Let us consider the standard $($statically determined$)$ beam bending with a constant body loading $($say$,$ resulting from gravity$).$

For a constant cross section $\backslash (($A$=$B H$)\backslash ),$ solve the problem by the finite element method with two elements $($of equal size$)$ with linear basis functions $($in $\backslash ($ x $\backslash ))$ and compare the FE approximations of the bending moment $\backslash (\backslash$left$($M$\_\{$h$\}\backslash$right$)\backslash )$ and shear force $\backslash (\backslash$left$($Q$\_\{$h$\}\backslash$right$)\backslash )$ to the corresponding exact solutions $($cf$.$ Theoretical exercise $1\mathrm{.}4).$

Hint. Before starting to calculate the required stiffness matrix $\backslash (\backslash$left$($K$\_\{$i j$\}\backslash$right$)\backslash )$ and force vector entries $(\backslash ($ f$\_\{$i$\}\backslash )),$ check how the boundary conditions $($at $\backslash ($ x$=0\backslash )$ and $\backslash ($ x$=$L $\backslash ))$ affect $($simplify$)$ the final equation system.