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 = 80 kNABsection4.5 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 mP = 80 kN at 4.5 mx = 4.5 m
Mx = kN·m
2.Easy
P = 30 kNAB2.5 m2.5 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 = 5 mP = 30 kN at 2.5 m
Vx = kN
3.Medium
P1​ = 55 kNP2​ = 15 kNAB4 m2 m4 m

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

L = 10 mP1 = 55 kN at 4 mP2 = 15 kN at 6 m
Mmax = kN·m
4.Medium
55 kN50 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.

55 kN @ 6 m50 kN @ 8 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)
5.Hard
w = 12 kN/mAB7 m2 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 = 10 mw = 12 kN/m from 7 to 9 m
x0 = m
6.Hard
w = 4 kN/mP = 30 kNABsection0.5 m2.5 m3 m

Find the bending moment Mx at the section x = 0.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 30 kN at 3 mw = 4 kN/m from 0 to 6 mx = 0.5 m
Mx = kN·m

Answer key

  1. 1. Mx = 90 kN·m
  2. 2. Vx = 15 kN
  3. 3. Mmax = 156 kN·m
  4. 4. D (x = 6 m)
  5. 5. x0 = 7.4 m
  6. 6. Mx = 13 kN·m

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