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
4 kN/mABCDEFG2 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.

4 kN/m, 0–10 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)
2.Easy
P = 10 kNABsection7 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 = 10 kN at 7 mx = 7 m
Mx = kN·m
3.Medium
w = 10 kN/mP = 10 kNABsection1 m3 m

The cantilever is fixed at A. It carries a uniformly distributed load w over its whole length and a point load P at 4 m from A. Find the bending moment Mx at the section x = 1 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 4 mP = 10 kN at 4 mw = 10 kN/m from 0 to 4 mx = 1 m
Mx = kN·m
4.Medium
w = 10 kN/mP = 35 kNABsection1 m1.5 m2.5 m

The cantilever is fixed at A. It carries a uniformly distributed load w over its whole length and a point load P at 2.5 m from A. Find the bending moment Mx at the section x = 1 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP = 35 kN at 2.5 mw = 10 kN/m from 0 to 5 mx = 1 m
Mx = kN·m
5.Hard
w = 10 kN/mP = 35 kNAB3.5 m1.5 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 = 5 mP = 35 kN at 3.5 mw = 10 kN/m from 0 to 5 m
Mmax = kN·m
6.Hard
w = 12 kN/mABC6 m1 m

The beam rests on a pin at A and a roller at B and overhangs B by 1 m to the free end C. A uniformly distributed load w acts over the whole length A–C. Find the maximum sagging bending moment Mmax between the supports.

L = 7 mw = 12 kN/m from 0 to 7 msupports at x = 0 and x = 6 m
Mmax = kN·m

Answer key

  1. 1. D (x = 6 m)
  2. 2. Mx = 8.75 kN·m
  3. 3. Mx = −75 kN·m
  4. 4. Mx = −132.5 kN·m
  5. 5. Mmax = 63 kN·m
  6. 6. Mmax = 51.04 kN·m

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