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 = 75 kNABsection1 m4 m

Find the bending moment Mx at the section x = 1 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP = 75 kN at 1 mx = 1 m
Mx = kN·m
2.Easy
55 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.

55 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)
3.Medium
P1​ = 30 kNP2​ = 65 kNAB1 m1 m2 m

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

L = 4 mP1 = 30 kN at 1 mP2 = 65 kN at 2 m
Mmax = kN·m
4.Medium
w = 2 kN/mP = 10 kNABsection0.5 m0.5 m1 m

The cantilever is fixed at A. It carries a uniformly distributed load w over its whole length and a point load P at 1 m from A. Find the bending moment Mx at the section x = 0.5 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 2 mP = 10 kN at 1 mw = 2 kN/m from 0 to 2 mx = 0.5 m
Mx = kN·m
5.Hard
w = 24 kN/mAB2 m4 m

The simply supported beam carries a uniformly distributed load over part of its span. Find the distance x0 from A to the section where the bending moment is largest.

L = 6 mw = 24 kN/m from 0 to 2 m
x0 = m
6.Hard
w = 3 kN/mP = 55 kNABsection4 m1 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 = 5 mP = 55 kN at 4 mw = 3 kN/m from 0 to 5 mx = 4 m
Mx = kN·m

Answer key

  1. 1. Mx = 60 kN·m
  2. 2. D (x = 3 m)
  3. 3. Mmax = 80 kN·m
  4. 4. Mx = −7.25 kN·m
  5. 5. x0 = 1.667 m
  6. 6. Mx = 50 kN·m

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