同济大学：《高等混凝土结构理论》课程电子教案（PPT课件）Chapter 2 Mechanical Behavior and Constitutive Relationships of Concrete and Steel Materials

Advanced Theory of Concrete Structures Chapter 2 Mechanical Behavior and Constitutive Relationships of Concrete and Steel Materials Xianglin Gu College of Civil Engineering,Tongji University 土本工程学院 gxl@tongji.edu.cn COLLEGEOP CIVILINGANEERING

Xianglin Gu College of Civil Engineering, Tongji University gxl@tongji.edu.cn Chapter 2 Mechanical Behavior and Constitutive Relationships of Concrete and Steel Materials Advanced Theory of Concrete Structures

闺 2.1 Basic Performance of Concrete Materials 士齐五鞋季悦 The compressive behavior of concrete materials is better than their tensile behavior

2 The compressive behavior of concrete materials is better than their tensile behavior 2.1 Basic Performance of Concrete Materials

2.2 Damage mechanisms of concrete 同俩大学 土苏三鞋季花 TONGUI UNVERSITY Development of microcracks

3 2.2 Damage mechanisms of concrete Development of microcracks

闺 2.3 Strength and Deformation of Concrete 同海大学 士齐工鞋季悦 2.3.1 Characteristic strength Properties of concrete materials vary because of the particles of materials are not uniform and the manufacturing processes are depend on the degree of control Frequency Mean strength Good control or even distribution of particles poor control or uneven distribution of particles Characteristic Strength strength

4 2.3 Strength and Deformation of Concrete 2.3.1 Characteristic strength Properties of concrete materials vary because of the particles of materials are not uniform and the manufacturing processes are depend on the degree of control Frequency Strength Mean strength Characteristic strength Good control or even distribution of particles poor control or uneven distribution of particles

2.3 Strength and Deformation of Concrete 同橘大学 土苏三鞋季花 汽0n号s7 2.3.3 Compressive strength under axial load Cube strength feu Loading plate Friction ↓↓↓小 ↓↓↓↓ Specimen 50×150×150 ↑↑↑↑↑ ↑↑↑↑↑ .Cubic strength of concrete is used in China to describe the grade of concrete C15,C20,C25,C30,C35,C40,C45,C50,C55,C60,C65,C70,C75, C80

5 2.3 Strength and Deformation of Concrete 2.3.3 Compressive strength under axial load Cube strength fcu Loading plate Specimen 150×150 ×150 Friction •Cubic strength of concrete is used in China to describe the grade of concrete ： •C15，C20，C25，C30，C35，C40，C45，C50，C55，C60，C65，C70，C75， C80

闺 2.3 Strength and Deformation of Concrete 同海大学 士齐工鞋学悦 2.3.3 Compressive strength under axial load Prism and Cylinder strengthf andf Loading plate Prism and cylinder strength are used in China and United states for the purpose of analysis or design Specimen 150×150X300 f-0.76fcu 0150×300 f'=0.79fcu

6 2.3 Strength and Deformation of Concrete 2.3.3 Compressive strength under axial load Prism and Cylinder strength fc and fc  •Prism and cylinder strength are used in China and United states for the purpose of analysis or design •fc=0.76fcu •fc '=0.79fcu Loading plate Specimen 150×150 ×300 or 150 ×300

2.3 Strength and Deformation of Concrete 同俩大学 土苏五鞋季花 0Jt期TN 2.3.3 Tensile strength under axial load Tensile strength fand split cylinder/cube strength fis 100 L150 .150 100 500 f0.395fm0.55 文应 f-0.19fu34 f-0.3f23 2F adl

7 2.3 Strength and Deformation of Concrete 2.3.3 Tensile strength under axial load Tensile strength ft and split cylinder/cube strength fts 100 100 150 150 500 d d f ts F F F F dl F f ts  2 = •ft=0.395fcu 0.55 •fts=0.19fcu 3/4 •fts=0.3fc  2/3

目 2.3 Strength and Deformation of Concrete 同海大学 士齐工鞋学悦 2.3.4 Factors affecting concrete strength Water/cement ratio Type of cement Supplementary cementitious materials Aggregate Mixing water Moisture conditions during curing Temperature conditions during curing Age of concrete Maturity of concrete Rate of loading

8 2.3 Strength and Deformation of Concrete 2.3.4 Factors affecting concrete strength Water /cement ratio Type of cement Supplementary cementitious materials Aggregate Mixing water Moisture conditions during curing Temperature conditions during curing Age of concrete Maturity of concrete Rate of loading

2.3 Strength and Deformation of Concrete 同两大学 土苏五鞋季花 0t期T 2.3.5 Failure criteria of concrete under biaxial loadings 1.21.0 -0.2 tention 02f -0.2 1.0 1.2 compression ō Many models have been proposed to describe the failure criteria of concrete under biaxial principle stresses

9 2.3 Strength and Deformation of Concrete 2.3.5 Failure criteria of concrete under biaxial loadings 1.0 1.0 1.2 1.2 -0.2  -0.2 2 /f c 1 /fc tention compression Many models have been proposed to describe the failure criteria of concrete under biaxial principle stresses

闺 2.3 Strength and Deformation of Concrete 同海大学 士齐五鞋学悦 2.3.5 Failure criteria of concrete under biaxial loadings Mohr's circle Principle tensile stress criterion Shear-compressive failure 近 ● 0.2 [(o/2)2+x205-o/2=f 01 π/f=(1+o/f)5 olf. -0.10.0 0.6 10 tensile strength Compressive strength

10 2.3 Strength and Deformation of Concrete 2.3.5 Failure criteria of concrete under biaxial loadings /fc /f c 0.2 0.1 -0.1     0.0 0.6 1.0 tensile strength Compressive strength Mohr’s circle  f t  0.5 t t t 2 2 0.5 / (1 / ) [( / 2) ] / 2 f f f      = + + − = Principle tensile stress criterion Shear–compressive failure