Keywords: biaxial bending, fiber model, failure surface, composite section.

This paper presents a generic fiber model algorithm for the analysis of arbitrary cross sections under biaxial bending and axial load. The strain distribution is based on the assumption that plane sections before bending remain plain after bending (Bernoulli-Euler assumption). This method distinguishes itself by using custom stress-strain diagrams for multiple non-intersecting graphical objects. Therefore, the cross section may have an irregular shape with or without openings and may consist of various materials. This algorithm is primarily used for the creation of failure surfaces but it can also address a variety of problems as shown in the examples. A special purpose computer program with full graphical interface has been developed.

In this algorithm, the isogonic or 3D method is used for the creation of the failure surface. The direction of the neutral axis is assumed from the very beginning and a full moment-curvature diagram is constructed until the cross section fails. The ultimate values of each analysis describe the conventional or real failure surface of the cross section.

The cross section is described by polygons and circles. Arcs are approximated by polygon chains to a specified accuracy. Complex cross sections may be described easily by assigning a "foreground" material and a "background" material to all graphical objects.

The stress-strain diagrams of all materials are composed of any number and any combination of consecutive parabolic or linear segments. Also, the material structure holds data related to the maximum compressive and tensile strain and whether reach of these values signifies the conventional failure of the cross section. Various effects such as concrete confinement, concrete tensile strength, strain hardening of the reinforcement etc. may be taken into account, providing full control to the designer over the entire model.

The calculation of the stress resultants itself is based on the trapezoidal decomposition of the cross section. The algorithm proved to be stable and fast while it provided accurate results. Moreover, it can address virtually any problem in which the Bernoulli-Euler assumption holds.

1

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2

Rodriguez, J.A., Aristizabal-Ochoa, J. Dario, "M-P- diagrams for reinforced, partially and fully prestressed concrete sections under biaxial bending and axial load", J Struct Engng, ASCE, 127(7):763-773, 2001. doi:10.1061/(ASCE)0733-9445(2001)127:7(763)

3

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4

Chen, S.F., Teng, J.G., Chan, S.L., "Design of biaxially loaded short composite columns of arbitrary cross section", J Struct Engng, ASCE, 127(6):678-685, 2001. doi:10.1061/(ASCE)0733-9445(2001)127:6(678)

5

Sfakianakis, M.G., "Biaxial bending with axial force of reinforced, composite and repaired concrete sections of arbitrary shape by fiber model and computer graphics", Advances in Engineering Software 33, 227-242, 2002. doi:10.1016/S0965-9978(02)00002-9

6

Yen, J.Y.R., "Quasi-Newton method for reinforced concrete column analysis and design", J Struct Engng, ASCE, 117(3):657-666, 1991. doi:10.1061/(ASCE)0733-9445(1991)117:3(657)

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