How to model structural concrete using finite element analysis?

How to Model Structural Concrete using Finite Element Analysis (FEA)?


How to Model Structural Concrete using Finite Element Analysis (FEA)










This book is part of the “How to” series and is the first NAFEMS publication that addresses the specialist area of modelling structural concrete with finite elements

Concrete is the most prolific man made material used in the World and although in 
the large majority of applications little detailed analysis is used there remains a 
significant number of structures where sophisticated analysis including finite 
element modelling is required to justify concrete structure design. These structures include the World’s largest man-made object (in terms of volume), the Three Gorges Dam which is built from 27 million m3 the World’s tallest building, Burj khalifa at 828m tall, Dubai, UAE. Also included are safety critical structures required for nuclear containment, structures for the storage of highly volatile chemicals and fuels, and some of the World’s longest spanning bridges. 

The use of structural concrete is highly prescribed and structures are nearly always designed and analysed to rules given in codes of practice. Generally, analysis of concrete structures is limited to linear techniques and these are now common place in many commercial design engines, and these techniques are briefly discussed in this book. However, there is increasing interest in more realistic simulation of concrete structures, were code of practice rules cannot be easily applied, and where a better understanding of performance is required. Hence, it is the more realistic simulation of concrete that is the subject of this book where aspects such as prediction of strength and cracking are considered.

This book is aimed primarily at engineers and analysts with some experience of 
concrete who are new, or nearly new to non-linear analysis
. It is anticipated, 
however, that it may also be useful to experienced analysts who are new to 
concrete
. Detailed formulation of material models and the derivation of relevant 
aspects of the finite element method are not included, but references for further 
reading are provided. Instead, the focus is on practical aspects of modelling 
 of concrete, Yangtze River in China, and including hints and tips which the author has found useful in tackling concrete simulation. Topics include an introductory discussion of material behaviour and non-linearity in reinforced concrete before moving on to finite element modelling. Traditional, non-linear and construction sequence analysis is then described before describing concrete and reinforcement material modelling. Because the behaviour of concrete is so non-linear there is also a discussion on solution procedures including hints on strategies to deal with cracking where sudden losses of stiffness can occur. 

Most importantly, a section is given to working with codes of practice and advice is 
given on how different types of finite element model can be used within a code of 
practice framework whilst aligning with established design principles.
Topics such 
as limit state design and partial safety factors are also described and the limitations that must be understood in modelling concrete structures in different ways. Understanding the limitations of simulation and the additional checks that may be necessary is key to the safe design and assessment of concrete structures. Finally, two sets of worked examples are given for the solution of simple concrete 
structures. The first considers different solution schemes, element types and mesh 
densities to solve the same problem, illustrates the variations to be expected and 
suggests the most appropriate representation. The second set compares predicted 
results with test results for several classic problems and indicates that good 
correlation can be achieved. 

This book is very much an introduction on finite element modelling of structural 
concrete.
Most topics are covered, albeit briefly, but references are provided for 
further reading. Subjects considered to beyond the scope of this introduction 
include detailed modelling of concrete maturity, creep and shrinkage although some discuss of these phenomena is included. Also, the analysis that has been considered is limited to static problems, dynamic analysis is not considered. So, for example, concrete material models that include strain rate are excluded from discussion.



Contents 

1. Introduction 1

1.1 Background 2
1.2 Scope 3

2. Material Behaviour 5

2.1 Concrete 5
2.2 Reinforcement 5
2.3 Design Concept 5

3. Non-linearity in Reinforced Concrete 7

3.1 Cracking 7
3.1.1 Plain 7
3.1.2 Reinforced 9
3.2 Crushing 10
3.3 Shrinkage 13
3.4 Creep 14
3.5 Reinforcement Yield 14
3.6 Reinforcement Relaxation 16
3.7 Reinforcement Bond 16
3.8 Geometric 17
3.9 Contact 17

