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 = 60 kNAB3 m

The cantilever is fixed at A and carries a point load P at its free end B. Find the bending moment MA at the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 3 mP = 60 kN at 3 m
MA = kN·m
2.Easy
P = 55 kNABsection1 m3 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 = 4 mP = 55 kN at 1 mx = 1 m
Mx = kN·m
3.Medium
w = 3 kN/mP = 70 kNABsection0.5 m4.5 m

The cantilever is fixed at A. It carries a uniformly distributed load w over its whole length and a point load P at 5 m from A. Find the bending moment Mx at the section x = 0.5 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP = 70 kN at 5 mw = 3 kN/m from 0 to 5 mx = 0.5 m
Mx = kN·m
4.Medium
30 kN50 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.

30 kN @ 10 m50 kN @ 4 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)
5.Hard
w = 4 kN/mABC5 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 = 7.5 mw = 4 kN/m from 0 to 7.5 msupports at x = 0 and x = 5 m
xc = m
6.Hard
w = 3 kN/mP = 50 kNABsection1.5 m1 m1.5 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 = 4 mP = 50 kN at 2.5 mw = 3 kN/m from 0 to 4 mx = 1.5 m
Mx = kN·m

Answer key

  1. 1. MA = −180 kN·m
  2. 2. Mx = 41.25 kN·m
  3. 3. Mx = −345.4 kN·m
  4. 4. C (x = 4 m)
  5. 5. xc = 3.75 m
  6. 6. Mx = 33.75 kN·m

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