9. a) For the frame shown, derive the equilibrium equation for translation at joint ②. 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]{δ, θ₂, θ₃} = {P}
DO NOT SOLVE THE EQUATIONS.
The unknowns of the problem shall be:
δ = translation at joint ② (positive in the direction shown)
θ₂ = rotation of joint ②
θ₃ = rotation of joint ③ (counter clockwise positive)