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Non-prismatic members are popular for civil engineering structures. This paper derives a set of unified beam-column formulations for nonlinear static and dynamic analyses of the structures made of members with tapered sections, addressing the problems in engineering design practices. The element shape-functions are established upon the local-axes by extracting the rigid-body movements for simplifying mathematical expressions. To represent the variations in the stiffness gradients of tapered sections, the tapered-variability indexes are proposed. The generalized tangent stiffness and consistent mass matrices are developed based on the indexes. When analyzing non-prismatic members, the conventional method for handling member loads is inapplicable because it is derived for prismatic sections. Therefore, a new approach for converting the member loads acting on tapered members into the equivalent …