Analyse the fixed beam:

The area of the negative/EI   diagram is that of the rectangle and is equal to - (M/EI) l.

As the algebraic sum of the two M/EI   diagrams is zero, we have

- (M _A/EI)x1 + wl³/12 EI =0

which gives M_A  = wl ²/12

Thus, the negative fixed end moments at A and B are both have the value -wl²/12 and the final BM diagram is as shown in Figure 12(e). The positive BM is maximum at centre and is equal to wl²/8 - wl²/12 - wl² / 24.

At the two ends we have the negative BM zones. The distance of the point of contraflexure (i.e. the points where the sign of BM changes) E and F from the ends is obtained by solving the quadratic equation

M_x   = - M_A +R_Ax -wx²/2=-wl²/12 +wl/2 x-wx²/2=0 giving x=0.211 I.