Draw the bending moment diagram and shear force diagram:

A cantilever beam of 8 m length is subjected to point loads of 15 kN, 10 kN, 25 kN and 20 kN at distances of 4 m, 2 m, 6 m and 8 m, respectively from the fixed end. Draw the bending moment diagram and shear force diagram.

Solution

Reaction at the support A = R_A = 10 + 15 + 25 + 20 = + 70 kN.

Shear Force

SF at A = F_A = + 70 kN

SF just left of C = + 70 kN

SF just right of C = + 70 - 10 = + 60 kN

SF just left of D = + 60 kN

SF just right of D = + 60 - 15 = + 45 kN

SF just left of E = + 45 kN

SF just right of E = + 45 - 25 = + 20 kN

SF just left of B = + 20 kN

SF just left of B = + 20 kN  (considering right side of the section)

Figure

 Bending Moment

BM at B, M_B = 0         (since the moment at the free end is equal to zero)

BM at E, M_E = - 20 × 2          (considering the right side)

                       = - 40 kN m

BM at D, M_D = - (20 × 4) - (25 × 2)

                      = - 130 kN m

BM at C, M_C  = - (20 × 6) - (25 × 4) - (15 × 2)       

                        = - 250 kN m

BM at A,   M_A = - (20 × 8) - (25 × 6) - (15 × 4) - (10 × 2)

                             = - 390 kN m.