An untopped, $12-$inch hollow$-$core section $($see figure below$),$ simply supported, floor system

spans, $36ft$ in a hotel corridor area. The service live load is $100psf,$ and the additional dead load

is $10psf.$ Consider only the dead load is sustained. The normal weight concrete has $f_{ci}=3500$

and $f_c=5000.$ Initially, try $6$ low$-$relaxation, $\frac{1}{2}$ inch diameter strands and

$\{$:$\frac{f_{py}}{f_{pu}}=0\mathrm{.}94)$ with a stress at transfer, $f_{si}=0\mathrm{.}67f_{pu}.$ After losses, the effective stress, $f_{se},$ in

the strands is $0\mathrm{.}57f_{pu}.$ Draping is not employed in shallow box sections.

a$)$ Check stresses at the ends and at midspan at transfer and under full service load for the

initial number of $6$ strands $($See Section $24\mathrm{.}5$ of $318-19)$ and determine if the section where

maximum moment occurs can be classified as $U,T$ or $C$ in accordance with ACI $318-19,$

Sec. $24\mathrm{.}5\mathrm{.}2\mathrm{.}1)$

b$)$ For the same loading, redesign the prestressing by reducing the number of strands to $4$ low$-$

relaxation, $\frac{1}{2}$ inch diameter, and determine whether the maximum moment section can

be classified as $U,T,$ or $C.$ Use same $f_{si}$ and $f_{se}$ values. Keep reinforcement symmetric

about the vertical axis of the cross section and at the same elevation.

c$)$ Using the ACI $318-19$ Chapter $22,$ check ultimate moment capacity for the two sections.

If necessary, in order to meet flexural strength requirements, supplement the flexural

capacity at the maximum moment section using GR$.60$ deformed bars placed with the

same centroid location of the prestressing strands. Determine the factor $\frac{M_n}{M_{cr}}($see

Chapter $21$ for the appropriate $)$ and estimate the cracking moment, $M_{cr},$ based on a

bottom fiber stress at midspan equal to $7\mathrm{.}5\sqrt[\phantom{2}]{f_c}.$

HOLLOW$-$CORE

$4\text{'}-0"$ x $12"$

Normal Weight Concrete

$f_c^{\text{'}}=5,000$

$f_{ci}^{\text{'}}=3,500$

Section Properties