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
w = 10 kN/mAB10 m

The simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum bending moment Mmax in the beam.

L = 10 mw = 10 kN/m from 0 to 10 m
Mmax = kN·m
2.Easy
15 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.

15 kN @ 8 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)
3.Medium
w = 2 kN/mABsection2 m3 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 = 5 mw = 2 kN/m from 0 to 5 mx = 2 m
Mx = kN·m
4.Medium
w = 5 kN/mABsection1 m5 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 = 6 mw = 5 kN/m from 0 to 6 mx = 1 m
Mx = kN·m
5.Hard
w = 5 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 = 5 kN/m from 0 to 9 msupports at x = 0 and x = 8 m
MB = kN·m
6.Hard
w = 5 kN/mABC5 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 bending moment MB at support B. Use sagging moments positive and upward shear on the left face positive.

L = 6.5 mw = 5 kN/m from 0 to 6.5 msupports at x = 0 and x = 5 m
MB = kN·m

Answer key

  1. 1. Mmax = 125 kN·m
  2. 2. A (x = 0 m)
  3. 3. Mx = 6 kN·m
  4. 4. Mx = 12.5 kN·m
  5. 5. MB = −2.5 kN·m
  6. 6. MB = −5.625 kN·m

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