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
45 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.

45 kN @ 6 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 = 25 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 = 25 kN at 5 mx = 5 m
Mx = kN·m
3.Medium
w = 4 kN/mABsection1 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 mw = 4 kN/m from 0 to 4 mx = 1 m
Mx = kN·m
4.Medium
P1​ = 25 kNP2​ = 75 kNAB2 m5 m1 m

The simply supported beam carries two point loads. Find the maximum bending moment Mmax in the beam.

L = 8 mP1 = 25 kN at 2 mP2 = 75 kN at 7 m
Mmax = kN·m
5.Hard
w = 12 kN/mP = 45 kNABsection2 m3 m

Find the bending moment Mx at the section x = 2 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP = 45 kN at 2 mw = 12 kN/m from 0 to 5 mx = 2 m
Mx = kN·m
6.Hard
w = 12 kN/mABC4 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. A uniformly distributed load w acts over the whole length A–C. Find the bending moment MB at support B. Use sagging moments positive and upward shear on the left face positive.

L = 6 mw = 12 kN/m from 0 to 6 msupports at x = 0 and x = 4 m
MB = kN·m

Answer key

  1. 1. D (x = 6 m)
  2. 2. Mx = 20.83 kN·m
  3. 3. Mx = 6 kN·m
  4. 4. Mmax = 71.88 kN·m
  5. 5. Mx = 90 kN·m
  6. 6. MB = −24 kN·m

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