A single$-$span timber joist supports one concentrated load as shown in

Figure $4.$

A$)$ Determine if the $416$ wood joist is adequate for bending and

deflections $($LL and DL$+$LL$).$

Given:

Point dead load, $P_{DL}=600lbs$

Point dead load, $P_{LL}=1100lbs$

Allowable bending stress, $F_b=1725$ psi

Modulus of Elasticity $($Young$\text{'}$s modulus$),E=1,900$ksi

Deflection limits:

DL$+$LL: L$/240$

LL: L$/360$

Assume the section profile is compact and the joist is adequately

braced.

Figure $4-$ Beam Diagram

Figure $5-$Joist Profile

Parameters:

$L=20ft($span$)$

$a=3\mathrm{.}5$ in $($design width$)$

$b=13\mathrm{.}25$ in $($design depth$)$

Hint:

$A=a^{*}b$

$I=a^{*}\frac{b^3}{12}$

$,S=a^{*}\frac{b^2}{6}$