Find the error in the following working

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

Find the error in the following working. "A mild-steel strut is pinned at both ends, with diameter d=8 mmd = 8\,\mathrm{mm}, length L=1.2 mL = 1.2\,\mathrm{m} and yield stress σY=250 MPa\sigma_Y = 250\,\mathrm{MPa}. Since it is loaded axially in compression, it fails when the compressive stress reaches yield: Pcr=σYA=250×106×π4(0.008)2=12.6 kN.”P_{\rm cr} = \sigma_Y A = 250\times10^6\times\frac{\pi}{4}(0.008)^2 = 12.6\,\mathrm{kN}.\text{''} Take E=200 GPaE = 200\,\mathrm{GPa}, and give the correct buckling load.

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