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 = 6 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 = 6 kN/m from 0 to 5 m
Mmax = kN·m
2.Easy
45 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.

45 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
P1​ = 55 kNP2​ = 45 kNABC1.5 m3.5 m1 m

The beam rests on a pin at A and a roller at B and overhangs B by 1 m to the free end C. It carries a point load P1 between the supports and a point load P2 at C. Find the shear force Vx just to the left of support B. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP1 = 55 kN at 1.5 mP2 = 45 kN at 6 msupports at x = 0 and x = 5 m
Vx = kN
4.Medium
w = 2 kN/mABsection2.5 m3.5 m

Find the shear force Vx at the section x = 2.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mw = 2 kN/m from 0 to 6 mx = 2.5 m
Vx = kN
5.Hard
w = 8 kN/mP = 20 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 = 20 kN at 1.5 mw = 8 kN/m from 0 to 4 mx = 1.5 m
Mx = kN·m
6.Hard
w = 10 kN/mABC5 m1 m

The beam rests on a pin at A and a roller at B and overhangs B by 1 m to the free end C. A uniformly distributed load w acts over the whole length A–C. Find the maximum sagging bending moment Mmax between the supports.

L = 6 mw = 10 kN/m from 0 to 6 msupports at x = 0 and x = 5 m
Mmax = kN·m

Answer key

  1. 1. Mmax = 18.75 kN·m
  2. 2. C (x = 4 m)
  3. 3. Vx = −25.5 kN
  4. 4. Vx = 1 kN
  5. 5. Mx = 33.75 kN·m
  6. 6. Mmax = 28.8 kN·m

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