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 = 20 kNABsection1 m7 m

Find the bending moment Mx at the section x = 1 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 20 kN at 1 mx = 1 m
Mx = kN·m
2.Easy
P = 10 kNABsection6 m2 m

Find the bending moment Mx at the section x = 6 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 10 kN at 6 mx = 6 m
Mx = kN·m
3.Medium
4 kN/m30 kNABCDEFG2 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.

30 kN @ 6 m4 kN/m, 0–10 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)
4.Medium
w = 6 kN/mP = 10 kNABsection0.5 m1.5 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 = 0.5 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 2 mP = 10 kN at 2 mw = 6 kN/m from 0 to 2 mx = 0.5 m
Mx = kN·m
5.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
6.Hard
w = 8 kN/mP = 35 kNAB5 m3 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 = 8 mP = 35 kN at 5 mw = 8 kN/m from 0 to 8 m
Mmax = kN·m

Answer key

  1. 1. Mx = 17.5 kN·m
  2. 2. Mx = 15 kN·m
  3. 3. D (x = 6 m)
  4. 4. Mx = −21.75 kN·m
  5. 5. MB = −6 kN·m
  6. 6. Mmax = 125.6 kN·m

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