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 = 35 kNAB3 m

The cantilever is fixed at A and carries a point load P at its free end B. Find the bending moment MA at the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 3 mP = 35 kN at 3 m
MA = kN·m
2.Easy
P = 20 kNAB3 m3 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 = 20 kN at 3 m
Vx = kN
3.Medium
5 kN/m50 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.

50 kN @ 4 m5 kN/m, 0–12 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)
4.Medium
P1​ = 10 kNP2​ = 15 kNAB2.5 m1 m1.5 m

The simply supported beam carries two point loads. Find the maximum bending moment Mmax in the beam.

L = 5 mP1 = 10 kN at 2.5 mP2 = 15 kN at 3.5 m
Mmax = kN·m
5.Hard
w = 4 kN/mAB3 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 = 4 mw = 4 kN/m from 0 to 3 m
x0 = m
6.Hard
w = 8 kN/mAB1 m7 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 = 8 mw = 8 kN/m from 1 to 8 m
Mmax = kN·m

Answer key

  1. 1. MA = −105 kN·m
  2. 2. Vx = 10 kN
  3. 3. C (x = 4 m)
  4. 4. Mmax = 23.75 kN·m
  5. 5. x0 = 1.875 m
  6. 6. Mmax = 62.02 kN·m

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