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 = 75 kNAB3.5 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 = 6 mP = 75 kN at 3.5 m
Vx = kN
2.Easy
w = 3 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 bending moment Mx 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 = 3 kN/m from 0 to 3 mx = 2.5 m
Mx = kN·m
3.Medium
w = 4 kN/mABsection0.5 m3.5 m

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

L = 4 mw = 4 kN/m from 0 to 4 mx = 0.5 m
Vx = kN
4.Medium
w = 6 kN/mABsection7.5 m0.5 m

Find the bending moment Mx at the section x = 7.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mw = 6 kN/m from 0 to 8 mx = 7.5 m
Mx = kN·m
5.Hard
w = 2 kN/mP = 30 kNABsection4.5 m1.5 m4 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 = 10 mP = 30 kN at 6 mw = 2 kN/m from 0 to 10 mx = 4.5 m
Mx = kN·m
6.Hard
w = 3 kN/mP = 50 kNABsection1.5 m0.5 m3 m

Find the bending moment Mx at the section x = 2 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP = 50 kN at 1.5 mw = 3 kN/m from 0 to 5 mx = 2 m
Mx = kN·m

Answer key

  1. 1. Vx = 31.25 kN
  2. 2. Mx = −0.375 kN·m
  3. 3. Vx = 6 kN
  4. 4. Mx = 11.25 kN·m
  5. 5. Mx = 78.75 kN·m
  6. 6. Mx = 54 kN·m

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