Problem $4(10$ points$)$

The design values of Red Maple species are given in the table below.

a$)$ Which grade has the highest bending strength

b$)$ Which grade$($s$)$ has the lowest shear strength?

c$)$ Which grade has the highest material stiffness?

d$)$ What is the allowable bending strength of a $\backslash (2^\{\backslash$prime $\backslash$prime$\}\backslash$times $6^\{\backslash$prime $\backslash$prime$\}\backslash )$ stud grade?

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline $\backslash$multirow$\{3\}\{*\}\{$Species and commercial grade$\}$ & $\backslash$multirow$\{3\}\{*\}\{$Size classification$\}$ & $\backslash$multicolumn$\{7\}\{|$c$|\}\{$Design values in pounds per square inch $($psi$)\}$ & $\backslash$multirow$[$b$]\{3\}\{*\}\{\backslash$begin$\{$tabular$\}\{$l$\}$

Specific $\backslash \backslash$

Gravity $\backslash (\{\}^\{4\}\backslash )$

$\backslash (\backslash$qquad $\backslash )$

$\backslash$end$\{$tabular$\}\}$ & $\backslash$multirow$\{3\}\{*\}\{\backslash$begin$\{$tabular$\}\{$l$\}$

Grading $\backslash \backslash$

Rules $\backslash \backslash$

Agency

$\backslash$end$\{$tabular$\}\}\backslash \backslash$

$\backslash$hline & & $\backslash$multirow$[$b$]\{2\}\{*\}\{\backslash [$

$\backslash$begin$\{$array$\}\{$c$\}$

$\backslash$text $\{$ Bending $\}\backslash \backslash$

F$\_\{\backslash$mathrm$\{$B$\}\}\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$array$\}$

$\backslash ]\}$ & $\backslash$multirow$[$t$]\{2\}\{*\}\{$Tension parallel to grain F$.\}$ & $\backslash$multirow$[$t$]\{2\}\{*\}\{\backslash$begin$\{$tabular$\}\{$l$\}$

Shear parallel to grain $\backslash \backslash$

$\backslash (\backslash$mathbf$\{$F$\}\_\{\backslash$gamma$\}\backslash )$

$\backslash$end$\{$tabular$\}\}$ & $\backslash$multirow$[$t$]\{2\}\{*\}\{$Compression perpendicular to grain $\backslash (\backslash$mathbf$\{$F$\}\_\{4\}\backslash )\}$ & $\backslash$multirow$[$t$]\{2\}\{*\}\{```$

Compression

parallel

to grain

F$6$

$```\}$ & $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Modulus of Elasticity$\}$ & & $\backslash \backslash$

$\backslash$hline & & & & & & & E & $\backslash (\backslash$mathrm$\{$E$\}\_\{\backslash$text $\{$man $\}\}\backslash )$ & & $\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{11\}\{|$l$|\}\{$RED MAPLE$\}\backslash \backslash$

$\backslash$hline Select Structurai & $\backslash$multirow$\{4\}\{*\}\{28$ wider$\}$ & $1,300$ & $750$ & $210$ & $615$ & $1,100$ & $1,700,000$ & $6200\mathrm{.}000$ & $\backslash$multirow$\{8\}\{*\}\{0\mathrm{.}58\}$ & $\backslash$multirow$\{8\}\{*\}\{$NELMA$\}\backslash \backslash$

$\backslash$hline No$.1$ & & $925$ & $550$ & $210$ & $615$ & $900$ & $\backslash (1\mathrm{.}600,000\backslash )$ & $580\mathrm{.}000$ & & $\backslash \backslash$

$\backslash$hline No$.2$ & & $900$ & $525$ & $210$ & $615$ & $700$ & $\backslash (1,500,000\backslash )$ & $550\mathrm{.}000$ & & $\backslash \backslash$

$\backslash$hline No$.3$ & & $525$ & $300$ & $210$ & $615$ & $400$ & $\backslash (1\mathrm{.}300,000\backslash )$ & $470\mathrm{.}000$ & & $\backslash \backslash$

$\backslash$hline Stud & $\backslash (2^\{2\}8\backslash )$ wider & $700$ & $425$ & $210$ & $615$ & $450$ & $\backslash (1\mathrm{.}300,000\backslash )$ & $470\mathrm{.}000$ & & $\backslash \backslash$

$\backslash$hline Construction & $\backslash$multirow$\{3\}\{*\}\{\backslash (2^\{*\}\backslash$cdot $4^\{*\}\backslash )$ wide$\}$ & $1\mathrm{.}050$ & $600$ & $210$ & $615$ & $925$ & $1,400,000$ & $510\mathrm{.}000$ & & $\backslash \backslash$

$\backslash$hline Standard & & $575$ & $325$ & $210$ & $615$ & $725$ & $1,300,000$ & $470,000$ & & $\backslash \backslash$

$\backslash$hline Utiity & & $275$ & $150$ & $210$ & $615$ & $475$ & $1\mathrm{.}200,000$ & $440\mathrm{.}000$ & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$