Age-adjusted Effective Modulus Method Research Articles

Long-Term Behavior of Composite Beams under Positive and Negative Bending. II: Analytical Study

The creep, shrinkage, and cracking of concrete may induce time-dependent changes in the stresses, internal forces, and deflections of steel-concrete composite beams. This paper presents an analytical model to consider these effects in analyzing the long-term behavior of composite beams under service loads using the step-by-step procedure. Under negative moments, the model accounts for the cracking, stress relaxing, tension stiffening, creep, and shrinkage of concrete. Meanwhile, a method is proposed to calculate the maximum crack width of the concrete slab by considering the shrinkage and creep effects. Four composite beams continuously loaded for about 3 years were analyzed using the proposed model. A good agreement is observed between the experimental results and the calculations by the proposed model. A discussion is also made about the aging coefficients in the age-adjusted effective modulus method under different loading conditions.

Sluoksniuotųjų Konstrukcijų Įtempių IR Deformacijų Būvio Bei Valkšnumo Analizė, Veikiant Ilgalaikei Apkrovai

The paper proposes numerical and analytical models of the time-dependent analysis of a multilayered composite. These models enable us to predict the time-dependent behaviour of composite structures made of materials having age-variable properties. The proposed numerical model deals with a numerical solution of linear Volterra integral equation implying the validity of the principle of superposition for the layers. Meanwhile, the proposed analytical approach is based on the application of the age-adjusted effective modulus method for the composite. The validity of these models has been proven by a direct calculation of the time-dependent stresses and strains for the three-layered composite wall structure comparing the obtained theoretical values with those determined numerically. In particular, it was demonstrated that the analytical approach gave the identical values of the time-dependent stress strain state parameters. Relying on the results obtained, the concluding remarks have been summarized as follows: a) Despite the fact of sustained load, acting on the composite made of layers with different time-dependent deformational properties does not always hold time-invariant layer stress. In particular, the layers possessing a higher strain tend to produce relaxation while the layers with a lower strain are undergone the stress increase to maintain the equilibrium between internal and external forces (Fig. 4, b, e). Therefore, the failure should primarily be originated from the layer with a lower strain; b) Time variation in the elastic modulii of the layers is responsible for the increased stresses at time t in a higher strain layer due to a partial recovery of instantaneous strains. This effect is more progressive at a young age of the composite loaded (cf. Fig. 4, b and e); c) The ageing coefficient between the layers is different and is mainly subjected by the history of the ageing process of the layers. However, at the age of loading exceeding 28 days, the difference in the ageing coefficient of the layers is insignificant (Fig. 4, a). Moreover, it should be emphasized that the ageing coefficients of the layers are coincident with each other for the case of the time invariant elastic properties of the layers (Fig. 4, d). d) For the most practical purposes requiring long creep periods (exceeding 360 days), an approximate value of the ageing coefficient of the layers equal to 0.8 should be recommended predicting the stress-strain state of the layered composite using the proposed analytical method. More sophisticated functions for the ageing coefficients proposed by Lacidogna and Tarantino (1996), Ghali et al. (2002), ACI 209R-92 may be implemented for the sake of analysis accuracy. e) The values of the creep coefficient for the whole composite are mainly within the values of the creep coefficients of the layers.

Long-Term Behavior of Prestressed Composite Beams at Service Loads for One Year

The combined effects of creep and shrinkage of concrete and relaxation of prestressing tendons cause gradual changes in the internal forces and deflections of composite beams. However, most of the research work conducted on prestressed steel–concrete composite beams has focused on short-term behavior; research findings on the long-term behavior are scarce in the literature. For the wide-scale use of prestressed composite beams in civil engineering applications, the long-term behavior must be investigated. This paper presents an experimental program designed to examine the long-term behavior of prestressed composite beams under sustained load conditions for one year. The test program consisted of two prestressed composite beams and one nonprestressed composite beam. On the basis of the age-adjusted effective modulus method and energy principle, the creep stiffness matrix and the creep force matrix of prestressed composite beams were developed. A time-dependent analytical model is presented to predict the l...

