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Calculate the Euler's limiting value of slenderness ratio for which it is not valid for long columns.Take $E=2 \times 10^{5}MPa, \sigma_{c}=320 N/mm^{2}$
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$$ \begin{array}{l}{\text { Data: } E=2 \times 10^{5} \mathrm{MPa}, \quad \sigma_{\mathrm{c}}=320 \mathrm{N} / \mathrm{mm}^{2}} \ {\text { Find: } \lambda_{\text {limiting }}} \ {\text { For long column, Euler's formula, }} \ {\quad \mathrm{P}_{\mathrm{E}}=\frac{\pi^{2} \text { EImin }}{\left(\mathrm{L}_{\mathrm{c}}\right)^{2}}}\end{array} $$ $$ \begin{array}{l}{\text { But } \mathrm{K}=\sqrt{\frac{\mathrm{I}}{\mathrm{A}}}} \ {\mathrm{K}^{2}=\frac{\mathrm{I}}{\mathrm{A}}} \ {\mathrm{I}=\mathrm{AK}^{2}} \ …

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