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 = 1.5 mE = 200 GPa (steel)b × h = 20 × 100 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 = 1 mE = 70 GPa (aluminium)d = 30 mm

P_cr = kN

3.Medium

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 P_cr.

L = 4 mE = 200 GPa (steel)b × h = 30 × 50 mm

P_cr = kN

4.Medium

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

L = 4 mE = 70 GPa (aluminium)d = 50 mm

P_cr = kN

5.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 = 5 mE = 200 GPa (steel)d = 40 mm

σ_cr = MPa

6.Hard

A solid round column of length L made of steel is fixed at the base and pinned at the top. It must carry 45 kN with a factor of safety of 2.5 against buckling. Find the smallest diameter d.

P = 45 kNn = 2.5L = 3 mE = 200 GPa (steel)

d = mm

Answer key

1. P_cr = 58.49 kN
2. P_cr = 27.47 kN
3. P_cr = 3.47 kN
4. P_cr = 52.99 kN
5. σ_cr = 1.974 MPa
6. d = 47.57 mm

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