$(10$ points$)$ Difficulty $(4/5)$

Dimensions:

Problem Statement:

A wooden deck is constructed to support a haystack as shown. The joists of the floor are to be made with dressed air$-$dry douglas fir lumber with nominal widths of $2$ inches. You know that a $14"$x$18"$x$36"$ square bale of this kind of hay

weighs $63$ lb $,$ and you are assuming the hay in the haystack has the same density as these square bales. $($This is probably a conservative estimate, since the bales are probably denser than the stack in reality.$)$ You would like to

design the joists to have a factor of safety of $4\mathrm{.}6$ against yielding. Determine the following:

$($a$)$ The maximum value of the distributed load applied to one joist.

$($b$)$ The maximum bending moment experienced by one joist.

$($c$)$ The minimum required height $h$ of the joists.

$($d$)$ The minimum required section modulus of the joists.

$($e$)$ The smallest standard lumber size acceptable to use for joists.

Answers:

$($a$)w_{\text{m}\text{a}\text{x}}=$

$($b$)M_{\text{m}\text{a}\text{x}}=$

$($c$)h_{\text{m}\text{i}\text{n}}=$

$($d$)S_{\text{m}\text{i}\text{n}}=$

$($e$)$ Lumber Choice $=$

be sure to include units with your answers