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 = 15 kNABsection3.5 m2.5 m

Find the bending moment Mx at the section x = 3.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 15 kN at 3.5 mx = 3.5 m
Mx = kN·m
2.Easy
w = 3 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 = 3 kN/m from 0 to 6 m
Mmax = kN·m
3.Medium
5 kN/m40 kNABCDEFG2 m2 m2 m2 m2 m2 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.

40 kN @ 8 m5 kN/m, 0–12 m
  1. 1A (x = 0 m)
  2. 2B (x = 2 m)
  3. 3C (x = 4 m)
  4. 4D (x = 6 m)
  5. 5E (x = 8 m)
  6. 6F (x = 10 m)
  7. 7G (x = 12 m)
4.Medium
w = 5 kN/mABsection7 m3 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 = 10 mw = 5 kN/m from 0 to 10 mx = 7 m
Mx = kN·m
5.Hard
w = 10 kN/mAB1 m4 m3 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 = 8 mw = 10 kN/m from 1 to 5 m
x0 = m
6.Hard
w = 5 kN/mP = 70 kNAB3 m5 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 = 8 mP = 70 kN at 3 mw = 5 kN/m from 0 to 8 m
Mmax = kN·m

Answer key

  1. 1. Mx = 21.88 kN·m
  2. 2. Mmax = 13.5 kN·m
  3. 3. E (x = 8 m)
  4. 4. Mx = 52.5 kN·m
  5. 5. x0 = 3.5 m
  6. 6. Mmax = 168.8 kN·m

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