Question

Draw shear force and bending moment diagram for the cantilever beam shown in Fig. (a).

Answer 1

Portion AB:

At distance x, from A,

F = –20 –20 x, linear variation. At 

x = 0, F_A = –20 kN At 

x = 1, F_B = –20 –20 × 1 = – 40 kN.

M = –20x –20x . x/2 , parabolic variation

x = 0, M_A = 0 

At x = 1 m, M_B = –20 –20 × 1 × 1/2 = – 30 kN-m.

Portion BC: 

Measuring x from A, 

F = –20 – 40 – 20x, linear variation. 

At x = 1 m, F_B = –80 kN 

At x = 3 m, F_C = –120 kN.

M = –20x –40(x – 1) –20x . x/2 parabolic variation;

x = 1 m, M = –30 kN-m

x = 3 m, M = – 60 – 40 × 2 – 20 × 3 × 3/2

= –230 kN-m

Hence SFD and BMD are shown in Fig.(b) and (c) respectively.