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
60 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.

60 kN @ 8 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 = 30 kNABsection2 m8 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 = 10 mP = 30 kN at 2 mx = 2 m
Mx = kN·m
3.Medium
P1​ = 65 kNP2​ = 20 kNABC1 m7 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 = 65 kN at 1 mP2 = 20 kN at 9 msupports at x = 0 and x = 8 m
Mx = kN·m
4.Medium
M0​ = 45 kN·mAB6 m2 m

The simply supported beam carries a clockwise couple M0 = 45 kN·m at x = 6 m from A, and no other load. Find the bending moment Mx just to the right of the couple. Use sagging moments positive and upward shear on the left face positive.

L = 8 mM0 = 45 kN·m clockwise, at 6 m
Mx = kN·m
5.Hard
w = 8 kN/mAB4 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 = 5 mw = 8 kN/m from 0 to 4 m
x0 = m
6.Hard
w = 20 kN/mAB1 m4 m

The simply supported beam carries a uniformly distributed load over part of its span. Find the maximum bending moment Mmax in the beam.

L = 5 mw = 20 kN/m from 1 to 5 m
Mmax = kN·m

Answer key

  1. 1. E (x = 8 m)
  2. 2. Mx = 48 kN·m
  3. 3. Mx = 54.38 kN·m
  4. 4. Mx = 11.25 kN·m
  5. 5. x0 = 2.4 m
  6. 6. Mmax = 57.6 kN·m

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