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 = 15 kNABsection1 m4 m

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

L = 5 mP = 15 kN at 1 mx = 1 m
Mx = kN·m
2.Easy
P = 75 kNABsection1.5 m4.5 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 = 6 mP = 75 kN at 1.5 mx = 1.5 m
Mx = kN·m
3.Medium
15 kN20 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.

15 kN @ 1 m20 kN @ 4 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)
4.Medium
P1​ = 80 kNP2​ = 80 kNABC3.5 m2.5 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 bending moment Mx under the load P1. Use sagging moments positive and upward shear on the left face positive.

L = 7 mP1 = 80 kN at 3.5 mP2 = 80 kN at 7 msupports at x = 0 and x = 6 m
Mx = kN·m
5.Hard
w = 4 kN/mABC4 m2 m

The beam rests on a pin at A and a roller at B and overhangs B by 2 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 = 4 kN/m from 0 to 6 msupports at x = 0 and x = 4 m
Mmax = kN·m
6.Hard
w = 6 kN/mP = 15 kNABsection2.5 m0.5 m3 m

Find the bending moment Mx at the section x = 3 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 15 kN at 2.5 mw = 6 kN/m from 0 to 6 mx = 3 m
Mx = kN·m

Answer key

  1. 1. Mx = 12 kN·m
  2. 2. Mx = 84.38 kN·m
  3. 3. E (x = 4 m)
  4. 4. Mx = 70 kN·m
  5. 5. Mmax = 4.5 kN·m
  6. 6. Mx = 45.75 kN·m

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