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
30 kNABCDEFG2 m2 m2 m2 m2 m2 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.

30 kN @ 8 m
  1. 1A (x = 0 m)
  2. 2B (x = 2 m)
  3. 3C (x = 4 m)
  4. 4D (x = 6 m)
  5. 5E (x = 8 m)
  6. 6F (x = 10 m)
  7. 7G (x = 12 m)
2.Easy
w = 3 kN/mAB6 m

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

L = 6 mw = 3 kN/m from 0 to 6 m
Mmax = kN·m
3.Medium
w = 2 kN/mP = 70 kNAB0.5 m1.5 m

The cantilever is fixed at A. It carries a uniformly distributed load w over its whole length and a point load P at 0.5 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 = 70 kN at 0.5 mw = 2 kN/m from 0 to 2 m
MA = kN·m
4.Medium
w = 8 kN/mP = 55 kNAB4 m

The cantilever is fixed at A. It carries a uniformly distributed load w over its whole length and a point load P at 4 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 = 4 mP = 55 kN at 4 mw = 8 kN/m from 0 to 4 m
MA = kN·m
5.Hard
w = 2 kN/mP = 50 kNABsection2.5 m3 m0.5 m

Find the bending moment Mx at the section x = 5.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 50 kN at 2.5 mw = 2 kN/m from 0 to 6 mx = 5.5 m
Mx = kN·m
6.Hard
w = 12 kN/mP = 30 kNAB1 m3 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 = 30 kN at 1 mw = 12 kN/m from 0 to 4 m
Mmax = kN·m

Answer key

  1. 1. A (x = 0 m)
  2. 2. Mmax = 13.5 kN·m
  3. 3. MA = −39 kN·m
  4. 4. MA = −284 kN·m
  5. 5. Mx = 13.17 kN·m
  6. 6. Mmax = 41.34 kN·m

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