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 @ 2 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
w = 10 kN/mABsection3 m2 m

The cantilever is fixed at A and carries a uniformly distributed load w over its whole length. Find the shear force Vx at the section x = 3 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mw = 10 kN/m from 0 to 5 mx = 3 m
Vx = kN
3.Medium
P1​ = 45 kNP2​ = 30 kNAB3 m1 m2 m

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

L = 6 mP1 = 45 kN at 3 mP2 = 30 kN at 4 m
Mmax = kN·m
4.Medium
w = 5 kN/mABsection2.5 m5.5 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 = 8 mw = 5 kN/m from 0 to 8 mx = 2.5 m
Mx = kN·m
5.Hard
w = 12 kN/mP = 35 kNAB2 m4 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 = 6 mP = 35 kN at 2 mw = 12 kN/m from 0 to 6 m
Mmax = kN·m
6.Hard
w = 2 kN/mP = 30 kNABsection1 m4.5 m2.5 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 = 8 mP = 30 kN at 1 mw = 2 kN/m from 0 to 8 mx = 5.5 m
Mx = kN·m

Answer key

  1. 1. C (x = 2 m)
  2. 2. Vx = 20 kN
  3. 3. Mmax = 97.5 kN·m
  4. 4. Mx = 34.38 kN·m
  5. 5. Mmax = 94.67 kN·m
  6. 6. Mx = 23.13 kN·m

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