Please use this identifier to cite or link to this item: https://hdl.handle.net/11681/10912
Title: A non-linear fracture mechanics numerical solution for reinforced concrete deep beams : a theoretical manual for the Fracture Mechanics Analysis of Reinforced Concrete Beams (FMARCB) Program
Authors: University of Missouri--Columbia. Department of Civil and Environmental Engineering.
Computer-Aided Structural Engineering Project (U.S.)
Riveros, Guillermo A.
Gopalaratnam, Vellore S. (Vellore Shroff), 1955-
Keywords: Bond slip High compressive strength Non-linear finite element analysis Non-linear fracture mechanics Normal compressive strength Reinforced concrete deep beams Shear Size effects Fracture mechanics Concrete beams
Computer-Aided Structural Engineering Project (U.S.)
Publisher: Information Technology Laboratory (U.S.)
Engineer Research and Development Center (U.S.)
Series/Report no.: ERDC/ITL TR ; 09-5.
Description: Technical Report
Abstract: A significant number of failures in reinforced concrete structures initiate in tension regions promoted by stress risers such as areas of high-stress concentrations or pre-existing cracks. Stable growth of these tensile cracks until peak loads are reached is associated with the development of large zones of fracture [fracture process zone (FPZ)]. The growth of the FPZ introduces the effect of structure size on the failure loads. An energy approach based on fracture mechanics concepts can be used to rationally analyze and design for size effects in brittle failures. Current design equations were developed based on strength analysis (as in the current American Concrete Institute code) where the margin of safety is higher for smaller structures than for larger ones. It is also conceivable that this approach would lead to unconservative designs for some very large structures (e.g., deep slabs for underground storage tanks). Since the empirical formulations of the code are based on data for concrete of normal strength, it places a limit on the maximum strength that can be effectively used in the design equations. As a result, promising high-performance concrete cannot be used to its fullest potential. Revisions to the shear design formulations are needed to ensure a uniform margin of safety for members of all sizes, strength, and geometries. This report describes a finite element analysis of reinforced concrete deep beams using nonlinear fracture mechanics. The development of a numerical model that incorporates compression and tension softening of concrete, bond slip between concrete and reinforcement, and the yielding of the longitudinal steel reinforcement is presented and discussed. 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 shear reinforcement. NOTE: This file is large. Allow your browser several minutes to download the file.
Rights: Approved for public release; distribution is unlimited.
URI: http://hdl.handle.net/11681/10912
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