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 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.

30 kN @ 4 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 = 4 kN/mAB8 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 = 8 mw = 4 kN/m from 0 to 8 m
Mmax = kN·m
3.Medium
w = 5 kN/mABsection3.5 m0.5 m

Find the shear force Vx at the section x = 3.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 4 mw = 5 kN/m from 0 to 4 mx = 3.5 m
Vx = kN
4.Medium
w = 2 kN/mABsection4 m1 m

Find the bending moment Mx at the section x = 4 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 = 4 m
Mx = kN·m
5.Hard
w = 8 kN/mP = 55 kNABsection2 m1 m2 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 = 5 mP = 55 kN at 2 mw = 8 kN/m from 0 to 5 mx = 3 m
Mx = kN·m
6.Hard
w = 4 kN/mP = 10 kNABsection1.5 m3.5 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 = 5 mP = 10 kN at 1.5 mw = 4 kN/m from 0 to 5 mx = 1.5 m
Mx = kN·m

Answer key

  1. 1. E (x = 4 m)
  2. 2. Mmax = 32 kN·m
  3. 3. Vx = −7.5 kN
  4. 4. Mx = 4 kN·m
  5. 5. Mx = 68 kN·m
  6. 6. Mx = 21 kN·m

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