$1.($Problem $6-14,$ Shigley$)$

This problem illustrates that the factor of safety for a machine element depends on the particular point selected for analysis. Here you are to compute factors of safety, based upon the distortionenergy theory, for stress elements at $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ of the member shown in the figure. This bar is made of AISI $1006$ cold$-$drawn steel and is loaded by the forces $\backslash ($ F$=0\mathrm{.}55\backslash$mathrm$\{$kN$\},$ P$=8\mathrm{.}0\backslash$mathrm$\{$kN$\}\backslash ),$ and $\backslash ($ T$=30\backslash$mathrm$\{$~N$\}\backslash$cdot $\backslash$mathrm$\{$~m$\}\backslash ).$