16 2 General Theory of Influence Lines
only that position of the load is arbitrary, i.e., this is astaticload, which may have
different positions along the beam. The time, velocity of the moving load, and any
dynamic effects are not taken into account. Thus, for convenience, from now on,
we will use notion of “moving” or “traveling” load for static load, which may have
differentposition along the beam.
Influence line for any functionZat a specified section of a structure may be
constructed using its definition as follows: the required function should be calcu-
lated for different position of unit load within the loaded portion. These values
are plotted at the points, which correspond to the position of the load. After that
all ordinates should be connected. However, such procedure is extremely annoy-
ing and cumbersome (especially for statically indeterminate structures). Because
of repetitive procedure of construction of influence lines, their advantages are
questionable.
In this book, the construction of influence lines is performed on the bases of a
different approach, i.e., deriving anequationof influence line for required func-
tionZ; this equation relates values ofZand positionxof the unit loadP. Thus
the required factorZis presented asanalytical function of the position of the
load. Such way of construction of influence lines is called static method. Appli-
cation of this method for construction of influence lines for reactions is presented
below.
2.1.1 Influence Lines for Reactions
The following types of beams are considered: simply supported beam, beam with
overhang, and cantilever beam.
2.1.1.1 Simply Supported Beam (Fig.2.1)
The beamABis loaded by moving loadPD 1. The moving load is shown by circle
and the dotted line indicates the loaded contour for possible positions of the load on
the structure The distance from the left-hand support to the load isx.
Influence Line forRA
Equilibrium equation in form of momentsof all external forces about the supportB
allows determine the reactionRAin terms ofx:
RA!X
MBD 0 WRAlCP.lx/D 0 !RADP.lx/
l: