Large displacement elastic analysis of space frames allowing for flexural-torsional buckling of beams

Abstract

A new method of structural design, called advanced analysis has already been suggested in advanced codes and specifications. In engineering practice, the geometric imperfection of a member is unavoidable. To fulfill the requirements of advanced analysis, the member initial imperfection effect should be accommodated implicitly within the element model. In this study, an exact imperfect element based on Timoshenko's beam-column theory, is developed in the co-rotational formulation. Force deformation equations, which can include the initial imperfection effect, are derived through solving the differential equilibrium equations. The exact secant and tangent stiffness matrices are extensions of Oran's equations for straight elements. Several stability functions and bowing coefficients are believed to be original. The use of a single element is adequate enough for the extreme case of a column with both ends fixed, in which even two cubic elements cannot generate an accurate result. The accuracy and efficiency of this developed element are compared with ones of the conventional cubic element or other currently available elements. The structural sensitivity analysis to imperfection is performed. Design check formulation is also formed and incorporated into the current program NAF-NIDA. Numerical examples prove that the element can conduct the second-order elastic analysis and design of practical skeletal frames. Another beam element for geometrically nonlinear analysis of space steel frames is obtained based on the finite element method in the updated Lagrangian formulation. In the proposed element formulation, three deformation matrices, which represent the higher order effects due to the axial force and moments in the element, are derived. These matrices are functions of element deformations and incorporate the coupling among axial, lateral and torsional deformations. The proposed matrices are used together with linear and geometric stiffness for beam elements to study the large deflection behavior of space frames. Numerical examples show that the proposed element formulation is accurate and efficient in predicting the non-linear behavior due to Euler, axial-torsional and flexural-torsional buckling of space frames even when fewer elements are used to model a member.