Given: A prestressed simply supported I$-$beam with cross section shown has a span of $200$ ft $,$ and is

subjected to self$-$weight of $1,240$ plf$.$

Concrete:

$f_c=10,000$ at shipping and final

$f_{ci}=8,000$ at release of prestress

$f_c=0\mathrm{.}45f_c$ allowable compressive stress

$fc=0\mathrm{.}6f_{ci}$ allowable compressive stress

$f_t=12\sqrt[\phantom{2}]{f_c^{\text{'}}}$ allowable tensile stress

Prestressing Strands:

$f_{pu}=270,000-$ ultimate strength

$f_{pj}=202,500-$ at jacking

$f_{pe}=145,000-$ at final after losses

$A_{ps}=0\mathrm{.}217i{n}^2$ per strand

Section properties are:

d $($girder depth$)=100\mathrm{.}0$ in

$A_g=1082\mathrm{.}78i{n}^2$

$I_g=1524912\mathrm{.}4i{n}^4$

$y{b}_b=48\mathrm{.}274$ in$.-$cgc to bot.

$y_t=51\mathrm{.}726$ in$.-$cgc to top

$S_b=31588\mathrm{.}9$ in ${?}^3$

$S_t=29480\mathrm{.}4i{n}^3$

Determine:

Use $52-0\mathrm{.}6$ in$.$ strands $(38$ straight, $14$ harped$)$ for the reminder of the problem

Transfer and development lengths of strands and stress diagram

$(10$ points$)$

Strand stress at $24$ in $.$ and at $48$ in $.$ from the end of beam

For pretensioned beam:

Prestress losses due to elastic shortening

Prestress Losses due to creep

Prestress losses due to shrinkage

Prestress losses due to relaxation of steel

For post$-$tensioned beam:

Elastic shortening losses if strands were jacked in $4$ equal sequences $(10$ points$)$

Prestress losses due to anchor set of $0\mathrm{.}375$ in$.$

Prestress losses due friction if polyethylene ducts were used

Draw initial and final stress diagram with PT from one end

$(10$ points$)$