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
30 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.

30 kN @ 4 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 = 40 kNABsection3 m2 m

The cantilever is fixed at A and carries a point load P at its free end B. Find the bending moment Mx at the section x = 3 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP = 40 kN at 5 mx = 3 m
Mx = kN·m
3.Medium
M0​ = 55 kN·mAB1 m4 m

The simply supported beam carries a clockwise couple M0 = 55 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 = 5 mM0 = 55 kN·m clockwise, at 1 m
Mx = kN·m
4.Medium
w = 4 kN/mABsection6 m4 m

Find the shear force Vx at the section x = 6 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mw = 4 kN/m from 0 to 10 mx = 6 m
Vx = kN
5.Hard
w = 10 kN/mP = 50 kNABsection1 m1 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 = 50 kN at 1 mw = 10 kN/m from 0 to 6 mx = 2 m
Mx = kN·m
6.Hard
w = 4 kN/mP = 10 kNABsection2.5 m1.5 m1 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 = 5 mP = 10 kN at 4 mw = 4 kN/m from 0 to 5 mx = 2.5 m
Mx = kN·m

Answer key

  1. 1. C (x = 4 m)
  2. 2. Mx = −80 kN·m
  3. 3. Mx = −11 kN·m
  4. 4. Vx = −4 kN
  5. 5. Mx = 73.33 kN·m
  6. 6. Mx = 17.5 kN·m

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