A pinned steel strut of diameter and length has an Euler buckling load

PHYSICS · Multi-part · 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

A pinned steel strut of diameter d=12 mmd = 12\,\mathrm{mm} and length L=0.90 mL = 0.90\,\mathrm{m} has an Euler buckling load Pcr,1P_{\rm cr,1}. A second strut of the same material and length is made with its diameter doubled to 24 mm24\,\mathrm{mm}. ((a)) By what factor does PcrP_{\rm cr} increase? ((b)) By what factor does the slenderness ratio λs\lambda_s change? ((c)) Separately, a tree trunk of diameter d=0.40 md = 0.40\,\mathrm{m}, made of the same wood throughout, has a self-weight buckling height Lc,1L_{c,1}. A second trunk of the same wood is twice as thick, 0.80 m0.80\,\mathrm{m} in diameter. By what factor does the self-weight buckling height increase?

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