Influence line

A line drawn to show how some quantity varies as unit load crosses a bridge. For example, the influence line for say the left-hand reaction of a beam would be a triangle, of unit height at the left-hand end, decreasing to zero at the right-hand end.

This would show that as unit load crossed the span the left-hand reaction would fall away to nothing when the load reached the right-hand abutment.

Again, suppose we drew the influence line for the force in a particular member. Then if a train of loads crossed, the sum of the heights of the influence line under each load would give the total force in that member for the chosen position of the train. With a suitable computer program the train could be moved about to find the maximum load in that member. This can be especially useful for the case of two trains crossing at the same time in opposite directions, a tedious calculation otherwise.

Influence lines can be drawn for shear at a particular point, bending moments , and so on.

You can see the drawing.