## 340 Influence Lines

In studies of the variation of the effects of a moving load, such as a reaction, shear, bending moment, or stress, at a given point in a structure, use of diagrams called influence lines is helpful. An influence line is a diagram showing the variation of an effect as a unit load moves over a structure.

An influence line is constructed by plotting the position of the unit load as the abscissa and as the ordinate at that position, to some scale, the value of the effect being studied. For example, Fig. 3.83a shows the influence line for reaction A in simple-beam AB. The sloping line indicates that when the unit load is at A, the reaction at A is 1.0. When the load is at B, the reaction at A is zero. When the unit load is at midspan, the reaction at A is 0.5. In general, when the load moves from B toward A, the reaction at A increases linearly: RA = (L - x)/L, where x is the distance from A to the position of the unit load.

Figure 3.83b shows the influence line for shear at the quarter point C. The sloping lines indicate that when the unit load is at support A or B, the shear at C is zero. When the unit load is a small distance to the left of C, the shear at C is -0.25; when the unit load is a small distance to the right of C, the shear at C is 0.75. The influence line for shear is linear on each side of C.

Figure 3.83c and d show the influence lines for bending moment at midspan and quarter point, respectively. Figures 3.84 and 3.85 give influence lines for a cantilever and a simple beam with an overhang.