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

Yoint $(3)$ below. Neglect the effects of axial strain. EI has the same value for all

members.

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 $(3)(positivein$ the direction shown$)$

${}_x=$ rotation $of$ joint $(2)$

${}_y=$ rotation $of$ joint $(3)(counter$ clockwise positive$)$

$($counter clockwise positive$)$