A simply supported beam is shown below. The beam is subjected to a uniform load $w_u=13t\frac{f}{m}.$ The cover depth is $4$ cm $.$ Use normal weight concrete with $f_c^{\text{'}}=350kg\frac{f}{c}{m}^2,$ uncoated longitudinal reinforcement with $f_y=5000kg\frac{f}{c}{m}^2,$ and transverse reinforcement with $f_x=4200kg\frac{f}{c}{m}^2.$ The transverse reinforcement is formed by an interior U $,$ an exterior U $,$ and a cap tie.

$($a$)$ Determine the maximum distance from the actual cutoff point to the center of the support if two tension reinforcing bars are to be terminated when the factored moment $M_u$ is reduced to a design moment strength $M_n$ corresponding to three tension reinforcing bars. Ignore the contribution of compression reinforcement when calculating $M_n.$

$($b$)$ Check whether the bars at the midspan section have sufficient embedment length to the actual cutoff point determined in $($a$)$ to develop $f_y.$ Check with the detailed calculation method for the development length

$($c$)$ Check whether the termination of the bars satisfies the code provisions related to reinforcement cutoff in a flexural tension zone. If extra stirrups are needed, use only the exterior U $($only two legs$).$

$($d$)$ Check the diameter of flexural reinforcement at the support. Use the simplified equation for development length calculation.