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 = 65 kNAB5 m1 m

The simply supported beam carries a single point load P. Find the shear force Vx just to the left of the load. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 65 kN at 5 m
Vx = kN
2.Easy
w = 10 kN/mAB8 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 = 8 mw = 10 kN/m from 0 to 8 m
Mmax = kN·m
3.Medium
w = 2 kN/mABsection8 m2 m

Find the bending moment Mx at the section x = 8 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 = 8 m
Mx = kN·m
4.Medium
w = 6 kN/mABsection1.5 m3.5 m

Find the bending moment Mx at the section x = 1.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mw = 6 kN/m from 0 to 5 mx = 1.5 m
Mx = kN·m
5.Hard
15 kN45 kN25 kNABCDEFG1 m1 m1 m1 m1 m1 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 @ 0 m45 kN @ 6 m25 kN @ 3 m
  1. 1A (x = 0 m)
  2. 2B (x = 1 m)
  3. 3C (x = 2 m)
  4. 4D (x = 3 m)
  5. 5E (x = 4 m)
  6. 6F (x = 5 m)
  7. 7G (x = 6 m)
6.Hard
w = 3 kN/mP = 50 kNABsection2 m2 m1 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 = 5 mP = 50 kN at 2 mw = 3 kN/m from 0 to 5 mx = 4 m
Mx = kN·m

Answer key

  1. 1. Vx = 10.83 kN
  2. 2. Mmax = 80 kN·m
  3. 3. Mx = 16 kN·m
  4. 4. Mx = 15.75 kN·m
  5. 5. F (x = 5 m)
  6. 6. Mx = 26 kN·m

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