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 = 4 m50 × 80 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 = 50 × 80 mm
Pcr = kN
2.Easy
PL = 6 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 = 6 mE = 70 GPa (aluminium)b × h = 40 × 100 mm
Pcr = kN
3.Medium
PL = 3 md = 50 mmcross-section

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

L = 3 mE = 200 GPa (steel)d = 50 mm
Pcr = kN
4.Medium
PL = 1 md = 40 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 = 1 mE = 70 GPa (aluminium)d = 40 mm
Pcr = kN
5.Hard
PL = 1.5 md = 20 mmcross-section

A column of length L made of aluminium is fixed at the base and pinned at the top. Find its slenderness and the critical buckling stress σcr from Euler’s formula.

L = 1.5 mE = 70 GPa (aluminium)d = 20 mm
σcr = MPa
6.Hard
P = 85 kNL = 4 md = ?cross-section

A solid round column of length L made of aluminium is fixed at the base and pinned at the top. It must carry 85 kN with a factor of safety of 3 against buckling. Find the smallest diameter d.

P = 85 kNn = 3L = 4 mE = 70 GPa (aluminium)
d = mm

Answer key

  1. 1. Pcr = 102.8 kN
  2. 2. Pcr = 10.24 kN
  3. 3. Pcr = 137.3 kN
  4. 4. Pcr = 21.7 kN
  5. 5. σcr = 15.67 MPa
  6. 6. d = 87.62 mm

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