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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
30 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.

30 kN @ 2 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)
2.Easy
P = 20 kNABsection3 m3 m

Find the bending moment Mx at the section x = 3 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 20 kN at 3 mx = 3 m
Mx = kN·m
3.Medium
w = 6 kN/mP = 55 kNABsection1.5 m0.5 m2 m

The cantilever is fixed at A. It carries a uniformly distributed load w over its whole length and a point load P at 2 m from A. Find the bending moment Mx at the section x = 1.5 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 4 mP = 55 kN at 2 mw = 6 kN/m from 0 to 4 mx = 1.5 m
Mx = kN·m
4.Medium
w = 12 kN/mABsection1 m9 m

Find the bending moment Mx at the section x = 1 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mw = 12 kN/m from 0 to 10 mx = 1 m
Mx = kN·m
5.Hard
w = 6 kN/mABC5 m2.5 m

The beam rests on a pin at A and a roller at B and overhangs B by 2.5 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 = 7.5 mw = 6 kN/m from 0 to 7.5 msupports at x = 0 and x = 5 m
MB = kN·m
6.Hard
w = 10 kN/mP = 50 kNAB1 m3 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 = 50 kN at 1 mw = 10 kN/m from 0 to 4 m
Mmax = kN·m

Answer key

  1. 1. B (x = 2 m)
  2. 2. Mx = 30 kN·m
  3. 3. Mx = −46.25 kN·m
  4. 4. Mx = 54 kN·m
  5. 5. MB = −18.75 kN·m
  6. 6. Mmax = 52.5 kN·m

Full step-by-step solutions: practise this topic on examproblems.com.