Abstract
The creep effects on the stresses induced in a concrete member by imposed deformations having a history similar to the shrinkage of concrete are analysed.
Direct solutions of the problem are deduced using two governing relationships of concrete judged in reference [1] as the best compromise between reality and simplicity.
The results are obtained in a general form and the influences of the most important parameters are plotted and compared.
Résumé
On évalue les effets du fluage sur les contraintes engendrées dans un élément de béton par des déformations imposées. Le cas répond à toute une gamme de problèmes pratiques.
L'exemple le plus simple en est le problème d'un béton armé symétriquement et où se produit un retrait.
Les solutions directes au problème sont obtenues à l'aide des méthodes Dischinger améliorées et de vitesse d'écoulement, que, dans un article précédent, on a considérées, comme le meilleur compromis entre la réalité physique et la simplicité mathématique.
On examine et compare sous une forme graphique les influences des paramètres les plus importants, tels que la vitesse de déformation imposée, le degré d'empêchement et l'âge du béton.
Les résultats des deux méthodes sont pratiquement égaux lorsque la déformation est imposée dans les deux premiers mois du béton, et diffèrent de plus en plus à mesure que l'âge où la déformation est imposée augmente.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- E :
-
modulus of elasticity. Throughout the present paperE is assumed age-independent
- t 0 :
-
the age of concrete on initial loading. For each problemt 0 is a constant
- t :
-
the time after loading;t=0 when the age of concrete ist 0
- t+t 0 :
-
the actual age of concrete at the momentt
- τ:
-
an intermediate time (0<τ≤t)
- σ(t,t 0):
-
the stress at the timet, measured from the aget 0. The positive values denote tension
- ε (t, t 0):
-
the total strain at the same time as σ (t, t 0). The positive values denote dilatation
- ɛϕ (t, t 0):
-
as ε but creep strain only. ɛϕ = ɛϕi + ɛϕr
- ɛϕr :
-
the recoverable component of ɛϕ
- ɛϕi :
-
the irrecoverable component of ɛϕ
- ɛ e (t, t 0):
-
σ (t, t 0)/E; the elastic strain
- ϕ (t, t 0):
-
\(\frac{{\varepsilon _\varphi (t,t_0 )}}{{\varepsilon _e (t,t_0 )}}\). ForE=const.\(\varphi = \frac{{\varepsilon _\varphi }}{\sigma }x E\), where\(\frac{{\varepsilon _\varphi }}{\sigma }\) is the specific creep strain (creep function). Also ϕ=ϕ i +ϕ r
- ϕ i (t, t 0):
-
\(\frac{{\varepsilon _{\varphi i} }}{{\varepsilon _e }}\)
- ϕ r (t, t 0):
-
\(\frac{{\varepsilon _{\varphi r} }}{{\varepsilon _e }}\) when ɛϕr is age-dependent
- ϕ r (t):
-
\(\frac{{\varepsilon _{\varphi r} }}{{\varepsilon _e }}\) when ɛϕr is age-independent
- β1 :
-
constant affecting the rate of time-development of ϕ i
- β2 :
-
constant similar to ϕ i but for ϕ r
- \(\bar \varphi _{i\infty } \) :
-
the final value of ϕ i including the influences of all the factors affecting the concrete creep, except the age of concrete
- ϕ i∞ :
-
\(\varphi _i (\infty ,t_0 ) = \bar \varphi _{i\infty } x e^{ - \beta _1 t_0 } ;\) the final value of ϕ i (t, t 0)
- ϕ r∞ :
-
the final value of ϕ r (t, t 0)
- λ2 :
-
β2 x (1+ϕ r∞ )
- R(t) :
-
a change in the unit length of the concrete due to an external cause (e.g. a temperature variation) or to an internal one (e.g. shrinkage). The positive value denote dilation
- \(\bar K\) :
-
the final value ofR.
- K :
-
\(\bar K \cdot E_c \); the elastic final value of σ c when α=1
- m :
-
a positive integer used to model aR-function faster than\(\frac{{\varphi _i (t,t_0 )}}{{\varphi _i \infty }} = 1 - e^{ - \beta _{1^t } } \)
- n :
-
the same asm but used to model aR-function slower than\(1 - e^{ - \beta _{1^t } } \)
- α:
-
the degree of restraint of the development ofR
- A :
-
the sectional area
- S :
-
the elastic stiffness
- r 1 ,r 2 :
-
the roots of the characteristic equation associated with the differential equation (4); see eq. (10)
- σ * c :
-
the particular solution of eq. (4)
- B, C :
-
constants of integration
- a :
-
α + + β2·(1 + αϕ r∞)
- A j :
-
constants
- c :
-
subscript associated with all the quantities concerning the concrete, or, generally, the part of the structure providing a time-dependent behaviour
- s :
-
similar toc but concerning the reinforcement or the part of the structure exhibiting elastic behaviour
References
Constantinescu D.R., Illston J.M.—Direct methods of analysing the structural effects of linear creep of ageing concrete. Materials and Structures. November–December 1974.
England G.L., Illston J.M.—Methods of computing stress in concrete from a history of measured strain. Civil Engineering and Public Works Review, April, May, June 1965.
Dischinger F.—Elastische und plastiche Verformungen der Eisenbetontragwerke und insbesondere der Bogenbruchen. Bauingenieur, No. 5/6, 1939.
Rüsch H., Jungwirth D., Hilsdorf H.—Kritische Sichtung der Verfahren zur Berucksichtigung der Einflusse von Kriechen und Schwinden des Betons auf das Verhalten der Tragwerke. Beton und Stahl-betonbau, Nos. 3, 4 and 6, 1973.
Illston J.M., England G.L.—Creep and shrinkage of concrete and their influence on structural behaviour — a review of methods of analysis. The Structural Engineer, July, 1970.
Illston J.M., Jordaan I.J.—Creep prediction for concrete under multiaxial stress. J.A.C.I., March 1972.
Courbon J.—L'influence du fluage linéaire sur l'équilibre des systèmes hyperstatiques en béton précontraint, Ann. ITBTP, Feb. 1968.
Author information
Authors and Affiliations
Additional information
currently undertaking research at King's College, London, England.
Rights and permissions
About this article
Cite this article
Constantinescu, D.R., Illston, J.M. Direct solutions to problems of time-dependent induced stresses in restrained concrete. Mat. Constr. 8, 11–17 (1975). https://doi.org/10.1007/BF02538953
Issue Date:
DOI: https://doi.org/10.1007/BF02538953