Abstract

This article presents a finite element analysis of reinforced concrete deep beams using nonlinear fracture mechanics. The article describes the development of a numerical model that includes several nonlinear processes such as compression and tension softening of concrete, bond slip between concrete and reinforcement, and the yielding of the longitudinal steel reinforcement. The development also incorporates the Delaunay refinement algorithm to create a triangular topology that is then transformed into a quadrilateral mesh by the quad-morphing algorithm. These two techniques allow automatic remeshing using the discrete crack approach. Nonlinear fracture mechanics is incorporated using the fictitious crack model and the principal tensile strength for crack initiation and propagation. The model has been successful in reproducing the load deflections, cracking patterns and size effects observed in experiments of normal and high-strength concrete deep beams with and without stirrup reinforcement.

Highlights

  • Reinforced concrete (RC) deep beams have useful applications in tall buildings, offshore structures, foundations, and military structures

  • If one was to design structures based on equations that were developed based on strength analysis, as in current American Concrete Institute (ACI) code [1], the margin of safety provided would depend upon the size of the structure

  • Because these models differ in material models, element formulations, and solution procedures, a specific approach will be more suited for specific structures and/or loading situations and less suited to others [13]; nonlinear fracture mechanics models are capable of analyzing the complete behavior of reinforced concrete beams of any size and loading geometry

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Summary

Introduction

Reinforced concrete (RC) deep beams have useful applications in tall buildings, offshore structures, foundations, and military structures. LEFM assumes that the fracture process is small and can be replaced, and that the rest of the member volume remains elastic; research in the last four decades has resulted in modifications to LEFM to account for the distributed nature of pre-peak micro-cracking and the presence of a large FPZ in concrete [3,4,5,6] These modifications have produced better results in the application of fracture mechanics concepts to brittle failure in reinforced concrete. Several numerical models have been developed to study the behavior of brittle failure (shear) of reinforced concrete beams [10,11,12,13] Because these models differ in material models, element formulations, and solution procedures, a specific approach will be more suited for specific structures and/or loading situations and less suited to others [13]; nonlinear fracture mechanics models are capable of analyzing the complete behavior of reinforced concrete beams of any size and loading geometry. The model has been successful in reproducing the load deflections, cracking patterns and size effects observed in experiments of normal and high-strength concrete deep beams with and without stirrup reinforcement [20] with shear-span-to-depth ratios a/d of 1.5 and 2.5

Experimental Evaluation
Nonlinear Fracture Mechanics Using the Fictitious Crack Model
Material Properties Characterization
Interface Element
Model Validation
Numerical Solution without Shear Reinforcement
Numerical Solution with Shear Reinforcement
10. Conclusions
Findings
11. Acknowledgements
Full Text
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