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
35 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.

35 kN @ 10 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)
2.Easy
w = 2 kN/mABsection2 m2 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 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 4 mw = 2 kN/m from 0 to 4 mx = 2 m
Mx = kN·m
3.Medium
M0​ = 60 kN·mAB1 m9 m

The simply supported beam carries a clockwise couple M0 = 60 kN·m at x = 1 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 = 10 mM0 = 60 kN·m clockwise, at 1 m
Mx = kN·m
4.Medium
P1​ = 40 kNP2​ = 10 kNABC4 m2 m1.5 m

The beam rests on a pin at A and a roller at B and overhangs B by 1.5 m to the free end C. It carries a point load P1 between the supports and a point load P2 at C. Find the bending moment MB at support B. Use sagging moments positive and upward shear on the left face positive.

L = 7.5 mP1 = 40 kN at 4 mP2 = 10 kN at 7.5 msupports at x = 0 and x = 6 m
MB = kN·m
5.Hard
w = 5 kN/mP = 30 kNABsection5.5 m3.5 m1 m

Find the bending moment Mx at the section x = 5.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 30 kN at 9 mw = 5 kN/m from 0 to 10 mx = 5.5 m
Mx = kN·m
6.Hard
w = 2 kN/mABC4 m1.5 m

The beam rests on a pin at A and a roller at B and overhangs B by 1.5 m to the free end C. A uniformly distributed load w acts over the whole length A–C. Find the maximum sagging bending moment Mmax between the supports.

L = 5.5 mw = 2 kN/m from 0 to 5.5 msupports at x = 0 and x = 4 m
Mmax = kN·m

Answer key

  1. 1. F (x = 10 m)
  2. 2. Mx = −4 kN·m
  3. 3. Mx = 54 kN·m
  4. 4. MB = −15 kN·m
  5. 5. Mx = 78.38 kN·m
  6. 6. Mmax = 2.954 kN·m

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