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 = 25 kNABsection2 m4 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 = 6 mP = 25 kN at 2 mx = 2 m
Mx = kN·m
2.Easy
P = 15 kNABsection2.5 m3.5 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 = 6 mP = 15 kN at 2.5 mx = 2.5 m
Mx = kN·m
3.Medium
M0​ = 20 kN·mAB2.5 m2.5 m

The simply supported beam carries a clockwise couple M0 = 20 kN·m at x = 2.5 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 = 5 mM0 = 20 kN·m clockwise, at 2.5 m
Mx = kN·m
4.Medium
M0​ = 15 kN·mAB1 m7 m

The simply supported beam carries a clockwise couple M0 = 15 kN·m at x = 1 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 = 8 mM0 = 15 kN·m clockwise, at 1 m
Mx = kN·m
5.Hard
4 kN/m55 kN50 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.

55 kN @ 0 m50 kN @ 12 m4 kN/m, 2–10 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 = 8 kN/mAB5 m2 m1 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 = 8 mw = 8 kN/m from 5 to 7 m
Mmax = kN·m

Answer key

  1. 1. Mx = 33.33 kN·m
  2. 2. Mx = 21.88 kN·m
  3. 3. Mx = −10 kN·m
  4. 4. Mx = −1.875 kN·m
  5. 5. B (x = 2 m)
  6. 6. Mmax = 21 kN·m

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