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 = 55 kNABsection1 m9 m

Find the bending moment Mx at the section x = 1 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 55 kN at 1 mx = 1 m
Mx = kN·m
2.Easy
P = 65 kNABsection3 m5 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 = 8 mP = 65 kN at 3 mx = 3 m
Mx = kN·m
3.Medium
P1​ = 65 kNP2​ = 30 kNAB1 m3.5 m1.5 m

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

L = 6 mP1 = 65 kN at 1 mP2 = 30 kN at 4.5 m
Mmax = kN·m
4.Medium
P1​ = 15 kNP2​ = 20 kNABC1.5 m3.5 m2 m

The beam rests on a pin at A and a roller at B and overhangs B by 2 m to the free end C. It carries a point load P1 between the supports and a point load P2 at C. Find the bending moment Mx under the load P1. Use sagging moments positive and upward shear on the left face positive.

L = 7 mP1 = 15 kN at 1.5 mP2 = 20 kN at 7 msupports at x = 0 and x = 5 m
Mx = kN·m
5.Hard
w = 20 kN/mAB1 m2 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 = 4 mw = 20 kN/m from 1 to 3 m
x0 = m
6.Hard
w = 2 kN/mP = 20 kNAB1.5 m2.5 m

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

L = 4 mP = 20 kN at 1.5 mw = 2 kN/m from 0 to 4 m
Mmax = kN·m

Answer key

  1. 1. Mx = 49.5 kN·m
  2. 2. Mx = 121.9 kN·m
  3. 3. Mmax = 61.67 kN·m
  4. 4. Mx = 3.75 kN·m
  5. 5. x0 = 2 m
  6. 6. Mmax = 22.5 kN·m

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