$*$Probs$.8\mathrm{.}6-44.$ Each of these two$-$spen continuous$-$beam problems involves a nonuniform beam with one degree of static indeterminacy. To solve these by Force$-$Method Superposition you can treat each of these problems as two simply supported beams that have compalible slope where they are joined together at $\backslash ($ B $\backslash ).$ One beam has flexural rigidity $\backslash ($ E I $\backslash ),$ and the other has flexural rigidity $\backslash (2$ E I $\backslash ).$ You can find the necessary subproblem solutions in Table E$\mathrm{.}2.$ You will have to consider carefully the internal shear force and bending moment acting on each beam at joint $\backslash ($ B $\backslash ).$ The free$-$body diagrams give you appropriate names for these internal shear forces and bending moments

For these nonuniform beams, $($a$)$ determine the internal moments at $\backslash ($ B$,\backslash$left$($M$\_\{1\}\backslash$right$)\_\{$B$\}\backslash )$ and $\backslash (\backslash$left$($M$\_\{2\}\backslash$right$)\_\{$B$\}\backslash )$; and $($b$)$ determine the reactions $\backslash ($ R$\_\{$A$\}\backslash )$ and $\backslash ($ R$\_\{$B$\}\backslash ).$

$($a$)$

$($b$)$