Consider the pin-jointed truss shown in the figure (not to scale). All members have the same axial rigidity, $A E$. Members $\mathrm{QR}, \mathrm{RS}$, and $\mathrm{ST}$ have the same length $L$. Angles QBT, RCT, SDT are all $90^{\circ}$. Angles BQT, CRT, DST are all $30^{\circ}$. The joint $\text{T}$ carries a vertical load $P$. The vertical deflection of joint $\mathrm{T}$ is $k \frac{P L}{A E}$. What is the value of $k$ ?
- $1.5$
- $4.5$
- $3.0$
- $9.0$