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 kNABsection1 m7 m

Find the bending moment Mx at the section x = 1 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 35 kN at 1 mx = 1 m
Mx = kN·m
2.Easy
P = 75 kNABsection2 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 = 75 kN at 2 mx = 2 m
Mx = kN·m
3.Medium
w = 12 kN/mABsection2 m6 m

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

L = 8 mw = 12 kN/m from 0 to 8 mx = 2 m
Vx = kN
4.Medium
M0​ = 60 kN·mAB3 m2 m

The simply supported beam carries a clockwise couple M0 = 60 kN·m at x = 3 m from A, and no other load. Find the bending moment Mx just to the right of the couple. Use sagging moments positive and upward shear on the left face positive.

L = 5 mM0 = 60 kN·m clockwise, at 3 m
Mx = kN·m
5.Hard
60 kN55 kN30 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.

60 kN @ 0 m55 kN @ 12 m30 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)
6.Hard
w = 10 kN/mP = 55 kNABsection7 m1 m

Find the bending moment Mx at the section x = 7 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 55 kN at 7 mw = 10 kN/m from 0 to 8 mx = 7 m
Mx = kN·m

Answer key

  1. 1. Mx = 30.63 kN·m
  2. 2. Mx = 90 kN·m
  3. 3. Vx = 24 kN
  4. 4. Mx = 24 kN·m
  5. 5. B (x = 2 m)
  6. 6. Mx = 83.13 kN·m

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