Computational Methods for Reinforced Concrete Structures
1st Edition
Published on 23. September 2014
354 pages
978-3-433-60363-5 (ISBN)
Description
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.
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.
More details
Other editions
Additional editions
Ulrich Haeussler-Combe
Computational Methods for Reinforced Concrete Structures
Software
11/2014
Ernst & Sohn
€82.75
No shipping information available
Ulrich Häussler-Combe
Computational Methods for Reinforced Concrete Structures
Book
10/2014
1st Edition
Ernst & Sohn
€61.90
Article exhausted; check for reprint
Person
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.
Content
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
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
Notations
The same symbols may have different meanings in some cases. But the different meanings are used in different contexts and misunderstandings should not arise.
firstly used General T transpose of vector or matrix Eq. (1.5) -1 inverse of quadratic matrix Eq. (1.13) d virtual variation of , test function Eq. (1.5) d solution increment of within an iteration of nonlinear equation solving Eq. (1.70) transformed in (local) coordinate system Eq. (5.15) time derivative of Eq. (1.4) Normal lowercase italics as reinforcement cross section per unit width Eq. (7.70) b cross-section width Section 3.1.2 bw crack-band width Section 2.1 d structural height Section 7.6.2 e element index Section 1.3 f strength condition Eq. (5.42) fc uniaxial compressive strength of concrete (unsigned) Section 2.1 fct uniaxial tensile strength of concrete Section 2.1 ft uniaxial failure stress - reinforcement Section 2.3 fyk uniaxial yield stress - reinforcement Section 2.3 fE probability density function of random variable E Eq. (9.2) gf specific crack energy per volume Section 2.1 h cross-section height Section 3.1.2 mx, my, mxy moments per unit width Eq. (7.8) n total number of degrees of freedom in a discretized system Section 1.2 nE total number of elements Section 3.3.1 ni order of Gauss integration Section 1.6 nN total number of nodes Section 3.3.1 nx, ny, nxy normal forces per unit width Eq. (7.8) p pressure Eq. (5.8) pF failure probability Eq. (9.18) distributed beam loads Eq. (3.58) r local coordinate Section 1.3 s local coordinate Section 1.3 sbf slip at residual bond strength Section 2.4 sb max slip at bond strength Section 2.4 t local coordinate Section 1.3 t time Section 1.2 tx, ty, txy couple force resultants per unit width Eq. (7.67) u specific internal energy Eq. (5.12) ?x, vy shear forces per unit width Eq. (7.8) w deflection Eq. (1.56) w fictitious crack width Eq. (2.4) wcr critical crack width Section 5.7.1 z internal lever arm Section 3.5.4 Bold lowercase roman b body forces Section 1.2 f internal nodal forces Section 1.2 p external nodal forces Section 1.2 n normal vector Eq. (5.5) t surface traction Section 1.2 tc crack traction Eq. (5.123) u displacement field Section 1.2 ? nodal displacements Section 1.2 wc fictitious crack width vector Eq. (5.123) Normal uppercase italics A surface Section 1.2, Eq. (1.5) A cross-sectional area of a bar or beam Eq. (1.54) As cross-sectional area reinforcement Example 2.4 At surface with prescribed tractions Section 1.2, Eq. (1.5) Au surface with prescribed displacements Eq. (1.53) C material stiffness coefficient Eq. (2.32) CT tangential material stiffness coefficient Eq. (2.34) D scalar damage variable Eq. (5.106) DT tangential material compliance coefficient Eq. (5.160) DcT tangential compliance coefficient of cracked element Eq. (5.132) DcLT tangential compliance coefficient of crack band Eq. (5.132) E Young's modulus Eq. (1.43) E0 initial value of Young's modulus Eq. (2.13) Ec initial value of Young's modulus of concrete Section 2.1 Es initial Young's modulus of steel Section 2.3 ET tangential modulus Eq. (2.2) F yield function Eq. (5.64) FE distribution function of random variable E Eq. (9.1) G shear modulus Eq. (3.8) G flow function Eq. (5.63) Gf specific crack energy per surface Eq. (2.7) I1 first invariant of stress Eq. (5.20) J determinantof Jacobian Eq. (1.67) J2, J3 second, third invariant of stress deviator Eq. (5.20) Lc characteristic length of an element Eq. (6.32) Le length of bar or beam element Section 1.3 M bending moment Section 3.1.2 N normal force Section 3.1.2 P probability Eq. (9.1) T natural period Eq. (3.211) V shear force Section 3.1.2 V volume Section 1.2, Eq. (1.5) Bold uppercase roman B matrix of spatial derivatives of shape functions Section 1.2, Eq....
