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
w = 2 kN/mABsection2.5 m0.5 m

The cantilever is fixed at A and carries a uniformly distributed load w over its whole length. Find the shear force Vx at the section x = 2.5 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 3 mw = 2 kN/m from 0 to 3 mx = 2.5 m
Vx = kN
2.Easy
P = 60 kNABsection8 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 mP = 60 kN at 8 mx = 8 m
Mx = kN·m
3.Medium
6 kN/m15 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.

15 kN @ 10 m6 kN/m, 2–8 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)
4.Medium
P1​ = 60 kNP2​ = 60 kNAB1 m4 m3 m

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

L = 8 mP1 = 60 kN at 1 mP2 = 60 kN at 5 m
Mmax = kN·m
5.Hard
w = 2 kN/mABC4 m1.5 m

The beam rests on a pin at A and a roller at B and overhangs B by 1.5 m to the free end C. A uniformly distributed load w acts over the whole length A–C. Find the maximum sagging bending moment Mmax between the supports.

L = 5.5 mw = 2 kN/m from 0 to 5.5 msupports at x = 0 and x = 4 m
Mmax = kN·m
6.Hard
w = 4 kN/mP = 30 kNABsection1.5 m2.5 m1 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 mP = 30 kN at 4 mw = 4 kN/m from 0 to 5 mx = 1.5 m
Mx = kN·m

Answer key

  1. 1. Vx = 1 kN
  2. 2. Mx = 96 kN·m
  3. 3. D (x = 6 m)
  4. 4. Mmax = 135 kN·m
  5. 5. Mmax = 2.954 kN·m
  6. 6. Mx = 19.5 kN·m

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