Question

A pre-tensioned (assume no losses) concrete rectangular $(b\times d)$ beam is designed on the basis of no tension. Concrete strength is ${\sigma }_c.$ The maximum moment that the beam can carry is

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

Answer 1

The correct option is D ${\sigma }_c.\frac{b{d}^2}{6}$

For no tension
$\frac{P}{A}=\frac{M}{Z}\Rightarrow M=\frac{P}{A}Z={\sigma }_{c}Z=\frac{b{d}^2{\sigma }_c}{6}$