Influence lines have important application for the design of structures
that resist large live loads. In this chapter we will discuss how to draw
the influence line for a statically determinate structure. The theory is
applied to structures subjected to a distributed load or a series of
concentrated forces, and specific applications to floor girders and
bridge trusses are given. The determination of the absolute maximum
live shear and moment in a member is discussed at the end of
the chapter.
In the previous chapters we developed techniques for analyzing the
forces in structural members due to dead or fixed loads. It was shown
that the shear and moment diagrams represent the most descriptive
methods for displaying the variation of these loads in a member. If a
structure is subjected to a live or moving load, however, the variation of
the shear and bending moment in the member is best described using
the influence line. An influence line represents the variation of either the
reaction, shear, moment, or deflection at a specific point in a member
as a concentrated force moves over the member. Once this line is
constructed, one can tell at a glance where the moving load should be
placed on the structure so that it creates the greatest influence at the
specified point. Furthermore, the magnitude of the associated reaction,
shear, moment, or deflection at the point can then be calculated from the
ordinates of the influence-line diagram. For these reasons, influence lines
play an important part in the design of bridges, industrial crane rails,
conveyors, and other structures where loads move across their span.
