Bending design of arbitrarily shaped steel fibre reinforced concrete sections using optimisation methods: Fid-Bau Portal

Bending design of arbitrarily shaped steel fibre reinforced concrete sections using optimisation methods

Mark, Peter / Strack, Mathias

The bending design often is of major concern in design procedures of steel fibre reinforced concrete (SFRC) members. Dimensions, material parameters as well as required amounts of bar and fibre reinforcements must be ascertained to achieve sufficient resistances of the cross sections against the actions of bending moments and axial forces. Besides such technical aspects, design procedures are also guided by economical considerations to save efforts in materials, time and construction. So the bending design of SFRC sections is treated with common mathematical techniques of optimisation to determine required amounts of bar reinforcement. First of all, the fundamental equations of the bending design are presented. They are incorporated into the mathematical framework of optimisation problems and solved using numerical optimisation methods. The governing equations of the bending design of arbitrarily shaped steel fibre reinforced concrete sections are then formulated in the form of an optimisation problem in order to calculate the minimum required bar reinforcements at given positions in the sections. Stress-strain-relations derived from the sigma-epsilon-design method model load-bearing effects of steel fibres. The optimisation problem is numerically solved using a Generalized Reduced Gradient algorithm and numerical integrations to determine the sectional forces of the resistance. The method is applied to the designs of slabs and girders. Therefore, stress-strain-relations recommended by the RILEM TC 162-TDF and an alternative, simplified approach are assumed. The calculated amounts of reinforcements together with the strain values at the top of the girder and at the lower reinforcement layer are presented for all three alternative fibre contributions. The bending design of reinforced concrete or steel fibre reinforced concrete sections subject to biaxial bending and axial forces can be performed with the presented optimisation method. The minimum amounts of bar reinforcements as well as the orientation of the plane of strains are obtained. The method allows for the treatment of arbitrarily shaped sections, as the sectional forces of the resistance are not analytically but numerically integrated. The method is especially suitable for practical applications, because it can efficiently be implemented into common spreadsheet analysis programs. The incorporation of stressstrain- relations according to the RILEM recommendations or of other desired relations require only small efforts, computing times usually remain negligible.