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 = 1.5 m25 × 50 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 = 1.5 mE = 70 GPa (aluminium)b × h = 25 × 50 mm
Pcr = kN
2.Easy
PL = 3 md = 25 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 = 3 mE = 200 GPa (steel)d = 25 mm
Pcr = kN
3.Medium
PL = 2.5 m40 × 50 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 = 2.5 mE = 70 GPa (aluminium)b × h = 40 × 50 mm
Pcr = kN
4.Medium
PL = 1.5 m25 × 50 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 = 1.5 mE = 200 GPa (steel)b × h = 25 × 50 mm
Pcr = kN
5.Hard
P = 130 kNL = 4 md = ?cross-section

A solid round column of length L made of aluminium is pinned at both ends. It must carry 130 kN with a factor of safety of 2.5 against buckling. Find the smallest diameter d.

P = 130 kNn = 2.5L = 4 mE = 70 GPa (aluminium)
d = mm
6.Hard
PL = 6 md = 60 mmcross-section

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

L = 6 mE = 200 GPa (steel)d = 60 mm
σcr = MPa

Answer key

  1. 1. Pcr = 19.99 kN
  2. 2. Pcr = 4.205 kN
  3. 3. Pcr = 117.9 kN
  4. 4. Pcr = 228.5 kN
  5. 5. d = 111.3 mm
  6. 6. σcr = 49.35 MPa

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