A rigid triangular frame is pivoted at C and held by two identical horizontal wires at points A and $B($see figure$).$ Each wire has an axial rigidity $EA=120$ kips and coefficient of thermal expansion $=12\mathrm{.}5\frac{{10}^{-6}}{}F.(25$ pts$)$

a$.$ If a vertical load $P=500lb$ acts at point D $,$ what are the tensile forces $T_A$ and $T_B$ in the wires at A and $B,$ respectively? $(10$ pts$)$

b$.$ If both wires have their temperatures raised by $180F$ while the load $P$ is acting, what are the forces $T_A$ and $T_B?(10$ pts$)$

c$.$ What further increase in temperature will cause the wire at $B$ to become slack?