a$)$ The maximum ULS design bending moment in a reinforced concrete beam is $300kNm.$ The beam cross$-$section is to be a solid rectangle, $270mm$ wide by $500mm$ deep.

Given:

$f_{ck}=25\frac{N}{m}{m}^2$ and $f_{yk}=500\frac{N}{m}{m}^2$

minimum cover is $30mm.$

bar diameter for longitudinal steel $=24mm$

link diameter $=8mm$

$($i$)$ Calculate the effective depth of the beam $($d$).(5$ marks$)$

$($ii$)$ Determine whether the beam is to be singly or doubly reinforced

$($iii$)$ Calculate how many reinforcement bars are needed to resist the maximum bending moment given

$(10$ marks$)$

$($iv$)$ Check the bar spacing if aggregate size is $20mm$

$(20$ marks$)$

$(5$ marks$)$

b$)$ A column has a length $($height$)$ of $3\mathrm{.}2m$ and is pinned and braced at both ends. Calculate the axial load capacity $(N)$ of the column if:

$($i$)$ a $30530597$ UC Section in Grade S$355$ steel is used

$($ii$)$ a reinforced concrete column is used that has a $280mm(30$ marks$)280mm$ square cross$-$section and is reinforced with eight $24mm$ diameter steel bars.

$(30$ marks$)$

Given: $f_{ck}=25\frac{N}{m}{m}^2,f_{yk}=500\frac{N}{m}m$

$3$