PROBLEM

The solid rod ABC in the figure is made of aluminum for which $E=70$GPa.

$(1)$ Knowing that force $P=5kN,$ determine the value of force Q so that the deflection at point A is zero

$(2)$ Find the corresponding deflection at point B

$(3)$ If instead of the loads a uniform temperature increase $T=50C$ had been applied to the rod, find the deflections at points A and B $.$

Given $[$:$A=\frac{d^2}{4},=\frac{{510}^{-6}}{C},{}_i=N_i\frac{L_i}{E}{A}_i+L_{i}T$