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 = 15 kNABsection2 m8 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 = 10 mP = 15 kN at 2 mx = 2 m
Mx = kN·m
2.Easy
P = 20 kNABsection1 m4 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 = 5 mP = 20 kN at 1 mx = 1 m
Mx = kN·m
3.Medium
M0​ = 50 kN·mAB6 m4 m

The simply supported beam carries a clockwise couple M0 = 50 kN·m at x = 6 m from A, and no other load. Find the bending moment Mx just to the left of the couple. Use sagging moments positive and upward shear on the left face positive.

L = 10 mM0 = 50 kN·m clockwise, at 6 m
Mx = kN·m
4.Medium
P1​ = 45 kNP2​ = 80 kNAB2 m4 m2 m

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

L = 8 mP1 = 45 kN at 2 mP2 = 80 kN at 6 m
Mmax = kN·m
5.Hard
6 kN/m35 kN25 kN45 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 @ 0 m25 kN @ 12 m45 kN @ 6 m6 kN/m, 2–8 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)
6.Hard
w = 4 kN/mAB3 m7 m

The simply supported beam carries a uniformly distributed load over part of its span. Find the maximum bending moment Mmax in the beam.

L = 10 mw = 4 kN/m from 0 to 3 m
Mmax = kN·m

Answer key

  1. 1. Mx = 24 kN·m
  2. 2. Mx = 16 kN·m
  3. 3. Mx = −30 kN·m
  4. 4. Mmax = 142.5 kN·m
  5. 5. E (x = 8 m)
  6. 6. Mmax = 13 kN·m

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