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Overview

1 Introduction

2 Theoretical Background

2.7.10.7 Calculation of distribution coefficient

Calculation of distribution coefficient

The maximum stress in the uncracked state is:

$σ_{m a x, ϕ_{1}} = \frac{n_{ϕ_{1}} + n_{s h, ϕ_{1}}}{A_{ϕ_{1}, l}} + \frac{m_{ϕ_{1}} - n_{ϕ_{1}} (χ_{l, ϕ_{1}} - \frac{h}{2}) + m_{s h, l, ϕ_{1}}}{I_{ϕ_{1}, l}} \cdot (h - χ_{l, ϕ_{1}}) = = \frac{- 100_{} \cdot_{} {10^{3}}_{} +_{} 101 . 5_{} \cdot_{} 10^{3}}{0.206} + {\frac{30_{} \cdot_{} {10^{3}}_{} -_{} (- 100_{} \cdot_{} 10^{3}) {(0 . 101_{} -_{} \frac{0.2}{2})}_{} +_{} 4.778 \cdot 10^{3}}{6.816 \cdot 10^{- 4}}}_{} \cdot_{} (0 . 2_{} -_{} 0.1) = 5.1 Mpa$

We assume a long-term loading:

$β_{φ_{1}} = 0.5$

Taking Tension Stiffening into account, the distribution coefficient is calculated according to the following equation:

for σ_max,φ1 > f_ctm:

$ζ_{d} = 1 - β_{ϕ_{1}} \cdot {(\frac{f_{c t m}}{σ_{m a x, ϕ_{1}}})}^{2}$

for σ_max,φ1 ≤ f_ctm:

$ζ_{s h, c, ϕ_{1}} = 0$

In the example, the maximum tension stress in the concrete is larger than the concrete tensile strength.

$σ_{m a x, ϕ_{1}} > f_{c t m}$

$5.1 > 2.9$

Thus, the distribution coefficient is:

$ζ_{ϕ_{1}} = 1 - β_{ϕ_{1}} \cdot {(\frac{f_{c t m}}{σ_{m a x, ϕ_{1}}})}^{2} = 1 - 0.5 \cdot {(\frac{2.9}{5.1})}^{2} = 0.835$

Image 2.123 Calculation of distribution coefficient (damage parameter)

Parent section

2.7.10 Example