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 = 50 kNABsection1.5 m4.5 m

Find the bending moment Mx at the section x = 1.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 50 kN at 1.5 mx = 1.5 m
Mx = kN·m
2.Easy
w = 3 kN/mAB10 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 = 10 mw = 3 kN/m from 0 to 10 m
Mmax = kN·m
3.Medium
P1​ = 20 kNP2​ = 15 kNAB4 m3 m1 m

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

L = 8 mP1 = 20 kN at 4 mP2 = 15 kN at 7 m
Mmax = kN·m
4.Medium
w = 10 kN/mP = 80 kNAB2 m3 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 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 = 80 kN at 2 mw = 10 kN/m from 0 to 5 m
MA = kN·m
5.Hard
w = 4 kN/mP = 55 kNABsection5 m0.5 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 = 55 kN at 5 mw = 4 kN/m from 0 to 8 mx = 5.5 m
Mx = kN·m
6.Hard
30 kN45 kN10 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.

30 kN @ 0 m45 kN @ 6 m10 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)

Answer key

  1. 1. Mx = 56.25 kN·m
  2. 2. Mmax = 37.5 kN·m
  3. 3. Mmax = 47.5 kN·m
  4. 4. MA = −285 kN·m
  5. 5. Mx = 113.4 kN·m
  6. 6. E (x = 4 m)

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