Prestressed Concrete:

Consider the rectangular $(b=1\mathrm{.}2m,h=0\mathrm{.}8m)$ simply supported beam of the figure below

Concrete: $C\frac{45}{55}{f}_{}=45$MPa

Ecm$=36$GPa

Applied Bending moment:

$-$Self weight $M=1\mathrm{.}2MN.m$

$-$Surchage $,M=2\mathrm{.}2MN.m$

The beam is reinforced with $57T15s$

$fpk=1860$MPa et $fp0\mathrm{.}1k=1674$MPa$(1(T)15(s)=150m{m}^2).$ Ep$=195000$MPa; $fpd=1390$MPa

The eccentricity of the tendons $e0=-0\mathrm{.}3m.$ The total losses are estimated at $20\%$

The concrete cover is $0\mathrm{.}1m$

Design the beam for the ultimate limit state

Problem $5$: $(2$ Points$)$

Consider the rectangular simply supported beam of the figure below

Loncrete:

$C\frac{25}{30}{f}_a=25$MPa

The applied prestressed force $Pm=2\mathrm{.}1MN($after all losses$)$

$=0\mathrm{.}03$rad

$A_{Sl}=12c{m}^2(Longitudinal$ passive steel$)$

$f_{ywk}=500$MPad$=0\mathrm{.}5m$

Applied shear force at a distance $d$ from the support $Vu(d)=0\mathrm{.}65MN$ under ultimate load

combination

Determine the required area of stirrups for the shear design. Consider $s=0\mathrm{.}1m$ for the stirrups spacing