The uniform brass bar AB has a rectangular cross section and is supported by pins and brackets as shown. Each end of the bar can rotate freely about a horizontal axis through the pin. but rotation about a vertical axis is prevented by the brackets. $($a$)$ Determine the ratio b$/$d for which the factor of safety is the same about the horizontal and vertical axes. $($b$)$ Determine the factor of safety if $P=1\mathrm{.}8$kips.$L=7ft.d=1\mathrm{.}5in.$ and $E=15\mathrm{.}06.$

Step $1$: Write what is known using the consistent units

Step $2$: Calculate Pcrh for buckling in horizontal plane knowing that Le$=0\mathrm{.}5$L and $lh=d^{**}\frac{b^3}{12}$

Step $3$: Calculate Pcrv for buckling in vertical plane knowing that Le$=$L and $Iv=b^{**}\frac{d^3}{12}$

Step $4$: Find b if Pcrh$=$Pcrv

Step $5$: Find Factor of Safety knowing that $FS=Pc\frac{r}{P}$