DEVELOPMENT OF INFLUENCE LINE DIAGRAM FOR A CONTINUOUS BEAM WITH VARYING MOMENT OF INERTIA

Abstract

Continuous bridges are used in units of two spans, three spans or four spans. Units of three spans are most common. As compared with simply supported bridges, the bending moments in continuous bridges are considerably less, thus resulting in smaller sections and economy in reinforcement and concrete. The degree of indeterminacy depends on number of spans. A three span unit is indeterminate to second degree, and a four span unit to third degree. It is thought that these bridges shall be more economically designed if the moment of inertia of the girder cross-section can be proportioned according to the bending moment envelopes due to dead and live loads. One of the main aspects of design of continuous bridges is for moving load. Analysis of such load is done by developing influence line diagram.. However, the design of these bridges involves tedious calculations as these structures are statically indeterminate. In order to reduce the tediousness of the preliminary analysis of continuous bridges with varying moment of inertia, it is necessary to develop a computer program with a user guide manual for computing the influence line diagrams so that the analysis become simpler and user friendly. This thesis is mainly emphasis on the development of programme - in MATLAB for influence line diagram for continuous girder with parabolic soffit along the spans, along its user guide. The programme is developed for two, three and four span of continuous girder with parabolic soffit. Influence line equations for members of variable cross-section will be derived by the same method as used for members of constant cross section. The only difference in approach is due to the fact that the second moment of area, I, is not constant which makes the computations more cumbersome The work is extended to find the appropriate shape of the girder i.e., finding the depth proportion at the centre and at the intermediate support. The results are tabulated separately for two, three and four span. The programme for two, three and four span is given in the appendix.