The current enclosure roof beam is a timber rectangular beam $5^{\text{'}\text{'}}$ wide and $24$ deep

$$

$6.$ Calculate the beam cross$-$section area

a$.A=80i{n}^2$

$($b$)A=120i{n}^2$

c$.A=245$ in ${?}^2$

d$.A=100i{n}^2$

$7.$ Calculate the beam centroid

a$.\stackrel{}{x}=2\mathrm{.}0in\frac{,}{b}ar(y)=10in$

b$.z=2\mathrm{.}0in\frac{,}{b}ar(y)=8in$

c$.\stackrel{}{x}=5\mathrm{.}0$ in$,\frac{?}{\text{b}\text{a}\text{r}}(y)=5$ in

$($d$.\stackrel{}{x}=2\mathrm{.}5in\frac{,}{b}ar(y)=12in$

$8.$ Calculate the beam second moment of area $(I_x$ and $I_4)$

$(10)$

a$.I_x=5760i{n}^4,I_y=250i{n}^4$

b$.I_x=240i{n}^4,I_y=50i{n}^4$

c$.I_s=2400$ in ${?}^4,I_y=1200$ in ${?}^4$

d$.I_x=4320i{n}^4,I_x=720i{n}^4$

$14.$ Calculate the allowable deflection limit for this spanning beam using the appropriate span ratio:

$(10)$

a$.$ linit $=0\mathrm{.}81$ in

b$.$ imet $=2\mathrm{.}13in$

c$.{}_{\text{m}\text{i}\text{t}\text{i}}=1\mathrm{.}07$ in

d$.$ limt $=0\mathrm{.}09$ in

$15.$ The cllent requests a specific deflection limit at the point of load, ${}_1$ for this project, of a maximum of $2.0in.$ What is the required second moment of area $1,$ for a steel beam $($with the elastic modulus of steel$)$ that has a deflection less than $2\mathrm{.}0$ in $($rearrange the deflection equation to find the value of $I_x?$

$(30)$

a$.I_x=358i{n}^6$

b$.I_x=713i{n}^6$

c$.l_x=271$ in ${?}^4$

d$.Is=167i{n}^4$

$16.$ What is the lightest $W-$shape steel beam from the tables that has an $I_{s\text{b}\text{i}\text{g}\text{g}\text{e}\text{r}\text{t}\text{h}\text{a}\text{n}}$ the needed for this new $2.$ Oin deflection limit$?$

$(10)$

b$.$ W$10122$

c$.$ W$10$x$49$

Section properties

The current enclosure roof beam is a timber rectangular beam $5^{\text{'}\text{'}}$ wide and $24$ deep

$$

$6.$ Calculate the beam cross$-$section area

$(5)$

a $A=80i{n}^2$

$($b$)A=120in$

c$.A=245$ in

d $A=100i{n}^2$

$7$ Calculate the beam centrold

$(5)$

a$.x=2.$ Oin, $y=10$ in

b $x=2$ oin, $y=8$ in

c$.\stackrel{}{x}=5\mathrm{.}0in,y=5in$

$($d$)x=2\mathrm{.}5$ in$,=12in$

$8$ Calculate the beam second moment of area $($I$.$ and $I_y$

$($a$)I_x=5760i{n}^4,I_y=250i{n}^4$

b$.I_x=240i{n}^4,I_y=50i{n}^4$

c$.I_x=2400i{n}^4,I_y=1200i{n}^4$

d$.I_x=4320i{n}^4,I_y=720i{n}^4$

$14.$ Calculate the allowable deflection limit for this spanning beam using the appropriate span ratio

$(10)$

a$.{}_{\text{i}\text{m}\text{u}\text{t}}=0\mathrm{.}81$ in

b$.$ i$.$ini $=2\mathrm{.}13in$

c$.{}_{\text{i}\text{m}\text{i}\text{t}}=1\mathrm{.}07$ in

d$.$ ilint $=0\mathrm{.}09in$

$15.$ The client requests a specific deflection limit at the point of load, $,$ for this project, of a maximum of $2.0$ in$.$ What is the required second moment of area $I_s$ for a steel beam $($with the elastic modulus of steel$)$ that has a deflection less than $2.$ Oin $($rearrange the deflection equation to find the value of $I_x)$

$(30)$

a$.I=358$ in ${?}^4$

b$.l_4=713i{n}^4$

c$.l_1=271i{n}^4$

d$.I_3=167l{n}^4$

$(10)$