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 = 65 kNABsection2 m0.5 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 = 2 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 2.5 mP = 65 kN at 2.5 mx = 2 m
Mx = kN·m
2.Easy
P = 45 kNABsection3 m1 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 = 4 mP = 45 kN at 3 mx = 3 m
Mx = kN·m
3.Medium
w = 2 kN/mP = 60 kNAB3 m

The cantilever is fixed at A. It carries a uniformly distributed load w over its whole length and a point load P at 3 m from A. Find the bending moment MA at the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 3 mP = 60 kN at 3 mw = 2 kN/m from 0 to 3 m
MA = kN·m
4.Medium
w = 12 kN/mABsection7 m3 m

Find the shear force Vx at the section x = 7 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mw = 12 kN/m from 0 to 10 mx = 7 m
Vx = kN
5.Hard
w = 5 kN/mP = 60 kNABsection9 m1 m

Find the bending moment Mx at the section x = 9 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 60 kN at 9 mw = 5 kN/m from 0 to 10 mx = 9 m
Mx = kN·m
6.Hard
12 kN/m50 kN50 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.

50 kN @ 6 m50 kN @ 3 m12 kN/m, 0–5 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)

Answer key

  1. 1. Mx = −32.5 kN·m
  2. 2. Mx = 33.75 kN·m
  3. 3. MA = −189 kN·m
  4. 4. Vx = −24 kN
  5. 5. Mx = 76.5 kN·m
  6. 6. D (x = 3 m)

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