Shear force & bending moment worksheet with answers

Free printable Shear force & bending moment worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
P = 45 kNABsection5 m1 m

Find the bending moment Mx at the section x = 5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 45 kN at 5 mx = 5 m
Mx = kN·m
2.Easy
P = 50 kNABsection2.5 m2.5 m

Find the bending moment Mx at the section x = 2.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP = 50 kN at 2.5 mx = 2.5 m
Mx = kN·m
3.Medium
w = 10 kN/mP = 15 kNABsection1.5 m1 m0.5 m

The cantilever is fixed at A. It carries a uniformly distributed load w over its whole length and a point load P at 2.5 m from A. Find the bending moment Mx at the section x = 1.5 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 3 mP = 15 kN at 2.5 mw = 10 kN/m from 0 to 3 mx = 1.5 m
Mx = kN·m
4.Medium
P1​ = 45 kNP2​ = 50 kNABC2 m4 m2 m

The beam rests on a pin at A and a roller at B and overhangs B by 2 m to the free end C. It carries a point load P1 between the supports and a point load P2 at C. Find the bending moment Mx under the load P1. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP1 = 45 kN at 2 mP2 = 50 kN at 8 msupports at x = 0 and x = 6 m
Mx = kN·m
5.Hard
w = 12 kN/mP = 40 kNABsection1.5 m3.5 m

Find the bending moment Mx at the section x = 1.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP = 40 kN at 1.5 mw = 12 kN/m from 0 to 5 mx = 1.5 m
Mx = kN·m
6.Hard
w = 8 kN/mP = 55 kNABsection3 m2 m

Find the bending moment Mx at the section x = 3 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP = 55 kN at 3 mw = 8 kN/m from 0 to 5 mx = 3 m
Mx = kN·m

Answer key

  1. 1. Mx = 37.5 kN·m
  2. 2. Mx = 62.5 kN·m
  3. 3. Mx = −26.25 kN·m
  4. 4. Mx = 26.67 kN·m
  5. 5. Mx = 73.5 kN·m
  6. 6. Mx = 90 kN·m

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