Estimate, to the nearest metre, the greatest height a uniform bamboo culm could reach…

PHYSICS · Subjective · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Buckling, plates and elastic foundations

Problem

Estimate, to the nearest metre, the greatest height a uniform bamboo culm could reach before it buckles under its own weight alone. Take the fresh bamboo fibre as an elastic solid with

E = 20\,\mathrm{GPa}

and density

\rho = 700\,\mathrm{kg\,m^{-3}}

, model the culm as a uniform solid circular column of diameter

d = 0.12\,\mathrm{m}

that is clamped at its base and free at its top, and use

g = 9.8\,\mathrm{m\,s^{-2}}

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