Matériaux et Construction

, Volume 6, Issue 4, pp 269–276

# Stochastic analysis for time-dependent load transfer in reinforced concrete columns

• A. B. O. Soboyejo
Article
• 55 Downloads

## Abstract

A stochastic process model is proposed for the phenomenon of time-dependent stress transfer from concrete to steel in reinforced concrete columns, subjected to axial loading. The phenomenon is caused by the mechanisms of creep and shrinkage. The importance of the stochastic model is brought out, in that it is now possible to have more meaningful information concerning the phenomenon under study. Furthermore, the importance of the stochastic model in practical problems involving the estimation of possible long-time stresses in structures, is mentioned. The results of the stochastic model are compared with practical tests results, and good agreements are obtained.

### Keywords

Shrinkage Creep Strain Creep Mechanism Concrete Column Shrinkage Strain

### Notation

Pc(0)

load on the concrete at the initial time of loading which in this case is considered as timet=0

Ps(0)

load on the steel at the initial time of loadingt=0

P

total load taken up by the column

As

area of steel

Ac

area of concrete

Es

modulus of elasticity of steel

Ec

modulus of elasticity of concrete; this value is assumed to be constant

c(t)

specific creep strain for concrete at any timet≥0, it has the dimensions of strain/stress, since it represents creep strain per unit stress

s(t)

shrinkage strain at any timet≥0 for the concrete

θ

$$\frac{{pEs}}{{1 + (n - 1)p}}$$

S

k(s) Ac

p

steel ratio

n

Es/Ec

μ

Θ/A

M1(t)

the mean or expected value

$$\sigma _{1^2 } (t, t)$$

the variance function

$$\sigma _{1^2 } (t, s)$$

the covariance function, of the load$$\bar Pc(t)$$ on the concrete due to creep mechanism alone

S

maximum shrinkage load capacity for the concrete

fc(t)

stress on concrete at timet

fs(t)

stress on steel at timet

## Résumé

On présente un modèle de traitement stochastique de transfert de charge en fonction du temps du béton à l'acier dans des poteaux de béton armé soumis à une charge axiale constante et permanente. Ce phénomène est principalement dû au fluage et au retrait du béton. On définit d'abord un modèle déterministe qui consiste en une représentation idéalisée et simplifiée susceptible de fournir une bonne approximation du phénomène réel.

Une fois le modèle mathématique mis au point, le choix du modèle de traitement stochastique dépend des mécanismes physiques réels du fluage et du retrait dans les poteaux de béton armé, ainsi que de la nature du modèle mathématique. Le modèle de traitement stochastique est un modèle probabiliste qui donne une fonction moyenne, reproduisant en fait le modèle mathématique et, en outre, les fonctions de variance et de covariance.

La fonction de variance autorise la formulation d'énoncés relatifs aux limites inférieures et supérieures de transfert de charge en fonction du temps, ainsi que pour le même phénomène, des énoncés relatifs aux écarts possibles de la fonction moyenne.

Les résultats fournis par le modèle de traitement stochastique sont comparés à ceux obtenus récemment en ce domaine par l'étude expérimentale; on constate que la concordance est très bonne.

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### References

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## Copyright information

© Secrétariat de Rédaction 1973

## Authors and Affiliations

• A. B. O. Soboyejo
• 1
1. 1.Faculty of EngineeringUniversity of LagosLagosNigeria