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The variation of shrinkage strain within beam depth was examined through four series of time-dependent laboratory experiments on unreinforced concrete beam specimens. Two types of beam specimens, horizontally cast and vertically cast, were tested; shrinkage variation was observed in the horizontally cast specimens. This indicated that the shrinkage...
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... measured shrinkage strains were compared to those measured from the horizontally cast test specimens to determine if the variation of shrinkage strains in Figures 4 and 5 were observed in the vertically cast beam specimens. Figure 7 plots the shrinkage strains measured from six surface-attached strain gages (gage numbering is illustrated in Figure 8). In Figure 7, the shrinkage strains measured from the vertically cast specimens range between 0.004 and 0.006 regardless of the locations of the strain gages, in contrast to the observations for horizontally cast beam specimens. ...
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... The shrinkage deformation of concrete mainly comes from the shrinkage of hardened cement paste, and when cement stone shrinks, aggregates limit the shrinkage of cement stone and then reduce the shrinkage effect of concrete. Therefore, the influence of aggregates and their force cannot be ignored in the analysis of the influence of average hydrostatic pressure (or pore hydraulic pressure) on the volume deformation of concrete [31,34,35]. Once a concrete mix proportion is determined, the amount (volume) of the concrete aggregate (coarse aggregate and fine aggregate) is fixed and remains stable in the development of concrete; the influence of aggregate on the linear strain of concrete can be considered by the volume fraction of the aggregate, V a /V c . ...
A crack caused by shrinkage could remarkably increase the permeability, heavily deteriorate the durability, and heavily deteriorate the service life of a concrete structure. However, different forms of thermal shrinkage can be predicted by directly applying a temperature load on a node. The prediction of moisture-induced stresses in cement-based materials by using the common finite element method (FEM) software is a big challenge. In this paper, we present a simple numerical calculation approach by using the proposed coefficient of hygroscopic expansion (CHE) to predict the moisture-induced deformation of concrete. The theoretical calculation formula of the linear CHE (LCHE) of cement-based material was deduced based on the Kelvin–Laplace equation and the Mackenzie equation. The hygroscopic deformation of cement mortar was investigated by inversion analysis; based on the results, the LCHE could be determined. Moreover, a case analysis of the application of LCHE to concrete is also conducted. The simulated results of concrete shrinkage were close to the experimental ones. As a whole, it is feasible to predict the drying shrinkage of concrete through simple calculation by using the proposed LCHE, which is also beneficial to the direct application of moisture loads on nodes in finite element analysis (FEA).
... Further, creep strain measurements are much influenced by minute changes in the humidity level and temperature of the laboratory [7,9,12]. A recent research study [27] revealed the variation of shrinkage strain within the beam depth of a rectangular concrete beam, and interpreted the phenomenon based on two causes-the diffusion of drying, which proceeds from the surface of the concrete section, and compaction during concrete casting and bleeding [28][29][30][31][32]. The bending creep in this paper was evaluated with consideration of the variation of shrinkage within the beam depth. ...
... The concrete mix proportions used in the three sets of experiments are listed in Table 1. TP-1 test series was aimed to evaluate the variation of shrinkage strain within the beam depth [27] as well as to identify the relation between bending creep and compressive creep strain. The water to cement ratio (W/C) of TP-1 test series in Table 1 was slightly higher than those of the other two test series of TP-2 and TP-3 to incorporate the former test aim. ...
... In the case of TP-1, embedded gauges were used in addition to surface-attached gauges to probe whether variations in shrinkage were developed within the beam depth of the concrete beam, similar to the case of surface-attached gauges. The detailed descriptions for the embedded gauge installation and the test results are provided in [27]. ...
Three types of creep experiments of compression, tension, and bending were implemented to identify quantitative relations among the three types of creep under drying atmospheric conditions. In case of the bending creep experiment, two types of unreinforced concrete beams with similar dimensions were cast for use in the beam creep and shrinkage tests. The variations in the shrinkage strain within the beam depth were measured to evaluate the effect of the shrinkage variations on the bending creep strain. The beam creep strain measured within the beam depth was composed of uniform and skewed parts. The skewed parts of the creep strain were found to be dominant whereas the uniform parts were small enough to be neglected in the bending creep evaluation. This indicated that the compressive bending creep at the top surface was close to the tensile bending creep at the bottom surface. The ratios of tensile and bending creep strains to compressive creep strain were approximately 2.9 and 2.3, respectively, and the ratio of bending creep strain to tensile creep strain was approximately 0.8. Particular attention is laid on the close agreement between tensile and compressive bending creep strains even if the creep in tension is 2.9 times larger than the creep strain in compression.
... Kaklauskas and Ghaboussi [19] and Kaklauskas et al. [20] presented methods for removing the shrinkage effect in the moment-curvature (M-k) relationship by adding the corresponding M-k induced by shrinkage in an RC section to the externally applied M-k. However, all these approaches accept uniform shrinkage strain through the height of the plain concrete section, whilst there is strong evidence that shrinkage strain is not necessarily uniform through the section and shrinkage strains at the top (cast surface) can be twice as much as the strains at the bottom of the section [1,18,27]. ...
