A pinned strut of solid circular cross-section

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 strut of solid circular cross-section, diameter d=30 mmd = 30\,\mathrm{mm}, is machined from 6061-T6 aluminium alloy (E=69 GPaE = 69\,\mathrm{GPa}, tensile yield stress σY=276 MPa\sigma_Y = 276\,\mathrm{MPa}). ((a)) Find the slenderness ratio λs\lambda_s at which the Euler buckling stress equals the yield stress, and the pinned length LcL_c of this rod at which that changeover occurs. ((b)) The rod is actually L=0.6 mL = 0.6\,\mathrm{m} long. Compute its slenderness ratio, its Euler buckling load and its yield load, and state which failure mode governs.

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