$(15$ marks$)$ Fig. $2-1$ shows a RC structure with symmetric and rectangular floor plan. The total height $H$ of the building is $120m$ with storey height of $4\mathrm{.}0m.$ The wind loads are defined based on Code of Practice on Wind Effects in Hong Kong $2019.$ Some information is given as follows:

$,$ The dimensions of the building $(L_x$ and $L_y)$ are given in Fig. $2-1.$

Take topographic multiplier $S_t=1\mathrm{.}2$ and directionality factor $S_{}=0\mathrm{.}85.$ Assume they are the same for both $x-$ and $y-$directions.

The fundamental frequencies of vibration along $x-$ and $y-$directions are equal to $0\mathrm{.}51Hz$ and $0\mathrm{.}73Hz,$ respectively.

Take damping ratio equal to $3\mathrm{.}0\%$ along both $x-$ and $y-$directions.

The wind pressure $Q_z$ are assumed to be uniformly distributed along the building's height, with value $Q_z=Q_h,$ where $Q_h$ is design wind pressure at the top.

Write down necessary assumptions $($if any$)$ in your solution. Show your steps clearly.

a$)$ Determine the along wind shear force, along$-$wind moment, and torsional moment at the base level due to wind along $x$ direction only.

$(5$ marks$)$

b$)$ When the building is subjected to wind along $y-$direction, it will also oscillate along $x-$ direction. Discuss the reason behind this phenomenon.

$(5$ marks$)$

c$)$ Compute the across$-$wind base moments due to winds along y$-$direction only. Check

$(5$ marks$)$

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