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 = 50 kNABsection9 m1 m

Find the bending moment Mx at the section x = 9 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 50 kN at 9 mx = 9 m
Mx = kN·m
2.Easy
P = 45 kNABsection2.5 m3.5 m

Find the bending moment Mx at the section x = 2.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 45 kN at 2.5 mx = 2.5 m
Mx = kN·m
3.Medium
5 kN/m40 kNABCDEFG2 m2 m2 m2 m2 m2 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.

40 kN @ 4 m5 kN/m, 0–12 m
  1. 1A (x = 0 m)
  2. 2B (x = 2 m)
  3. 3C (x = 4 m)
  4. 4D (x = 6 m)
  5. 5E (x = 8 m)
  6. 6F (x = 10 m)
  7. 7G (x = 12 m)
4.Medium
M0​ = 10 kN·mAB1.5 m2.5 m

The simply supported beam carries a clockwise couple M0 = 10 kN·m at x = 1.5 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 = 10 kN·m clockwise, at 1.5 m
Mx = kN·m
5.Hard
w = 12 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 distance xc from A to the point of contraflexure between the supports (where the bending moment changes sign).

L = 5.5 mw = 12 kN/m from 0 to 5.5 msupports at x = 0 and x = 4 m
xc = m
6.Hard
w = 16 kN/mAB3 m2 m1 m

The simply supported beam carries a uniformly distributed load over part of its span. Find the distance x0 from A to the section where the bending moment is largest.

L = 6 mw = 16 kN/m from 3 to 5 m
x0 = m

Answer key

  1. 1. Mx = 45 kN·m
  2. 2. Mx = 65.63 kN·m
  3. 3. C (x = 4 m)
  4. 4. Mx = 6.25 kN·m
  5. 5. xc = 3.438 m
  6. 6. x0 = 3.667 m

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