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
35 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.

35 kN @ 3 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 = 6 kN/mABsection1.5 m1 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 = 1.5 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 2.5 mw = 6 kN/m from 0 to 2.5 mx = 1.5 m
Mx = kN·m
3.Medium
w = 12 kN/mABsection6 m2 m

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

L = 8 mw = 12 kN/m from 0 to 8 mx = 6 m
Vx = kN
4.Medium
w = 12 kN/mABsection5 m3 m

Find the bending moment Mx at the section x = 5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mw = 12 kN/m from 0 to 8 mx = 5 m
Mx = kN·m
5.Hard
w = 3 kN/mABC8 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 = 9.5 mw = 3 kN/m from 0 to 9.5 msupports at x = 0 and x = 8 m
Mmax = kN·m
6.Hard
w = 2 kN/mP = 45 kNABsection1 m5.5 m1.5 m

Find the bending moment Mx at the section x = 6.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 45 kN at 1 mw = 2 kN/m from 0 to 8 mx = 6.5 m
Mx = kN·m

Answer key

  1. 1. D (x = 3 m)
  2. 2. Mx = −3 kN·m
  3. 3. Vx = −24 kN
  4. 4. Mx = 90 kN·m
  5. 5. Mmax = 22.34 kN·m
  6. 6. Mx = 18.19 kN·m

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