Creep buckling of imperfect thin-walled shallow concrete domes

Engineering Structures, 1993

This paper presents an approximate solution of the stress redmtribu-t=on due to concrete creep in a rectangular orthogonal anisotropic thin plate subjected to uniformly distributed loads. Using the aging theory and the conversion modulus, simply supported concrete thin plates were analysed by the approximate solution developed in this paper. It was found that there are a significant stress redistribution and a notable deflection increase due to concrete creep in an anisotropic plate. The larger the difference of creep characteristics of two directions, the larger the stress redistribution. The calculated results are very close for both the aging theory and the conversion modulus theory when the stress redistribution is not very large. It is found that the results predicated by the theory of conversion modulus are adequate for engineering practme for all situations considered. Creep is one of the major properties of concrete_ This time-dependent behawour has very sigmficant effects on stress and deflections of concrete structures. Since Hatt of Purdue University first reported the creep results of a series of deflection tests of beams m 1907, experimental and theoretical studies on concrete creep have provided a good understanding of the nature of concrete creep under well-defined laboratory condmons ~-t4. Design considerations of effects of concrete creep are discussed in detail m the two ACI pubhcations 36 A comprehenswe state-of-the-art summary of recent experimental and theoretical studies on creep and shrinkage m concrete structures is contained in the excellent book edited by Bazant and Wlttmann ~5

Transient creep strain has to be included within the constitutive relationships for concrete at high temperatures. However, the necessity of taking into account this term explicitly is not clearly defined. In the Eurocode 2 uniaxial concrete material model, transient creep is included implicitly. This paper aims to highlight the capabilities and limitations of concrete uniaxial models at elevated temperatures for thermomechanical behaviour modelling, depending on the implicit or explicit consideration of transient creep strain in the model. The characteristics inherent to the two types of models are described and compared. It appears that one of the major limitations of implicit models concerns the unloading stiffness because implicit models treat transient creep as reversible. Based on numerical analysis performed on loaded concrete columns subjected to natural fire, it is shown that the stress-temperature paths experienced by structural concrete are varied and complicated and that concrete material models cannot handle properly these complex situations of unsteady temperatures and stresses without explicit consideration of transient creep. The paper proposes a new formulation of the Eurocode 2 concrete material model that contains an explicit term for transient creep. The new model is implemented in the software SAFIR and validated against experimental data of the mechanical strain developed by concrete cylinders under different unsteady temperatures and loads. It is shown that the actual material behaviour is better matched with the new explicit model than with the current implicit Eurocode 2 model. Finally, a comparison is given between experimental and calculated results on an axially restrained concrete column subjected to heating and cooling.

Engineering Structures, 2009

This paper investigates the long-term and thermal behaviour of spherical shallow, thin walled concrete domes. Although these structures are vulnerable to creep, shrinkage and thermal effects, a thorough understanding of their time-dependent behaviour has hitherto not been fully established. The paper aims to provide outcomes and insight to enhance the effective design and safe use of shallow concrete domes, and a theoretical model, which accounts for the membrane and bending behaviour, as well as for creep, shrinkage and thermal effects, is developed for this purpose. The analytical model uses variational principles, equilibrium requirements, and the time-dependent constitutive relations of the concrete material. The equilibrium equations derived from this boundary value problem are solved via the so-called multiple shooting numerical method, which enables the incorporation of the variable thickness of the shell, its different boundary conditions, and various types of axisymmetric loadings in the solution. A numerical example and a parametric study, which highlight the capabilities of the proposed theoretical model and which provide some insight into the long-term and thermal behaviour of shallow concrete domes, are presented. The results show that long-term and thermal effects play important roles in the behaviour and structural safety of shallow, thin-walled concrete domes, and so these effects need to be fully understood and quantifiable.

International Journal of Damage Mechanics, 2005

Softening and time-dependence of fracture are two complex and coupled phenomena that have to be taken into account in order to simulate realistic concrete behaviour. Understanding the interaction between these two phenomena is important to design reliable civil engineering structures subjected to high level-loading for a long time. The aim of this paper is to develop a simple time-dependent softening model applied to concrete. Presentation is restricted to compression behaviour. A constitutive viscodamage model describes concrete phenomena like relaxation, creep and rate-dependent loading using a unified framework. The model could be viewed as a generalisation of a time-independent damage model and is based on strong thermodynamical arguments. The determination of the material parameters linked to the proposed constitutive equation results from constant strain rate experiments. Using these parameters values, creep and relaxation numerical tests give satisfactory qualitative responses. Phenomena as creep failure under high-sustained load are explained quite simply within stability theory. Creep failure appears as the manifestation of a bifurcation phenomenon. Conversely, for low-sustained load, the motion asymptotically converges towards an equilibrium configuration. Consequently, this model is able to predict creep failure for various stress levels. Implementation of this rheological model in a structural code is envisaged in the future: a non-local approach would be probably necessary in order to simulate objective structural behaviour.

2014

This paper presents a numerical model for the analysis of concrete creep in plane deformation. Creep deformations of concrete were determined by means of correcting the modulus of elasticity of concrete in the principal directions for the current state of stresses. The correction of the modulus of elasticity, in an direction, depends on the current creep coefficient and the current elasticity modulus of concrete in this direction. With this numerical model it is possible to analyze the creep deformations of reinforced and prestressed concrete structures. Based on comparison of the results obtained by this numerical model and the numerical and experimental results of other authors, a verification of the numerical model was done.

