Example 4.7 Determine the slope at A and deflection of B of the beam shown in Figure 4.9(a) using the conjugate beam method.
Solution: The vertical reaction at A in the real beam is given by
The bending moment at any point X at a distance x from A is given by
The corresponding conjugate beam and loading acting on it are shown in Figure 4.9(b). The loading on the beam varies parabolically with maximum value as
.
The slope at A ,
in the original beam will be equal to the shear force at A in the conjugate beam, thus,
(clockwise direction)
The deflection of B in the real beam will be equal to the bending moment at B in conjugate beam i.e.
. 
in the original beam will be equal to the shear force at A in the conjugate beam, thus, 
(clockwise direction) 
(downward direction) 
