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 = 40 kNABsection0.5 m1.5 m

The cantilever is fixed at A and carries a point load P at its free end B. 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 = 40 kN at 2 mx = 0.5 m
Mx = kN·m
2.Easy
30 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.

30 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)
3.Medium
w = 12 kN/mP = 80 kNABsection0.5 m0.5 m1 m

The cantilever is fixed at A. It carries a uniformly distributed load w over its whole length and a point load P at 1 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 = 80 kN at 1 mw = 12 kN/m from 0 to 2 mx = 0.5 m
Mx = kN·m
4.Medium
w = 3 kN/mABsection3.5 m2.5 m

Find the bending moment Mx at the section x = 3.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mw = 3 kN/m from 0 to 6 mx = 3.5 m
Mx = kN·m
5.Hard
w = 10 kN/mP = 15 kNAB3 m5 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 = 15 kN at 3 mw = 10 kN/m from 0 to 8 m
Mmax = kN·m
6.Hard
w = 3 kN/mP = 35 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 = 35 kN at 6 mw = 3 kN/m from 0 to 8 mx = 6 m
Mx = kN·m

Answer key

  1. 1. Mx = −60 kN·m
  2. 2. A (x = 0 m)
  3. 3. Mx = −53.5 kN·m
  4. 4. Mx = 13.13 kN·m
  5. 5. Mmax = 104.1 kN·m
  6. 6. Mx = 70.5 kN·m

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