Find the shape function of the longitudinal total coordinate system coordinate $(x)$ of the beam element with $3\mathrm{.}1(5$ points$)$ length $L$ and cross$-$sectional second moment I. Young's Modulus Ei$.$

$3\mathrm{.}2(10$ points$)$ Show that the element strength matrix in the entire coordinate system of the auxiliary element is as follows.

$([M_1],[V_1],[M_2],[V_2])=[K{]}^{(e)}([U_{11}],[U_{12}],[U_{j1}],[U_{j2}]),[K{]}^{(e)}=\frac{EI}{L^3}{\left[\begin{array}{cccc}12& 6L& -12& 6L\\ 6L& 4L^2& -6L& 2L^2\\ -12& -6L& 12& -6L\\ -6L& 2L^2& -6L& 4L^2\end{array}\right]}^2$

Find the shape function of the longitudinal total coordinate system coordinate $(x)$ of the beam element with $3\mathrm{.}1(5$ points$)$ length $L$ and cross$-$sectional second moment I. Young's Modulus Ei$.$

$3\mathrm{.}2(10$ points$)$ Show that the element strength matrix in the entire coordinate system of the auxiliary element is as follows. Please explain detali ex dof

$([M_1],[V_1],[M_2],[V_2])=[K{]}^{(e)}([U_{11}],[U_{12}],[U_{j1}],[U_{j2}]),[K{]}^{(e)}=\frac{EI}{L^3}{\left[\begin{array}{cccc}12& 6L& -12& 6L\\ 6L& 4L^2& -6L& 2L^2\\ -12& -6L& 12& -6L\\ -6L& 2L^2& -6L& 4L^2\end{array}\right]}^2$