Two identical bars and a beam is placed between two rigid ends. The top and bottom elastic bars are identical $(E=20$GPa, Area $=0\mathrm{.}001m^2$ and thermal expansion coefficient $={10}^{-5}\frac{1}{}C).$ Bars are connected to the rigid ends with pins at both ends. Beam is perfectly connected to the rigid ends to make sure plane sections remain plane during bending. Elasticity modulus of the beam is $200$ GPa.

If the temperature of the top bar is decreased by $20C$ and the bottom bar is increased by $20C($temperature of the beam is kept constant$),$

a$.$ Find the internal normal forces in the elastic bars. $($Answer: $1923$ N $)$

b$.$ Calculate the radius of curvature of the beam. $($Answer: $1444$ m $)$

Hint: The compatibility equation is given by ${}_x=-\frac{y}{}$