Example 4.16 Using the diagram multiplication method, determine the deflection under the load and end slopes of a non-prismatic simply supported beam.
Solution: Bending moment (B.M.) diagram (i.e.
diagram) due to concentrated load W on the beam is shown in Figure 4.22(b).
Mid-span deflection : Apply a unit load in the downward direction at C . Deflection at C is given by multiplying the diagrams of Figure 4.22 (b) and (c) as follows
Slope at A : Apply a unit couple at A acting in the clockwise direction and plot the bending moment diagram of the beam as shown in Figure 4.22(d). The slope at A is given by multiplying the diagrams of Figure 4.22 (b) and (d) as follows
(clockwise direction)
Slope at B : Apply a unit couple at B acting in the anti-clockwise direction and plot the bending moment diagram of the beam as shown in Figure 4.22(e). The slope at B is given by multiplying the diagrams of Figure 4.22 (b) and (e) as follows
diagram) due to concentrated load W on the beam is shown in Figure 4.22(b). 
(clockwise direction)
