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 m20 × 100 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 = 1 mE = 200 GPa (steel)b × h = 20 × 100 mm
Pcr = kN
2.Easy
PL = 5 m25 × 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 = 5 mE = 70 GPa (aluminium)b × h = 25 × 60 mm
Pcr = kN
3.Medium
PL = 6 md = 40 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 = 6 mE = 200 GPa (steel)d = 40 mm
Pcr = kN
4.Medium
PL = 3 m40 × 60 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)b × h = 40 × 60 mm
Pcr = kN
5.Hard
PL = 6 md = 50 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 = 6 mE = 200 GPa (steel)d = 50 mm
σcr = MPa
6.Hard
P = 50 kNL = 3 md = ?cross-section

A solid round column of length L made of steel is fixed at the base and pinned at the top. It must carry 50 kN with a factor of safety of 3 against buckling. Find the smallest diameter d.

P = 50 kNn = 3L = 3 mE = 200 GPa (steel)
d = mm

Answer key

  1. 1. Pcr = 131.6 kN
  2. 2. Pcr = 2.159 kN
  3. 3. Pcr = 27.56 kN
  4. 4. Pcr = 143.2 kN
  5. 5. σcr = 8.567 MPa
  6. 6. d = 51.12 mm

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