Cantilever beam - shear force diagrams:
Illustrate the shear force & bending moment diagrams for the cantilever beam illustrated in Figure.
Figure
Solution
Reaction at the support A,
R_{A} = (2 × 2) + 3 + 4 = + 11 kN
Shear Force (Beginning from the Left End A)
SF at A, F_{A} = + 11 kN
SF at B, F_{B} = + 11 - (2 × 2) = + 7 kN
SF just left of D, F_{D} = + 7 kN
SF just right of D, F_{D} = + 7 - 3 = + 4 kN
SF just left of F, F_{F} = + 4 kN = load at F
Bending Moment (Beginning from the Right End F)
BM just right of E, M _{E} = - 4 × 2 = - 8 kN-m
BM just left of E, M _{E} = - 8 - 1 = - 9 kN-m
BM at D, M _{D} = - 4 × 4 - 1 = - 17 kN-m
BM just right of C, M _{C} =- (4 × 6) - 1 - (3 × 2) =- 31 kN-m
BM just left of C, M _{C} =- 31 + 4 =- 27 kN-m
BM at B, M _{B} = - (4 × 8) - 1 - (3 × 4) + 4 = - 41 kN-m
BM at A, M_{A} =- (4 × 10) - 1 - (3 × 6) + 4 - (2 × 2 × (2 /2)) =- 59 kN-m