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Stress-Strain Curves for Concrete and Reinforcement Materials


A s = Longitudinal reinforcement area
a i = Distance between the axes of the vertical reinforcement around the section
b o = Cross section size between the axes of the stirrupssurrounding thecore concrete
E c = Elasticity module of concrete
E s = Elasticity modulus of reinforcement steel
f c = Concrete compressive stress in confined concrete
f cc = Confined concretestrength
f co = Compressive strength of unconfined concrete
f e = Effective wrapping pressure
f s = Stress in reinforcing steel
f sy = Yield strength of reinforcement steel
f su = Tensile strength of reinforcing steel
f yw = Yield strength of transverse reinforcement
h o = Size of cross section between the axes of stirrupssurroundingcore concrete
k e = Coiling Efficiency Coefficient
s = Transverse reinforcement range
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


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.


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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