$(15$ marks$)$ The rigid beam resting on three $20$ mm $-$diameter posts is subjected to a concentrated force $P$ as shown in the figure below. Posts $AC$ and $EF$ are made of steel while post $BD$ is made of aluminum. The allowable stress for each material is given as ${}_{st}=200$MPa and ${}_{dl}=80$MPa, and the Young's modulus for each material is given as $E_{st}=210$GPa, and $E_d=70$GPa. Determine the maximum value of $P$ that can be sustained by the rigid beam.