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.