Problem $1[40$ points$]$

Consider the statically indeterminate frame shown below. All members have wide$-$flange W$310$x$21$ steel cross$-$sections made of steel with $\backslash ($ E$=210,000\backslash$mathrm$\{$MPa$\}\backslash ).$ Use the flexibility method with the horizontal reaction force at D as the redundant to solve the following problems.

a$)[20$ points$]$ Determine the bending moment diagram $($BMD$)$ due to the load that is shown in the figure. Neglect axial deformations.

b$)[20$ points$]$ Determine the BMD when the temperature increases by $\backslash (30^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ on the outside but not on the inside of the frame. Include the fact that the temperature change causes a net elongation of each member, but continue to neglect the effect of axial deformations on the BMD$.$ The coefficient of thermal expansion, $\backslash (\backslash$alpha $\backslash ),$ is $\backslash (1\mathrm{.}2\backslash$cdot $10^\{-5\}/\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$