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 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.

15 kN @ 5 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)
2.Easy
w = 8 kN/mABsection2.5 m1.5 m

The cantilever is fixed at A and carries a uniformly distributed load w over its whole length. Find the bending moment Mx at the section x = 2.5 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 4 mw = 8 kN/m from 0 to 4 mx = 2.5 m
Mx = kN·m
3.Medium
w = 5 kN/mABsection3 m2 m

Find the bending moment Mx at the section x = 3 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mw = 5 kN/m from 0 to 5 mx = 3 m
Mx = kN·m
4.Medium
w = 10 kN/mABsection2.5 m1.5 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 = 4 mw = 10 kN/m from 0 to 4 mx = 2.5 m
Mx = kN·m
5.Hard
w = 3 kN/mABC6 m2 m

The beam rests on a pin at A and a roller at B and overhangs B by 2 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 = 8 mw = 3 kN/m from 0 to 8 msupports at x = 0 and x = 6 m
MB = kN·m
6.Hard
w = 12 kN/mAB1 m3 m6 m

The simply supported beam carries a uniformly distributed load over part of its span. Find the maximum bending moment Mmax in the beam.

L = 10 mw = 12 kN/m from 1 to 4 m
Mmax = kN·m

Answer key

  1. 1. F (x = 5 m)
  2. 2. Mx = −9 kN·m
  3. 3. Mx = 15 kN·m
  4. 4. Mx = 18.75 kN·m
  5. 5. MB = −6 kN·m
  6. 6. Mmax = 57.38 kN·m

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