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 = 15 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 = 15 kN at 2.5 mx = 2.5 m
Mx = kN·m
2.Easy
10 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 @ 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)
3.Medium
w = 2 kN/mABsection2 m2 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 = 4 mw = 2 kN/m from 0 to 4 mx = 2 m
Mx = kN·m
4.Medium
P1​ = 20 kNP2​ = 20 kNAB3 m4 m1 m

The simply supported beam carries two point loads. Find the maximum bending moment Mmax in the beam.

L = 8 mP1 = 20 kN at 3 mP2 = 20 kN at 7 m
Mmax = kN·m
5.Hard
w = 2 kN/mP = 50 kNABsection4 m2 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 = 6 mP = 50 kN at 4 mw = 2 kN/m from 0 to 6 mx = 4 m
Mx = kN·m
6.Hard
w = 3 kN/mP = 40 kNABsection1.5 m2.5 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 = 4 mP = 40 kN at 1.5 mw = 3 kN/m from 0 to 4 mx = 1.5 m
Mx = kN·m

Answer key

  1. 1. Mx = 14.06 kN·m
  2. 2. C (x = 4 m)
  3. 3. Mx = 4 kN·m
  4. 4. Mmax = 45 kN·m
  5. 5. Mx = 74.67 kN·m
  6. 6. Mx = 43.13 kN·m

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