Nonlinear Finite Element Analysis of Concrete Structures

CONTENTS
Page
PREFACE 5
1. INTRODUCTION 7
2. CONSTITUTIVE MODELLING OF CONCRETE 9
2.1. Failure strength 9
2.1.1. Geometrical preliminaries 10
2.1.2. Evaluation of some failure criteria — . 13
2.1.3. The two adopted failure criteria 19
2.1.4. Adopted cracking criteria 26
2.2. Stress-strain relations 28
2.2.1. Nonlinearity index 32
2.2.2. Change of the secant value of Young's
modulus 35
2.2.3. Change of the secant value of Poisson's
ratio 39
2.2.4. Experimental verification 41
2.3. Creep 45
2.4. Summary 4 7
3. CONSTITUTIVE EQUATIONS FOR REINFORCEMENT AND PR£-
STRESSING 48
4. FINITE ELEMENT MODELLING 55
4.1. Fundamental equations of the finite element
method 57
4.2. Concrete element 66
4.2.1. Basic derivations 67
4.2.2. Cracking in the concrete element 72
4.3. Reinforcement elements 81
4.3.1. Elastic deformation of reinforcement ... 84
4.3.2. Plastic deformation of reinforcement ... 95
4.4. Prestressing 99
4.5. Plane stress and strain vs. axisymmetric
formulation 100
4.6. Computational schemes 102