A $400400mm$ column supports a flat slab floors in a residential building. Slab thickness at each floor level is $200mm.$ Dimensions

of drop panel is $20002000mm$ w ith thickness of $300mm.$ Overall height between the top of the slab levels in each floor as shown in

the Figure is $3250mm.$ Shear wall of the building structure takes lateral loads and prevents sway movement. Column subjects only to

uni axial bending. Design analysis carried out found that the column has to support design axial force $N^{**}$ and associated moment $M^{**}$

values at the two ends which causes column to bend in $Y-Y$ axis. $($Refer to the Figure$).$ It is decided to provide $4N$ longitudinal

reinforcement bars at a distance $60mm$ to their centroids from each faces $(2$ bars at each face$).$ Using the design data and Figure below.

a$.$ Calculate the effective length of the column based on simplified method given in Clause $10\mathrm{.}3\mathrm{.}1$ AS$3600-2009?$

b$.$ What is the radius of gyration based on simplified method given in Clause $10\mathrm{.}5\mathrm{.}2$ AS$3600-2009?$

c$.$ Show that column can design as a short column based on the slenderness ratio?

d$.$ Calculate the $\frac{N^{**}}{b}D$ and $\frac{M^{**}}{b}{D}^2$

e$.$ What is the required proportion of steel area p to the nearest $0\mathrm{.}005$ and what is the steel area required? Use the design chart available

in the text and indicate which chart used to determine steel percentage $p.$

f$.$ Which minimum bar diameter w ould you select from the available bar diameters of $20mm,24mm,28mm,32mm.36mm$ and $40mm?$

g$.$ Has your selected reinforcement area satisfy the minimum and max imum steel percentage requirement for the column as for AS$3600-$

$2009?$ If not what's your recommendation?

h$.$ What is the minimum tie bar diameter for lateral reinforcement w ould you select from the available bar diameters of $10mm,12mm$

and $16mm?$ What is the recommend the maximum spacing of tie bars w ithin $5mm$ accuracy as for the AS$3600-2009$ requirements?

i$.$ Design check verifier recommends to use the immediate smaller size of the bar diameter you have selected for the longitudinal

reinforcement $w$ ith a different reinforcement configuration. Without carrying out any further calculation state the best arrangement

with minimum number of bars, considering that the bending is only around $Y-Y$ axis? $($State how many bars, bar diameter and

corresponding number of bars in the faces. Provide a sketch of bar arrangement. If you have used $24mm,28mm,32mm36mm$ in

the previous answer $($f$),$ it should be $20mm,24mm,28mm$ and $32mm$ respectively for this answer.$)$

j$.$ For the updated reinforcement arrangement is it possible for you to use the same tie bar diameter determined for the previous answer

$($h$),$ without violating AS$3600-2009$ requirements. $($State Yes or No$).$

k$.$ For the updated reinforcement arrangement is it possible for you to use the same tie bar spacing determined for the prev ious answ er

$($h$)$ without violating AS$3600-2009$ requirements. $($State Y es or No$).$