The plan and elevation of steel special moment frame building are shown in Figures 1 and 2, respectively. The code-specified gravity loading is given as follows: Dfloor 85 psf Droof=68 psf Lfloor 50 psf Curtain wall = 175 lb/ft along building perimeter at every level Young's modulus for steel may be assumed to be 29*106 psi. Consider the response of the building in the plane of the moment-resisting frames. Ignore axial and shear deformations. A) Estimate the fundamental mode period and mode shape using Rayleigh's quotient method. B) Estimate the modal properties (period, mode shape) of the building. Consider the first four translational modes only. Plot the mode shapes. As an approximation, you may want to, but not required to, model the building as a 4-DOF moment-resisting frame structure with lumped masses at floor levels. C) Consider the Newhall station record from the 1994 Northridge earthquake (the one you used for your HW #4). Assume that the building has damping ratio of 2% of the critical damping. 1) Plot the displacement spectra (2% damped and 10% damped) for the 1994 Newhall ground motion. (Use Spector, Prism, or other software to generate the displacement spectra.) 2) Using the displacement spectra form part 1), determine the maximum roof drift, maximum roof (mean) drift ratio, and maximum story drift and story drift ratio for each story, by considering a) each mode, separately; b) combination of all four modes. Give two sets of results: using 2% vs. using 10% spectra. 3) Assuming 2% damping ratio for all four modes, plot the story drift ratio vs. time for each story if the building was subject to the 1994 Newhall station ground motion. D) Estimate max roof drift and max mean drift ratio using "velocity of displacement." Estimate peak story drift ratio (max in all stories) using the same. How do your estimates compare with your estimates from B) and C)? B 25'-0" 25'-0" A 25'-0" 30'-0" Roof W21x44 Fourth Level W14x68 W21x44 Third Level W24x76 Second Level Base W14x132 W24x76 W14×176 W14x82 30'-0" 2 ◄H▶ 2 3 4 30'-0" 30'-0" Figure 1 Floor Plan 30'-0" W21x44 W21x44 W24x76 W24×76 BM-1 JT-1 W14x176 W14x82 Column splice 48" above finished floor, typ. Figure 2 Special Moment Frame - Elevation 3 30'-0" W21x44 W21x44 W24x76 W24×76 4 W14x132 W14×68 14'-0" 12'-6" 12'-6" 12'-6" 5 30'-0"