RF-CONCRETE Surfaces – Online Manual Version 5

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RF-CONCRETE Surfaces – Online Manual Version 5

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2.7.6 Distribution Coefficient

Distribution Coefficient

The calculation of the distribution coefficient ζd is shown for a reinforcement direction Φ. First, the maximum concrete tension stress σmax,Φ is calculated under the assumption of a 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 influence of tension stiffening is taken into account in the deformation calculation according to EN 1992-1-1.

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

ζϕ = 1 - β · fctmσmax,ϕn 

  • for σmax,Φ ≤ fctm :

ζϕ = 0 

where

Table 2.2

β

parameter for the load duration

ftm

mean tensile strength of concrete

n

2 for EN 1992-1-1

Distribution coefficient ζΦ without taking tension stiffening into account
  • for σmax,Φ > fctm :

ζϕ = 1 

  • for σmax,Φ ≤ fctm :

ζϕ = 0 

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