The two steel channels are to be laced together to form a 30 -ft-long bridge column assumed to be pin connected at its ends. Each channel has a cross-sectional area of \(A=3.10 \mathrm{in}^{2}\) and moments of inertia \(I_{x}=55.4 \mathrm{in}^{4}, I_{y}=0.382 \mathrm{in}^{4}\). The centroid \(C\) of its area is located in the figure. Determine the proper distance \(d\) between the centroids of the channels so that buckling can occur about the \(x-x\) and \(y^{\prime}-y^{\prime}\) axes due to the same load. What is the value of this critical load? Neglect the effect of the lacing. Take \(E_{\mathrm{st}}=29\left(10^{3}\right) \mathrm{ksi}, \sigma_{Y}=50 \mathrm{ksi}\).

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MA 0.269 in.. 1.231 in. x C x y -d