RF-CONCRETE Surfaces – Online Manual Version 5

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RF-CONCRETE Surfaces – Online Manual Version 5

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2.8.2.1 Theoretical approaches

Theoretical approaches

"Nonlinear calculation" refers to the determination of internal forces and deformations considering the nonlinear behavior of internal forces and deformations (physical).

Planar structures can be described as two-dimensional structures with the following state quantities: surface loads, deformations, internal forces, and strains in the surface centroids. However, since material properties that vary over the surface depth must be considered for the nonlinear reinforced concrete model, it becomes necessary to extend the 2D model by additionally taking the depth of the cross-section into account. The cross-section of the reinforced concrete is divided into a certain number of steel and concrete layers (see Figure 2.126).

Based on the strains in the surface centroids and under the assumption of the Bernoulli hypothesis, the strains leading to the stresses after the corresponding steel or concrete material law has been applied are obtained for each layer. Then, the resulting stresses per layer can be integrated into the internal forces of the gross cross-section.

Figure 2.126 Layer model for reinforced concrete surfaces

If the concrete's tension strength is reached in a point of the structure, a discontinuity occurs in the form of a crack. Strictly speaking, this discontinuity would require an adjustment of the discretization (remeshing) so that every crack is included in the calculation in its actual position and size. In case of several cracks, this method would result in a high numerical effort because every crack would increase the number of elements. Therefore, occurring cracks are "smeared" within an element and the stiffness-reducing influences of the cracks are taken into account in the calculation by adjusting the material rule.

If the first principal stress in a concrete layer reaches the concrete tensile strength, a crack is formed perpendicular to the first principal stress direction. This principal direction may change if the load changes. Here we can assume that a forming crack does not change its position and orientation (the so-called fixed crack model) or that the crack always runs orthogonally to the variable principal directions (rotating crack model). RF-CONCRETE NL uses the rotating crack model.

Figure 2.127 Crack models in reinforced concrete surface elements