RF-CONCRETE Surfaces Version 5

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RF-CONCRETE Surfaces Version 5

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2.7.6 Distribution Coefficient

Distribution Coefficient

The calculation of the distribution coefficient ζd is shown for one reinforcement direction Φ. First, the program calculates the maximum concrete tension stress σmax,Φ under the assumption of linear-elastic material behavior:

σmax,ϕ = nϕ + nsh,ϕAϕ,I + mϕ - nϕ · xϕ,I - h2 + msh,ϕ,lIϕ,I · h - xϕ,l 

where

Table 2.2

nΦ

axial force from external loading in reinforcement direction Φ

nsh,Φ

additional axial force from shrinkage in reinforcement direction Φ

mΦ

moment from external loading in reinforcement direction Φ

msh,Φ,I

additional moment from shrinkage in reinforcement direction φ in state I

xΦ,I

depth of concrete compression zone in uncracked state in reinforcement direction Φ

h

depth of cross-section

AΦ,I

ideal cross-section area in state I in reinforcement direction Φ

IΦ,I

ideal moment of inertia in state I in reinforcement direction Φ

The influence of the shrinkage forces on the maximum tension stress σmax,Φ is considered via the additional internal forces from shrinkage.

The calculation of the distribution coefficient ζΦ depends on whether the tension stiffening is taken into account in the deformation calculation according to EN 1992-1-1.

Distribution coefficient ζΦ taking into account tension stiffening
  • for σmax,Φ > fctm :

ζϕ = 1 - β · fctmσmax,ϕn 

  • for σmax,Φ ≤ fctm :

ζϕ = 0 

Equation 2.83 (2.83)

mit

Table 2.2

β

parameter to take load duration into account

ftm

mean tensile strength of concrete

n

2 for EN 1992-1-1

Coefficient of distribution ζΦ without consideration of tension stiffening
  • for σmax,Φ > fctm :

ζϕ = 1 

  • for σmax,Φ ≤ fctm :

ζϕ = 0 

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