4. Finite Element Modelling 19

4.1 Traditional Linear Analysis 19
4.1.1 Frames 19
4.1.2 Grillages 19
4.1.3 Plates and Shells 19
4.1.4 Solids 20
4.2 Non-linear Analysis 20
4.3 Construction Sequence Analysis 20


5. Concrete Material Modelling 23

5.1 General 23
5.2 Dimensions 23
5.3 Plasticity 24
5.3.1 Compression 24
5.3.2 Tension 26
5.3.3 Tension/Compression Combination 27
5.4 Cracking General 27
5.5 Smeared Crack Modelling 28
5.5.1 Fixed Direction 28
5.5.2 Rotating Direction 29
5.5.3 Tension Softening 29
5.5.4 Shear Retention 31
5.6 Discrete Cracking 31
5.6.1 Interfaces 31
5.6.2 Adaptivity 31
5.7 Total Strain 32
5.7.1 Directional Concepts 32
5.7.2 Multiaxial Behaviour 33
5.7.3 Tensile Behaviour 33
5.7.4 Shear Behaviour 33

6. Reinforcement Modelling 35

6.1 General 35
6.2 Smeared Representations 36
6.3 Embedded Equivalence 37
6.4 Explicit 39
6.5 Homogeneous 40
6.6 Bond Interface 40

7. Prestressed Reinforcement Modelling 41

7.1 General 41
7.2 External Loads 42
7.2.1 Prestressing by Pre-tensioning 42
7.2.2 Prestressing by Post-tensioning 44
7.3 Initial Strain 46
7.4 Stressing Analysis 48

8. Solution Procedures 49

8.1 General 49
8.2 Implicit Solvers 50
8.2.1 Time Increments 50
8.2.2 Equilibrium Iterations 51
8.2.3 Convergence Tolerance 52
8.3 Explicit Solvers 54

9. Working with Codes of Practice 55

9.1 Significance 55
9.2 Design Code Principles 55
9.2.1 Allowable Stress Design 55
9.2.2 Limit State Design 56
9.2.3 Partial Safety Factors 56
9.3 Linear Elastic Analysis of Beams 56
9.3.1 Principles and Treatment of Safety Factors 56
9.3.2 ULS Flexure 57
9.3.3 ULS Shear 58
9.3.4 ULS Torsion 58
9.3.5 SLS Stress 58
9.3.6 SLS Cracking 60
9.3.7 SLS Deflection 60
9.4 Linear Analysis of Slabs 60
9.4.1 ULS Torsion 60
9.4.2 SLS Cracking 61
9.4.3 ULS Shear 61
9.5 Linear Analysis using 3D Shell or Solid Elements 61
9.5.1 ULS 61
9.5.2 SLS 63
9.6 Non-linear Analysis 63
9.6.1 Partial Safety Factors 63
9.6.2 ULS Flexure 64
9.6.3 ULS Shear 65
9.6.4 SLS 66
9.6.5 Concrete Tensile Strength 66
9.6.6 Bond 67

10. Hints and Tips 69


11. Worked Examples 73

11.1 Modelling a Simply Supported Reinforced Concrete Beam 73
11.1.1 Description 73
11.1.2 Section Capacity Calculation 75
11.1.3 2D Line Beam Representation 76
11.1.4 2D Plane Stress Representation 78
11.1.5 3D Solid Representation 83
11.1.6 Solution Comparison 86
11.2 Benchmarking Against Physical Tests 87
11.2.1 Non-linear Analysis of Reinforced Concrete Beam 88
11.2.2 Non-linear Analysis of Reinforced Concrete Deep Beam 90
11.2.3 Non-linear Analysis of Reinforced Concrete Slab 93
11.2.4 3D Non-linear Analysis of Standard Concrete Cube 96
11.2.5 Summary 99


12. Glossary 103

13. References 105



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About

C.L. Brookes

First Published - January 2016

Softback, 106 Pages