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 = 70 kNAB3 m1 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 = 4 mP = 70 kN at 3 m
Vx = kN
2.Easy
P = 25 kNAB1 m7 m

The simply supported beam carries a single point load P. Find the shear force Vx just to the right of the load. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 25 kN at 1 m
Vx = kN
3.Medium
w = 2 kN/mABsection3.5 m1.5 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 = 5 mw = 2 kN/m from 0 to 5 mx = 3.5 m
Mx = kN·m
4.Medium
15 kN/m55 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.

55 kN @ 3 m15 kN/m, 0–6 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)
5.Hard
w = 2 kN/mABC4 m1.5 m

The beam rests on a pin at A and a roller at B and overhangs B by 1.5 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 = 5.5 mw = 2 kN/m from 0 to 5.5 msupports at x = 0 and x = 4 m
Mmax = kN·m
6.Hard
w = 5 kN/mP = 50 kNABsection4 m1 m5 m

Find the bending moment Mx at the section x = 4 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 50 kN at 5 mw = 5 kN/m from 0 to 10 mx = 4 m
Mx = kN·m

Answer key

  1. 1. Vx = 17.5 kN
  2. 2. Vx = −3.125 kN
  3. 3. Mx = 5.25 kN·m
  4. 4. D (x = 3 m)
  5. 5. Mmax = 2.954 kN·m
  6. 6. Mx = 160 kN·m

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