Problem $1$: $(45$ points$)$ Repeat the example problem in class, but this time use LRFD to solve it$.$ You only

need to check the beam for bending and not for shear or deflection. In addition, this time the beam used

is known to be located in the unventilated rafter space of a commercial barn in Louisiana. As such, the

beam will routinely experience both elevated temperatures and humidity. Assume that the temperature

up in the rafters is often between $1100$F and $1200$F$.$ In addition, assume that the beam often has a

moisture content around $21\%.$ You can keep all the original assumptions as the example in class. Take

the time dependent variable for LRFD $($$)$ as $1\mathrm{.}0.$ Also assume that bending governs the design and not

shear or deflection. Draw a quick sketch of the beam, supports and loading as a free$-$body diagram. Show

all work.

Hints: For the final answer, keep in mind that the problem is asking for the $$actual$$ load $($inc$.$ the hoist

weight$)$ that can be hung on the beam. The $$actual$$ load is often referred to as the service load and does

not include any load factors. When you solve this problem using LRFD that includes the load factors such

as $1\mathrm{.}2$ for dead loads and $1\mathrm{.}6$ for live loads. Think of what type of load the hoisted load is$?$ Also note that

the LRFD Format Conversion Factor $($KF$)$ is only applied to the stress value you are calculating at the end.

Last, the resistance factor $($$)$ is also applied at the end once you are comparing a nominal moment to the

factored moment. For example, Mn $$ Mu in the case of checking this beam in flexure.