Problem $1(10$ points$)$

A three bars system consisting of a central bar of length $\backslash ($ L $\backslash )$ and two bars inclined at an angle $\backslash (\backslash$theta$\_\{0\}\backslash )$ is loaded by a downward tensile force $\backslash ($ P $\backslash ),$ as shown in the following figure. Assume that axial rigidity $\backslash ($ E A $\backslash )$ of all bars are the same. Given $\backslash ($ E A$,$ L $\backslash )$ and $\backslash (\backslash$theta$\_\{0\}\backslash ).$

$(1)(5$ points$)$ Determine the displacement $(\backslash (\backslash$delta $\backslash ))$ under the force as a function of the input data. Note that this is a statically indeterminate problem.

$(2)(5$ points$)$ Solve the problem using the Castigliano's theorem or minimization of total potential energy.