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 = 40 kNABsection3 m7 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 = 10 mP = 40 kN at 3 mx = 3 m
Mx = kN·m
2.Easy
P = 65 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 = 65 kN at 2 mx = 2 m
Mx = kN·m
3.Medium
4 kN/m10 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.

10 kN @ 6 m4 kN/m, 4–12 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)
4.Medium
w = 5 kN/mABsection0.5 m5.5 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 = 6 mw = 5 kN/m from 0 to 6 mx = 0.5 m
Vx = kN
5.Hard
w = 24 kN/mAB5 m1 m

The simply supported beam carries a uniformly distributed load over part of its span. Find the distance x0 from A to the section where the bending moment is largest.

L = 6 mw = 24 kN/m from 0 to 5 m
x0 = m
6.Hard
w = 4 kN/mP = 40 kNABsection2.5 m1.5 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 = 4 mP = 40 kN at 2.5 mw = 4 kN/m from 0 to 4 mx = 2.5 m
Mx = kN·m

Answer key

  1. 1. Mx = 84 kN·m
  2. 2. Mx = 86.67 kN·m
  3. 3. D (x = 6 m)
  4. 4. Vx = 12.5 kN
  5. 5. x0 = 2.917 m
  6. 6. Mx = 45 kN·m

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