Computational Methods for Reinforced Concrete Structures

Ulrich Häußler-Combe

• Publisher: Ernst & Sohn
• Year: 2014
• ISBN:
  9783433603635
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

The book covers the application of numerical methods to reinforced concrete structures. To analyze reinforced concrete structures linear elastic theories are inadequate because of cracking, bond and the nonlinear and time dependent behavior of both concrete and reinforcement. These effects have to be considered for a realistic assessment of the behavior of reinforced concrete structures with respect to ultimate limit states and serviceability limit states.
The book gives a compact review of finite element and other numerical methods. The key to these methods is through a proper description of material behavior. Thus, the book summarizes the essential material properties of concrete and reinforcement and their interaction through bond. These basics are applied to different structural types such as bars, beams, strut and tie models, plates, slabs and shells. This includes prestressing of structures, cracking, nonlinear stressstrain relations, creeping, shrinkage and temperature changes.
Appropriate methods are developed for each structural type. Large displacement and dynamic problems are treated as well as short-term quasi-static problems and long-term transient problems like creep and shrinkage. Most problems are illustrated by examples which are solved by the program package ConFem, based on the freely available Python programming language. The ConFem source code together with the problem data is available under open source rules at concrete-fem.com.
The author aims to demonstrate the potential and the limitations of numerical methods for simulation of reinforced concrete structures, addressing students, teachers, researchers and designing and checking engineers.

Chapter 1

Finite Elements Overview

1.1 Modeling Basics

“There are no exact answers. Just bad ones, good ones and better ones. Engineering is the art of approximation.” Approximation is performed with models. We consider a reality of interest, e.g., a concrete beam. In a first view, it has properties such as dimensions, color, surface texture. From a view of structural analysis the latter ones are irrelevant. A more detailed inspection reveals a lot of more properties: composition, weight, strength, stiffness, temperatures, conductivities, capacities, and so on. From a structural point of view some of them are essential. We combine those essential properties to form a conceptual model. Whether a property is essential is obvious for some, but the valuation of others might be doubtful. We have to choose. By choosing properties our model becomes approximate compared to reality. Approximations are more or less accurate.

On one hand, we should reduce the number of properties of a model. Any reduction of properties will make a model less accurate. Nevertheless, it might remain a good model. On the other hand, an over-reduction of properties will make a model inaccurate and therefore useless. Maybe also properties are introduced which have no counterparts in the reality of interest. Conceptual modeling is the art of choosing properties. As all other arts it cannot be performed guided by strict rules.

The chosen properties have to be related to each other in quantitative manner. This leads to a mathematical model. In many cases, we have systems of differential equations relating variable properties or simply variables. After prescribing appropriate boundary and initial conditions an exact, unique solution should exist for variables depending on spatial coordinates and time. Thus, a particular variable forms a field. Such fields of variables are infinite as space and time are infinite.

As analytical solutions are not available in many cases, a discretization is performed to obtain approximate numerical solutions. Discretization reduces underlying infinite space and time into a finite number of supporting points in space and time and maps differential equations into algebraic equations relating a finite number of variables. This leads to a numerical model.

Figure 1.1: Modeling (a) Type of models following [83]. (b) Relations between model and reality.

A numerical model needs some completion as it has to be described by means of programming to form a computational model. Finally, programs yield solutions through processing by computers. The whole cycle is shown in Fig. 1.1. Sometimes it is appropriate to merge the sophisticated sequence of models into the model.

A final solution provided after computer processing is approximate compared to the exact solution of the underlying mathematical model. This is caused by discretization and round-off errors. Let us assume that we can minimize this mathematical approximation error in some sense and consider the final solution as a model solution. Nevertheless, the relation between the model solution and the underlying reali...

Table of contents

• Cover
• Contents
• Title page
• Copyright page
• Preface
• Notations
• Chapter 1: Finite Elements Overview
• Chapter 2: Uniaxial Structural Concrete Behavior
• Chapter 3: Structural Beams and Frames
• Chapter 4: Strut-and-Tie Models
• Chapter 5: Multiaxial Concrete Material Behavior
• Chapter 6: Plates
• Chapter 7: Slabs
• Chapter 8: Shells
• Chapter 9: Randomness and Reliability
• Appendix A: Solution of Nonlinear Algebraic Equation Systems
• Appendix B: Crack Width Estimation
• Appendix C: Transformations of Coordinate Systems
• Appendix D: Regression Analysis
• Appendix E: Reliability with Multivariate Random Variables
• Appendix F: Programs and Example Data
• Bibliography
• Index