Column buckling worksheet with answers

Free printable Column buckling 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
PL = 3 m40 × 100 mmcross-section

A column of length L made of aluminium is pinned at both ends. Using Euler’s formula, find its critical buckling load Pcr.

L = 3 mE = 70 GPa (aluminium)b × h = 40 × 100 mm
Pcr = kN
2.Easy
PL = 4 m30 × 40 mmcross-section

A column of length L made of steel is pinned at both ends. Using Euler’s formula, find its critical buckling load Pcr.

L = 4 mE = 200 GPa (steel)b × h = 30 × 40 mm
Pcr = kN
3.Medium
PL = 2 md = 30 mmcross-section

A column of length L made of aluminium is fixed at both ends. Using Euler’s formula, find its critical buckling load Pcr.

L = 2 mE = 70 GPa (aluminium)d = 30 mm
Pcr = kN
4.Medium
PL = 5 md = 60 mmcross-section

A column of length L made of aluminium is fixed at the base and free at the top. Using Euler’s formula, find its critical buckling load Pcr.

L = 5 mE = 70 GPa (aluminium)d = 60 mm
Pcr = kN
5.Hard
P = 10 kNL = 1.5 md = ?cross-section

A solid round column of length L made of steel is pinned at both ends. It must carry 10 kN with a factor of safety of 2 against buckling. Find the smallest diameter d.

P = 10 kNn = 2L = 1.5 mE = 200 GPa (steel)
d = mm
6.Hard
P = 145 kNL = 6 md = ?cross-section

A solid round column of length L made of aluminium is pinned at both ends. It must carry 145 kN with a factor of safety of 3 against buckling. Find the smallest diameter d.

P = 145 kNn = 3L = 6 mE = 70 GPa (aluminium)
d = mm

Answer key

  1. 1. Pcr = 40.94 kN
  2. 2. Pcr = 11.1 kN
  3. 3. Pcr = 27.47 kN
  4. 4. Pcr = 4.395 kN
  5. 5. d = 26.11 mm
  6. 6. d = 146.6 mm

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