A $10-$ft simply$-$supported beam has a uniform flexural rigidity El of $50({10}^6)$ kip$-$in$^2$ and uniform weight per unit length of $200l\frac{b}{f}t.$ Assuming

$(x)=\frac{x(x-L)}{L^2}$ where $L$ is the length, the generalized stiffness tilde$(k)($kip$/$in$.)$ is most nearly:

$9\mathrm{.}65$

$833,000$

$200,000,000$

$116$