A straight prismatic circular bar $AD$ has diameter $d$ and length $L$ in its undeformed state. Its left

end is fixed while its right end is displaced by ${}_D.$ A uniformly distributed axial force, $p$ per unit

length, is applied on segment $AB,$ and a concentrated force, $P_c,$ on cross$-$section $C.$ The bar

undergoes linear elastic deformation with a homogeneous Young's modulus, $E.$ The original

lengths of segments $AB$ and $BC$ are $L_{AB}$ and $L_{BC},$ respectively. Please i$)$ calculate the elongations

of segments $AB$ and $BC,$ ii$)$ calculate the axial displacement as a piecewise function of $x.$