22.314/1.56/2.084/13.14 Fall 2006� Problem Set IX Due 11/21/06 This problem set illustrates some features of seismic analysis. A response spectrum modal (lumped mass) method is to be used. 1)Geometry, Properties, Supports: The reactor component of interest is represented by a pipe. The pipe is subjected to a seismic ground motion that acts parallel to the x-direction. The axis of the pipe in the z-direction. The pipe has an outside diameter of 210mm, a wall thickness of 7mm, and a length of 3m. The pipe is made of a material with Young’s modulus = 200 Gpa and density = 8500 kg/m3 . Liquid water (density = 750 kg/m3 ) is present both inside and outside of the pipe. The added mass coefficient for the outside water is 1.1. Neglect direct treatment of fluid friction, fluid drag, and solid friction – these effects are incorporated in the damping matrix of item 2. The support at z = 0 is fixed (zero displacement and zero slope). The support at the other end (z=L=3 m) is a roller (zero displacement, zero moment, and zero axial force).
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