2.2 Application of Influence Lines for Fixed and Moving Loads 27
2.2 Application of Influence Lines for Fixed and Moving Loads
Influence lines, which describe variation of any functionZ(reaction, bending
moment, shear, etc.) in the fixed section due to moving concentrated unit loadPD 1
may be effectively used for calculation of this functionZdue toarbitrary fixed
andmovingloads.
2.2.1 Fixed Loads
Three types of fixed loads will be considered: concentrated loads, uniformly dis-
tributed loads, and couples as shown in Fig.2.10. Let us consider effect of each load
separately.
Fig. 2.10 Application of
influence line for fixed loads α
y (^1) y
2
w
P 1 P (^2) q M
Inf. line for Z
Concentrated Loads
If a structure is loaded by a loadP.P ¤ 1/, then functionZdue to this load is
ZD ̇Py, withythe ordinate of influence line for functionZat the point where
loadPis applied. The sign ofZdepends on the sign of ordinateyof influence line.
If a structure is loaded by several loadsPi, then according to superposition principle
ZD ̇
X
i
Piyi: (2.8)
In order to compute the value of any function (reaction, internal forces in any section
of the beam, frame, or any member of the truss, etc.) arising under the action of
several concentrated loadsPi, the corresponding influence line must be constructed,
each load should be multiplied by the ordinate of the influence line measured at the
load point, and the obtained products must be summed up.
It is easy to check that units of ordinate of influence lines, which have been
discussed early, lead to the required units for functionZ.