Question $1(29$ points$)$

Consider that a sawn lumber joist that supports a balcony $($Figure $1$a$)$ is modeled as a cantilever with a fixed end and is subjected to the shown loading $($Figure $1$b$).$ Design the joist using ASD.

$\backslash (>\backslash )$ Consider that the loading includes only dead and live load and the distributed loading in Figure $1$b represents the Dead $+$ Live load combination, which is the critical load combination that the design should be based on$.$

Material is No$.1\backslash$& Btr Douglas Fir$-$Larch. Consider dry$-$service and normal temperature conditions and no incising. Joist spacing is $30".$

The maximum deflection of a cantilever beam due to distributed loading is provided in Figure $1$b$.$ Deflection limits are those for floor members.

The joists rest on the perimeter girders as shown in Figure $1$c$.$

$($b$)$

downward

$\backslash [$

$\backslash$delta $\backslash$max $=\backslash$frac$\{$w L$^\{4\}\}\{8$ E I$\}$

$\backslash ]$

Figure $1.($a$)$ Balcony with sawn lumber joists, $($b$)$ joist cantilever configuration and loading, $($c$)$ the support conditions of the joist.