Second-order analysis of non-prismatic steel members by tapered beam-column elements

Certain benefits in terms of the efficiency in material consumption can be achieved by adopting tapered steel members in long-span structures. In this paper, analytical solutions for second-order analysis of non-prismatic steel members by a series of tapered beam-column elements are firstly proposed. The exact stiffness matrices for five common types of sections, e.g. circular solid, circular hollow, rectangular solid, rectangular hollow and symmetric I sections, are derived using the Hermite interpolation shape function and the co-rotational (CR) description to simplify the derivations and formulations. Large deformation is considered by the incremental secant stiffness method based on the updated Lagrangian approach. Descriptions for the kinematic motion using the CR description are elaborated. A distinct feature of the proposed method is to analytically express the flexural rigidity of tapered sections in the stiffness matrices using a series of stiffness factors, such as the αi and βi factors, accurately reflecting the stiffness variation along the member length. Several examples are presented to examine the validity and accuracy of the proposed formulations. The examples indicate that only two elements per member can produce very accurate analysis results, where the computational savings in the numerical procedure are considerable.