Problem $2$: Analysis of frames by the Slope$-$Deflection method.

Determine the reactions and draw the axial force, shear and bending moment diagrams for the frame with sidesway shown in Fig. $2$ using the slope$-$deflection method.

The moment of inertia for the columns AB and CD is $\backslash (\backslash$mathrm$\{$Icol$\}=100\backslash$times $106\backslash$mathrm$\{$~mm$\}4\backslash )$ and for the beam BC is Ibeam $\backslash (=200\backslash$times $106\backslash$mathrm$\{$~mm$\}4\backslash ).$ Young's modulus is $\backslash ($ E$=200\backslash$mathrm$\{$GPa$\}\backslash ).$

The loads and dimensions are given in Fig $2.$ The ends $\backslash ($ A $\backslash )$ and $\backslash ($ D $\backslash )$ of the frame are fully fixed.

The following tasks are to be performed and reported:

$1.$ Identify the spans, nodes and degrees of freedom.

$2.$ Derive slope$-$deflection equations for each span.

$3.$ Derive equilibrium equations required to find the unknown rotations and lateral displacement.

$4.$ Calculate the unknown displacements and rotations.

$5.$ Calculate the member end moments.

$6.$ Calculate the support reactions.

$7.$ Draw the axial force, shear and bending moment diagrams.

Fig $2.$ Frame with sidesway

$\backslash [$

$\backslash$mathrm$\{$n$\}1=3,\backslash$mathrm$\{$n$\}2=1,\backslash$mathrm$\{$n$\}3=0$

$\backslash ]$