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 = 30 kNAB1.5 m3.5 m

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

L = 5 mP = 30 kN at 1.5 m
Vx = kN
2.Easy
P = 40 kNABsection1 m1 m

The cantilever is fixed at A and carries a point load P at its free end B. Find the bending moment Mx at the section x = 1 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 2 mP = 40 kN at 2 mx = 1 m
Mx = kN·m
3.Medium
P1​ = 20 kNP2​ = 50 kNAB2.5 m2.5 m1 m

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

L = 6 mP1 = 20 kN at 2.5 mP2 = 50 kN at 5 m
Mmax = kN·m
4.Medium
w = 10 kN/mABsection4 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 mw = 10 kN/m from 0 to 5 mx = 4 m
Mx = kN·m
5.Hard
w = 2 kN/mABC6 m1 m

The beam rests on a pin at A and a roller at B and overhangs B by 1 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 = 7 mw = 2 kN/m from 0 to 7 msupports at x = 0 and x = 6 m
Mmax = kN·m
6.Hard
w = 4 kN/mP = 10 kNABsection3 m6 m1 m

Find the bending moment Mx at the section x = 9 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 10 kN at 3 mw = 4 kN/m from 0 to 10 mx = 9 m
Mx = kN·m

Answer key

  1. 1. Vx = −9 kN
  2. 2. Mx = −40 kN·m
  3. 3. Mmax = 50 kN·m
  4. 4. Mx = 20 kN·m
  5. 5. Mmax = 8.507 kN·m
  6. 6. Mx = 21 kN·m

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