$(3)$ Consider a loaded statically indeterminate beam, as shown in Figure $3.$ The symbols $k_s$ and $k_{}$ denote the axial spring constant and the rotational spring constant, respectively, and $k_s=E\frac{\text{I}}{L^3}$ and $k_{}=E\frac{\text{I}}{L}.$

$($a$)$ Select the spring force $(F_s)$ as the redundant force and determine its value using the consistent deformation method. The conjugate$-$beam method is required for the involved calculation. $(15\%)$

$($b$)$ Select the spring moment $)$ as the redundant moment and determine its value using the consistent deformation method. The unit$-$load method is required for the involved calculation. $,(15\%)$