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 = 50 kNABsection2.5 m3.5 m

Find the bending moment Mx at the section x = 2.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 50 kN at 2.5 mx = 2.5 m
Mx = kN·m
2.Easy
15 kNABCDEFG1 m1 m1 m1 m1 m1 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 @ 1 m
  1. 1A (x = 0 m)
  2. 2B (x = 1 m)
  3. 3C (x = 2 m)
  4. 4D (x = 3 m)
  5. 5E (x = 4 m)
  6. 6F (x = 5 m)
  7. 7G (x = 6 m)
3.Medium
w = 3 kN/mABsection2 m8 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 = 10 mw = 3 kN/m from 0 to 10 mx = 2 m
Vx = kN
4.Medium
w = 5 kN/mABsection4 m2 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 = 6 mw = 5 kN/m from 0 to 6 mx = 4 m
Mx = kN·m
5.Hard
w = 6 kN/mP = 55 kNABsection0.5 m3 m1.5 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 = 5 mP = 55 kN at 3.5 mw = 6 kN/m from 0 to 5 mx = 0.5 m
Mx = kN·m
6.Hard
w = 6 kN/mABC6 m2.5 m

The beam rests on a pin at A and a roller at B and overhangs B by 2.5 m to the free end C. A uniformly distributed load w acts over the whole length A–C. Find the bending moment MB at support B. Use sagging moments positive and upward shear on the left face positive.

L = 8.5 mw = 6 kN/m from 0 to 8.5 msupports at x = 0 and x = 6 m
MB = kN·m

Answer key

  1. 1. Mx = 72.92 kN·m
  2. 2. B (x = 1 m)
  3. 3. Vx = 9 kN
  4. 4. Mx = 20 kN·m
  5. 5. Mx = 15 kN·m
  6. 6. MB = −18.75 kN·m

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