(Solved): 2. ( 50 points) Given the structure below, where all members share the same square cross-section and ...

2. ( 50 points) Given the structure below, where all members share the same square cross-section and a 50 kN lateral load is applied at the midspan of member CD. Take \( \mathrm{E}=200 \mathrm{GPa} \). Assume point \( \boldsymbol{D} \) is a pin support. Use the virtual work method: (a) ( 25 points) Considering bending effects only, determine the minimum required moment of inertia \( I \) for the members such that the horizontal displacement at point A does not exceed \( \pm 30 \mathrm{~mm} \). (b) ( 25 points) One claims that the internal strain energy due to axial forces should also be considered. Do you agree? Justify your answer by calculating and comparing the percentage change in the required \( I \) when axial effects are included. For square cross-sections, \( A=\sqrt{12 I} \).