Simply supported beam subjected to moving unit load P is presented in Fig. 2.4. Construction of influence lines for bending moment and shear force induced at section k are shown below.
Bending Moment Mk
The bending moment in section k is equal to the algebraic sum of moments of all forces, which are located to the left (or right) of section k, about point k. Since the expression for bending moment depends on whether the load P is located to the left or to the right from the section k, then two positions of the load P need to be considered, i.e., to the left and to the right of section k.
Load P = 1 Is Located to the Left of Section k
In this case, it is convenient to calculate the bending moment Mk using the right forces (Fig. 2.4). The only reaction RB is located to the right of point k, so the
To summarize, in order to construct the influence line for bending moment at section k it is necessary to:
1. Plot ordinates a and b on the left and right vertical lines passing through the left-hand and right-hand support, respectively.
2. Join each of these points with base point at the other support; both lines intersect at section k.
3. Show the operating ranges of influence line. The hatching (operating range) corresponds to the position of the load but not to the part of the beam which is used for computation of bending moment.
