A simply supported beam with $14-$feet span has a rectangular section having $\backslash ($ b$=14\backslash$mathrm$\{$in$\}\backslash ).,\backslash ($ d$=22\mathrm{.}5\backslash$mathrm$\{$in$\}\backslash ).$ and $\backslash ($ h$=25\backslash$mathrm$\{$in$\}\backslash ).$ It is reinforced for flexure with reinforcing bars that continue uninterrupted to the ends of the span. The beam needs to carry service dead load $\backslash (\backslash$mathrm$\{$w$\}\_\{$D$\}=3\mathrm{.}0\backslash$mathrm$\{$kips$\}/\backslash$mathrm$\{$ft$\}\backslash ).($excluding self$-$weight$)$ and service live load $\backslash (\backslash$mathrm$\{$w$\}\_\{$L$\}=6\backslash$mathrm$\{$kips$\}/\backslash$mathrm$\{$ft$\}\backslash ).,$ both uniformly distributed along the span. Design the shear reinforcement for the beam using $\backslash$#$3$ vertical $\backslash ($ U $\backslash )-$stirrups or closed ties. The material strengths are $\backslash ($ f$\_\{$c$\}^\{\backslash$prime$\}\backslash )\backslash (=4,000\backslash$mathrm$\{$psi$\}\backslash )$ and $\backslash ($ f$\_\{$y$\}=60,000\backslash$mathrm$\{$psi$\}\backslash ).$ Assume that the width of the supports at the ends is $6$ inches as shown in the figure.

$($i$)$ Determine the shear reinforcement spacing for a factored shear force at a distance of the effective depth $(\backslash ($ d $\backslash ))$ plus half the bearing pad length $(3$ inches$)$ from the centreline of each support, and use the corresponding spacing as uniform spacing throughout the beam length. Show a neat scaled sketch of the arrangement of the shear reinforcement in elevation clearly showing the spacing $($AutoCAD or MicroStation drawings are preferred$).$ Show a typical beam cross$-$section as well.

$($ii$)$ Determine the distance from the mid$-$span over which a spacing of shear reinforcement of $\backslash (9^\{\backslash$prime $\backslash$prime$\}\backslash$mathrm$\{$O$\}/\backslash$mathrm$\{$C$\}\backslash )$ will work for this beam, even though we know that such variable spacing is not practical. Show the shear force diagram to determine the relavant distance on either side of the mid$-$span for the proposed $\backslash (9"\backslash )$ spacing. For the rest of the length, you may use a spacing as determined for the shear force at the critical section in Part $($i$).$ Show a scaled drawing to show the details for this Part $($ii$).$

Elevation View

Note: Span $=\backslash (14^\{\backslash$prime$\}-0^\{\backslash$prime $\backslash$prime$\}\backslash )$ and Bearing Pad Length at the Ends $\backslash (=\backslash$mathrm$\{$N$\}=6^\{\backslash$prime $\backslash$prime$\}\backslash )$

Critical section for shear design is at a distance of $\backslash (\backslash$boldsymbol$\{$d$\}\backslash )$ plus half the length of the bearing pad $(\backslash (3^\{\backslash$prime $\backslash$prime$\}\backslash ))$ from the centerline of the supports at the ends.