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 = 10 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 = 10 kN at 8 mx = 8 m
Mx = kN·m
2.Easy
w = 4 kN/mAB5 m

The simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum bending moment Mmax in the beam.

L = 5 mw = 4 kN/m from 0 to 5 m
Mmax = kN·m
3.Medium
35 kN60 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.

35 kN @ 4 m60 kN @ 5 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)
4.Medium
w = 5 kN/mABsection4.5 m1.5 m

Find the shear force Vx at the section x = 4.5 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 = 4.5 m
Vx = kN
5.Hard
w = 6 kN/mABC8 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 distance xc from A to the point of contraflexure between the supports (where the bending moment changes sign).

L = 10.5 mw = 6 kN/m from 0 to 10.5 msupports at x = 0 and x = 8 m
xc = m
6.Hard
w = 6 kN/mP = 15 kNABsection1.5 m4.5 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 = 6 mP = 15 kN at 1.5 mw = 6 kN/m from 0 to 6 mx = 1.5 m
Mx = kN·m

Answer key

  1. 1. Mx = 16 kN·m
  2. 2. Mmax = 12.5 kN·m
  3. 3. E (x = 4 m)
  4. 4. Vx = −7.5 kN
  5. 5. xc = 7.219 m
  6. 6. Mx = 37.13 kN·m

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