Please solve this problem using $$Matrix Stiffness Method step $by$ step. Consider the structure on the right. Determine the support reactions with the displacement

method. Draw the bending moment and shear force diagrams.

Requirements:

Conduct the structural analysis twice based on the following two different definitions of structural

nodes:

$($a$)$ Node definition $1$: three structural nodes at $A,B,$ and $C$;

$($b$)$ Node definition $2$: four structural nodes at $A,E,B,$ and $C.$

Verify your results by comparing the diagrams from the two analyses.

Notes:

$E=200$GPa,$I=1\mathrm{.}8({10}^9)m{m}^4.$ The values are constant from $A$ to $C.$

For node definition $1,$ complete the analysis with hand calculation and FE$-$approved

calculators

For node definition $2,$ outline the solution steps on the answer sheets and complete the

computation using the excel template provided on Canvas.

Hints:

For node definition $1,$ use superposition to get the fixed$-$end forces of element $AB($note

that there is a typo on FEF equations in the textbook, use the updated version in the

course slide$).$

For node definition $1,$ free body diagrams may be needed for the diagrams along AB$.$