Influence Lines for Truss Member Forces

In trusses, influence lines are used to determine axial member forces caused by moving loads. In the classical truss model, loads enter the truss through joints, so a load moving between adjacent panel points is transferred to those joints through the deck system or an equivalent linear distribution.

Joint-load transfer

When a unit load lies between two adjacent panel points, its effect on the truss is replaced by two joint loads whose magnitudes vary linearly with load position. The influence line for a member force is therefore normally linear between panel points.

Method of sections

Pass a section through the member of interest and write equilibrium for one part of the truss. Consider the unit load separately in the characteristic regions of its path. A moment equation can often isolate one cut-member force directly.

Method of joints

If influence lines are needed for several members meeting near one joint, determine the joint loads for characteristic unit-load positions and apply joint equilibrium successively.

Force sign

With tension taken as positive, positive influence-line ordinates represent tension and negative ordinates compression. If the influence line changes sign, the same member may change from tension to compression as the load moves.

Application

After the influence line is known, the extreme force from a train of moving loads is found by placing the loads on regions that are most favorable in sign and magnitude. This is particularly important in bridge trusses and similar structures subjected to traffic loads.