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 = 25 kNABsection0.5 m2 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 = 2.5 mP = 25 kN at 2.5 mx = 0.5 m
Mx = kN·m
2.Easy
w = 12 kN/mAB4 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 = 4 mw = 12 kN/m from 0 to 4 m
VA = kN
3.Medium
50 kN10 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.

50 kN @ 10 m10 kN @ 4 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)
4.Medium
w = 8 kN/mABsection3.5 m2.5 m

Find the shear force Vx 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 = 8 kN/m from 0 to 6 mx = 3.5 m
Vx = kN
5.Hard
w = 10 kN/mP = 25 kNABsection1.5 m1 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 = 4 mP = 25 kN at 2.5 mw = 10 kN/m from 0 to 4 mx = 1.5 m
Mx = kN·m
6.Hard
w = 2 kN/mP = 20 kNABsection1 m3 m

Find the bending moment Mx at the section x = 1 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 4 mP = 20 kN at 1 mw = 2 kN/m from 0 to 4 mx = 1 m
Mx = kN·m

Answer key

  1. 1. Mx = −50 kN·m
  2. 2. VA = 48 kN
  3. 3. F (x = 10 m)
  4. 4. Vx = −4 kN
  5. 5. Mx = 32.81 kN·m
  6. 6. Mx = 18 kN·m

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