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.

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1.Easy
PL = 2.5 m40 × 60 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 = 2.5 mE = 70 GPa (aluminium)b × h = 40 × 60 mm
Pcr = kN
2.Easy
PL = 5 md = 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 = 5 mE = 200 GPa (steel)d = 80 mm
Pcr = kN
3.Medium
PL = 1 md = 20 mmcross-section

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

L = 1 mE = 200 GPa (steel)d = 20 mm
Pcr = kN
4.Medium
PL = 2.5 m30 × 100 mmcross-section

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

L = 2.5 mE = 200 GPa (steel)b × h = 30 × 100 mm
Pcr = kN
5.Hard
P = 40 kNL = 1 md = ?cross-section

A solid round column of length L made of aluminium is fixed at the base and free at the top. It must carry 40 kN with a factor of safety of 3 against buckling. Find the smallest diameter d.

P = 40 kNn = 3L = 1 mE = 70 GPa (aluminium)
d = mm
6.Hard
PL = 2.5 md = 30 mmcross-section

A column of length L made of steel is pinned at both ends. Find its slenderness and the critical buckling stress σcr from Euler’s formula.

L = 2.5 mE = 200 GPa (steel)d = 30 mm
σcr = MPa

Answer key

  1. 1. Pcr = 35.37 kN
  2. 2. Pcr = 158.8 kN
  3. 3. Pcr = 3.876 kN
  4. 4. Pcr = 284.2 kN
  5. 5. d = 61.34 mm
  6. 6. σcr = 17.77 MPa

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