Consider the pin-jointed truss shown (not to scale). All members have the same axial rigidity, $AE$. Members $QR,\;RS,\;ST$ have the same length $L$. Angles $QBT,\;RCT,\;SDT$ are $90^\circ$ and angles $BQT,\;CRT,\;DST$ are $30^\circ$. A vertical load $P$ acts at joint $T$. If the vertical deflection of joint $T$ is $ \displaystyle \Delta_T=k\,\frac{PL}{AE}$, what is the value of $k$?
