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 = 50 kNABsection4.5 m0.5 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 = 4.5 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP = 50 kN at 5 mx = 4.5 m
Mx = kN·m
2.Easy
P = 30 kNAB2 m6 m

The simply supported beam carries a single point load P. Find the shear force Vx just to the right of the load. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 30 kN at 2 m
Vx = kN
3.Medium
10 kN/m55 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.

55 kN @ 6 m10 kN/m, 0–12 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 = 4 kN/mABsection0.5 m7.5 m

Find the bending moment Mx at the section x = 0.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mw = 4 kN/m from 0 to 8 mx = 0.5 m
Mx = kN·m
5.Hard
w = 8 kN/mP = 35 kNABsection2 m3 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 = 5 mP = 35 kN at 2 mw = 8 kN/m from 0 to 5 mx = 2 m
Mx = kN·m
6.Hard
w = 8 kN/mP = 45 kNABsection5 m3 m

Find the bending moment Mx at the section x = 5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 45 kN at 5 mw = 8 kN/m from 0 to 8 mx = 5 m
Mx = kN·m

Answer key

  1. 1. Mx = −25 kN·m
  2. 2. Vx = −7.5 kN
  3. 3. D (x = 6 m)
  4. 4. Mx = 7.5 kN·m
  5. 5. Mx = 66 kN·m
  6. 6. Mx = 144.4 kN·m

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