DEFLECTIONS OF MEMBERS WITH VARIABLE CIRCULAR CROSS-SECTION

The paper presents the closed form solutions of the elastic deflections of one-dimensional bending members having circular cross-section with linearly and (in the binomial form) parabolically varying radius along the member's length. The solutions are obtained by transforming the fourth-order differential equations with variable coefficients into fourth-order differential equations with constant coefficients. For each radius variability four load conditions are considered: concentrated; uniformly distributed; linearly varying distributed; and parabolically varying distributed. The solutions give the distribution of the deflections, the rotations, the curvatures, the moments and the shearing forces of statically determinate and statically indeterminate members. Closed form solutions of the axial displacements are also presented. Numerical examples of structures commonly utilized in civil and mechanical engineering are provided.