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 @ 5 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 = 40 kNABsection8 m2 m

Find the bending moment Mx at the section x = 8 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 40 kN at 8 mx = 8 m
Mx = kN·m
3.Medium
P1​ = 65 kNP2​ = 20 kNABC4 m1 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 = 7 mP1 = 65 kN at 4 mP2 = 20 kN at 7 msupports at x = 0 and x = 5 m
MB = kN·m
4.Medium
M0​ = 35 kN·mAB2 m8 m

The simply supported beam carries a clockwise couple M0 = 35 kN·m at x = 2 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 = 10 mM0 = 35 kN·m clockwise, at 2 m
Mx = kN·m
5.Hard
w = 2 kN/mABC8 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 distance xc from A to the point of contraflexure between the supports (where the bending moment changes sign).

L = 9.5 mw = 2 kN/m from 0 to 9.5 msupports at x = 0 and x = 8 m
xc = m
6.Hard
w = 8 kN/mABC8 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. 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 = 9 mw = 8 kN/m from 0 to 9 msupports at x = 0 and x = 8 m
MB = kN·m

Answer key

  1. 1. F (x = 5 m)
  2. 2. Mx = 64 kN·m
  3. 3. MB = −40 kN·m
  4. 4. Mx = 28 kN·m
  5. 5. xc = 7.719 m
  6. 6. MB = −4 kN·m

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