Optimization of Double Track Railway Bridge Superstructure Using FEM

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International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 5, May 2015)

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Optimization of Double Track Railway Bridge Superstructure

Using FEM

A. S. Jamadar

1

, H. S. Jadhav

2

1

M. Tech Scholar at Rajarambapu Institute of Technology, Islampur-415414

2_{Proffessor at Rajarambapu Institute of Technology, Islampur-415414}

Abstract— The purpose of this paper is to optimize truss bridges with a span of 50 m and 60 m long at different heights while they are subjected to wind and railway loading. Later the bridges are compared according to the most important analysis outcome such as deflection in order to identify the optimum bridge height. The analysis and design of double track bridge for modified broad gauge loading is done and further the optimization process is carried out. Principal of static analysis is applied keeping limit state design as its constraint. The optimization is carried by varying heights so that the top chords are located on approximately curved parabolic shape and designing the members using Jindal flat flange sections. Use of Jindal flat flange sections add newness to the structure. In the present paper an effort has been made to use the method of actual wheel load application and to optimize the through truss bridges with different span. Analysis and design of these bridges is done using STAAD PRO-V8i (SS5) (finite element analysis) software. In general the output of the work shows that the weight minimization can be done by designing the bridge somewhat deeper than they are normally built and the performance of bridge regarding the use of Jindal sections.

Keywords—Actual wheel load, double track railway bridge, finite element analysis (FEM), Jindal flat flanges, limit state design.

I. INTRODUCTION

Generally the analysis of bridges are carried out applying the live load in the form of equivalent uniformly distributed load concept. The finite element analysis is required and is the most preferred method for understanding the structural behavior of these bridges for actual application wheel loads. Since the earliest time of design of bridges, designers have considered the problem of weight minimization of bridge.

Much work has been done in finding the economic solutions and more needs to be done. In recent years, construction of steel arched and truss bridges became more common when span range of 40 to 550 meters. One important factor in bridge economy is the quantity of material used in the structure. This is influenced greatly by the general geometry and shape chosen for the main structural framework. The determination of optimum height of bridge trusses designed to satisfy modern specifications is therefore a problem of continuing interest and importance. Many researchers have carried out study considering the equivalent uniformly distributed load rather than applying actual wheel loads and conventional use of built-up members. The design of bridges should be done for actual wheel loads, but theoretically it is very difficult to analyse the bridge at actual wheel loads. Due to this limitation the bridges are designed for standard design loading. Therefore a study regarding the actual application of wheel loads needs to be done. Together with this the optimal design with respect to shape and size of structural framework needs to be done. Therefore, this paper can be divided in to two main parts bridge analysis (for actual wheel load) and bridge optimal design using Jindal flat flanges. The limit state design is done conforming to IS800-2007.

II. FINITE ELEMENT MODELLING OF TRUSS BRIDGE

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International Journal of Emerging Technology and Advanced Engineering

TABLE I

PARAMETERS OF INPUT DATA

Sr.

No. Particulars

For validation of Software

1 Effective span of

bridge 50 m.

2 Spacing of cross

girders 5.00 m

3 Spacing of stringers 2.00 m 4 Spacing of main girders 7.00 m

5 Type of material FE250

6 Member Properties Built-up members 7 Weight of stock rails 0.60 kN 8 Weight of check rails 0.40 kN 9 Spacing of sleepers 0.45 m 10 Weight of sleepers 7.85 kN/m3

11 Weight of stringers per

track per meter (assumed) 3.00 kN/m(say)

12

Weight of cross girders per track per meter

(assumed)

5.00 kN/m(say)

13 Live load

Modified broad gauge loading as

per IRS

14 Design Constraints Working Stress method

TABLE I(CONTINUED...) PARAMETERS OF INPUT DATA

Sr. No.

Double track bridge

50 m 60m

1 50 m 60m

2 5.00 m 5.00 m

3 1.676 m 1.676 m

4

4.724 m with intermediate gap of 1.052

m

4.724 m with intermediate gap of

1.052 m

5 FE250 FE250

FE 350 FE 350

6 Jindal Flat Flange Sections

Jindal Flat Flange Sections

7 0.60 kN 0.60 kN

8 0.40 kN 0.40 kN

9 0.45 m 0.45 m

10 7.85 kN/m3 7.85 kN/m3

11 3.00 kN/m(say) 3.00 kN/m(say) 12 5.00 kN/m(say) 5.00 kN/m(say)

13 Modified broad gauge loading as per IRS

Modified broad gauge loading as per

IRS Limit state

A. Validation Problem Statement

The bridge considered for validation of software results is of 50 m span with the height of 6 m. The structural behaviour of the bridge for axial forces in the chord members under modified broad gauge loading considering one end hinged and to be roller supported is presented. The geometrical details of the bridge are given in Fig. 1, 2, 3. The self-weight of both truss girder by fullers formula is 13 kN/m calculated manually. The finite element analysis of through truss Railway Bridge using Staad Pro-V8i software is carried out and the results are verified with the manual calculations done.

