$4.$ A structural engineer must determine which type of steel to

select for a beam, but the weight limitation cannot exceed $7$ tons.

The project has narrowed the choices down to A$36$ steel $(\backslash$rho $=7800$

kg$/$m$3)$ and A$992$ steel $(\backslash$rho $=7850$ kg$/$m$3).$ However, the engineer needs

to determine the load difference between an A$36$ and A$992$ steel box

beam with an inertia of $356$ in$4,$ and has an elastic modulus of $30$ x

$106$ PSI & $35$ x $106$ PSI, respectively. The A$36$ steel is designed

to deflect $0\mathrm{.}107$ while the A$992$ steel is designed to deflect

$0\mathrm{.}118.$ Both beams have a span length of $12\mathrm{.}3$ meters, a distributed

stress of $101\mathrm{.}45$ kN$/$m$2,$ full length of$15\mathrm{.}78$ m$,$ and the beam is in a

simple load configuration. Determine the load difference between

the two beam options at the design limit$.$ What is your calculated

answer most closely to$?$a$.1\mathrm{.}5$ tonb. $20\mathrm{.}5$ tonsc. $104\mathrm{.}7$ tonsd. $8924\mathrm{.}1$ tons