Problem $1$

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

end is fixed. A uniformly distributed axial force, $p$ per unit length, is applied on segment $AB,$ a

concentrated force, $P_c,$ on cross$-$section $C,$ and a concentrated force, $P_D,$ on the rigat end $D.$ 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$)$ describe the stress$/$strain

states in the bar as piecewise functions of $x,$ ii$)$ calculate the elongations of segments $AB,BC,$

and $CD,$ the total elongation of bar $AD,$ and the axial displacements at cross sections $B,C,$ and

D$.$