Materials with Rheological Properties : Calculation of Structures

__Materials with Rheological Properties__ presents the evolution of the mathematical models used to calculate the resistance structures and the conditions which enable progress to be made in this field. The author presents equations describing the behavior of each possible type of resistance structure (with discrete collaboration, continuous collaboration and complex composition). These equations are then redefined in the particular concrete form for each type of structure, by using the notions and known parameters from the construction's statics. The mathematical models are then tested using practical case studies.Content: Chapter 1 Introduction (pages 1–7): Chapter 2 The Rheological Behavior of Building Materials (pages 9–43): Chapter 3 Composite Resistance Structures with Elements Built from Materials Having Different Rheological Properties (pages 45–128): Chapter 4 Applications on Resistance Structures for Constructions (pages 129–188): Chapter 5 Numerical Application (pages 189–222): Chapter 1 The Initial Stresses and Strains State of the Structures with Continuous Collaboration (pages 223–239): Chapter 2 Systems of Integral and Integro?differential Equations (pages 241–282): Materials with Rheological Properties......Page 5 Table of Contents......Page 7 1.1. Historical background......Page 11 1.2. Considering the plastic and rheological properties of materials in calculating and designing resistance structures for constructions......Page 13 1.3. The basis of the mathematical model for calculating resistance structures by taking into account the rheological properties of the materials......Page 14 2.1. Preamble......Page 19 2.2.1. Structural steel for metal construction......Page 29 2.2.2. Reinforcing steel (non-prestressed)......Page 32 2.2.3. Reinforcements, steel wire and steel wire products for prestressed concrete......Page 33 2.3. Concrete......Page 42 3.1. Mathematical model for calculating the behavior of composite resistance structures: introduction......Page 55 3.2.1. The effects of the long-term actions and loads: overview......Page 59 3.2.1.1. Composite structures with discrete collaboration......Page 71 3.2.1.2. Composite structures with continuous collaboration......Page 77 3.2.1.3. Composite structures with complex composition......Page 90 3.2.2. The effect of repeated short-term variable load actions: overview......Page 96 3.3.1. The effect of long-term actions and loads: overview......Page 105 3.3.1.1. Composite structures with discrete collaboration......Page 112 3.3.1.2. Composite structures with continuous collaboration......Page 116 3.3.1.3. Composite structures with complex composition......Page 125 3.3.2. The effect of repeated short-term variable actions and loads: overview......Page 130 3.4. Conceptual aspects of the mathematical model of resistance structure behavior according to the rheological properties of the materials from which they are made......Page 135 4.1. Correction matrix......Page 139 4.1.1. The displacement matrix of the end of a perfectly rigid body due to unit displacements successively applied to the other end of a rigid body......Page 140 4.1.2. The reaction matrix of the end of a perfectly rigid body due to unit forces successively applied to the other end of a rigid body......Page 142 4.2.1. Preliminaries necessary to systematize the calculation of composite structures in the formulation according to the creep......Page 143 4.2.2. Composite structures with discrete collaboration......Page 146 4.2.3. Composite structures with continuous collaboration......Page 150 4.2.4. Composite structures with complex composition......Page 165 4.3.1. Preliminaries necessary to systematize the calculation of the composite structures in the formulation according to the stress relaxation......Page 171 4.3.2. Composite structures with discrete collaboration......Page 175 4.3.3. Composite structures with continuous collaboration......Page 182 4.3.4. Composite structures with complex composition......Page 189 5.1. Considerations concerning the validation of the mathematical model proposed for estimation through calculation of the behavior of the resistance structures by considering the rheological properties of the materials......Page 199 5.2. The RALUCA computer applications system......Page 201 5.3. The resistance structure......Page 208 5.4.1. The first series of experiments......Page 213 5.4.1.1. The particular conditions for the analysis of the mathematical model......Page 214 5.4.2.1. The particular conditions for the analysis of the mathematical model......Page 216 5.4.3.1. The influence of the parameters defining the creep function......Page 221 5.4.3.2. The stresses state in the structure caused by the contraction of the concrete......Page 224 5.4.3.3. The influence of the deformability of the connection elements on the effort’s distribution among the elements of the structure......Page 227 Appendix 1. The Initial Stresses and Strains State of the Structures with Continuous Collaboration......Page 233 A.1. Simply supported beam with uniformly distributed load......Page 237 A.2. Simply supported beam loaded with a concentrated force......Page 240 A.3. Simply supported beam loaded with a concentrated moment at each end......Page 243 A.4. Simply supported beam loaded with concentrated forces applied eccentrically, acting on a direction parallel with the axis of the beam......Page 245 Appendix 2. Systems of Integral and Integro-differential Equations......Page 251 1. Integro-differential equations whose unknown factors are functions of one variable......Page 252 2. Integro-differential equations whose unknown factors are functions of two variables......Page 261 3. Integro-differential equations whose unknown factors are functions of one or two variables......Page 270 Bibliography......Page 293 Index......Page 297 "This book presents the evolution of the mathematical models used to calculate the resistance structures and the conditions which enable progress to be made in this field. The author presents equations describing the behavior of each possible type of resistance structure (with discrete collaboration, continuous collaboration and complex composition). These equations are then redefined in the particular concrete form for each type of structure, by using the notions and known parameters from the construction's statics. The mathematical models are then tested using practical case studies."--Jacket