20 2 General Theory of Influence Lines
SincePD 1 , the equation of influence line becomes
IL.RA/D1: (2.4)It means that reactionRAequals to 1 for any position of concentrated loadPD 1.
The MomentM 0 at Support A
This moment may be calculated considering the equilibrium equation in form of
moment of all the external forces with respect to pointA
M 0!X
MAD 0 WM 0 PxD 0 !M 0 DPx:Since loadPD 1 , then equation of influence line is
IL.M 0 /Dx: (2.5)It means that moment varies according to linear law. If the loadPD 1 is located at
xD 0 (pointA), then the momentM 0 at the fixed support does not arise. Maximum
moment at supportAcorresponds to position of the loadP D 1 at pointB;this
moment equals to1l. The units of the ordinates of influence line forM 0 are meters.
2.1.2 Influence Lines for Internal Forces
Simply supported beam subjected to moving unit loadPis presented in Fig.2.4.
Construction of influence lines for bending moment and shear force induced at sec-
tionkare shown below.
2.1.2.1 Bending MomentMk
The bending moment in sectionkis equal to the algebraic sum of moments of all
forces, which are located to the left (or right) of sectionk, about pointk. Since the
expression for bending moment depends on whether the loadPis located to the
left or to the right from the sectionk, then two positions of the loadPneed to be
considered, i.e., to the left and to the right of sectionk.
LoadPD 1 Is Located to the Left of Sectionk
In this case, it is convenient to calculate the bending momentMkusing the right
forces (Fig. 2.4). The only reactionRBis located to the right of pointk,sothe