Problem $5$

A rectangular reinforced concrete beam has a width of $300mm$

and an effective depth of $450mm$ to centroid of the tension bars. The

beam is reinforced with six $32mm\frac{O}{?}$ tension bars placed in two layers

with the outer layer having a depth of $478mm,$ and two $28mm\frac{O}{?}$

compression bars with centroid $65mm$ from the extreme concrete

fiber. Use the $2010NSCP,f_c^{\text{'}}=34\mathrm{.}5$MPa and $f_y=345$MPa. Assume

that the concrete displaced by the compression steel shall not be

neglected and that the compression steel yields. Det. the following:

The balanced steel ratio if the beam is singly reinforced.

The maximum steel ratio for a singly$-$reinforced section in

tension control.

The maximum steel ratio for a doubly$-$reinforced section in

tension control.