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
40 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.

40 kN @ 1 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 = 45 kNABsection2 m6 m

Find the bending moment Mx at the section x = 2 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 45 kN at 2 mx = 2 m
Mx = kN·m
3.Medium
w = 12 kN/mP = 35 kNABsection1 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 2.5 m from A. Find the bending moment Mx at the section x = 1 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 2.5 mP = 35 kN at 2.5 mw = 12 kN/m from 0 to 2.5 mx = 1 m
Mx = kN·m
4.Medium
P1​ = 50 kNP2​ = 45 kNAB2 m3 m1 m

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

L = 6 mP1 = 50 kN at 2 mP2 = 45 kN at 5 m
Mmax = kN·m
5.Hard
w = 3 kN/mP = 60 kNAB1 m9 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 = 10 mP = 60 kN at 1 mw = 3 kN/m from 0 to 10 m
Mmax = kN·m
6.Hard
w = 6 kN/mP = 50 kNABsection4 m2 m

Find the bending moment Mx at the section x = 4 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 50 kN at 4 mw = 6 kN/m from 0 to 6 mx = 4 m
Mx = kN·m

Answer key

  1. 1. B (x = 1 m)
  2. 2. Mx = 67.5 kN·m
  3. 3. Mx = −66 kN·m
  4. 4. Mmax = 81.67 kN·m
  5. 5. Mmax = 73.5 kN·m
  6. 6. Mx = 90.67 kN·m

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