Problem $3$

The simply supported $T$ beam represented in the figure spans $60ft$ and is subjected to a uniformly distributed load, $w.$ Estimate the load $(w)$ at which web$-$shear cracking occurs using the ACl approach $($ignore the selfweight$).$ The section where to perform the calculation is at distance $1\mathrm{.}75ft$ from the support.

The following information is provided: normal weight concrete is used; the prestressing steel consists of twelve low$-$relaxation strands $($area of each strand is $0\mathrm{.}153i{n}^2)$ with eccentricities of $14\mathrm{.}95$ in at the ends and $24\mathrm{.}03$ in at midspan. Assume the stress in the strands after all losses is $152$ksi. $Ac=686i{n}^2,I=74,607i{n}^4,y_b=27\mathrm{.}28in,y_t=8\mathrm{.}72in,f_c^{\text{'}}=5,000.$