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 = 30 kNABsection4 m2 m

Find the bending moment Mx at the section x = 4 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 30 kN at 4 mx = 4 m
Mx = kN·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 = 8 kN/mP = 60 kNABsection2.5 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 3 m from A. Find the bending moment Mx at the section x = 2.5 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 3 mP = 60 kN at 3 mw = 8 kN/m from 0 to 3 mx = 2.5 m
Mx = kN·m
4.Medium
P1​ = 80 kNP2​ = 55 kNAB1 m1 m2 m

The simply supported beam carries two point loads. Find the maximum bending moment Mmax in the beam.

L = 4 mP1 = 80 kN at 1 mP2 = 55 kN at 2 m
Mmax = kN·m
5.Hard
w = 12 kN/mP = 35 kNABsection5 m1 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 = 6 mP = 35 kN at 5 mw = 12 kN/m from 0 to 6 mx = 5 m
Mx = kN·m
6.Hard
w = 20 kN/mAB2 m3 m1 m

The simply supported beam carries a uniformly distributed load over part of its span. Find the distance x0 from A to the section where the bending moment is largest.

L = 6 mw = 20 kN/m from 2 to 5 m
x0 = m

Answer key

  1. 1. Mx = 40 kN·m
  2. 2. Mmax = 150 kN·m
  3. 3. Mx = −31 kN·m
  4. 4. Mmax = 95 kN·m
  5. 5. Mx = 59.17 kN·m
  6. 6. x0 = 3.25 m

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