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)d = 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 = 2 mE = 70 GPa (aluminium)b × h = 30 × 50 mm

P_cr = kN

3.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 = 6 mE = 200 GPa (steel)b × h = 20 × 80 mm

P_cr = kN

4.Medium

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

L = 2.5 mE = 200 GPa (steel)d = 50 mm

P_cr = kN

5.Hard

A solid round column of length L made of aluminium is fixed at both ends. It must carry 105 kN with a factor of safety of 2 against buckling. Find the smallest diameter d.

P = 105 kNn = 2L = 5 mE = 70 GPa (aluminium)

d = mm

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 against buckling. Find the smallest diameter d.

P = 45 kNn = 2L = 6 mE = 200 GPa (steel)

d = mm

Answer key

1. P_cr = 269.2 kN
2. P_cr = 19.43 kN
3. P_cr = 5.968 kN
4. P_cr = 387.6 kN
5. d = 78.87 mm
6. d = 63.62 mm

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