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 = 30 kNABsection2.5 m3.5 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 = 6 mP = 30 kN at 2.5 mx = 2.5 m
Mx = kN·m
2.Easy
w = 3 kN/mAB2 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 = 2 mw = 3 kN/m from 0 to 2 m
VA = kN
3.Medium
w = 6 kN/mP = 50 kNABsection0.5 m0.5 m2 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 = 3 mP = 50 kN at 1 mw = 6 kN/m from 0 to 3 mx = 0.5 m
Mx = kN·m
4.Medium
45 kN45 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.

45 kN @ 4 m45 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)
5.Hard
w = 2 kN/mP = 60 kNABsection2 m4 m4 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 = 10 mP = 60 kN at 2 mw = 2 kN/m from 0 to 10 mx = 6 m
Mx = kN·m
6.Hard
w = 10 kN/mP = 60 kNABsection2 m8 m

Find the bending moment Mx at the section x = 2 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 60 kN at 2 mw = 10 kN/m from 0 to 10 mx = 2 m
Mx = kN·m

Answer key

  1. 1. Mx = 43.75 kN·m
  2. 2. VA = 6 kN
  3. 3. Mx = −43.75 kN·m
  4. 4. E (x = 4 m)
  5. 5. Mx = 72 kN·m
  6. 6. Mx = 176 kN·m

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