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
40 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.

40 kN @ 2 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
P = 35 kNABsection2.5 m2.5 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 = 5 mP = 35 kN at 2.5 mx = 2.5 m
Mx = kN·m
3.Medium
P1​ = 55 kNP2​ = 30 kNABC3.5 m1.5 m1 m

The beam rests on a pin at A and a roller at B and overhangs B by 1 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 = 6 mP1 = 55 kN at 3.5 mP2 = 30 kN at 6 msupports at x = 0 and x = 5 m
Mx = kN·m
4.Medium
w = 6 kN/mP = 45 kNABsection4 m1 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 = 4 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP = 45 kN at 5 mw = 6 kN/m from 0 to 5 mx = 4 m
Mx = kN·m
5.Hard
w = 5 kN/mP = 35 kNABsection5 m1 m

Find the bending moment Mx at the section x = 5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 35 kN at 5 mw = 5 kN/m from 0 to 6 mx = 5 m
Mx = kN·m
6.Hard
w = 12 kN/mAB2 m2 m

The simply supported beam carries a uniformly distributed load over part of its span. Find the distance x0 from A to the section where the bending moment is largest.

L = 4 mw = 12 kN/m from 0 to 2 m
x0 = m

Answer key

  1. 1. B (x = 2 m)
  2. 2. Mx = 43.75 kN·m
  3. 3. Mx = 36.75 kN·m
  4. 4. Mx = −48 kN·m
  5. 5. Mx = 41.67 kN·m
  6. 6. x0 = 1.5 m

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