Solution: The conjugate beam of the actual beam is shown in Figure 4.8(b). A linearly varying distributed upward elastic load with intensity equal to zero at A and equal to PL/EI at B. The free-body diagram for the conjugate beam is shown in Figure 4.8(c). The reactions at A of the conjugate beam are given by
The slope at A , and the deflection at the free end A of the actual beam in Figure 4.8(d) are respectively, equal to the “shearing force” and the “bending moment” at the fixed end A of the conjugate beam in Figure 4.8(d).
Note that points downward because causes tension in bottom fiber of the beam at A (i.e. sagging moment) .
and the deflection 
at the free end A of the actual beam in Figure 4.8(d) are respectively, equal to the “shearing force” 
and the “bending moment” 
at the fixed end A of the conjugate beam in Figure 4.8(d). 
points downward because 
causes tension in bottom fiber of the beam at A (i.e. sagging moment) . 
