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
15 kN/mABCDEFG2 m2 m2 m2 m2 m2 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.

15 kN/m, 0–12 m
  1. 1A (x = 0 m)
  2. 2B (x = 2 m)
  3. 3C (x = 4 m)
  4. 4D (x = 6 m)
  5. 5E (x = 8 m)
  6. 6F (x = 10 m)
  7. 7G (x = 12 m)
2.Easy
w = 4 kN/mAB4 m

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

L = 4 mw = 4 kN/m from 0 to 4 m
VA = kN
3.Medium
w = 10 kN/mABsection5 m1 m

Find the shear force Vx at the section x = 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 m
Vx = kN
4.Medium
M0​ = 25 kN·mAB7 m1 m

The simply supported beam carries a clockwise couple M0 = 25 kN·m at x = 7 m from A, and no other load. Find the bending moment Mx just to the right of the couple. Use sagging moments positive and upward shear on the left face positive.

L = 8 mM0 = 25 kN·m clockwise, at 7 m
Mx = kN·m
5.Hard
w = 6 kN/mP = 30 kNAB1 m9 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 = 10 mP = 30 kN at 1 mw = 6 kN/m from 0 to 10 m
Mmax = kN·m
6.Hard
w = 12 kN/mABC5 m1 m

The beam rests on a pin at A and a roller at B and overhangs B by 1 m to the free end C. A uniformly distributed load w acts over the whole length A–C. Find the bending moment MB at support B. Use sagging moments positive and upward shear on the left face positive.

L = 6 mw = 12 kN/m from 0 to 6 msupports at x = 0 and x = 5 m
MB = kN·m

Answer key

  1. 1. A (x = 0 m)
  2. 2. VA = 16 kN
  3. 3. Vx = −20 kN
  4. 4. Mx = 3.125 kN·m
  5. 5. Mmax = 90.75 kN·m
  6. 6. MB = −6 kN·m

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