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

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

L = 3 mE = 200 GPa (steel)b × h = 40 × 50 mm

P_cr = kN

2.Easy

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

L = 6 mE = 70 GPa (aluminium)d = 40 mm

P_cr = kN

3.Medium

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

L = 4 mE = 70 GPa (aluminium)b × h = 20 × 60 mm

P_cr = kN

4.Medium

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 P_cr.

L = 1.5 mE = 200 GPa (steel)b × h = 30 × 60 mm

P_cr = kN

5.Hard

A solid round column of length L made of steel is pinned at both ends. It must carry 135 kN with a factor of safety of 2.5 against buckling. Find the smallest diameter d.

P = 135 kNn = 2.5L = 2.5 mE = 200 GPa (steel)

d = mm

6.Hard

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

L = 1.5 mE = 200 GPa (steel)d = 40 mm

σ_cr = MPa

Answer key

1. P_cr = 58.49 kN
2. P_cr = 2.412 kN
3. P_cr = 3.525 kN
4. P_cr = 241.7 kN
5. d = 68.31 mm
6. σ_cr = 21.93 MPa

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