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 kNAB4 m2 m

The simply supported beam carries a single point load P. Find the shear force Vx just to the right of the load. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 20 kN at 4 m
Vx = kN
2.Easy
P = 15 kNABsection2 m2 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 = 4 mP = 15 kN at 2 mx = 2 m
Mx = kN·m
3.Medium
w = 8 kN/mP = 80 kNAB0.5 m2.5 m

The cantilever is fixed at A. It carries a uniformly distributed load w over its whole length and a point load P at 0.5 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 = 80 kN at 0.5 mw = 8 kN/m from 0 to 3 m
MA = kN·m
4.Medium
w = 10 kN/mP = 50 kNAB2 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 2 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 = 4 mP = 50 kN at 2 mw = 10 kN/m from 0 to 4 m
MA = kN·m
5.Hard
w = 8 kN/mP = 50 kNABsection1.5 m3 m1.5 m

Find the bending moment Mx at the section x = 1.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 50 kN at 4.5 mw = 8 kN/m from 0 to 6 mx = 1.5 m
Mx = kN·m
6.Hard
12 kN/m40 kN20 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.

40 kN @ 12 m20 kN @ 6 m12 kN/m, 0–8 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)

Answer key

  1. 1. Vx = −13.33 kN
  2. 2. Mx = 15 kN·m
  3. 3. MA = −76 kN·m
  4. 4. MA = −180 kN·m
  5. 5. Mx = 45.75 kN·m
  6. 6. E (x = 8 m)

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