上海交通大学：《钢筋混凝土基本原理》课程教学资源（PPT课件）Chapter 4 Analysis Methods of Reinforced Concrete Members

Chapter 4 Analysis Methods of Reinforced Concrete Members

Chapter 4 Analysis Methods of Reinforced Concrete Members

4.1 Design and analysis Analysis Design Known Sectional dimensions Loads Reinforcement Properties of materials Strength of material Inner force Solve Load carrying capacity Structures which can satisfy Deformation predicted functions Crack width Characteristics Certainty problem Uncertainty Comprehensive

4.1 Design and analysis Analysis Design Known Sectional dimensions Reinforcement Strength of material Inner force Loads Properties of materials Solve Load carrying capacity Deformation Crack width Structures which can satisfy predicted functions Characteristics Certainty problem Uncertainty Comprehensive

4.2 Analysis methods for R.C. structures 对承受各种内力（轴力、弯矩、剪力、扭矩）的一维 构件和二维、三维结构，应力分析后都可以找到主应 力方向，在主应力方向无非是压力或拉力。 ·沿主拉力方向配筋当然最为有效，在主压力方向加设 钢筋也有增强作用。 ·钢筋混凝土轴心受力构件是最简单，也是最基本的受 力状态，掌握其受力性能的一般规律，是了解其它构 件性能的基础。从中可以得到钢筋混凝土构件截面分 析的一般方法

4.2 Analysis methods for R.C. structures • 对承受各种内力（轴力、弯矩、剪力、扭矩）的一维 构件和二维、三维结构，应力分析后都可以找到主应 力方向，在主应力方向无非是压力或拉力。 • 沿主拉力方向配筋当然最为有效，在主压力方向加设 钢筋也有增强作用。 • 钢筋混凝土轴心受力构件是最简单，也是最基本的受 力状态，掌握其受力性能的一般规律，是了解其它构 件性能的基础。从中可以得到钢筋混凝土构件截面分 析的一般方法

4.2.1 Basic functions in structural analysis Load Deformation Equilibrium Compatibility condition Stress Strain Constitutive law 下面通过轴心受力构件来表示以上材料力学基本方程在钢筋混凝土截面受力分 析中的应用方法。并从中得到受力分析的基本规律（注：实际工程中严格意义 的轴心受拉、受压是不存在的)

4.2.1 Basic functions in structural analysis Load Deformation Stress Strain E q u i l i b r i u m condition Constitutive law Compatibility 下面通过轴心受力构件来表示以上材料力学基本方程在钢筋混凝土截面受力分 析中的应用方法。并从中得到受力分析的基本规律（注：实际工程中严格意义 的轴心受拉、受压是不存在的）

N 4.2.2 Analysis of axially loaded short column E0元、二E (compression) A.=uth Ae (a)

4.2.2 Analysis of axially loaded short column (compression)

Concept ·Reinforcement ratio A A In practical design,Ac is usually taken as the normal concrete area,without deduction (for the area of longitudinal reinforcement(纵向钢筋)

• Reinforcement ratio c s A A   In practical design, Ac is usually taken as the normal concrete area, without deduction (扣除） for the area of longitudinal reinforcement（纵向钢筋）. Concept

Basic functions ·Compatibility: Es=8c Constitutive law: Constitutive law for steel bar When s,≤8y( s=EEs When &3 o=fy=const f E。E0Em Constitutive law for concrete Oc=f(8c)=AE08c A-k Plastic coefficient Ee

Basic functions • Compatibility: s c    • Constitutive law: Constitutive law for steel bar When s y    s Es s    When s y    f const  s  y  Constitutive law for concrete c c E c  f   0  ( )  E0 Ec   Plastic coefficient

When 8e=0 λ=1 E c=p 入 Eo a EcrEp 元↓ Concept Stress ratio (under the condition of compatibility) o-6,E=6,E2=E/E=n 0.6eE。 eE。 由于混凝土的软化 (入↓)钢筋承受的压 力占总额的比例随总压 Where n= Es modular ratio (const. Eo 力的上升而上升

When  0 c   1 c p    E a Ep 1 0    c p              E E n E E E E s c s s c c s s c s     0 0 Stress ratio (under the condition of compatibility) Where E0 E n s  modular ratio (const.) 由于混凝土的软化 （λ↓）钢筋承受的压 力占总额的比例随总压 力的上升而上升。 Concept

Equilibrium condition N=a,A+a,A,=0,A1+7p)=a,A 4=A+月p)=A+贸 Concept n As is transform section or equivalent section for reinforcement(折算为混凝土截面积)

• Equilibrium condition 0 (1 ) A n N c Ac s As c Ac   c            n A A n A  Ac   c  s (1 ) 0  n As is transform section or equivalent section for reinforcement（折算为混凝土截面积） Concept

4.2.2.1 Loading process e y<e p (HPB300) fy fc +8 Ey Ep 1500*10-6 2000*10-6

4.2.2.1 Loading process εy<εp (HPB300) fy fc εy εp ε σ 1500 * 10 -6 2000*10-6