$10\mathrm{.}28$ Two steel bars $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ support a load $\backslash ($ P $\backslash ),$ as shown. Bar $\backslash ($ A $\backslash )$ has an area of $\backslash (580\backslash$mathrm$\{$~mm$\}^\{2\}\backslash )$ and bar $\backslash ($ B $\backslash )$ has an area of $\backslash (700\backslash$mathrm$\{$~mm$\}^\{2\}\backslash ).$ The yield stress is $275$ MPa $.$ Both bars elongate equally at point $\backslash ($ O $\backslash ).$ Neglect the slope of the bars.

a$.$ Assume an allowable stress of $185$ MPa and determine the allowable load using an elastic design approach.

b$.$ Assume a factor of safety of $1\mathrm{.}80$ and determine the allowable load using an ultimate strength design approach.