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 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.

40 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 = 80 kNABsection1.5 m3.5 m

Find the bending moment Mx at the section x = 1.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP = 80 kN at 1.5 mx = 1.5 m
Mx = kN·m
3.Medium
w = 3 kN/mABsection0.5 m3.5 m

Find the bending moment Mx at the section x = 0.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 4 mw = 3 kN/m from 0 to 4 mx = 0.5 m
Mx = kN·m
4.Medium
M0​ = 50 kN·mAB9 m1 m

The simply supported beam carries a clockwise couple M0 = 50 kN·m at x = 9 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 9 m
Mx = kN·m
5.Hard
w = 4 kN/mP = 45 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 = 45 kN at 2.5 mw = 4 kN/m from 0 to 6 mx = 2.5 m
Mx = kN·m
6.Hard
w = 4 kN/mP = 35 kNABsection1 m5 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 = 10 mP = 35 kN at 6 mw = 4 kN/m from 0 to 10 mx = 1 m
Mx = kN·m

Answer key

  1. 1. E (x = 4 m)
  2. 2. Mx = 84 kN·m
  3. 3. Mx = 2.625 kN·m
  4. 4. Mx = −45 kN·m
  5. 5. Mx = 83.13 kN·m
  6. 6. Mx = 32 kN·m

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