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 = 70 kNAB6 m2 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 = 8 mP = 70 kN at 6 m
Vx = kN
2.Easy
20 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.

20 kN @ 3 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)
3.Medium
P1​ = 25 kNP2​ = 10 kNAB2 m2 m1 m

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

L = 5 mP1 = 25 kN at 2 mP2 = 10 kN at 4 m
Mmax = kN·m
4.Medium
w = 5 kN/mABsection5.5 m2.5 m

Find the shear force Vx at the section x = 5.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mw = 5 kN/m from 0 to 8 mx = 5.5 m
Vx = kN
5.Hard
w = 3 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 = 3 kN/m from 0 to 6 msupports at x = 0 and x = 5 m
Mmax = kN·m
6.Hard
w = 6 kN/mP = 30 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 = 30 kN at 2 mw = 6 kN/m from 0 to 5 mx = 2 m
Mx = kN·m

Answer key

  1. 1. Vx = 17.5 kN
  2. 2. D (x = 3 m)
  3. 3. Mmax = 34 kN·m
  4. 4. Vx = −7.5 kN
  5. 5. Mmax = 8.64 kN·m
  6. 6. Mx = 54 kN·m

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