(Solved): 2. Consider the structure represented in the figure, consisting of an infinitely rigid bar \( \math ...

2. Consider the structure represented in the figure, consisting of an infinitely rigid bar \( \mathbf{A B C} \) and two deformable steel ties BD and CE. Data: BD: \( E=200 \mathrm{GPa} ; \mathrm{A}=8 \mathrm{~cm}^{2} \) CE: \( E=200 G P a ; A=12 \mathrm{~cm}^{2} \) Yield Stress: \( \sigma_{\text {vieal }}=235 \mathrm{MPa} \) a) Calculate the axial forces on the steel ties and the vertical displacement of node \( \mathrm{C} \) for \( \mathbf{P}=250 \mathrm{kN} \). b) Determine the value of the load \( \mathbf{P} \) at which one of the steel ties enters the plastic phase. c) Determine the value of \( \mathbf{P} \) that causes the collapse of the structure. d) Plot the graph of the displacement of point \( \mathbf{C} \) as a function of load \( \mathbf{P} \) until the collapse of the structure. e) Calculate the residual displacement of point \( \mathbf{C} \) after unloading the structure, assuming that the maximum value reached by \( \mathrm{P} \) is \( 490 \mathrm{kN} \). Also calculate the residual (i.e, after unloading) axial forces on the steel ties. 2. a) \( \mathrm{N}_{\mathrm{BD}}=53,571 \mathrm{kN} \) (traction) \( \mathrm{N}_{\mathrm{CE}}=160,714 \mathrm{kN} \) (traction) \( \delta_{C}{ }^{\text {vert }}=2,009 \mathrm{~mm}(\downarrow) \) b) \( \mathrm{P}=438,(6) \mathrm{kN} \) c) \( \mathrm{P}=501,(3) \mathrm{kN} \) d) e) \( \delta_{C}=2,475 \mathrm{~mm}(\downarrow) \) \( \mathrm{N}_{\mathrm{BD}}=66 \mathrm{kN} \) (traction) \( \mathrm{N}_{\mathrm{CE}}=-33 \mathrm{kN} \) (compression)