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 = 10 kNAB2 m

The cantilever is fixed at A and carries a point load P at its free end B. 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 = 10 kN at 2 m
MA = kN·m
2.Easy
4 kN/mABCDEFG2 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.

4 kN/m, 0–10 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)
3.Medium
P1​ = 75 kNP2​ = 55 kNAB5 m2 m1 m

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

L = 8 mP1 = 75 kN at 5 mP2 = 55 kN at 7 m
Mmax = kN·m
4.Medium
w = 12 kN/mP = 60 kNAB0.5 m4.5 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 = 5 mP = 60 kN at 0.5 mw = 12 kN/m from 0 to 5 m
MA = kN·m
5.Hard
w = 4 kN/mAB7 m2 m1 m

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

L = 10 mw = 4 kN/m from 7 to 9 m
Mmax = kN·m
6.Hard
w = 8 kN/mP = 60 kNABsection2 m2 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 = 4 mP = 60 kN at 2 mw = 8 kN/m from 0 to 4 mx = 2 m
Mx = kN·m

Answer key

  1. 1. MA = −20 kN·m
  2. 2. D (x = 6 m)
  3. 3. Mmax = 175 kN·m
  4. 4. MA = −180 kN·m
  5. 5. Mmax = 11.52 kN·m
  6. 6. Mx = 76 kN·m

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