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 = 70 kNAB1 m3 m

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

L = 4 mP = 70 kN at 1 m
Vx = kN
2.Easy
P = 70 kNABsection3 m7 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 = 10 mP = 70 kN at 3 mx = 3 m
Mx = kN·m
3.Medium
w = 10 kN/mP = 45 kNAB2 m0.5 m

The cantilever is fixed at A. It carries a uniformly distributed load w over its whole length and a point load P at 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 = 2.5 mP = 45 kN at 2 mw = 10 kN/m from 0 to 2.5 m
MA = kN·m
4.Medium
M0​ = 30 kN·mAB2 m3 m

The simply supported beam carries a clockwise couple M0 = 30 kN·m at x = 2 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 = 5 mM0 = 30 kN·m clockwise, at 2 m
Mx = kN·m
5.Hard
25 kN35 kN45 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.

25 kN @ 0 m35 kN @ 6 m45 kN @ 3 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)
6.Hard
w = 4 kN/mP = 30 kNABsection4 m2 m4 m

Find the bending moment Mx at the section x = 6 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 30 kN at 4 mw = 4 kN/m from 0 to 10 mx = 6 m
Mx = kN·m

Answer key

  1. 1. Vx = 52.5 kN
  2. 2. Mx = 147 kN·m
  3. 3. MA = −121.3 kN·m
  4. 4. Mx = 18 kN·m
  5. 5. E (x = 4 m)
  6. 6. Mx = 96 kN·m

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