A uniform rectangular rigid slab of total mass M and mass mo

A uniform rectangular rigid slab of total mass M and mass moment of inertia Icm is supported on four light (massless) columns that are fixed at base and axially rigid. The flexural rigidity of each column is shown in the figure and same about the two principal axes. 2EI 2EI EI EI 12EI where h is the height of column. The lateral stiffness for a column with rigidity EI is given by k- Develop the equation of motion for this structure with respect to the three degrees of freedom located at center of mass and shown in the figure above.

Solution

use stiffness equation and flexural equation, find the displacement in terms of force & deflection and calculate force.