So long effect of fixed loads have been studied in the form of Bending moment, shear force and deflection. In many cases , however , loads are not fixed. In a bridge structures apart from its own dead weight which is fixed we have a large number of moving vehicles or even moving pedestrians. As the loads move its effect on bending moment, shear force or deflection at a particular section goes on changing . This variation is studied with the help of influence line where a unit load is allowed to move and a particular function say, Bending moment , shear force or deflection at a section is plotted with respect to different position of loads. The difference between a Bending moment diagram and a diagram for influence line for Bending moment should be emphasized. In a bending moment diagram , the loads are fixed . The section is varied to compute the Bending moment at a different section and plotted. In influence line for Bending moment, the section is fixed the unit load is varied to compute the Bending moment at the fixed section for all the load positions. Therefore , influence line can be defined as the diagram of a function , say , of bending moment , shear force or deflection at a particular section when a unit load rolls over the span.
An influence line diagram is a graph which depicts the variation of a particular response for different position of a unit concentrated load on the span of a structure.
Uses of I.L.D
- To identify locations of moving loads , that would results in the maximum values of support reactions and internal force resultant.
- To enable a quick calculation of these forces response function under any loading configuration.
Different moving loads on the bridge
- Single point load
- Uniformly distributed load longer than span
- Uniformly distributed load shorter than the span.
- Multiple loads/a train of point loads.
Example 1: use the beam below to calculate the reactions at support, shear force & bending moment.
Example 2
Example 3
Example 4
