Problem $3$

Determine the kinematic indeterminacy $($KI$)$ values and label the global DOFs in the beams shown below. Use the displacement method to determine the support reactions. Plot the bending moment and shear force diagrams.

Notes:

Use element$-$based assemblage for determining structural stiffness matrix;

Assign your own $E$ and $/$ values based on the following assumptions

For structure $($a$),$ the material is reinforced concrete and the cross section is rectangular. The shape should maintain the ratio of $\frac{?}{?}$ values between $AB$ and $BC.$

For structure $($b$),$ the material is steel and the cross section follows the American Institute of Steel Construction $($AISC$)$ shapes