Influence Lines - Structural and Stress Analysis - page 640

Chapter 20 / Influence Lines
The structures we have considered so far have been subjected to loading systems that
were stationary, i.e. the loads remained in a fixed position in relation to the structure.
In many practical situations, however, structures carry loads that vary continuously.
For example, a building supports a system of stationary loads which consist of its self-
weight, the weight of any permanent fixtures (such as partitions, machinery, etc.) and
also a system of imposed or 'live' loads which comprise snow loads, wind loads or any
movable equipment. The structural elements of the building must then be designed
to withstand the worst combination of these fixed and movable loads.
Other forms of movable load consist of vehicles and trains that cross bridges and
viaducts. Again, these structures must be designed to support their self-weight, the
weight of any permanent fixtures such as a road deck or railway track and also the
forces produced by the passage of vehicles or trains. It is then necessary to determine
the critical positions of the vehicles or trains in relation to the bridge or viaduct.
Although these loads are moving loads, they are assumed to be moving or changing at
such a slow rate that dynamic effects (such as vibrations and oscillating stresses) are
absent.
The effects of loads that occupy different positions on a structure can be studied by
means of influence lines . Influence lines give the value at a particular point in a structure
of functions such as shear force, bending moment and displacement for all positions
of a travelling unit load; they may also be constructed to show the variation of support
reaction with the unit load position. From these influence lines the value of a function
at a point can be calculated for a system of loads traversing the structure. For this we
use the principle of superposition so that the structural systems we consider must be
linearly elastic.
20.1 I NFLUENCE L INES FOR B EAMS IN C ONTACT WITH THE L OAD
We shall now investigate the construction of influence lines for support reactions and
for the shear force and bending moment at a section of a beam when the travelling
load is in continuous contact with the beam.
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