Interaction of Continuous Frames and Soil Media

A solution to the response of fully continuous orthogonal space frames supported on a viscoelastic soil media is presented. Matrix expressions containing slope-deflection equilibrium equations are used to formulate the structural problem in terms of joint rotations and elemental translations. The support reactions, derived in terms of the deformations, are incorporated into the equations of motion describing the consolidation of the soil mass. These expressions are written for mechanical models which are assumed to have viscoelastic characteristics analogous to the time-displacement properties of soils. Finite differences are used to reduce the differential equations of motion to linear algebraic forms such that a composite solution can be found when these expressions are substituted in the equilibrium equations. The methods of converting soil properties into equivalent viscoelastic mechanical model factors are examined and illustrative examples demonstrate the method.