results for LL analysis are as follows:

RA = 720 kN

RB = 780 kN

Comparison of result

Manual Analysis CSI BRIDGE

Analysis

Difference (%)

DL LL DL LL DL LL

Bending moment 16000 5746 16027 5764 0.16 0.31

Support reactions

(��)

2126.25 709 2137 720 0.5 1.5

(��) 2126.25 785 2137 780 0.5 0.64

RESULT AND DISCUSSION

General

It shows the model developed by using CSI Bridge software is having close agreement with analytical

result. Therefore, this mode can be used for future study.

Comparison Between Analytical and CSI BRIDGE Solution

The observations between analytical and CSI BRIDGE solution are as follows

1. The shear forces developed in the bridge deck slab computed by CSI Bridge software are

very close to manual result.

2. The bending moment developed in the bridge deck slab computed by CSI Bridge software

are very close to manual result.



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Comparison of bending moment developed in deck between analytical and CSI BRIDGE

Solution

Comparison of shear force developed in deck between analytical and CSI BRIDGE Solution

FINDING AND SUGGESTIONS

1. This project was mainly focused on response of box girder deck only. However

additional work needed to study responses of other type of bridge decks.

2. This study includes response of deck only 70R wheel load. So additional work is

needed to study the response of deck for other types of loading as per IRC 6.

16000

5746

16027

5764

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

DEAD LOAD LIVE LOAD

BE

ND

ING

MO

ME

NT

LOADING CONDITION

ANALYTICAL

CSI BRIDGE

2126

785

2137

780

0

500

1000

1500

2000

2500

DEAD LOAD LIVE LOAD

SH

EA

R F

OR

CE

LOADING CONDITION

ANALYTICAL

CSI BRIDGE



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CONCLUSION

Results obtained by CSI BRIDGE analysis is validated by comparing it with

analytical solution. The result reveals the response obtained by CSI BRIDGE analysis

are very close to analytical solution for dead and live loading condition.

REFERENCES

1. References

[1] Agarwal M. S. and Chidiac S. E. “Finite Strip Analysis of Bridges “, First

Edition 1996.

[2] Hambly E. C. “Bridge Deck Behavior”. “, First Edition 1991.

[3] IRC 6-2000. “Standard Specification and Code of Practice for Bridges “, Section: II,

“Loads and Stresses” (Fourth Revision).

[4] IRC 21-2000. “Standard Specification and Code of Practice for Bridges “, Section:

III, “Cement Concrete (Plain and Reinforced Concrete) “, Third Revision.

[5] IS 456-2000. “Indian Standard Plain and Reinforced Concrete – Code of Practice”,

Fourth Revision. Buru of Indian steel, New Delhi.

[6] Kristek V. “Theory of Box Girder”. “, First Edition 1979.

[7] Kar Ansuman, Khatri Vikash, Maiti P. R., Singh P. K., “Study on Effect of Skew

Angle in Skew Bridges.” International Journal of Engineering Research and

Development E-ISSN: 2278-067X,( August 2012).

[8] Naresh K, Rao Sanjeev C., “Analysis of Skew Bridge.” International Journal of

Research Sciences and Advanced Engineering Volume 2. Issue 10 (2015).



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ANALYSIS OF BRIDGE DECK · Courbon’s Method Orthotropic Plate Theory Finite Difference Method...

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