A thin plate with width $2w=6$ in$.$ and thickness $t=0\mathrm{.}06$ in$,$ is

made of Ti$-6$A$1-4$V annealed titanium alloy, with properties of

$S_u=130$ksi, and $S_y=120$ksi. It has a fracture toughness of

$K_{Ic}=110$ksi$-i{n}^{\frac{1}{2}}.$ It is used in a car structural component that

will be inspected periodically for cracks. Estimate the highest

load, P $($see the figure$),$ that car be applied to the component

without causing sudden fracture when a central crack grows to a

length, $2$ c $,$ of $1\mathrm{.}0$ in $.$