A procedure for creep and shrinkage analysis of frames with low beam stiffness

AbstractAdjacent vertical members in tall buildings undergo differential time‐dependent deformations due to creep and shrinkage. These deformations result in differential deflections at floor levels and redistribution of forces. An available practical procedure in the literature to estimate these deformations, taking into account the sequential nature of the loading, utilizes the rate of creep method (RCM) to evaluate the stress transfer between concrete and steel. This procedure is designated as Procedure(RCM) and is prone to errors since the creep recovery of concrete is neglected in RCM. A more accurate procedure designated as Procedure(AEMM) using the age‐adjusted effective modulus method (AEMM) as a stress transfer method, and taking into account the sequential nature of the loading, is proposed. The proposed procedure is more accurate than Procedure(RCM) since creep recovery of concrete is considered in AEMM. Numerical studies are carried out in this paper to compare the results from these two procedures. Copyright © 2007 John Wiley & Sons, Ltd.

Creep Buckling of Shallow Parabolic Concrete Arches

This paper addresses, both theoretically and experimentally, the buckling of shallow concrete arches that may occur due to the effects of creep and shrinkage deformations of the concrete. Under sustained loading, these viscoelastic effects cause time-dependent changes of the deflections of a shallow arch and can lead to the establishment of a geometric configuration at which the arch is no longer stable, and which heralds the onset of creep buckling. By using a virtual work formulation, the equilibrium and buckling equations of an arch with horizontal spring supports are derived in closed form, and using the algebraically tractable age-adjusted effective modulus method to model the time-dependent behavior of the concrete allows the buckling load and the prebuckled life of the arch to be determined using prescriptive equations. Long-term tests on three 4.25 m span arches under sustained loading are described. Each arch failed because of creep buckling several months after first loading. These tests are used to validate the theory developed in the paper and to provide benchmark data for calibration. The study shows that creep and shrinkage of the concrete have a profound influence on the structural behavior of shallow concrete arches.

Composite model for basic creep of high-strength concrete

Most of the reported work on creep of high-strength concrete (HSC) covers measurements of total creep on standard specimens kept in a standard environment of 50% relative humidity and 23 °C. The results of these studies are used to establish the basic creep factor of high-strength concrete, assuming that the environmental effect on creep of HSC is similar to that for normal-strength concrete (NSC). However, some recent work has shown that the effect of the environment on creep of HSC is different from that observed for NSC, which indicates that a realistic creep model for HSC needs to be developed based on more fundamental material behaviour. This paper reports a theoretical study of a composite model for predicting basic creep of concrete, considering it as a composite material of coarse aggregate, fine aggregate and cement paste. The model is based on the age-adjusted effective modulus method proposed by Bazant, and can take into account the composition of the concrete, the degree of compaction and the hydration of cement paste. The model is shown to predict basic creep measurements reported in the literature with reasonable accuracy.

Time analysis of composite beams with partial interaction using available modelling techniques: A comparative study

This paper presents a comparison of available numerical structural formulations for the short- and long-term analysis of composite beams with partial shear interaction. The finite difference method, the finite element method, the direct stiffness method and the exact analytical model have been considered, and both the instantaneous analysis and the time analysis based on the age-adjusted effective modulus method (AEMM) have been carried out. For modelling based on the first two of these formulations, a spatial discretisation and a discretisation in the time domain are required, while only the time discretisation needs to be specified for the direct stiffness method. The results obtained using these formulations are compared qualitatively and their accuracy is estimated, adopting the exact analytical model as a benchmark reference with the objective of establishing the minimum spatial discretisations required to keep the error within an acceptable tolerance. These comparisons are carried out for simply supported beams, propped cantilevers and fixed ended beams, from which the qualitative behaviour of these formulations in the modelling of continuous beams can also be deduced.