Recent compilation of data on numerous large-span prestressed segmentally erected box girder bridges revealed gross underestimation of their multi-decade deflections. The main cause has been identified as incorrect and obsolete creep prediction models in various existing standard recommendations, and is being addressed under a separate study. But previous analyses of the excessive deflections of the the Koror-Babeldaob (KB) Bridge in Palau and of four Japanese bridges further have shown that a more accurate method of multi-decade creep analysis is also required. Its systematic and comprehensive presentation, appropriate not only for bridges but also for any large creep-sensitive structure, is the objective of this paper. For each time step, the solution is reduced to an elastic structural analysis with generally orthotropic elastic moduli and eigenstrains. This analysis should normally be three-dimensional. It can be accomplished A member of the National Academy of Sciences and the National Academy of Engineering, he is the founding Past Chair and a member of Joint ACI-ASCE Committee 446, Fracture mechanics of Concrete. He is also a member of ACI Committees 209, Creep and shrinkage in Concrete; 348, structural safety; and Joint ACI-ASCE Committees 334, Concrete shell design and Construction; 445, shear and torsion; and 447, Finite element analysis of reinforced Concrete structures. He is a licensed structural engineer in Illinois.

An analytical model based on the experimental trend of the creep deformation of concrete in direct tension is developed. The model is calibrated for normal and high strength concretes and the results show close agreement with experimental data. The inclussion of the stress level is a unique feature of the model and presents a prospect for predicting concrete deformation for any regime of loading. The model confirm that the creep strain of concrete in tension are non-linear right frm the begining of loading therby ruling out the applicability of the principle of superposition The model presents a means for incorporating the nonlinearlity of creep into other predictive models of concrete.

Cement and Concrete Research, 2015

Concrete creep models have to consider several important phenomena (nonlinearity, multi-axiality, hydration, and thermal and drying effects) to be relevant in structural applications. A selection of experimental results of creep tests found in the scientific literature are used to highlight these phenomena. Firstly, regarding the creep rate in different directions of a specimen under various loads, it is shown that creep rate under moderate loading can derive from elastic strains. Secondly, the reason why a Drucker Prager criterion can be chosen to model non-linear creep is discussed. Thirdly the interest of resorting to a creep theory able to decouple ageing (or hydration) effects and consolidation effects is explained. Moreover, interest using a poro-mechanical formulation, in which Biot coefficient depends on stress state, to model drying creep and shrinkage is discussed in the light of short meso-scopic analysis. The effect of temperature on creep is also addressed. The numerical implementation of the proposed modelling is briefly exposed and the model responses are confronted with experimental results.

CRC Press eBooks, 2010

Background 1 1.1.1 Concrete strain components 2 1.1.2 Typical concrete strain magnitudes 4 1.2 Creep of concrete S 1.2.1 Creep mechanisms and influencing factors 5 1.2.2 Creep components 7 1.2.3 Effects of ageing 8 1.2.4 The creep coefficient, <p {t, r), and the creep function, J(t,z) 8 1.2.5 The principle of superposition 9 1.2.6 Tensile creep 14 1.2.7 The effects of creep on structural behaviour 14 1.3 Shrinkage of concrete 17 1.3.1 Types of shrinkage 17 1.3.2 Factors affecting shrinkage 18 1.3.3 The effects of shrinkage on structural behaviour 18 1.4 Time analysisthe basic problem 22 1.5 References 22 2 Material properties 24 2.1 Concrete 24 2.1.1 Introductory remarks 24 2.1.2 Compressive and tensile strength 24 2.1.3 Elastic modulus 25 2.1.4 Creep coefficient 26 2.1.5 Shrinkage strain 29 Contents 2.2 Steel reinforcement 31 2.2.1 General 31 2.2.2 Conventional, non-prestressed reinforcement 32 2.2.3 Prestressing steel 33 2.3 References 36

2015

The time-dependent behaviour of concrete structures can be modelled by viscoelastic integral equations, which in most cases cannot be solved in a closed form. As an alternative, an algebraic method, the Age Adjusted Effective Modulus method (AAEM) was introduced. However, in cases were the load history on the structural element exhibits a significant amount of load changes, the use of numerical step-by-step methods, in which the stiffness matrix is multiplied with such viscoelastic integral equations, poses an advantage. Since the concrete strain is a function of the load history, this load history needs to be stored for each structural element. However this poses no longer a problem with computers. The load history results from the construction and the in-service stages of a structure. The loads during the construction period or the early service life invoke time-dependent deformations and can compromise the later serviceability of the structure. Due to the time effects, unacceptable deformations may be latent for several years. Commonly the construction sequence is neglected in the design of concrete structures with respect to creep and shrinkage. Furthermore, it is recognized that only part of the creep deformations can be recovered, even if loads are applied during a short period of time. This can have a significant effect on the later deformation occurring at a higher age. The fact that only a partial recovery is observed means that the viscoelastic behaviour of concrete is different for unloading. In this paper an existing numerical approach is extended in order to handle the viscoelastic behaviour for both the loading and unloading of concrete, taking into account the modelling of non-recoverable creep. Hereby, constitutive viscoelastic laws for loading and unloading suggested in the literature are used. Measurements of T-shaped concrete beams that are subjected to load changes are used to verify the suggested calculation method.