# Stress-Strain Curves for Concrete and Reinforcement Materials

**ICONS**

* A _{s} =* Longitudinal reinforcement area

*Distance between the axes of the vertical reinforcement around the section*

**a**_{i }=*Cross section size between the axes of the stirrupssurrounding thecore concrete*

**b**_{o}=*Elasticity module of concrete*

**E**_{c}=*Elasticity modulus of reinforcement steel*

**E**_{s}=*Concrete compressive stress in confined concrete*

**f**_{c }=*Confined concretestrength*

**f**_{cc}=*Compressive strength of unconfined concrete*

**f**_{co }=*Effective wrapping pressure*

**f**_{e}=*Stress in reinforcing steel*

**f**_{s}=*Yield strength of reinforcement steel*

**f**_{sy}=*Tensile strength of reinforcing steel*

**f**_{su}=*Yield strength of transverse reinforcement*

**f**_{yw}=*Size of cross section between the axes of stirrupssurroundingcore concrete*

**h**_{o }=*Coiling Efficiency Coefficient*

**k**_{e}=*Transverse reinforcement range*

**s =****ρ**

_{s }*Volumetric proportion of the total transverse reinforcement (rectangular in cross-section ρ*

**=**_{s}= ρ

_{x}+ ρ

_{y})

**ρ**,

_{x}**ρ**

_{y }*transverse reinforcement volume fraction in the appropriate direction*

**=****ε**

_{c }*concrete compressive unit deformation of*

**=****ε**

_{c }*maximum pressure unit strain of the confined concrete*

**=****ε**

_{s }*the reinforcing steel the strain*

**=****ε**

_{sy }*flow volume of deformation of the reinforcing steel*

**=****ε**

_{sh }*Unit deformation of reinforcement steel at the beginning of hardening*

**=****ε**

_{water }*rupture strain of reinforcing steel*

**=****5A.1. WRAPPED AND NON-WRAPPED CONCRETE MODELS**

*The* following stress-strain relations are defined for confined and unconfined concrete to be used in the evaluation according to deformation with *Nonlinear Methods* , when no other model is selected **(Figure 5A.1)** .

**(a) In** confined concrete, the concrete compressive stress f _{c} is given by the equation in **Equation (5A.1)** as a function of the pressure strain ε _{c} :

Confined concrete strength in this equation f _{cc} raw edge strength concrete with f _{co} relationship between **Eq. (5A.2)** are given.

Here, the *effective winding pressure* f _{e} can be taken as the average of the values given in **Equation (5A.3)** for two perpendicular directions in rectangular sections :

In these relations, f _{yw is the} yield strength of the transverse reinforcement, ρ _{x} and ρ _{y} are the volumetric ratios of the transverse reinforcement in the respective directions, and k _{e} is the *coefficient ***of winding ***efficiency* defined in **Equation (5A.4)** .

Here, a _{i shows the} distance between the axes of the longitudinal reinforcements around the section, b _{o} and h _{o} the section dimensions between the axes of the stirrups surrounding the core concrete, s is the spacing between the axes of the stirrups in the longitudinal direction, and A _{s} indicates the longitudinal reinforcement area. **Eq. (5A.1)** wherein the normalized correlation with concrete units related to strain the x variable r **Eq. (5A.5)** and **Eq. (5A.6)** are given in.

**5A.2. REINFORCEMENT STEEL MODEL**

*Nonlinear methods* for use in the evaluation according to the deformation, for the reinforcement steel **in Eq. (5A.7)** wherein the stress-strain relationship are defined **(Figure 5A.2)** :

The elastic modulus of reinforcement steel is E _{s} = 2x10 ^{-5} MPa. Other information on reinforcement steels are given in **Table 5A.1** .

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