On a small building project, lumber $($nominal size $4x14$ and dressed size $3\mathrm{.}5$

in$.$ X $13\mathrm{.}5$ in$)$ will be used in resisting bending $($flexural loading$).$ The piece of

lumber, with self$-$weight $($density$)$ of $25l\frac{b}{f}{t}^3$ and spanning $30ft,$ simply

supported, will carry two unknown point loads $P$ lbs$.,$ each at a point $5ft.$ left

and right of the midspan, as shown in the figure below. It was observed that

the $6x14$ beam is defected with a knot in the top $2\mathrm{.}5in.$ of the beam depth.

The knot is located on the beam at the midspan. The Modulus of Rupture

$($MOR$)$ of the clear wood is $8,200$ psi. Assuming the neutral axis to be located

at half the depth of beam,

a$.$ Estimate the flexural strength $($MOR$)$ of this defected $4x14$ wood

beam at the $x-$section with the knot.

b$.$ Determine the maximum load P $($lbs$.)$ that the piece of lumber can

carry at each of these two points.

$(40$ pts$.)$