Age-Adjusted Effective Modulus Method for Creep of High-Performance Concrete

This paper discusses the suitability of using several creep theories of common concrete for creep of high-performance concrete (HPC). Based on the Age-Adjusted Effective Modulus method (AEMM) for creep of concrete, Improved Dischinger (ID) method and the Elastic Continuation and Plastic Flow (ECPF) theory for calculating relaxation coefficient and considering characteristics of HPC, a method is set up for calculating the creep of HPC under changing stresses, and comparing results gotten by the method with some experimental data, it can be considered that the above methods are suit for the calculation of creep of HPC.

Analytical solutions for the time-dependent behaviour of composite beams with partial interaction

This paper presents a generic modelling for the time-dependent analysis of composite steel–concrete beams with partial shear interaction that occurs due to the deformation of the shear connection. The time effects considered in this modelling are those that arise from shrinkage and creep deformations of the concrete slab, and these effects are modelled using algebraic representations such as those of the age-adjusted effective modulus method (AEMM) and the mean stress method (MS), which are viscoelastic models for concrete deformation that can be stated algebraically. The generic model lends itself to closed form solutions for the analysis of composite beams subjected to a generic applied loading under a variety of end conditions. In this paper, the generic model is applied for the time-dependent analysis of composite beams that are simply supported and encastré, and to a propped cantilever, that are subjected to uniformly distributed loading and shrinkage deformations. Various representations of the structural behaviour of these beams are given in closed form which can also be used to benchmark available modelling techniques, i.e. finite element and finite difference formulations, which require a spatial discretisation to be specified as well as the time discretisation to perform a time analysis.

Time analysis of structural concrete elements using the equivalent displacement method

This paper presents a modelling technique referred to as the equivalent displacement method (EDM) which describes the behaviour in time of structural concrete elements, such as reinforced concrete beams and composite beams with full shear interaction, accounting for time effects, such as creep, of the concrete component. The time-dependent behaviour of the concrete is modelled using the algebraic representations, such as the age-adjusted effective modulus method (AEMM), while the steel joist and reinforcement are assumed to behave in a linear-elastic fashion. The main advantage of the EDM method is that it requires only one analysis to obtain the deformation state of the structural system at one step in time based on the AEMM methods, instead of the two required by available modelling techniques (i. e. one performed at timet 0 and one performed one step in timet). The EDM method is then applied to the analysis of structural concrete elements using the stiffness analysis and the results obtained based on this modelling technique are validated against other modelling methods. The advantages of using the EDM method in design applications are also illustrated.

Innovative Composite Precast Prestressed Precambered U-Shaped Concrete Deck for Belgium’s High Speed Railway Trains

During the past decade, an innovative composite precast, prestressed U-shaped bridge deck has been developed for use in the construction of the high speed railway system in Belgium. This deck is also used for replacing the old structural steel bridges that are being phased out. This article presents a method of analysis to measure the creep and shrinkage effects on the long-term behavior of the decks. The authors first review the origins and basic principles of this hybrid beam, then discuss their implementation. They note that, while these bridge decks have performed according to expectations, some variability has been observed between the measured and computed camber just after the transfer of prestressing. To explain the observed variability in camber, a multivariable statistical analysis was conducted on 42 bridge decks; results are reported in this paper. Variables studied include age of concrete at release, compressive strength, influence of curing temperatures, steel tensile stress versus strength, steel compressive stress versus strength, and bending moment. The most significant variables to explain camber measurement discrepancies at prestress transfer are the maximum tensile stress-to-yield strength ratio in the steel girders at prebending, and the steel girder type. In an instrumented bridge deck, the authors found that the computed strain values derived from an approximate, pseudo-elastic analysis with imposed modular ratios are quite different from the measured strains, especially 2 1/2 years after construction. The authors conclude that, in general, the step-by-step method is a more precise evaluator of the time-dependent redistribution of strains between steel and concrete than the age-adjusted effective modulus method.

