IntermediateTopic 44 of 112Civil & Structural
Influence lines
Show how a moving load affects reactions or internal forces.
In depth
An influence line shows the variation of a reaction, shear or moment at a point as a unit load moves across the structure. Used to find the worst load positions for moving loads (cranes, vehicles). Müller-Breslau principle: influence line = deflected shape from unit displacement.
Key points
- Absolute maximum moment
- Multiple wheel loads
- Bridge design
ExampleThe maximum midspan moment of a bridge occurs with the heaviest axle near the centre.
What is Influence lines?
Show how a moving load affects reactions or internal forces.
Why is it important to understand influence lines?
Influence lines show how a moving load changes a reaction or force, so they are used to find the worst position of traffic or cranes.
What is an influence line?
A graph that shows the value of a force or reaction as a unit load moves across the structure.
How do I use an influence line?
Place the loads at the positions where the ordinates are largest and multiply the load by the ordinate, summed across all loads.
How is Influence lines used in practice?
Typical applications include finding the position of trucks that maximises the moment in a bridge girder, locating the worst position of a crane wheel load on a runway beam and checking the maximum shear in a continuous beam under a moving load.
What should I learn before Influence lines?
Study "Statically determinate structures" first (topic 43 of 112 in Civil & Structural). It covers the groundwork this topic builds on.
What are the key points of Influence lines?
Absolute maximum moment. Multiple wheel loads. Bridge design.
Can you give an example of Influence lines?
The maximum midspan moment of a bridge occurs with the heaviest axle near the centre.
What comes after Influence lines?
The next topic is "Slope-deflection method", which builds directly on this one.
How difficult is Influence lines?
It is classed as Intermediate in Civil & Structural (topic 44 of 112). It is an intermediate topic. Work through the beginner topics in Civil & Structural first.