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 = 45 kNABsection4.5 m1.5 m

Find the bending moment Mx at the section x = 4.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 45 kN at 4.5 mx = 4.5 m
Mx = kN·m
2.Easy
w = 5 kN/mAB5 m

The cantilever is fixed at A and carries a uniformly distributed load w over its whole length. Find the bending moment MA at the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mw = 5 kN/m from 0 to 5 m
MA = kN·m
3.Medium
w = 3 kN/mP = 25 kNABsection1.5 m0.5 m

The cantilever is fixed at A. It carries a uniformly distributed load w over its whole length and a point load P at 2 m from A. Find the bending moment Mx at the section x = 1.5 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 2 mP = 25 kN at 2 mw = 3 kN/m from 0 to 2 mx = 1.5 m
Mx = kN·m
4.Medium
w = 10 kN/mABsection2 m8 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 = 10 mw = 10 kN/m from 0 to 10 mx = 2 m
Mx = kN·m
5.Hard
w = 2 kN/mP = 60 kNABsection2.5 m1.5 m6 m

Find the bending moment Mx at the section x = 2.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 60 kN at 4 mw = 2 kN/m from 0 to 10 mx = 2.5 m
Mx = kN·m
6.Hard
w = 12 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 distance xc from A to the point of contraflexure between the supports (where the bending moment changes sign).

L = 6.5 mw = 12 kN/m from 0 to 6.5 msupports at x = 0 and x = 5 m
xc = m

Answer key

  1. 1. Mx = 50.63 kN·m
  2. 2. MA = −62.5 kN·m
  3. 3. Mx = −12.88 kN·m
  4. 4. Mx = 80 kN·m
  5. 5. Mx = 108.8 kN·m
  6. 6. xc = 4.55 m

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