B. Load Combination Considered for validation

Following load combination is considered for study DL+LL

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International Journal of Emerging Technology and Advanced Engineering

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Fig.2. Defining moving load

Fig.3. Actual application of moving load

C. Results

The results of member axial forces obtained by analysis from STAAD PRO V8i (SS5) and analytical calculations done manually are given in table below.

TABLE II

COMPARISON OF DESIGN FORCES

Member

Design forces(Analytical)

Design forces(Software)

Dead load +Live

load Dead load +Live load

Compre ssion

(kN)

Tension (kN)

Compressi on (kN)

Tension (kN)

U4U5 3571.36 - 3678.77 -

U3U4 3434.56 - 3408.72 -

L4L5 - 3409.56 - 3213.55

U4L4 487.42 272.51 464.05 248.02

U4L5 355.89 620.05 358.36 594.58

From the results of analysis it is observed that, the application of exact wheel load may be complex for analysis theoretically but using the software approach it can easily achieved through very realistic way.

The software results are in good agreement with manual calculations and thus the software is validate.

III. FINITE ELEMENT MODELLING OF DOUBLE TRACK

BRIDGE

The loads to be taken into account in the bridge modelling are presented in the following sections. Some of them are applied vertically to the structure, others horizontally.

A. The various types of horizontal and vertical loads acting on the structure

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International Journal of Emerging Technology and Advanced Engineering

2) Live load: As per clause 2.3 of IRS Bridge rules, 25t Loading -2008 with maximum axle load of 245.2 kN is to be used for broad gauge loading. Thus live load per wheel is 122.6 kN and is applied as moving load with wheel spacing of 1.676 m.

3) Impact load: As per clause 2.4.1.1 (c) of IRS Bridge rules, the augmentation in load due to dynamic effect is considered. This augmentation in load due to dynamic effect adding a load equivalent to coefficient of dynamic augment multiplied by live load giving maximum stress in the member. For a given span,

Impact load = Impact factor 0.6 122.6 = 21.55 kN to

be added in live load.

4) Longitudinal Forces: As per clause 2.8 of IRS Bridge rules, provisions are made for longitudinal loads arising

from either the tractive effort or the braking force.

5) Racking force: As per clause 2.8 of IRS Bridge rules, lateral bracing are provided to resist the racking force of 5.88 kN/m to be treated as moving load laterally.

6) Wind Pressure effect: As per clause 2.11 of IRS Bridge

rules, if the wind pressure of 1.47 kN/m2 or more is acting

at the deck level then no moving load should be considered on the bridge.

B. Load Combination Considered for study

Following load combinations are considered for study.

1) 1.5(DL+ LL)

2) 1.2 (DL ± LL ± WLX)

Of the above conditions the load case (1) comes out to be the governing.

C. Optimization Process

The objective function of the optimisation process is the weight of the truss bridge also satisfying the serviceability requirements. The target of the optimisation process was to minimise the objective function. Shape optimisation of the truss was conducted by selecting its height at midspan as the design variable. The cross-sectional areas of the members constitute the sizing optimisation design variables. For each cycle of the shape optimisation process, iterations for different heights are performed and analysis is carried out to determine the amount of member forces generated in each model as the chords and web members being the subject for design.

Iterations for selecting the member are performed to obtain the least weight of the truss, while the structure conformed to all design requirements. In the optimization process top chord utilised is to form an approximately curved parabolic shape. This is done by keeping the height of first vertical member constant throughout the process.

The initial height of bridge is kept 5.5 m for 50 m and 6 m for 60 m conforming to the clearance requirement of double track through truss bridge. The variation of height of is done by increasing it by every 0.5 m depending location of height so that they are on the parabola. The limit state design is done conforming to IS800-2007. Member properties are composed of Jindal flat flange sections. For all models static analysis is done.

