Problem $1(35$ points$)$:

The support bracket shown below is subjected to a factored load Puy$=220$ kip, and is to be attached to a column flange with two identical vertical rows of ASTM A$325-$X$,7/8"$ diameter bolts. The bolts depicted in the figure are for illustration only, and may not represent the actual number of bolts needed. Filler plates will not be used. Bolts will be spaced at $\backslash (3^\{\backslash$prime $\backslash$prime$\}\backslash )$ on center. The load eccentricity is ex$=10".$ The supporting bracket plate thicknesses are $\backslash ($ t f$=5/8^\{\backslash$prime $\backslash$prime$\}\backslash ),$ and the bracket width $($parallel to column flange$)$ is $\backslash (\backslash$mathrm$\{$bf$\}=8^\{\backslash$prime $\backslash$prime$\}\backslash ).$ The vertical edge distance from outer bolt centers to edge of bracket plate is $\backslash (2^\{\backslash$prime $\backslash$prime$\}\backslash ).$ Assume that the connection design is controlled by bolt strength only $($ignore any other limit state$).$

a$)$ Using the elastic method of analysis, calculate the smallest number of bolts per vertical row required to safely resist the applied load, if the connection is a bearing$-$type connection

b$)$ If the design obtained in part a$)$ is to be used in a slip$-$critical connection, what is the maximum load Puy that may be safely applied?