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
50 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.

50 kN @ 4 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)
2.Easy
P = 75 kNABsection4 m4 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 = 8 mP = 75 kN at 4 mx = 4 m
Mx = kN·m
3.Medium
w = 12 kN/mABsection2.5 m1.5 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 = 4 mw = 12 kN/m from 0 to 4 mx = 2.5 m
Mx = kN·m
4.Medium
P1​ = 40 kNP2​ = 25 kNABC3 m5 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 Mx under the load P1. Use sagging moments positive and upward shear on the left face positive.

L = 9.5 mP1 = 40 kN at 3 mP2 = 25 kN at 9.5 msupports at x = 0 and x = 8 m
Mx = kN·m
5.Hard
w = 5 kN/mP = 55 kNABsection3 m1 m

Find the bending moment Mx at the section x = 3 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 4 mP = 55 kN at 3 mw = 5 kN/m from 0 to 4 mx = 3 m
Mx = kN·m
6.Hard
w = 10 kN/mP = 30 kNAB1 m5 m

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

L = 6 mP = 30 kN at 1 mw = 10 kN/m from 0 to 6 m
Mmax = kN·m

Answer key

  1. 1. E (x = 4 m)
  2. 2. Mx = 150 kN·m
  3. 3. Mx = 22.5 kN·m
  4. 4. Mx = 60.94 kN·m
  5. 5. Mx = 48.75 kN·m
  6. 6. Mmax = 61.25 kN·m

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