$(10$ Points$)$ The A$-36$ steel rod shown in the figure has a diameter of $50mm$ and is lightly attached to the rigid supports at A and $B$ when $T_1=25C.$ Determine the force $P$ that must be applied to the collar at its midpoint so that, when $T_2=30C,$ the reaction at $B$ is zero.

Note; Dimension $a$ is given for each student in the attached table.