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 = 25 kNAB2 m6 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 2 m
Vx = kN
2.Easy
P = 65 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 = 65 kN at 2 mx = 2 m
Mx = kN·m
3.Medium
M0​ = 15 kN·mAB3 m1 m

The simply supported beam carries a clockwise couple M0 = 15 kN·m at x = 3 m from A, and no other load. Find the bending moment Mx just to the left of the couple. Use sagging moments positive and upward shear on the left face positive.

L = 4 mM0 = 15 kN·m clockwise, at 3 m
Mx = kN·m
4.Medium
P1​ = 65 kNP2​ = 45 kNABC5 m3 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. It carries a point load P1 between the supports and a point load P2 at C. Find the bending moment MB at support B. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP1 = 65 kN at 5 mP2 = 45 kN at 10 msupports at x = 0 and x = 8 m
MB = kN·m
5.Hard
w = 4 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 = 4 kN/m from 0 to 5.5 msupports at x = 0 and x = 4 m
Mmax = kN·m
6.Hard
w = 10 kN/mAB1 m3 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 = 4 mw = 10 kN/m from 1 to 4 m
Mmax = kN·m

Answer key

  1. 1. Vx = −6.25 kN
  2. 2. Mx = 65 kN·m
  3. 3. Mx = −11.25 kN·m
  4. 4. MB = −90 kN·m
  5. 5. Mmax = 5.908 kN·m
  6. 6. Mmax = 17.58 kN·m

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