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
w = 10 kN/mAB5 m

The simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum bending moment Mmax in the beam.

L = 5 mw = 10 kN/m from 0 to 5 m
Mmax = kN·m
2.Easy
P = 35 kNAB3.5 m2.5 m

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

L = 6 mP = 35 kN at 3.5 m
Vx = kN
3.Medium
w = 3 kN/mABsection0.5 m4.5 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 = 5 mw = 3 kN/m from 0 to 5 mx = 0.5 m
Mx = kN·m
4.Medium
45 kN45 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.

45 kN @ 2 m45 kN @ 5 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)
5.Hard
w = 3 kN/mP = 10 kNABsection6 m3.5 m0.5 m

Find the bending moment Mx at the section x = 9.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 10 kN at 6 mw = 3 kN/m from 0 to 10 mx = 9.5 m
Mx = kN·m
6.Hard
w = 8 kN/mP = 55 kNABsection6 m2 m

Find the bending moment Mx at the section x = 6 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 55 kN at 6 mw = 8 kN/m from 0 to 8 mx = 6 m
Mx = kN·m

Answer key

  1. 1. Mmax = 31.25 kN·m
  2. 2. Vx = 14.58 kN
  3. 3. Mx = 3.375 kN·m
  4. 4. C (x = 2 m)
  5. 5. Mx = 10.13 kN·m
  6. 6. Mx = 130.5 kN·m

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