CIVL2007 Theory and Design of Structures II
Analytical Component (2 March 2007)
page 94
TOPIC 4: INFLUENCE LINES FOR STATICALLY
INDETERMINATE STRUCTURES
 LECTURE NOTES 
Introduction
Dead loads
are always fixed in magnitude and position, whereas
live loads
can have a variety of positions on the structure although they are fixed in
magnitude. Engineering structures, particularly bridges, are frequently
subjected to moving live loads such as cars and trains.
Axial force, shear force and bending moment diagrams are the best
descriptive methods of displaying their variation along a member (i.e.
beam or frame) due to a
dead
or
fixed
load.
An Influence Line (IL) best represents the variation of axial force, shear
force and bending moment along a member (i.e. beam or frame) due to
live
or
moving
loads. Influence lines can also represent the variation of the
reactions and deflection.
“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” (Hibbeler 2002)
Influence Lines therefore play an important part in the design of structures
(e.g. bridges, crane rails and conveyors) where loads
move
across their
span. They consider the problem of how to place loads on a structure in
order to realise the most severe stresses.
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CIVL2007 Theory and Design of Structures II
Analytical Component (2 March 2007)
page 95
Sometimes we may be able to determine by inspection how to place a
system of loads on a structure to realise the most severe stresses. For more
complicated structures and loading conditions one may not be able to rely
on common sense to determine the most severe load position and a trial
anderror solution may be required. In all cases the problem may be
simplified by the use of Influence Lines which shows graphically how the
changing position of loads influences quantities such as reactions, bending
moments, shear forces, and deflections (Timoshenko and Young 1965).
An important difference between shear and moment diagrams to Influence
Lines is influence lines represent the effect of a moving (live) load at a
specific point on a member whilst shear force and bending moment
diagrams represent the effect of fixed loads at all points along a member
The basic procedure for constructing Influence Lines for indeterminate
structures is the same as that for determinate structures. For determinate
structures, the Influence Lines for forces and moments consist of straight
line segments, hence, only the ordinates of a few positions of the unit load
need to be evaluated. However, Influence Lines for indeterminate
structures are generally curved lines or curvedline segments, hence they
require calculation of many more ordinates.
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 Spring '09
 A.smith
 Force, iL, analytical component

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