Repeat Problem 9.14 using the DOFs shown in Fig. P.9.16.
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Figure P9.14 shows a uniform slab supported on four columns rigidly attached to the slab and clamped at the base. The slab has a total mass m and is rigid in plane and out of plane. Each column is of circular cross section, and its second moment of cross-sectional area about any diametrical axis is as noted. With the DOFs selected as ux , uy , and uθ at the center of the slab, and using influence coefficients:
(a) Formulate the mass and stiffness matrices in terms of m and the lateral stiffness k = 12 /h3 of the smaller column; h is the height.
(b) Formulate the equations of motion for ground motion in (i) the x-direction, (ii) the y-direction, and (iii) the direction d–b.