$2$

a$)$

A $10m$ span prestressed simply prestressed beam, with the section shown in

Figure $2\mathrm{.}1,$ carries a total maximum working load of $24\mathrm{.}7k\frac{N}{m}.$ Assuming that the centroid of the prestressing tendons is at a constant level of $55mm$ above the lower face of the beam, compute the prestressing force $(P)$ required for the maximum moment location. Assume $f_{ck}=40\frac{N}{m}{m}^2,{}_w=0\mathrm{.}8,f_w=3\mathrm{.}5\frac{N}{m}{m}^2$ and $f_{cw}=24\frac{N}{m}{m}^2.$ Use only the bottom tension working condition.

Once you have calculated $P$ you do not need to show that all inequalities are satisfied. This would, however, be essential in practice.

$($b$)$ An existing simply supported reinforced concrete beam, with the section shown in Figure$21\mathrm{.}2,$ spans $10m.$ The assessed loading is self$-$weight plus an additional permanent load of $20k\frac{N}{m}$ and a variable load of $15k\frac{N}{m}.$ Check the design crack width by detailed calculation.

Assume $E_s=200k\frac{N}{m}{m}^2,E_{cm}=18k\frac{N}{m}{m}^2,$

$f_{ck}=40\frac{N}{m}{m}^2,f_{yk}=500,\frac{N}{m}{m}^2,f_{ct,\text{e}\text{f}\text{f}}=3\mathrm{.}5\frac{N}{m}{m}^2,$

links $=8mm,$ cover $=30mm.,$

Figure $2\mathrm{.}2$