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
20 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.

20 kN @ 3 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 = 60 kNAB4 m

The cantilever is fixed at A and carries a point load P at its free end B. Find the bending moment MA at the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 4 mP = 60 kN at 4 m
MA = kN·m
3.Medium
w = 12 kN/mABsection3.5 m1.5 m

Find the bending moment Mx at the section x = 3.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mw = 12 kN/m from 0 to 5 mx = 3.5 m
Mx = kN·m
4.Medium
w = 2 kN/mABsection1.5 m3.5 m

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

L = 5 mw = 2 kN/m from 0 to 5 mx = 1.5 m
Vx = kN
5.Hard
w = 3 kN/mP = 35 kNABsection4.5 m1.5 m

Find the bending moment Mx at the section x = 4.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 35 kN at 4.5 mw = 3 kN/m from 0 to 6 mx = 4.5 m
Mx = kN·m
6.Hard
w = 10 kN/mP = 50 kNABsection3 m1 m

Find the bending moment Mx at the section x = 3 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 4 mP = 50 kN at 3 mw = 10 kN/m from 0 to 4 mx = 3 m
Mx = kN·m

Answer key

  1. 1. A (x = 0 m)
  2. 2. MA = −240 kN·m
  3. 3. Mx = 31.5 kN·m
  4. 4. Vx = 2 kN
  5. 5. Mx = 49.5 kN·m
  6. 6. Mx = 52.5 kN·m

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