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 = 60 kNABsection2.5 m1.5 m

Find the bending moment Mx at the section x = 2.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 4 mP = 60 kN at 2.5 mx = 2.5 m
Mx = kN·m
3.Medium
w = 3 kN/mABsection0.5 m3.5 m

Find the shear force Vx at the section x = 0.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 4 mw = 3 kN/m from 0 to 4 mx = 0.5 m
Vx = kN
4.Medium
M0​ = 45 kN·mAB2.5 m2.5 m

The simply supported beam carries a clockwise couple M0 = 45 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 = 5 mM0 = 45 kN·m clockwise, at 2.5 m
Mx = kN·m
5.Hard
w = 3 kN/mP = 40 kNABsection4 m3 m1 m

Find the bending moment Mx at the section x = 7 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 40 kN at 4 mw = 3 kN/m from 0 to 8 mx = 7 m
Mx = kN·m
6.Hard
w = 12 kN/mP = 50 kNABsection6 m2 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 = 8 mP = 50 kN at 6 mw = 12 kN/m from 0 to 8 mx = 6 m
Mx = kN·m

Answer key

  1. 1. Mmax = 36 kN·m
  2. 2. Mx = 56.25 kN·m
  3. 3. Vx = 4.5 kN
  4. 4. Mx = 22.5 kN·m
  5. 5. Mx = 30.5 kN·m
  6. 6. Mx = 147 kN·m

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