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2 Theoretical Background

2.7.3 Critical Surface

Critical Surface

To determine the critical surface, each reinforcement direction φ is considered separately. The state of stress is analyzed on both surfaces s – bottom surface (in the direction of the local +z-axis) and top surface (in the direction of the local -z-axis). The side with the greatest tensile stress in the concrete is classified as governing. The internal forces on the critical side are designated as nΦ and mΦ.

The axial force nΦ,s that is transformed in the reinforcement direction Φ has the same value for both surfaces s (nΦ = nΦ,top = nΦ,bottom). The axial forces are therefore not relevant for determining the critical side; only the moments are considered in finding the governing surface. The algebraic signs for the bending moments nΦ,s are determined regarding whether the moments cause tension or compression on the respective surface s. Therefore, the critical surface is the side with the larger bending moment (i.e. the side that is more strongly subjected to tension).

For the calculation of the stiffness, only the internal forces nΦ and mΦ on the critical side are taken into account. Until now, the term "bottom surface" has referred to the local +z-axis; in the following, however, "bottom surface" refers to the critical side of the surface.