Simplified Analytical Solution for Tapered Circular Elements on Homogeneous or Non-homogeneous Soil

Abstract

Abstract This paper presents a simplified method to examine the response of circular tapered Euler-Bernoulli beam-columns. The Di˙erential Transformation Method (DTM) is implemented to solve the di˙erential equation (DE) that governs the response of the element. When conventional analytical approaches (i.e., discrete or continuum approaches) are used to solve the DE, and because of the introduction of the non-uniform cross-section and the soil non-homogeneity, the analysis becomes rather di˚cult and the solution complex to obtain. Here, the rather complex DE and corresponding boundary conditions (B.Cs.) are expressed as a system of linear algebraic expressions which solution is readily available. The proposed formulation includes the e˙ects of i) semi-rigid connections and lateral restraints at the ends of the element, ii) an external transverse load, iii) flexible and short elements, iv) soil/element sti˙ness, and v) an elastic homogeneous or non-homogeneous Pasternak soil. Both static and buckling analysis can be carried out using the same formulation.