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
w = 8 kN/mAB6 m

The simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum bending moment Mmax in the beam.

L = 6 mw = 8 kN/m from 0 to 6 m
Mmax = kN·m
2.Easy
P = 30 kNABsection3 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 = 3 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP = 30 kN at 5 mx = 3 m
Mx = kN·m
3.Medium
15 kN/m60 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.

60 kN @ 2 m15 kN/m, 4–12 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
M0​ = 15 kN·mAB7 m1 m

The simply supported beam carries a clockwise couple M0 = 15 kN·m at x = 7 m from A, and no other load. Find the bending moment Mx just to the right of the couple. Use sagging moments positive and upward shear on the left face positive.

L = 8 mM0 = 15 kN·m clockwise, at 7 m
Mx = kN·m
5.Hard
w = 3 kN/mP = 40 kNABsection1.5 m3.5 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 = 5 mP = 40 kN at 1.5 mw = 3 kN/m from 0 to 5 mx = 1.5 m
Mx = kN·m
6.Hard
w = 4 kN/mP = 55 kNABsection3 m0.5 m6.5 m

Find the bending moment Mx at the section x = 3.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 55 kN at 3 mw = 4 kN/m from 0 to 10 mx = 3.5 m
Mx = kN·m

Answer key

  1. 1. Mmax = 36 kN·m
  2. 2. Mx = −60 kN·m
  3. 3. D (x = 6 m)
  4. 4. Mx = 1.875 kN·m
  5. 5. Mx = 49.88 kN·m
  6. 6. Mx = 152.8 kN·m

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