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
w = 3 kN/mAB6 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 = 6 mw = 3 kN/m from 0 to 6 m
Mmax = kN·m
2.Easy
P = 10 kNAB4 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 = 4 mP = 10 kN at 4 m
MA = kN·m
3.Medium
w = 10 kN/mABsection0.5 m4.5 m

Find the shear force Vx at the section x = 0.5 m from 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 = 0.5 m
Vx = kN
4.Medium
12 kN/m20 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.

20 kN @ 3 m12 kN/m, 0–6 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)
5.Hard
w = 6 kN/mP = 20 kNAB1 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 = 5 mP = 20 kN at 1 mw = 6 kN/m from 0 to 5 m
Mmax = kN·m
6.Hard
w = 6 kN/mABC8 m1.5 m

The beam rests on a pin at A and a roller at B and overhangs B by 1.5 m to the free end C. A uniformly distributed load w acts over the whole length A–C. Find the maximum sagging bending moment Mmax between the supports.

L = 9.5 mw = 6 kN/m from 0 to 9.5 msupports at x = 0 and x = 8 m
Mmax = kN·m

Answer key

  1. 1. Mmax = 13.5 kN·m
  2. 2. MA = −40 kN·m
  3. 3. Vx = 20 kN
  4. 4. D (x = 3 m)
  5. 5. Mmax = 30.08 kN·m
  6. 6. Mmax = 44.68 kN·m

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