Question

The below figure represents a section of a prestressed beam. For a no-tension design where ${\sigma }_c$ is the permissible stress in concrete, the total moment carrying capacity is

• A. $\frac{b{d}^2{\sigma }_c}{3}$
• B. $\frac{b{d}^2{\sigma }_c}{4}$
• C. $\frac{b{d}^2{\sigma }_c}{6}$
• D. $\frac{b{d}^2{\sigma }_c}{12}$

Answer 1

The correct option is D $\frac{b{d}^2{\sigma }_c}{12}$

For maximum compression
$\frac{P}{bd}+\frac{M}{\frac{b{d}^2}{6}}\le {\sigma }_c\cdots \left(i\right)\text{For no tension}\frac{P}{bd}-\frac{M}{\frac{b{d}^2}{6}}=0\Rightarrow \frac{P}{bd}=\frac{M}{\frac{b{d}^2}{6}}\Rightarrow P=\frac{6M}{d}\text{Put value of P in eq. (i)}\Rightarrow \frac{2M}{\frac{b{d}^2}{6}}\le {\sigma }_c\Rightarrow \frac{12M}{b{d}^2}\le {\sigma }_{c}M\le \frac{{\sigma }_{c}b{d}^2}{12}$