Nonlinear analysis of space R/C frames with non-uniform torsion

Abstract

This paper presents a numerical model of stability and load-bearing capacity of space reinforced concrete (R/C) frame structures taking into account the material and geometric nonlinearity. The developed model describes the behavior of space frames with composite cross sections under a monotonically increasing load, from zero up to the ultimate load, i.e. collapse of the structure. The collapse of the structure occurs due to exceeding the limit load and/or loss of stability of space beams or whole structure.

The fibre decomposition procedure is developed to solve material and geometrical nonlinear behaviour of composite cross-section in three-dimensional frames. The filaments in the fibre decomposition model of the cross-section, which describe uniaxial behaviour of materials, are extended over corresponding finite element and create a separate prismatic body discretised by brick finite elements. After mapping of boundary forces on prismatic body, i.e. ‘comparative body’, the capture of non-uniform torsion is applied. The main attention in this approach is concentrated on the evaluation of the torsional stiffness, which are strongly nonlinear.

Three integration levels exist: the first along the beam-column finite element, the second over the fibre decomposed cross-section and the third over a prismatic comparative body. Behaviour of the space frames shall be more realistically described in this way, especially flexural, lateral and torsional stability effects.

The global procedure includes an incremental-direct iteration step approach. The incremental step model of gravitational load level is applied. Geometrical nonlinearity is assumed by Total Lagrange small displacement formulation. The perfect bond-slip effect between concrete and rebars as well as smeared crack model is assumed.

Two examples are studied to verify the accuracy of the program and demonstrate its application in practical engineering.