Design-Oriented Nonlinear Modeling of Reinforced Concrete Wall Structures for Numerical Limit State Analysis

Daniel Vestergaard

Research output: Book/ReportPh.D. thesis

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Abstract

Reinforced concrete (RC) plays a significant role in modern construction due to its versatility, durability, and low cost. As a consequence, concrete has become the world’s most-used building material, the second-most-used substance after water, and the source of more than 8% of global CO2 emissions. Design processes for building structures of, e.g., reinforced concrete involve multiple parties, such as clients, architects, and engineers from different disciplines, often resulting in frequent changes to the design. Combined with time constraints, this requires structural engineers to adopt tools for limit state verification based not only on their accuracy but also their computational robustness and modeling complexity. As a result, limit state verification of complex RC structures is often carried out using efficient but inaccurate linear-elastic methods leading to unnecessarily conservative designs.

Finite Element Limit Analysis (FELA) has emerged as an efficient and reliable alternative for ultimate limit state analysis of normally reinforced concrete structures by combining the extremum principles of plasticity with convex optimization.
Since the concept does not involve finite deformations, however, it is ill-suited for assessing strain- and stiffness-based phenomena such as crack widths, reinforcement ductility, and structural instability.

This thesis presents a design-oriented numerical tool with low modeling complexity for nonlinear limit state analysis of RC wall structures. Based on FELA’s high computational performance and low modeling complexity, the presented tool
draws inspiration from the field by formulating the elastic field problem as a convex optimization problem using the principle of minimum complementary energy. Using this approach, the framework enables integrated collapse and deformation analysis of large-scale RC wall structures.

The presented framework is based on nonlinear-elastic constitutive models for concrete and steel reinforcement, which allow the inclusion of the concrete strength reduction due to cracking as well as fire-induced thermal strain and reduced material stiffness. The constitutive models are coupled with a stress-based finite membrane element for modeling walls with in-plane loading, and a novel stress-based finite shell element for modeling walls with combined in-plane and transverse loading. These models are demonstrated to be capable of analyzing large-scale finite element models of RC wall structures with more than 13,000 finite membrane elements and 2,400 finite shell elements, respectively, within minutes on a standard laptop computer. Finally, the framework enables nonlinear instability analysis of slender RC wall structures through an iterative two-step procedure where the cracked section stiffness is derived from the geometrically linear response and used in a subsequent displacement-based linearized buckling analysis. This method is demonstrated also to enable instability analysis of large-scale models with more than 3,200 finite elements on a standard laptop computer.
Original languageEnglish
Place of PublicationKgs. Lyngby
PublisherTechnical University of Denmark
Number of pages182
ISBN (Electronic)978-87-7475-705-4
DOIs
Publication statusPublished - 2022
SeriesDCAMM Special Report
NumberS319
ISSN0903-1685

Keywords

  • Reinforced concrete
  • Convex optimization
  • Finite element models
  • Elasto-plasticity
  • Complementary energy
  • Buckling

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