(Solved): 4. The stiffness and mass matrices, modal frequencies and mode shapes of the frame shown in Fig. 4 ...

4. The stiffness and mass matrices, modal frequencies and mode shapes of the frame shown in Fig. 4 are given below. Using Response Spectrum method, determine the base shear of the frame for the El Centro earthquake (Fig. 5). Assume \( 2 \% \) damping. Use SRSS method of combination. (20) \[ \mathbf{m}=\left(1 \text { kip- } \sec ^{2} / \text { in }\right)\left[\begin{array}{ccc} 1.0 & 0 & 0 \\ 0 & 1.5 & 0 \\ 0 & 0 & 2.0 \end{array}\right] \mathbf{k}=(600 \text { kips/in })\left[\begin{array}{rrr} 1 & -1 & 0 \\ -1 & 3 & -2 \\ 0 & -2 & 5 \end{array}\right] \] Fig. 4 Fig. 5