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 = 40 kNAB2.5 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 = 2.5 mP = 40 kN at 2.5 m
MA = kN·m
2.Easy
w = 2 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 = 2 kN/m from 0 to 10 m
Mmax = kN·m
3.Medium
w = 10 kN/mABsection5.5 m0.5 m

Find the shear force Vx at the section x = 5.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mw = 10 kN/m from 0 to 6 mx = 5.5 m
Vx = kN
4.Medium
w = 3 kN/mABsection3.5 m0.5 m

Find the bending moment Mx at the section x = 3.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 4 mw = 3 kN/m from 0 to 4 mx = 3.5 m
Mx = kN·m
5.Hard
w = 10 kN/mP = 30 kNAB2.5 m3.5 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 = 30 kN at 2.5 mw = 10 kN/m from 0 to 6 m
Mmax = kN·m
6.Hard
w = 8 kN/mABC5 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 = 6.5 mw = 8 kN/m from 0 to 6.5 msupports at x = 0 and x = 5 m
Mmax = kN·m

Answer key

  1. 1. MA = −100 kN·m
  2. 2. Mmax = 25 kN·m
  3. 3. Vx = −25 kN
  4. 4. Mx = 2.625 kN·m
  5. 5. Mmax = 87.5 kN·m
  6. 6. Mmax = 20.7 kN·m

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