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The use of subgrade modulus in structural analysis and design is often poorly coordinated between geotechnical and structural engineers, leaving a possibility for misuse and error. Ideally, foundation design should account for soil stiffness, footing stiffness, and soil structure interaction through selection of the proper modulus value. The subgra...
Context in source publication
Context 1
... increase is at least 25 percent of the pressure on the footing. This zone may be called the pressure bulb, and its typical shape is presented in Figure 1. The depth of the pressure bulb is roughly proportional to the width of the footing. For a stiff clay, where the deformation characteristics are roughly independent of depth, settlement will result from compression of the soil under the footing. Because the depth of soil that will experience compression will be roughly proportional to the width of the footing, settlement can be considered as roughly proportional to the width of the footing. Thus, it can be shown ...
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Citations
In this paper, an analytical method is presented in order to determine the static bending response of an axisymmetric thin circular/annular plate with different boundary conditions resting on a spatially inhomogeneous Winkler foundation. To this end, infinite power series expansion of the deflection function is exploited to transform the governing differential equation into a new solvable system of recurrence relations. Singular points of the governing equation are effectively treated by applying the Frobenius theorem in the solution, which in turn permits the use of more-general analytical functions to describe the variation of the foundation modulus along the radius of the plate. Moreover, no special limitation is imposed on the transverse loading function as applied to the system. On employing the proposed method, the deflection response is obtained through an illustrative example for various boundary conditions along the plate edges, considering free, clamped, hinged, and elastically restrained boundaries. In addition, analytical results are validated and compared with those obtained using a finite element analysis, where an excellent agreement is found. Finally, the extension of the method to solve the more-general case of a variable two-parameter (Pasternak) foundation is indicated.
An exact solution is established pertaining to the problem of undamped free vibration of a thin circular plate resting on a Winkler foundation with variable subgrade modulus. The solution is performed by applying the infinite power series method. Moreover, the solution procedure is demonstrated through an illustrative example, wherein the general frequency equation is derived for two different boundary conditions. The correctness of the solution is also verified using results available in the literature. Finally, it is shown that the proposed method of solution is directly applicable to the more-general problem of circular plates on a variable-modulus Pasternak-type foundation.
