Chapter 20 – Influence Lines

The structures we have considered so far have been subjected to loading systems that were stationary, i.e. the loads remained in a fixed position in relation to the structure. In many practical situations, however, structures carry loads that vary continuously. For example, a building supports a system of stationary loads which consist of its selfweight, the weight of any permanent fixtures (such as partitions, machinery, etc.) and also a system of imposed or ‘live’ loads which comprise snow loads, wind loads or any movable equipment. The structural elements of the building must then be designed to withstand the worst combination of these fixed and movable loads. The effects of loads that occupy different positions on a structure can be studied by means of influence lines. Influence lines give the value at a particular point in a structure of functions such as shear force, bending moment and displacement for all positions of a travelling unit load; they may also be constructed to show the variation of support reaction with the unit load position. From these influence lines the value of a function at a point can be calculated for a system of loads traversing the structure. For this we use the principle of superposition so that the structural systems we consider must be linearly elastic.