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 = 55 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 = 55 kN at 2.5 mx = 2.5 m
Mx = kN·m
2.Easy
12 kN/mABCDEFG1 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.

12 kN/m, 0–6 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)
3.Medium
w = 12 kN/mABsection5.5 m2.5 m

Find the shear force Vx at the section x = 5.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mw = 12 kN/m from 0 to 8 mx = 5.5 m
Vx = kN
4.Medium
w = 12 kN/mABsection0.5 m4.5 m

Find the shear force Vx at the section x = 0.5 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 = 0.5 m
Vx = kN
5.Hard
w = 8 kN/mP = 50 kNABsection4 m1 m

Find the bending moment Mx at the section x = 4 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP = 50 kN at 4 mw = 8 kN/m from 0 to 5 mx = 4 m
Mx = kN·m
6.Hard
w = 2 kN/mP = 30 kNABsection1 m2.5 m0.5 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 = 4 mP = 30 kN at 1 mw = 2 kN/m from 0 to 4 mx = 3.5 m
Mx = kN·m

Answer key

  1. 1. Mx = 80.21 kN·m
  2. 2. A (x = 0 m)
  3. 3. Vx = −18 kN
  4. 4. Vx = 24 kN
  5. 5. Mx = 56 kN·m
  6. 6. Mx = 5.5 kN·m

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