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004785

Dipl.-Ing. Georg Dlubal

2025-01-08

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Overview

1 Introduction

2 Theoretical Background

3 Input Data

4 Calculation

5 Results

6 Result Evaluation

7 Printout

8 General Functions

9 Literature

2.8.4.1 Considering creep

Considering creep

Creep describes the time-dependent deformation of the concrete with loading within a particular period of time. The essential influence values are similar to those of shrinkage (see chapter 2.8.4.2). Additionally, the so-called "creep-producing stress" has a considerable effect on the creep deformations.

Online Manual RF-CONCRETE Surfaces | 2.8.4.2 Consideration of Shrinkage

Attention must be paid to the load duration, the time of load application, as well as the extent of the loading. Creep is taken into account by the creep coefficient φ(t,t0) at the point of time t.
In RF-CONCRETE Surfaces, the specifications for determining the creep coefficient are set in window 1.3 Surfaces. In it, you can specify the concrete's age at the considered point of time and at the beginning of loading, the relative air humidity, as well as the type of cement. Based on these specifications, the program determines the creep coefficient φ.

Figure 2.144 Window 1.3 Surfaces, Tab Creep

We now will briefly look at the determination of the creep coefficient φ according to EN 1992-1-1, clause 3.1.4. Using the following equations requires the creep-producing stress σ_c of the acting permanent load to not exceed the following value.

σ_c ≤ 0.45 · f_ckj
where
f_ckj - Zylinderdruckfestigkeit des Betons zum Zeitpunkt des Aufbringens der kriecherzeugenden Spannung

Unter Annahme eines linearen Kriechverhaltens (σ_c << 0.45 ⋅ f_ckj) kann das Kriechen des Betons durch eine Abminderung des Beton-Elastizitätsmoduls erfasst werden.

E_{c, eff} = \frac{E_{cm}}{1.0 + φ (t, t_{0})}

E_cm	Mean modulus of elasticity according to EN 1992-1-1, Table 3.1
φ(t,t₀)	Creep coefficient
t	Age of concrete at relevant point of time in days
t₀	Age of concrete when load application starts in days

Creep of Concrete

According to EN 1992-1-1, clause 3.1.4, the creep coefficient φ(t,t0) at the analyzed point of time t can be calculated as follows.

ϕ (t, t_{0}) = ϕ_{RH} \cdot β (f_{cm}) \cdot β (t_{0}) \cdot β (t, t_{0})

β(f_cm)	Coefficient for considering the concrete compressive strength
β(t₀)	Coefficient for considering the age of concrete

Creep Coefficient φ(t,t₀) at Analyzed Point of Time t

β (f_{cm}) = \frac{16 . 8}{\sqrt{f_{cm}}}

Coefficient for Considering Concrete Compressive Strength

β (t_{0}) = \frac{1}{0.1 + {t_{0 . eff}}^{0.2}}

Coefficient for Considering Age of Concrete

φ_{RH} = 1 + \frac{1 - \frac{RH}{100}}{0.10 \cdot \sqrt[3]{h_{0}}} \cdot α_{1} \cdot α_{2}

h₀	Effective thickness of structural component [mm] (for surfaces: h₀ = h)
α₁	Adaptation factor
α₂	Adaptation factor

Formula φ_RH

h_{0} = \frac{2 \cdot A_{c}}{u}

A_c	Cross-sectional area
u	Cross-section perimeter

Effective Thickness of Structural Component [mm] (for Surfaces: h₀ = h)

α_{1} = {(\frac{35}{f_{cm}})}^{0.7}

f_cm	Mean value of cylinder compressive strength

Adjustment Factor α₁

α_{2} = {(\frac{35}{f_{cm}})}^{0.2}

f_cm	Mean value of cylinder compressive strength

Adjustment Factor α₂

t_{0 . eff} = t_{0} {[1 + \frac{9}{2 + {t_{0}}^{1.2}}]}^{α} \geq 0.5 \cdot d

Formula t_0.eff

β (t, t_{0}) = {[\frac{t - t_{0}}{β_{H} + t - t_{0}}]}^{0.3}

t	Age of concrete at relevant point of time in days
t₀	Age of concrete when load application starts in days

Coefficient for Considering Load Duration

β_{H} = 1.5 \cdot {[1 + {(0.012 \cdot RH)}^{18}]}^{α} \cdot h_{0} + 250 \cdot α_{3} \leq 1500 \cdot α_{3}

RH	Relative humidity [%]
h₀	Effective component thickness [mm]
α₃	Adaptation factor

Formula β_H

α_{3} = {(\frac{35}{f_{cm}})}^{0.5}

f_cm	Mean value of cylinder compressive strength

Adjustment Factor α_3rd

The influence of the type of cement on the concrete's creep coefficient can be taken into account by modifying the load application age t0 with the following equation:

t_{0} = t_{0, T} \cdot {(1 + \frac{9}{2 + {(t_{0, T})}^{1.2}})}^{α} \geq 0.5

t₀

Effective age of concrete when load application starts, taking the influence of temperature into account

Exponent depending on type of cement:

-1: Slow-hardening cements (S) (32,5)
0: Normal- or rapid-hardening cements (N) (32.5 R; 42.5)
1: Rapid-hardening, high-strength cements (R) (42.5 R; 52.5)

Loading age t₀

Considering creep in the calculation

If the strains at the point of time t = 0 as well as at a later point of time t are known, it is possible to determine the creep coefficient φ for a calculational consideration in the model.

φ_{t} = \frac{ε_{t}}{ε_{t = 0}} - 1

Creep Coefficient

This equation is rearranged to the strain at the point of time t. Es ergibt sich folgender Zusammenhang, der für konstante Spannungen Gültigkeit besitzt:

ε_{t} = ε_{t = 0} \cdot (φ_{t} + 1)

Relation Valid for Uniform Stresses

For stresses higher than approximately 0.4 ⋅ f_ck, the strains increase disproportionately, resulting in the loss of the linearly assumed reference.
The calculation in RF-CONCRETE NL uses a common solution that is reasonable for construction purposes. The stress-strain diagram of the concrete is distorted by the factor (1 + φ).

Image 2.146 Distortion of Stress-Strain Relation for Determining Creep Effect

Wie im Bild 2.146 ersichtlich, handelt es sich bei der Berücksichtigung des Kriechens um den Fall konstanter kriecherzeugender Spannungen über die Belastungszeit. Because of neglected stress redistributions, the deformation is slightly overestimated due to this assumption. The stress reduction without a change in strain (relaxation) is only taken into account to a limited degree in this model. If we assume a linear elastic behavior, a proportionality could be presumed and the horizontal distortion would also reflect the relaxation at a ratio of (1 + φ). This correlation, however, is lost for the nonlinear stress-strain relationship.

Thus, it becomes clear that this procedure must be understood as an approximation. Therefore, a reduction of the stresses due to relaxation as well as nonlinear creep cannot or can only be approximately represented.

Parent Chapter

2.8.4 Creep and Shrinkage