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
15 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.

15 kN @ 10 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)
2.Easy
P = 70 kNAB2 m

The cantilever is fixed at A and carries a point load P at its free end B. Find the bending moment MA at the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 2 mP = 70 kN at 2 m
MA = kN·m
3.Medium
w = 4 kN/mABsection2.5 m2.5 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 = 5 mw = 4 kN/m from 0 to 5 mx = 2.5 m
Mx = kN·m
4.Medium
w = 2 kN/mABsection1 m9 m

Find the shear force Vx at the section x = 1 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mw = 2 kN/m from 0 to 10 mx = 1 m
Vx = kN
5.Hard
w = 6 kN/mP = 30 kNABsection5 m0.5 m2.5 m

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

L = 8 mP = 30 kN at 5 mw = 6 kN/m from 0 to 8 mx = 5.5 m
Mx = kN·m
6.Hard
w = 8 kN/mABC6 m2.5 m

The beam rests on a pin at A and a roller at B and overhangs B by 2.5 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 = 8.5 mw = 8 kN/m from 0 to 8.5 msupports at x = 0 and x = 6 m
Mmax = kN·m

Answer key

  1. 1. F (x = 10 m)
  2. 2. MA = −140 kN·m
  3. 3. Mx = 12.5 kN·m
  4. 4. Vx = 8 kN
  5. 5. Mx = 88.13 kN·m
  6. 6. Mmax = 24.59 kN·m

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