Problem #$1(30$ pts$)$:

Given:

Reinforced concrete beams are composed of both concrete $($strong in compression$),$ and steel $($equally strong in

both compression and tension$).$

Your company needs to determine how much a reinforced concrete beam deforms with a $20-$kip load, and you

have been assigned to the case.

Both the steel and concrete started with zero stress before the external load is applied.

The length of the beam before the external load is applied is $20$ feet.

Steel rebar properties: $E=29,000$ksi, there are $8$ pieces of rebar in the beam, and each solid rebar piece has a

diameter of $0\mathrm{.}375-$inches.

Concrete beam properties: $E=5,000$ksi, and it is a $10-$inch diameter beam. Hint: Don't forget to subtract the area

of the rebar from the full cross$-$section to get the cross$-$section of the concrete.

Find:

Report answers to $3$ sig$-$figs and include the sign if appropriate.

${}_{\text{c}\text{o}\text{n}}={}_{\text{s}\text{t}\text{e}\text{a}}=0,$ before loud

$L_D=$delDft

Steel:

$E=$del$9,000ks$;

Spieces of rebar

$8$pieces $of$ rebas

evach has a diameter $of{0\mathrm{.}3755}^{\text{'}\text{'}}$

Concrete:

$E=5,000KS$

ciameter $={10}^{\text{'}\text{'}}$

${}_{r\frac{e}{b}ar}=\frac{p}{8A}$

$=\frac{\text{d}\text{e}\text{l}0}{8*\frac{}{4}(375{)}^2}$

$=22\mathrm{.}64$kSi

${}_{\text{c}\text{o}\text{n}}=\frac{P}{A}$

$=\frac{\text{d}\text{e}\text{l}0}{\frac{}{4}({10}^2-(8\mathrm{.}375{)}^2)}$