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
35 kNABCDEFG1 m1 m1 m1 m1 m1 m

The marks A to G split the beam into six equal parts. At which mark is the bending moment largest in size, sagging or hogging? Click it in the diagram.

35 kN @ 3 m
  1. 1A (x = 0 m)
  2. 2B (x = 1 m)
  3. 3C (x = 2 m)
  4. 4D (x = 3 m)
  5. 5E (x = 4 m)
  6. 6F (x = 5 m)
  7. 7G (x = 6 m)
2.Easy
P = 65 kNABsection3 m7 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 = 10 mP = 65 kN at 3 mx = 3 m
Mx = kN·m
3.Medium
P1​ = 55 kNP2​ = 80 kNAB7 m1 m2 m

The simply supported beam carries two point loads. Find the maximum bending moment Mmax in the beam.

L = 10 mP1 = 55 kN at 7 mP2 = 80 kN at 8 m
Mmax = kN·m
4.Medium
w = 10 kN/mP = 30 kNAB2 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 m from A. Find the bending moment MA at the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 2 mP = 30 kN at 2 mw = 10 kN/m from 0 to 2 m
MA = kN·m
5.Hard
w = 4 kN/mABC4 m1 m

The beam rests on a pin at A and a roller at B and overhangs B by 1 m to the free end C. A uniformly distributed load w acts over the whole length A–C. Find the maximum sagging bending moment Mmax between the supports.

L = 5 mw = 4 kN/m from 0 to 5 msupports at x = 0 and x = 4 m
Mmax = kN·m
6.Hard
w = 8 kN/mP = 50 kNAB2.5 m1.5 m

The simply supported beam carries a uniformly distributed load w over its whole span and a point load P. Find the maximum bending moment Mmax in the beam.

L = 4 mP = 50 kN at 2.5 mw = 8 kN/m from 0 to 4 m
Mmax = kN·m

Answer key

  1. 1. A (x = 0 m)
  2. 2. Mx = 136.5 kN·m
  3. 3. Mmax = 227.5 kN·m
  4. 4. MA = −80 kN·m
  5. 5. Mmax = 7.031 kN·m
  6. 6. Mmax = 61.88 kN·m

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