a$)$ For the frame shown, derive the equilibrium equation for translation at

joint $(3).$ Neglect the effects of axial strain. All members have the same EI

value.

b$)$ Derive the equilibrium equations for moment equilibrium at joints $(2)$ and $(3).$

c$)$ Present your results in matrix form by giving the terms of the stiffness matrix $[$K$]$

and the load vector $\{P\}$ in the following equation:

$[K]\{[],[{}_2],[{}_3^{}]\}=\{P\}$

DO NOT SOLVE THE EQUATIONS.

The unknowns of the problem shall be:

$=$ translation $at$ joint$(3)(positiveto$ the right$)$

${}_2=$ rotation $of$ joint $(2)(counter$ clockwise positive$)$

${}_3=$ rotation $of$ joint $(3)$