Learning topic
Influence Lines and Moving Loads
Definition of an influence line, its difference from an internal-force diagram, and the response to a moving unit load.
An influence line for a response $S$ is the graph of $S(x)$ as a unit load moves along a specified path on the structure. The response may be a support reaction, shear force, bending moment, or axial force in a particular member.
What changes during construction
The reaction, section, or member for which the influence line is constructed remains fixed. Only the coordinate of the moving load changes. This is the essential distinction between an influence line and an ordinary internal-force diagram.
Unit load
In the classical construction, a dimensionless unit force is moved across the structure. The ordinate at each load position is numerically equal, including sign, to the selected response caused by that unit force.
Superposition
For a linear structural system, once the influence line is known, a set of concentrated loads gives
$$S=\sum_i P_i y_i,$$
where $y_i$ is the influence-line ordinate beneath $P_i$. For a distributed load,
$$S=\int q(x)y(x)\,dx.$$
Sign of an ordinate
A positive ordinate means that a unit load at that position produces a positive value of the selected response under the adopted sign convention; a negative ordinate produces the opposite response.
About this topic
This topic introduces the influence line as a graph of a selected response quantity as a unit load moves across a structure and explains how it differs from a diagram produced by a fixed load system.