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As discussed above, bridge decks are required to support both static and
moving loads. Each element of a bridge must be designed for the most severe
conditions that can possibly be developed in that member. Live loads should be
placed in such a way that they will produce the most severe conditions. The
critical positions of live loads will not be the same for every member. A useful
method for determining the most severe condition of loading is by using
“influence lines”.
An influence line represents some internal force such as shear force,
bending moment etc. at a particular section or in a given member of girder, as a
unit load moves over the span. The ordinate of influence line represents the
value of that function when the unit load is at that particular point on the
structure. Influence lines provide a systematic procedure for determining how the
force (or a moment or shear) in a given part of a structure varies as the applied
load moves about on the structure. Influence lines of responses of statically
determinate structures consist only of straight lines whereas this is not true of
indeterminate structures. It may be noted that a shear or bending moment
diagram shows the variation of shear or moment across an entire structure for
loads fixed in one position. On the other hand an influence line for shear or
moment shows the variation of that response at one particular section in the
structure caused by the movement of a unit load from one end of the structure to
the other. In the following section, influence lines only for statically determinate
structures are discussed.
A unit force is placed at various locations and the shear force at sections
1-1 is obtained for each position of the unit load. These values give the ordinates
of influence line with which the influence line diagram for shear force at sections
1-1 can be constructed. Note that the slope of the influence line for shear on the
left of the section is equal to the slope of the influence line on the right of the
section. This information is useful in drawing shear force influence line in all
cases.
Influence line for bending moment at the same section 1-1 of the simple
beam is shown in Fig. 7.12(b). For a section, when the sum of the moments of all
the forces to the left is clockwise or when the sum to the right is counterclockwise,
the moment is taken as positive. The values of bending moment at
sections 1-1 are obtained for various positions of unit load and influence line is
plotted. The detailed calculation of ordinates of influence lines is illustrated for
members of the truss girder in the following section.
7.5.2 Influence lines for truss girders
Influence lines for support reactions and member forces for truss may be
constructed in the same manner as those for beams. They are useful to
determine the maximum force that may act on the truss members. The truss
shown in Fig.7.13 is considered for illustrating the construction of influence lines
for trusses.
The member forces in U3U4, U3L4 and L3L4 are determined by passing a
section X-X and considering the equilibrium of the free body diagram of one of
the truss segments.