A composite bar of length $L = 1$ m consists of a steel segment and a brass segment clamped between two rigid walls so it cannot expand. The steel segment is $0.5$ m long, has area $A_s = 200$ mm$^2$, Young's modulus $E_s = 200$ GPa, and thermal expansion coefficient $\\alpha_s = 12 \\times 10^{-6}$ /^\\circC. The brass segment is $0.5$ m long, has area $A_b = 200$ mm$^2$, $E_b = 100$ GPa, and $\\alpha_b = 20 \\times 10^{-6}$ /^\\circC. If the temperature increases by \\Delta T = 50^\\circC, what is the compressive force generated in the bar?