Problem #$1$:

A simply$-$supported singly$-$reinforced concrete beam must be

able to carry a uniformly distributed factored load $($including

self weight$)$ of $25k\frac{N}{m}.$ If the beam has a span of $4\mathrm{.}0$ metres

and has the dimensions and reinforcement details shown in

the accompanying figure, design the strengthening system

using carbon FRP sheets according to CSA S$806-12$ to obtain

the required flexural capacity. The material properties are as

follows:

Concrete strength, $f_c^{\text{'}}=40$MPa

Internal steel reinforcement: $410M$ bars

Steel yield strength, $f_y=400$MPa

Steel elastic modulus, $E_s=200$GPa

Carbon FRP thickness, $t_{frp}=0\mathrm{.}9mm$

$,$ CFRP failure strain, ${}_{\text{f}\text{i}\text{p}\text{u}}=1\mathrm{.}26\%$

$,$ CFRP elastic modulus, $E_{frp}=120$GPa