Learning topic
Influence Lines
Learn influence lines for reactions, shear, bending moments, and truss forces under moving loads, including construction methods and the Müller-Breslau principle.
An influence line shows how a selected reaction, internal force, or other structural response changes as a unit moving load occupies successive positions on the structure. Influence lines are fundamental for bridges, crane girders, and other systems subjected to loads whose position is not fixed.
Influence line versus internal-force diagram
A shear or bending-moment diagram gives an internal force at different sections for a fixed load system. An influence line instead refers to one selected response quantity and gives its value as a function of the position of a moving load.
Construction
For statically determinate structures, influence-line ordinates can be obtained directly from equilibrium as a unit load moves across the structure. A kinematic approach relates the influence-line shape to the displacement mechanism created by releasing the restraint associated with the response quantity.
Use with real loads
Once the influence line is known, the effect of concentrated loads is obtained by summing each load multiplied by the corresponding ordinate. Distributed loads are handled by integration, or by signed influence-line areas when the load intensity is constant.
Critical load position
The sign and shape of an influence line indicate where moving concentrated or distributed loads should be placed to maximize or minimize the selected structural response.
About this topic
This section covers influence lines for statically determinate structures: moving loads, influence lines for reactions, shear forces and bending moments, static and kinematic construction methods, the Müller-Breslau principle, loading of influence lines, hinged multispan beams, and trusses.