A $24in.$ deep, $8ft$ wide, $70ft$ long double $T$ beam carries a girder weight of $420plf,$ a sustained dead load of $10psf,$ and superimposed live load of $30psf.$ It is prestressed with twelve $\frac{1}{2}$ in$.$ diameter $270$ksi low$-$relaxation strands with a midspan eccentricity of $12\mathrm{.}3in.$ and an end eccentricity of $5\mathrm{.}0in.$ Section properties are $A_c=401i{n}^2,I_g=20,985i{n}^4,y_b=17\mathrm{.}15in.,y_t=6\mathrm{.}85$ in$.,$ and $h_f=2in.$ Concrete strength is $5000,f_{ci}^{\text{'}}=3500,$ and $R=0\mathrm{.}80.$ Determine the class of the beam.