TABLE III

PARAMETRIC STUDY FOR OPTIMUM HEIGHT FOR GIVEN SPAN

Span (m) Length of each panel (between two verticals) (m) Height of first vertical (m) Height at middle vertical (max,m)

50 5 5.51

6.5

7.01 7.43

8.22

8.88

60 5 6.15

7.15 7.65 8.13 8.68 9.11 9.66 10.51

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International Journal of Emerging Technology and Advanced Engineering

[image:5.612.337.557.264.603.2]

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Fig. 4 Model of double track K-type truss bridge

Fig. 5 Types of loads applied

IV. RESULT AND DISCUSSION

A. For 50 m Bridge:

The variation in height is done by changing the height of middle vertical and thus forming an approximately curved parabolic top chord members. The interval of change of height is kept as 0.5 m each depending on their location on the parabola. And its results for member forces are compared. The truss bridge with 50 m span is increased from the height of 5.51 m to up to 8.88 m for investigating the optimum height for the bridge.

Fig. 6 Variation of deflection for Fe 250

[image:5.612.60.276.411.689.2]

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International Journal of Emerging Technology and Advanced Engineering

[image:6.612.326.559.106.653.2]

Fig. 9 Variation in weight For Fe350

1) Closure:From graph 6, 7 it is observed that for Fe 250 grade of steel the deflection goes on reducing as the height goes on increasing. The weight of bridge gradually reduces till 7.43 m later goes on increases giving optimum height of 7.43 m. The serviceability criteria at that height is also met. Thus the optimum height is 7.43 m with reduction in deflection of about 19.41%.

From graph 8, 9 it is observed that for Fe 350 grade of steel the weight of bridge reduces till 7.43 m later goes on increases giving optimum height of 7.43 m. But the serviceability criteria is met at 8.22 m of the considered height ranges. Thus the feasible height requirement is 8.22 m.

B. For 60 m Bridge

Similar to the 50 m bridge, the truss bridge with 60 m span is increased from the height of 6.15 m to up to 10.51 m. keeping the height of first vertical as 6.15 m and changing the midspan height.

[image:6.612.65.285.130.456.2]

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1) Closure: From graph 10, 11 it is observed that for Fe 250 grade of steel the deflection goes on reducing with increase in height. The optimum at which bridge weight is minimum is 8.68 m. But the serviceability criteria at that height is not met. Thus the optimum height is 9.11 m with reduction in deflection of about 31.20%.

From graph 12, 13 it is observed that for Fe 350 grade of steel the serviceability criteria is achieved at greater height. Thus the feasible height requirement is not obtained as far as weight minimization is concerned.

V. CONCLUSION

For 50 m span of bridge using Jindal flat flanges the optimum height is obtained at 7.43 m conforming to FE250 grade of steel satisfying the serviceability criteria as well. The reduction in deflection observed is 19.41%.

For 60 m span of bridge using Jindal flat flanges the optimum height is obtained at 8.22 m conforming to FE250 grade of steel but not satisfying the serviceability criteria at that height. Thus optimum height is 9 m. The reduction in deflection observed is 31.20%.

For both the spans it is observed that Fe350 grade of steel is not feasible as far as weight minimization is concerned.

Acknowledgement

The author is very thankful to Mr. Rahul Dhinganefrom

Vaastustruct,Pune andMr. Satish Mane from Conciv, Pune

for their unconditional guidance for the fulfilment of the present work.

REFERENCES

[1] Maraveas C, Papagiannakis A, Miamis K, Tasioulia K. 2014. Optimal design of through–truss steel bridges. The 2014 International Conference on High Performance and Optimum Design of Structures and Materials.

[2] Sankar Midhun B, Jacob Priya A. 2013. Comparison of design standards for steel railway bridges. International Journal of Engineering Research and Applications (IJERA).Vol 2 (Mar-Apr), 1131-1138.

[3] Pandia Raj R, Kalyanaraman V. 2005. GA based optimal design of steel truss bridge.26th World Congresses of Structural and Multidisciplinary Optimization. Rio de Janeiro, Brazil (May 30-Jun 03).

[4] Togan Vedat, Daloglu Ayse T. 2013. ―Bridge truss optimization under moving load using continuous and discrete design variables in optimization methods‖. Indian Journal of Engineering and Material Sciences. August;16: 245-258.

[5] Bridge rules (IN SI UNITS). Rules specifying the loads for design of super-structure and sub-structure of bridges and for assessment of the strength of existing bridges. Adopted-1941, second reprinting– 2008.

[6] Indian railway standard. Code of practice for the design of steel or wrought iron bridges carrying rail, road or pedestrian traffic. Adopted–1941,reprint- 2003.

[7] I. S. 1915-1961:The Indian standard code of practice of steel bridges.

[8] Ram Chandra. Design of steel structures. 7th ed. Delhi 6: Standard Book House; 2006 (vol 2)