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Overview

1 Introduction

2 Theoretical Background

2.7.6 Distribution Coefficient

Distribution Coefficient

The calculation of the distribution coefficient ζ_d is shown for a reinforcement direction Φ. First, the maximum concrete tension stress σ_max,Φ is calculated under the assumption of linear-elastic material behavior:

$σ_{max, ϕ} = \frac{n_{ϕ} + n_{s h, ϕ}}{A_{ϕ, I}} + \frac{m_{ϕ} - n_{ϕ} \cdot (x_{ϕ, I} - \frac{h}{2}) + m_{s h, ϕ, l}}{I_{ϕ, I}} \cdot (h - x_{ϕ, l})$

where

Table 2.2
n_Φ	axial force from external loading in reinforcement direction Φ
n_sh,Φ	additional axial force from shrinkage in reinforcement direction Φ
m_Φ	moment from external loading in reinforcement direction Φ
m_sh,Φ,I	additional moment from shrinkage in reinforcement direction φ in state I
x_Φ,I	depth of concrete compression zone in uncracked state in reinforcement direction Φ
h	depth of cross-section
A_Φ,I	ideal cross-section area in state I in reinforcement direction Φ
I_Φ,I	ideal moment of inertia in state I in reinforcement direction Φ

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

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

Distribution coefficient ζ_Φ while taking tension stiffening into account

for σ_max,Φ > f_ctm :

$ζ_{ϕ} = 1 - β \cdot {(\frac{f_{c t m}}{σ_{m a x, ϕ}})}^{n}$

for σ_max,Φ ≤ f_ctm :

$ζ_{ϕ} = 0$

where

Table 2.2
β	parameter for the load duration
f_tm	mean tensile strength of concrete
n	2 for EN 1992-1-1

Distribution coefficient ζ_Φ without taking tension stiffening into account

for σ_max,Φ > f_ctm :

$ζ_{ϕ} = 1$

for σ_max,Φ ≤ f_ctm :

$ζ_{ϕ} = 0$

Parent section

2.7 Deformation Analysis with RF-CONCRETE Deflect