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
25 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.

25 kN @ 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)
2.Easy
P = 40 kNABsection1 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 = 1 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 2.5 mP = 40 kN at 2.5 mx = 1 m
Mx = kN·m
3.Medium
M0​ = 60 kN·mAB3 m5 m

The simply supported beam carries a clockwise couple M0 = 60 kN·m at x = 3 m from A, and no other load. Find the bending moment Mx just to the left of the couple. Use sagging moments positive and upward shear on the left face positive.

L = 8 mM0 = 60 kN·m clockwise, at 3 m
Mx = kN·m
4.Medium
w = 10 kN/mABsection3.5 m0.5 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 = 4 mw = 10 kN/m from 0 to 4 mx = 3.5 m
Vx = kN
5.Hard
w = 10 kN/mP = 60 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 = 60 kN at 3 mw = 10 kN/m from 0 to 8 m
Mmax = kN·m
6.Hard
w = 6 kN/mP = 60 kNABsection1.5 m4 m0.5 m

Find the bending moment Mx at the section x = 5.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 60 kN at 1.5 mw = 6 kN/m from 0 to 6 mx = 5.5 m
Mx = kN·m

Answer key

  1. 1. E (x = 8 m)
  2. 2. Mx = −60 kN·m
  3. 3. Mx = −22.5 kN·m
  4. 4. Vx = −15 kN
  5. 5. Mmax = 187.5 kN·m
  6. 6. Mx = 15.75 kN·m

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