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 = 10 kNABsection4 m4 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 = 8 mP = 10 kN at 4 mx = 4 m
Mx = kN·m
2.Easy
15 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.

15 kN @ 6 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)
3.Medium
w = 3 kN/mABsection4.5 m1.5 m

Find the bending moment Mx at the section x = 4.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mw = 3 kN/m from 0 to 6 mx = 4.5 m
Mx = kN·m
4.Medium
w = 10 kN/mABsection7.5 m0.5 m

Find the shear force Vx at the section x = 7.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mw = 10 kN/m from 0 to 8 mx = 7.5 m
Vx = kN
5.Hard
w = 4 kN/mAB1 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 = 4 mw = 4 kN/m from 1 to 4 m
x0 = m
6.Hard
w = 5 kN/mP = 45 kNAB4 m4 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 = 45 kN at 4 mw = 5 kN/m from 0 to 8 m
Mmax = kN·m

Answer key

  1. 1. Mx = 20 kN·m
  2. 2. D (x = 6 m)
  3. 3. Mx = 10.13 kN·m
  4. 4. Vx = −35 kN
  5. 5. x0 = 2.125 m
  6. 6. Mmax = 130 kN·m

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