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
50 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.

50 kN @ 1 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
w = 10 kN/mAB2 m

The cantilever is fixed at A and carries a uniformly distributed load w over its whole length. Find the shear force VA at the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 2 mw = 10 kN/m from 0 to 2 m
VA = kN
3.Medium
M0​ = 30 kN·mAB1 m3 m

The simply supported beam carries a clockwise couple M0 = 30 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 = 30 kN·m clockwise, at 1 m
Mx = kN·m
4.Medium
w = 6 kN/mABsection1.5 m2.5 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 = 4 mw = 6 kN/m from 0 to 4 mx = 1.5 m
Mx = kN·m
5.Hard
w = 2 kN/mP = 30 kNABsection2.5 m1.5 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 = 4 mP = 30 kN at 2.5 mw = 2 kN/m from 0 to 4 mx = 2.5 m
Mx = kN·m
6.Hard
w = 8 kN/mAB1 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 = 4 mw = 8 kN/m from 1 to 3 m
x0 = m

Answer key

  1. 1. B (x = 1 m)
  2. 2. VA = 20 kN
  3. 3. Mx = 22.5 kN·m
  4. 4. Mx = 11.25 kN·m
  5. 5. Mx = 31.88 kN·m
  6. 6. x0 = 2 m

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