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
10 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.

10 kN @ 4 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)
2.Easy
w = 12 kN/mAB10 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 = 10 mw = 12 kN/m from 0 to 10 m
Mmax = kN·m
3.Medium
w = 3 kN/mABsection3 m2 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 = 5 mw = 3 kN/m from 0 to 5 mx = 3 m
Mx = kN·m
4.Medium
M0​ = 20 kN·mAB2.5 m1.5 m

The simply supported beam carries a clockwise couple M0 = 20 kN·m at x = 2.5 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 = 4 mM0 = 20 kN·m clockwise, at 2.5 m
Mx = kN·m
5.Hard
w = 4 kN/mP = 40 kNABsection2 m2 m4 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 = 8 mP = 40 kN at 4 mw = 4 kN/m from 0 to 8 mx = 2 m
Mx = kN·m
6.Hard
w = 5 kN/mP = 55 kNABsection5 m3 m

Find the bending moment Mx at the section x = 5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 55 kN at 5 mw = 5 kN/m from 0 to 8 mx = 5 m
Mx = kN·m

Answer key

  1. 1. E (x = 4 m)
  2. 2. Mmax = 150 kN·m
  3. 3. Mx = 9 kN·m
  4. 4. Mx = 7.5 kN·m
  5. 5. Mx = 64 kN·m
  6. 6. Mx = 140.6 kN·m

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