Problem 1: A structure was originally designed as a moment-resisting frame (with rigid connections between beams and columns). An engineer in your office suggested adding braces to the structure to control the maximum drift. The braces can be assumed to act both in tension and in compression (no buckling). The geometry and properties of the frame and braces are givenin the following figure.
a) Define and calculate the mass, stiffness, spectral and modal matrices of the frame with and without the braces.
b) For the unbraced frame, using the design response spectrum for Melbourne and assuming that the structure has 5% damping in each mode, compute the maximum displacement at each floor, the maximum inter-storey drift, the maximum base shear as well as the maximum moment and shear in each column of the frame. Clearly indicate on the spectra which spectral values were used in the response spectrum analysis.
c) For the braced frame, using the design response spectrum for Melbourne, and assuming that the structure has 5% damping in each mode, compute the maximum displacement at each floor, the maximum inter-storey drift, the maximum base shear as well as the maximum moment and shear in each column of the frame. Clearly indicate on the spectra which spectral values were used in the response spectrum analysis.
d) Compare the response of these two structures and discuss the pros and cons of each design.
Problem 2:
An elevated water tank is to be built at a site where an existing two-storey moment frame (with rigid connections between the beams and the columns) equipped with braces (effective in both tension and compression) is located. Preliminary calculations indicate that the
estimated period of the elevated tank will be approximately 2.0 s. The geometry and properties of the frame are given in the following figure. The structure is assumed to have 5% damping in both modes of vibration. The design acceleration spectrum for 5% damping for this site is also given below.
a) Define the mass and stiffness matrices of the braced-frame structure.
b) Compute the spectral and modal matrices of the braced-frame structure.
c) Compute the damping matrix of this system (for a Rayleigh damping model).
d) Using a response spectrum analysis, estimate the maximum displacement of the top floor relative to the ground as well as the maximum base shear of the braced-frame structure when it is subjected to the design ground motion.
e) For this design ground motion, determine the minimum distance D at which the elevated water tank can be built in order to avoid pounding between the two structures under the design earthquake.
