Question

A prestressed concrete beam of cross-sectional area $A$, moment of inertial ${}^{\prime }{l}^{\prime }$, distance of top extreme fibre from neutral axis ${}^{\prime }{y}^{\prime }$ and distance of bottom extreme fibre from neutral axis ${}^{\prime }{y}_b^{\prime }$ is subjected to a prestressing force such that stress at top fibre is zero. What is the value of eccentricity ('r' is radius of gyration)?

• A. $A/y_b$
• B. $r^2/y_b$
• C. $r^2/y_r$
• D. $r{y}_b/y_t$

Answer 1

The correct option is C $r^2/y_r$

The compressive stress $=\frac{P}{A}$
The tension at top fibre$=\frac{Pe}{Z_t}=\frac{Pe{y}_t}{I}$
For zero stress at top fiber $\frac{P}{A}=\frac{Pe{y}_t}{I}$
$\therefore e=\frac{\left(I/A\right)}{y_t}=\frac{r^2}{y_t}$