RASHTREEYA SIKSHANA SAMITHI TRUST

R.V.COLLEGE OF ENGINEERING BANGALORE 560 059

(An Autonomous Institution affiliated to VTU, Belgaum)DEPARTMENT OF MECHANICAL ENGINEERING

ASSIGNMENT

TOPIC: Preliminary static analysis of suspension bridges

COURSE: FINITE ELEMENT METHODCOURSE CODE: 12ME71

NAME OF THE STUDENT (IN CAPS) USN

SUMIT KUMAR 1RV12ME104

SEMESTER: VIISECTION: C

TOTAL : 10 MARKS

10

1. IntroductionSuspension bridges are designed today by makingextensive use of discretisation methods of analysis (i.e. the finite element method). Examples of application of these methods to the analysis of suspension bridges, both in the static and dynamic fields, include the works of Chaudhury and Brotton [1], Jennings and Mairs [2], Abdel-Ghaffar [3] and Arzoumanidis and Bienek [4].

These methods normally lead to analysis with a large number of variables involved, difficult to verify and that tend to obscure the influence of key parameters on the overall behaviour of the bridge.In contrast, the majority of the existing long span suspension bridges were correctly designed (when making use of the so-called deflection theory) before the computer era. A historical review of the approximate methods that lead to the deflection theory can be found elsewhere [5,6].

The well-established deflection theory[6–8], by solving the differential equilibrium equations in the deformed position, correctly accounts for the stiffening effect of the tension force in the cable. Although analytical expressions for some loading cases exist, their use is often cumbersome [8].

Furthermore, with basic references out of print, the direct use of the deflection theory appears to be too antiquated to offer a useful check to results from numerical analysis.In this paper, numerical methods are applied to solve the dimensionless analytical equations of the deflection theory [9] and to perform parametrical studies that can be helpful in the understanding of the static behavior of suspension bridges. Dimensionless charts that include displacements and bending moments under concentrated loading and maximum displacements

and bending moments under distributed loading are presented for single-span suspension bridges. Based on these charts, approximate formulae useful for design are given and trends in the static behaviour of suspension bridges are readily explained. Extension to the analysis of three span suspension bridges is performed. The accuracy of this extension is checked by presenting the results obtained

from a number of existing and hypothetical three span suspension bridges.

Whereas this load may correspond to the live loadactually considered in the design of some of thesebridges (for the George Washington Bridge and the Golden Gate, 4000 lb/ft_59 kN/m were considered (Ammann et al. [13, p. 77])), in other bridges the actual design live load may be very different. For example, for the Tacoma Narrows bridge the design live load was 1500 lb/ft_22 kN/m; the Severn and theHumber have only four lanes; the Akashi-Kaykio is designed also for railway loading. These should be considered when comparing the results between different bridges.

The results are calculated assuming that the boundary conditions for each bridge are as in Fig. . This is clearly different both in the real Tagus Bridge where a clamp exists between the cable and the stiffening truss at midspan and in the Great Belt Bridge, which is designed with a continuous girder in a manner