Question

The cross-section of a pretensioned prestressed concrete beam is shown in figure. The reinforcement is place concentrically. If the stress in steel at transfer is 1000 MPa, compute the stress in steel immediately after transfer. The modular ratio is 6.

Answer 1

Prestressing force $=1000\times 500$
= 500 kN
Stress in concrete at the level of steel
$f_c=\frac{P}{A}=\frac{500\times {10}^3}{200\times 300}$
$=8.33N/m{m}^2$
Just after pretensioning there would be a elastic shortening loss only.
Hence,
Elastic shortening loss $=m{f}_c$
$=6\times 8.33$
$=50N/m{m}^2$
Stress in steel immediately after transfer
= 1000 - 50
$=950N/m{m}^2$