$$

CES $5715$ HW#$3$

Table $24\mathrm{.}5\mathrm{.}3\mathrm{.}1-$Concrete compressive stress limits immediately after transfer of prestress

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Problem $1$

A foot bridge uses a simply supported precast pretensioned double Tee section as shown in the figure in its invert position. The properties and weight of the available sections are listed in the table below. $f_c^{\text{'}}=7000,.f_{ci}^{\text{'}}=5000,\frac{P_e}{P_i}=0\mathrm{.}8,(e{)}_{mp}=y_b-2in,$ span length $=60ft,$ live load $=500l\frac{b}{f}t,f_{pe}=153$ksi, area of one strand $=0\mathrm{.}153i{n}^2.$ This section is to be designed as a class $U$ section.

Consider allowable stress limit per ACl code $($provided next page$),$ choose the least weight section from the available sections.

Construct the feasibility domain and determine the minimum effective prestressing force $P_e$ and corresponding eccentricity $e_0.$ How many strands are required?

Using the number of strands selected from $2),$ determine the range of eccentricity $($e$)$ at end span such that allowable stress limits are not violated.

Check whether this section satisfied minimum reinforcement requirement.

Check whether the section is adequate under ultimate strength condition. $($No need to redesign$)$

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