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 kNABsection4 m6 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 = 10 mP = 10 kN at 4 mx = 4 m
Mx = kN·m
2.Easy
4 kN/mABCDEFG1 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.

4 kN/m, 0–6 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 = 6 kN/mP = 15 kNAB0.5 m2.5 m

The cantilever is fixed at A. It carries a uniformly distributed load w over its whole length and a point load P at 0.5 m from A. 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 = 15 kN at 0.5 mw = 6 kN/m from 0 to 3 m
MA = kN·m
4.Medium
P1​ = 60 kNP2​ = 25 kNABC1.5 m4.5 m2 m

The beam rests on a pin at A and a roller at B and overhangs B by 2 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 Mx under the load P1. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP1 = 60 kN at 1.5 mP2 = 25 kN at 8 msupports at x = 0 and x = 6 m
Mx = kN·m
5.Hard
w = 12 kN/mP = 45 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 = 45 kN at 2.5 mw = 12 kN/m from 0 to 4 mx = 1.5 m
Mx = kN·m
6.Hard
w = 12 kN/mP = 40 kNABsection3 m2.5 m2.5 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 = 8 mP = 40 kN at 3 mw = 12 kN/m from 0 to 8 mx = 5.5 m
Mx = kN·m

Answer key

  1. 1. Mx = 24 kN·m
  2. 2. A (x = 0 m)
  3. 3. MA = −34.5 kN·m
  4. 4. Mx = 55 kN·m
  5. 5. Mx = 47.81 kN·m
  6. 6. Mx = 120 kN·m

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