Problem $1-$Analysing a Beam $(9$ Points$)$:

The beam in the figure below is Southern Pine No$.1/$ Lumber and has $6"12"$ nominal size crosssection. Assuming the fixed connection has been applicable, allowable bending and shear stresses are $Fb=550$ and $Fv=45.$

a$.$ Determine the maximum bending and shear stresses.

b$.$ Determine if the beam is safely designed for bending and shearing.

J Draw load$/$FBD$,$ shear, and moment diagrams for the beam.

Show all the calculations including the calculation for drawing shear and moment diagram.

$$ Ignore beam self$-$weight.