Q$1.$ A civil engineer has designed a $25$ m long simply supported prestressed beam $($Figure

Q$1)$ for a club hall. The beam is used to support a uniformly distributed service load of

$25k\frac{N}{m}($exeluding its own self$-$weight$).$

Assume that:

Concrete characteristic strength, $f_d=50\frac{N}{m}{m}^2$

Concrete strength at transfer, $fo{k}_{(1)}=45\frac{N}{m}{m}^2$

Eccentricity for the duct is $150$ mm

Losses of prestress $=10\%$

Minimum stress at transfer is $4\mathrm{.}1\frac{N}{m}{m}^2$

The properties of different M$-$beams are shown in Table $1.$

$($a$)$ Explain the transfer stage and service stage. Also, calculate the stress limits at

transfer and service stage.

$(5$ marks$)$

$($b$)$ Compute the post$-$tensioned section and select the most appropriate and

economical section for the post$-$tensioned concrete M $-$beam from Table $1$

provided.

$(5$ marks$)$

$($c$)$ Determine the minimum prestress force at the mid span of the M$-$beam using

four inequalities equations.

$(15$ marks$)$

$[$Total: $25$ marks$]$