• Deü, Jean-François
• Rouleau, Lucie
• Pais, Joseph
• Larbi, Walid
• Benakli, Sarah
• Ayoub, Naim

Abstract

The main objective of this research is to create a structural reinforced concrete shell finite element model that accounts for non-linear material behavior in seismic analysis. This shell model should be relatively accurate and computationally fit in order to be integrated into finite element analysis softwares. In addition, the whole structural model should be capable of under- going pushover analysis (non-linear static) and time history analysis (non-linear dynamic). During the initial stage of this research, we will start with a beam element. The first target is to model beams (frame structures) that account for non-linear material behavior in seismic analysis. This model will be then tested for accuracy and computational fitness in pushover and time history analysis. After passing all the validation requirements, the established concept will be generalized on shell elements. Modeling the plasticity of an element as a single concentrated node at the middle of the sec- tion can give acceptable results for beams since generally the dimensions of a beam’s transverse section are relatively small. However, this is not the case for shells, which usually possess a relatively large length. As a result, we can no longer model the entire section’s plasticity as one concentrated node at the middle. For this reason we considered the principle of fiber hinges which distributes the plasticity all over the section. The fiber hinge concept consists in dividing the reinforced concrete section into a set of fibers. Each fiber follows the non-linear uniaxial stress strain curve corresponding to its proper mate- rial (unconfined concrete, confined concrete or steel reinforcement). The overall behavior of the section is then obtained from the summation of all the fibers. A fiber hinge model is implemented in Matlab and the Newton-Raphson method is used to calculate the non-linear deformations in a section corresponding to its internal forces. Then by integrating this procedure all over the length of structural elements, the resulting tangent stiffness matrix and node displacements that consider material non-linearity are obtained. As a first step of validation, the ultimate loads computed by the proposed Matlab method (for beam elements) are compared to those predicted by classic reinforced concrete calculations. Secondly, the deflections obtained with this Matlab method are compared to the results of an engineering non-linear analysis software.

Topics

• impedance spectroscopy
• steel
• plasticity
• size-exclusion chromatography