For the beam shown in figure below, using the stiffness method, calculate all

the unknown nodal displacements and member forces in beams ab and bc$.$

Temperature: Member AB has temperature change such that:

Tu $=150,$ Tt $=0$ and Tc $=75,$ Section is symmetric with height $=12$ in and alpha $=6\mathrm{.}5\backslash$times $106$ ft$/($ft$)$

Fabrication error: Member BC has out of straightness fabrication error ebc $=0\mathrm{.}5$ in$.$

Support Settlement: The support A settles down by $0\mathrm{.}5$ in$.$

For all members:

E $=207360$ k$/$ft$2$

I $=1/12$ ft$4$

L $=12$ ft

Area: Aab $=0\mathrm{.}25$ ft$2$

and Abc $=0\mathrm{.}1$ ft$2$

Spring: ks $=$ EI$/$L$^3$

Note: I and A is different for members AB and BC$,$ and concentrated force is applied at

the center of the span.

Hint: Use a consistent unit system and you need to include axial dofs in this problem.