Problem #$4(25$ pts$)$: A wooden beam needs to be elongated for a renovation project. An extension is added by nailing $($no glue$)$

two wooden boards at the connection joint. Nails go all the way through both boards and the beam.

Given:

The wooden boards are $1\mathrm{.}5$ inches thick.

The shear strength of the wooden boards is $1\mathrm{.}5$ksi.

The nails have a diameter of $0\mathrm{.}238$ inches.

Assume that $10$ nails are installed on each side $($this is not necessarily the answer for problem #$2$ or #$3).$

The beams have an axial load of $25$ kips.

Find:

$(1)$ The minimum nail installation distance away from the board's edge to the center of the nail to prevent tear$-$out. You do not

need to analyze the beams, only the boards. Report answer with three significant figures.

Minimum distance $($inches$)$