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 = 20 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 = 20 kN at 4 mx = 4 m
Mx = kN·m
2.Easy
35 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.

35 kN @ 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)
3.Medium
w = 3 kN/mABsection5.5 m4.5 m

Find the shear force Vx at the section x = 5.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mw = 3 kN/m from 0 to 10 mx = 5.5 m
Vx = kN
4.Medium
w = 2 kN/mABsection9 m1 m

Find the bending moment Mx at the section x = 9 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mw = 2 kN/m from 0 to 10 mx = 9 m
Mx = kN·m
5.Hard
w = 2 kN/mP = 10 kNABsection4 m2 m2 m

Find the bending moment Mx at the section x = 6 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 10 kN at 4 mw = 2 kN/m from 0 to 8 mx = 6 m
Mx = kN·m
6.Hard
w = 20 kN/mAB4 m1 m

The simply supported beam carries a uniformly distributed load over part of its span. Find the maximum bending moment Mmax in the beam.

L = 5 mw = 20 kN/m from 0 to 4 m
Mmax = kN·m

Answer key

  1. 1. Mx = 40 kN·m
  2. 2. A (x = 0 m)
  3. 3. Vx = −1.5 kN
  4. 4. Mx = 9 kN·m
  5. 5. Mx = 22 kN·m
  6. 6. Mmax = 57.6 kN·m

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