36 2 General Theory of Influence Lines
Fig. 2.17 Calculation of
bending momentMkusing
influence line forRA
PRAk
RB
1CInf. line RAa+
yCRA(orRB). Using moving load approach, we need to construct the influence line
for bending moment at sectionk. However, we can combine both approaches. For
this, show the influence line for reactionRA. According to this influence line, the
reactionRADPyC. Immediately, the bending moment at sectionKequalsMKD
RAaDPyCa. This idea will be used later for analysis of structures.
2.5 Properties of Influence Lines
Fundamental properties of influence lines are the following:
1.For statically determinate structures influence lines for reactions and internal
forces are linear
2.In case of a simply supported beam with overhangs, the influence lines for reac-
tions and internal forces for section between supports should be constructed as
for beam without overhangs and extended along the overhangs
3.In case of indirect load application influence line between two joint points is
linear
4.Units of ordinate of any influence line of factorZare unit ofZdivided by unit
of loadP(kN, lb)
Influence lines describe fundamental properties of a structure, which are inde-
pendent from the load; therefore, they may be considered as a fundamental and
reference data for the structure. Influence lines allow finding internal forces and re-
actions in case of fixed and moving loads.Influences lines allow performing quick
analysis of a structure when it is modified, in particularly in case of indirect load
application.
Influence line for some factor is used for determination of this factor only; and
after this factor may be used for determination of some other parameters. For exam-
ple, we can determine reactions due to any fixed loads using influence line. Then this
reaction can be used for determination of internal forces by definition. Such com-
bination of two approaches is a very effective way of analysis of complex statically
determinate structures and especially of statically indeterminate structures.