Theoretical Study on Short-Term and Long-Term Deflections of Fiber Reinforced Polymer Prestressed Concrete Beams

This paper presents the methods for predicting the short-term and time-dependent deflections of fully or partially prestressed concrete beams with fiber reinforced polymer (FRP) tendons under sustained bending moment and axial force. The age-adjusted effective modulus method is used to model the creep behavior in the concrete and the relaxation in the FRP prestressing tendons. A tension-stiffening model is proposed to evaluate the stiffness of the section after cracking. The analytical values are compared to the test results and it is found that the analytical values are in good agreement with the experimental results.

Numerical Analysis of Continuous Composite Beams under Service Loading

This paper presents a method for the service-load analysis of continuous composite beams. Both short-term and time-dependent analyses are carried out, in which cracking, creep and shrinkage of the concrete slab are considered. The time-dependent response of individual cross-sections is modelled using the Age-Adjusted Effective Modulus Method coupled with a relaxation procedure, and the lengthwise or longitudinal analysis of the member makes use of the force method of structural analysis. Both propped and unpropped construction may be modelled. The numerical solution requires iteration, but is suited to straightforward spreadsheet or conventional programming on a personal computer, on which the analysis is performed rapidly. The scope of the method is demonstrated in a simple example of the behaviour of a two-span beam with the same sustained loading that is cast propped or unpropped.

Triaxial Composite Model for Basic Creep of Concrete

This paper shows how the mechanics of elastic composite materials can be adapted to predict the basic creep of concrete with aging caused by hydration. The prediction is made on the basis of the given composition of concrete, the elastic constants of the aggregate, and the aging viscoelastic properties of the portland cement mortar. The triaxial action of the composite is approximated by Dvorak's transformation field analysis. To convert the aging creep problem to an elastic problem of a composite material with inelastic strains, Granger and Bazant's approach is used. This approach relies on Bazant's age-adjusted effective modulus method that reduces the integral-type stress-strain relation for linear aging creep with nonconvolution kernel to a quasi-elastic incremental stress-strain relation with inelastic incremental strain. Explicit expressions for the aging creep properties of concrete as a composite are deduced. The model is calibrated and verified by Ward and colleagues and Counto's test data. The predictions obtained are almost as close as those recently obtained by Granger and Bazant's model. While the present model has the advantage of describing the triaxial composite action in a rational manner, it does not yet capture the effect of the deviation of the aggregate configuration from the case of a continguous aggregate skeleton of maximum possible compactness. Further refinements in this respect are needed. Another refinement might be needed to take into account possible enhancement of creep in the interface layers between the mortar and the aggregate.

SHORT- AND LONG-TERM BEHAVIOUR OF AXIALLY LOADED COMPOSITE PROFILED WALLS.

Keywords NEW SOUTH WALES UNIVERSITY, STRATHCLYDE UNIVERSITY, WOLLONGONG UNIVERSITY WALLS, COMPOSITE, PROFILED, AXIALLY, LOADED, AXIAL, LOADS, BEHAVIOUR, SHORT TERM, LONG TERM, WALLING, FORMWORK, SHEETING, STEEL, INFILLED, CONCRETE, CORES, SUSTAINED, TESTS, DEFORMATION, EFFECTIVE, MODULUS, METHODS, DESIGN, INFILL, RESPONSES, TIME DEPENDENT, COLUMNS, REINFORCED, SLENDERNESS, EFFECT, ECCENTRICITY, STRUCTURES... Show All

Drying creep of concrete in terms of the age-adjusted effective modulus method

The problem of drying creep of concrete is considered. It is emphasized that there is no single explanation of the paradoxical concrete performance known as the Pickett effect. The existing experimental data cannot clearly distinguish between the different mechanisms of drying creep, namely microcracking and stress-induced shrinkage. The phenomenological approach describing drying creep under tension as a sum of shrinkage-induced creep and creep-induced shrinkage is corrected by taking into account the swelling deformation of sealed concrete in basic creep tests. In such a way, the drying creep strain represents only the extra creep component, and therefore the mechanism of drying creep based on the stress-induced shrinkage is called into question. A new phenomenological approach to the problem of drying creep using the terms of the age-adjusted effective modulus method is demonstrated. The work done by a concrete element under simultaneous loading and drying is represented as restrained shrinkage in addition to basic creep under gradually developed stresses. It is shown that the drying creep strain depends on the values of the ageing coefficients for basic and drying creep and on the individual components of the concrete deformation; instantaneous strain, basic creep and free shrinkage. It is found that the instantaneous strain plays a minor role. The experimental data from the creep tests under tension are used to calculate the ageing coefficient ofconcrete for basic creep.

