Computational Methods for Reinforced Concrete Structures

by Hä; uß; ler-Combe, Ulrich

• ISBN13: 9783433030547
• ISBN10: 3433030545
• Edition: 1st
• Format: Paperback
• Copyright: 2014-11-24
• Publisher: Ernst & Sohn

Summary

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.

Author Biography

Ulrich Häussler-Combe, Prof. Dr.-Ing. habil. studied structural engineering at the Technical University Dortmund and gained his doctorate from the Karlsruhe Institute of Technology (KIT). Following ten years of construction engineering and development in computational engineering, he came back to KIT as a lecturer for computer aided design and structural dynamics. Since 2003 he has been professor of special concrete structures at Dresden University of Technology.

Table of Contents

1 FINITE ELEMENTS OVERVIEW
Modeling Basics
Discretization Outline
Elements
Material Behavior
Weak Equilibrium and Spatial Discretization
Numerical Integration and Solution Methods for Algebraic Systems
Convergence

2 UNIAXIAL STRUCTURAL CONCRETE BEHAVIOR
Scales and Short-Term Stress-Strain Behavior of Homogenized Concrete
Long-Term Behavior -
Creep and Imposed Strains
Reinforcing Steel Stress-Strain Behavior
Bond between Concrete and Reinforcing Steel
The Smeared Crack Model
The Reinforced Tension Bar
Tension Stiffening of Reinforced Tension Bar

3 STRUCTURAL BEAMS AND FRAMES
Cross-Sectional Behavior
1 Kinematics -
2 Linear Elastic Behavior -
3 Cracked Reinforced Concrete Behavior -
4 Compressive Zone and Internal Forces -
5 Linear Concrete Compressive Behavior with Reinforcement -
6 Nonlinear Behavior of Concrete and Reinforcement
Equilibrium of Beams
Finite Element Types for Plane Beams
1 Basics -
2 Finite Elements for the Bernoulli Beam -
3 Finite Elements for the Timoshenko Beam -
4 System Building and Solution Methods -
5 Elementwise Integration -
6 Transformation and Assemblage -
7 Kinematic Boundary Conditions and Solution
Further Aspects of Reinforced Concrete
1 Creep -
2 Temperature and Shrinkage -
3 Tension Stiffening -
4 Shear Stiffness for Reinforced Cracked Concrete Sections
Prestressing
Large Deformations and Second-Order Analysis
Dynamics of Beams

4 STRUT-AND-TIE MODELS
Elastic Plate Solutions
Modeling
Solution Methods for Trusses
Rigid-Plastic Truss Models
More Application Aspects

5 MULTIAXIAL CONCRETE MATERIAL BEHAVIOR
Basics
1 Continua and Scales -
2 Characteristics of Concrete Behavior
Continuum Mechanics
1 Displacements and Strains -
2 Stresses and Material Laws -
3 Coordinate Transformations and Principal States
Isotropy, Linearity, and Orthotropy
1 Isotropy and Linear Elasticity -
2 Orthotropy -
3 Plane Stress and Strain
Nonlinear Material Behavior
1 Tangential Stiffness -
2 Principal Stress Space and Isotropic Strength -
3 Strength of Concrete -
4 Phenomenological Approach for the Biaxial Anisotropic Stress-Strain Behavior
Isotropic Plasticity
1 A Framework for Multiaxial Elastoplasticity -
2 Pressure-Dependent Yield Functions
Isotropic Damage
Multiaxial Crack Modeling
1 Basic Concepts of Crack Modeling -
2 Multiaxial Smeared Crack Model
The Microplane Model
Localization and Regularization
1 Mesh Dependency -
2 Regularization -
3 Gradient Damage
General Requirements for Material Laws

6 PLATES
Lower Bound Limit Analysis
1 The General Approach -
2 Reinforced Concrete Contributions -
3 A Design Approach
Crack Modeling
Linear Stress-Strain Relations with Cracking
2D Modeling of Reinforcement and Bond
Embedded Reinforcement

7 SLABS
A Placement
Cross-Sectional Behavior
1 Kinematic and Kinetic Basics -
2 Linear Elastic Behavior -
3 Reinforced Cracked Sections
Equilibrium of Slabs
1 Strong Equilibrium -
2 Weak Equilibrium -
3 Decoupling
Structural Slab Elements
1 Area Coordinates -
2 A Triangular Kirchhoff Slab Element
System Building and Solution Methods
Lower Bound Limit Analysis
1 General Approach and Principal Moments -
2 Design Approach for Bending -
3 Design
Approach for Shear
Kirchhof Slabs with Nonlinear Material Behavior

8 SHELLS
Approximation of Geometry and Displacements
Approximation of Deformations
Shell Stresses and Material Laws
System Building
Slabs and Beams as a Special Case
Locking
Reinforced Concrete Shells
1 The Layer Model -
2 Slabs as Special Case -
3 The Plastic Approach

9 RANDOMNESS AND RELIABILITY
Basics of Uncertainty and Randomness
Failure Probability
Design and Safety Factors

10 APPENDICES
A Solution of Nonlinear Algebraic Equation Systems
B Crack Width Estimation
C Transformations of Coordinate Systems
D Regression Analysis
E Reliability with Multivariate Random Variables
F Programs and Example Data