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 kNABsection3 m5 m

Find the bending moment Mx at the section x = 3 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 20 kN at 3 mx = 3 m
Mx = kN·m
2.Easy
60 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.

60 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)
3.Medium
M0​ = 15 kN·mAB1 m3 m

The simply supported beam carries a clockwise couple M0 = 15 kN·m at x = 1 m from A, and no other load. Find the bending moment Mx just to the left of the couple. Use sagging moments positive and upward shear on the left face positive.

L = 4 mM0 = 15 kN·m clockwise, at 1 m
Mx = kN·m
4.Medium
w = 3 kN/mABsection3.5 m2.5 m

Find the shear force Vx at the section x = 3.5 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 = 3.5 m
Vx = kN
5.Hard
w = 24 kN/mAB4 m1 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 = 5 mw = 24 kN/m from 0 to 4 m
x0 = m
6.Hard
w = 10 kN/mP = 50 kNAB2.5 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 = 4 mP = 50 kN at 2.5 mw = 10 kN/m from 0 to 4 m
Mmax = kN·m

Answer key

  1. 1. Mx = 37.5 kN·m
  2. 2. D (x = 3 m)
  3. 3. Mx = −3.75 kN·m
  4. 4. Vx = −1.5 kN
  5. 5. x0 = 2.4 m
  6. 6. Mmax = 65.63 kN·m

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