Simplified Approach to Evaluate Creep and Shrinkage Effects in Steel-Concrete Composite Beams

A simplified approach to evaluate creep and shrinkage effects in a steel-concrete composite beam with rigid or deformable connections, based on the age-adjusted effective modulus method, is presented. An aging coefficient, χ, evaluated in the absence of connection is adopted and exactly characterized by a theoretical point of view. Simplified expressions to evaluate χ and an easy to use, closed-form solution in the hypothesis of rigid connections and uncracked concrete are proposed. Numerical comparisons show how the proposed approach provides accurate results independently of the connection stiffness and load condition, and how it can substitute appropriately the more popular effective modulus method.

LONG-TERM SERVICE-LOAD BEHAVIOUR OF SIMPLY SUPPORTED PROFILED COMPOSITE SLABS.

This paper is concerned with the time-dependent behaviour of simply supported profiled composite slabs which are used as both the floor systems for buildings and bridge deck construction. Creep and shrinkage strains and their effects on the time-dependent behaviour are considered using the age-adjusted effective modulus method and a relaxation procedure in the time domain. The theoretical model allows the analysis of both a cracked and an uncracked cross-section. A numerical integration technique is implemented in order to monitor the member behaviour of simply supported composite slabs. A parametric study is undertaken to study the effects of span to depth ratio, slab depth, material properties and applied service loads on the long-term behaviour of these slabs. The effects which are monitored in the parametric study are the long-term strains, stresses and deflections. The results of long-term deflections are then compared with the current British code for composite slab construction, BS 5950: Part 4, and are shown to agree well. However, the method shows that the long-term stresses induced from the concrete into the steel are increased over time and suggests that these also be incorporated in international codes, particularly for use in buildings with a varying load history. (A)

Modified AAEM Method for Composite Beams with Post-Connected Slab

This paper proposes a simplified method to analyze the long-term behavior of continuous composite beams with precast prestressed concrete slab and flexible shear connection. The integral terms, which appear in the rigorous integral-differential solving system, are approximated with algebraic formulas in the spirit of the age-adjusted effective modulus method. The proposed method provides the solution of the problem in two steps, namely at the time at which the slab is connected to the beam and at the final time of the analysis, so that it is not necessary to know the whole history of the stress of the concrete. For this problem, a new creep modulus for the concrete has been defined. Useful information on performing a simplified creep analysis by means of routine computer programs for elastic analysis are given. Finally, a practical example is considered to test the proposed method on the basis of the results given by the general step-by-step procedure.

Creep and Shrinkage Deflections of RC Beams with Steel Fibers

In this paper, two analytical approaches based on the effective modulus method (EMM) and the age‐adjusted effective modulus method (AEMM), are proposed for the prediction of deflections due to creep and shrinkage in reinforced‐concrete beams with a steel‐fiber concrete matrix under sustained loads. In the EMM‐based approach, the deflection due to creep is evaluated from an elastic analysis using a modulus of elasticity that accounts for the reduced creep coefficient in steel‐fiber concrete, while the deflection due to shrinkage is analyzed using the equivalent tensile‐force method, which accounts for the reduced shrinkage strains in the steel‐fiber concrete. The AEMM‐based approach considers the aging of steel‐fiber concrete and involves a simultaneous linear‐elastic analysis for deflections due to creep and shrinkage using an age‐adjusted effective modulus of elasticity. Tests on 12 SFRC beams as well as on the material properties were carried out. The proposed methods, using creep coefficients and shrin...