(Solved): Problem 1: The given single story, single bay frame (which can be idealized as a SDOF system) with ...

Problem 1: The given single story, single bay frame (which can be idealized as a SDOF system) with a lumped mass of \( m=4 \) tons and the total lateral stiffness of \( k=1500 \mathrm{kN} / \mathrm{m} \) is designed elastically in Part(a) and with an elasto-plastic behavior in Part(b) and Part(c). Using the elastic design acceleration response spectrum and the \( R_{\mu}-\mu-T \) spectrum given below; a) Find the maximum elastic displacement \( \left(u_{e}\right) \) at the top of the frame and the elastic base shear force \( \left(F_{c}\right) \). b) If the strength reduction factor is taken as \( R_{\mu}=6 \), calculate the maximum (inelastic) displacement (umax) at the top of the frame. c) This time if the base shear capacity is limited to \( \mathrm{F}_{\mathrm{y}}=\mathrm{W} / 2 \) where \( \mathrm{W} \) is the weight of the structure, calculate the maximum (inelastic) displacement \( \left(u_{\max }\right) \) at the top of the frame.