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 = 75 kNABsection1.5 m3.5 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 = 5 mP = 75 kN at 1.5 mx = 1.5 m
Mx = kN·m
2.Easy
10 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.

10 kN @ 2 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
w = 8 kN/mABsection5.5 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 mw = 8 kN/m from 0 to 8 mx = 5.5 m
Mx = kN·m
4.Medium
P1​ = 55 kNP2​ = 20 kNABC4 m4 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 = 9 mP1 = 55 kN at 4 mP2 = 20 kN at 9 msupports at x = 0 and x = 8 m
Mx = kN·m
5.Hard
w = 20 kN/mAB5 m1 m

The simply supported beam carries a uniformly distributed load over part of its span. Find the distance x0 from A to the section where the bending moment is largest.

L = 6 mw = 20 kN/m from 0 to 5 m
x0 = m
6.Hard
w = 10 kN/mP = 15 kNABsection2 m2 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 = 4 mP = 15 kN at 2 mw = 10 kN/m from 0 to 4 mx = 2 m
Mx = kN·m

Answer key

  1. 1. Mx = 78.75 kN·m
  2. 2. B (x = 2 m)
  3. 3. Mx = 55 kN·m
  4. 4. Mx = 100 kN·m
  5. 5. x0 = 2.917 m
  6. 6. Mx = 35 kN·m

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