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A prestressed T beam below is pretensioned using low relaxation stress$-$relieved Grade $270$ strands. The steel area $A_{ps}=1\mathrm{.}1i{n}^2.$ The tensile strength is $f_{pu}=270$ksi, and the concrete compressive strength is $f_c^{\text{'}}=6000.$

$($a$)$ Calculate the nominal moment capacity $M_n$ with $h_f=3$ in$.$

$($B$)$ The nominal moment capacity $M_n$ increases with a thicker flange depth $h_f.$ However, $M_n$ may stop increasing if $h_f$ reaches a certain value. Determine the minimum thickness $h_f$ from which $M_n$ does not increase. Also, calculate the corresponding maximum nominal moment capacity $M_n$ that this beam can attain with varying $h_f.$