Keywords: cross section, nonlinear analysis, reinforced concrete, frames, membrane elements, shear models.

For slender concrete structures material and geometrical nonlinearities have to be taken into account on grounds of safety and economy. The material nonlinearity of frame elements can be captured by a nonlinear analysis on a cross-sectional level. The analysis of the cross-sections is based on establishing the strain and corresponding stress distribution states. From these states the relation between the state of strain and the internal forces of the frame element is derived. For spatial frame elements six internal forces have to be considered.

This paper summarises previously proposed models for the cross-sectional analysis of spatial frames. The structural behaviour of a reinforced concrete frame element under torsion is studied in detail with three-dimensonal finite elements based on a damaged plasticity model. The analysis shows only accurate results as long as crack formation is not completed, after that the computed curve shows a large discrepancy. Taking into account existing models [1] and the preliminary finite element study a new approach for reinforced and prestressed spatial frame elements with arbitrary cross sections is derived. The approach is based on a notional division of the cross section into two interacting systems.

In the first system, the bending moments and axial force act on the concrete section and the longitudinal reinforcement. A cross-sectional integration is iteratively applied. The surface integral is numerically solved by line integration along its border. In the second system, the torsional moments and the shear forces are assigned to an assumed thin-walled hollow section which is assembled from membrane elements. From the wide range of membrane models the FASTM [2] seems most appropriate, because the important contribution of concrete is considered, and a simple but consistent smeared strain concept is applied.

1

K.N. Rahal, M.P. Collins, "Combined Torsion and Bending in Reinforced and Prestressed Concrete Beams", ACI Structural Journal, 100(2), 157-165, 2003.

2

R.R.H. Zhu, T.T.C. Hsu, J.Y. Lee, "Rational Shear Modulus for Smeared-Crack Analysis of Reinforced Concrete", ACI Structural Journal, 98(4), 443-450, 2001.

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