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 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.

60 kN @ 2 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 = 30 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 = 30 kN at 1.5 mx = 1.5 m
Mx = kN·m
3.Medium
M0​ = 45 kN·mAB1 m3 m

The simply supported beam carries a clockwise couple M0 = 45 kN·m at x = 1 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 = 4 mM0 = 45 kN·m clockwise, at 1 m
Mx = kN·m
4.Medium
P1​ = 60 kNP2​ = 25 kNABC1 m3 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 = 60 kN at 1 mP2 = 25 kN at 5 msupports at x = 0 and x = 4 m
Vx = kN
5.Hard
w = 6 kN/mP = 75 kNAB2 m2 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 = 75 kN at 2 mw = 6 kN/m from 0 to 4 m
Mmax = kN·m
6.Hard
w = 6 kN/mABC6 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. A uniformly distributed load w acts over the whole length A–C. Find the bending moment MB at support B. Use sagging moments positive and upward shear on the left face positive.

L = 8 mw = 6 kN/m from 0 to 8 msupports at x = 0 and x = 6 m
MB = kN·m

Answer key

  1. 1. C (x = 2 m)
  2. 2. Mx = 31.5 kN·m
  3. 3. Mx = 33.75 kN·m
  4. 4. Vx = −21.25 kN
  5. 5. Mmax = 87 kN·m
  6. 6. MB = −12 kN·m

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