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
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)
2.Easy
P = 80 kNAB4 m4 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 = 80 kN at 4 m
Vx = kN
3.Medium
w = 5 kN/mABsection3.5 m2.5 m

Find the bending moment Mx at the section x = 3.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mw = 5 kN/m from 0 to 6 mx = 3.5 m
Mx = kN·m
4.Medium
P1​ = 15 kNP2​ = 15 kNABC2.5 m1.5 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 shear force Vx just to the left of support B. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP1 = 15 kN at 2.5 mP2 = 15 kN at 5 msupports at x = 0 and x = 4 m
Vx = kN
5.Hard
w = 8 kN/mP = 40 kNABsection6 m1 m3 m

Find the bending moment Mx at the section x = 6 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 40 kN at 7 mw = 8 kN/m from 0 to 10 mx = 6 m
Mx = kN·m
6.Hard
w = 4 kN/mP = 30 kNAB3 m1 m

The simply supported beam carries a uniformly distributed load w over its whole span and a point load P. Find the maximum bending moment Mmax in the beam.

L = 4 mP = 30 kN at 3 mw = 4 kN/m from 0 to 4 m
Mmax = kN·m

Answer key

  1. 1. D (x = 3 m)
  2. 2. Vx = 40 kN
  3. 3. Mx = 21.88 kN·m
  4. 4. Vx = −13.13 kN
  5. 5. Mx = 168 kN·m
  6. 6. Mmax = 28.5 kN·m

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