Current recommendations by fib Model Code 2010 only consider the effect of shrinkage strains on long-term crack width calculations of reinforced concrete (RC) elements. However, shrinkage strains develop fairly early and can influence mean strains as well as short-term crack width and deflection calculations. This paper examines the effect of shrinkage strains on short-term deformations using experiments on eight RC beams, with and without steel fibres, at the age of 4-5 months. The results show that due to shrinkage, measured strains, deflections and crack widths are higher than expected for fully cracked sections. The MC-2010 predictive equation for crack widths is amended to account for shrinkage strains and induced curvatures. This work will lead to better design equations and less serviceability problems in RC structures.
... Younis [34] and Jeong et al. [27] report that shrinkage strains vary through the height of plain rectangular sections, and the ratio between top and bottom shrinkage strains can be higher than two. Younis [34] attributed strain differences to concrete bleeding and porosity, while Jeong et al. [27] linked it to uncertainty of concrete properties and nonuniform distribution of coarse aggregates, having found that more aggregates settled in the bottom half (55%) compared to 45% in the top half of the section. ...
... Younis [34] and Jeong et al. [27] report that shrinkage strains vary through the height of plain rectangular sections, and the ratio between top and bottom shrinkage strains can be higher than two. Younis [34] attributed strain differences to concrete bleeding and porosity, while Jeong et al. [27] linked it to uncertainty of concrete properties and nonuniform distribution of coarse aggregates, having found that more aggregates settled in the bottom half (55%) compared to 45% in the top half of the section. ...
... Shrinkage of cement paste in concrete is initially restrained by the adsorbed free water in the capillary pores and then by solid particles such as un-hydrated cement particles, calcium hydroxide crystals and aggregates as well as reinforcement [23,8,31]. However, several factors can lead to uneven evolution of shrinkage through the section height: (1) available amount of water, which is higher towards the top of the section due to bleeding and surface tamping; (2) level of restraint provided by solid particles, which is higher towards the bottom where more particles settle [27]; (3) differential loss of water particles from the cement matrix into the surrounding environment, due to variable porosity and permeability which is normally higher at the top [7]; (4) variation of concrete mechanical properties through the depth of the section [24], such as compressive strength, density and elastic modulus, which are affected by water-to-binder ratio, vibration and tamping of fresh concrete. ...
Shrinkage induced curvatures in reinforced concrete elements are thought to be affected only by section geometry and distribution/ratio of reinforcement. The variation in the level of internal restraint caused by the non-uniform distribution of concrete constituents within the section, however, can also lead to additional shrinkage induced deformations, and potentially to larger than expected deformations in critical structural elements, even under service conditions. This study examines experimentally the development of non-uniform shrinkage strains in unreinforced as well as symmetrically and asymmetrically reinforced concrete elements. Results confirm that shrinkage is non-uniform due to the variations in internal restrains (coarse aggregates and reinforcement). The addition of steel fibres mitigates this effect and reduces overall shrinkage curvature. A prediction model for shrinkage induced curvature of plain and reinforced concrete is proposed, taking into account the non-uniform distribution of concrete constituents. The proposed model yields results in good agreement with experimentally observed values of shrinkage curvature and can be used to improve the predictions of design guidelines.
... It is also known that aggregates tend to settle and concentrate at the bottom of the mould whilst water and air rise due to vibration and surface tamping. These phenomena can cause differences in compressive strength and elastic modulus at the top and bottom of the element [24,25]. As more paste and water are found near the top surface, this can cause much higher shrinkage strains in that region. ...
... The varying amounts of coarse aggregates at the bottom of the section resulted in varying degrees of restrain and thus a higher scatter in shrinkage resistance. Non-uniform shrinkage strains in these rectangular sections can be the result of non-uniform distribution of the coarse aggregates across the depth of concrete section, which also creates curvature that will contribute to the global deformation of the members [25,45]. ...
The effect of restrained shrinkage on the mechanical performance of concrete and steel fibre reinforced concrete (SFRC) requires more investigation, especially when using recycled tyre steel fibre (RTSF). This paper examines the free and restrained shrinkage strains and the mechanical performance of seven SFRC mixes. Results show that both free and restrained average shrinkage strains are very similar in all blends of fibres and they exhibited non-uniform shrinkage through the height of the section. All examined blends meet strength requirements by MC-2010 for fibres to replace part of the conventional reinforcement in RC structures.
... These differential strains are caused by differences in the concrete structure due to vibration of the fresh concrete to minimize the air void content, by aggregate sedimentation and surface bleeding (Hoshino, 1989). Jeong et al. (2015) observed that more course aggregates settle in the bottom half (55%) compared to 45% in the top half of the section and thus the centroid of the course aggregate sits below the centroid of the section. The sedimentation and bleeding led to a decrease in the strength of the concrete in the upper section compared to the bottom section (Hoshino, 1989). ...
... This is not considered in the Euro-code and fib Model Code 2010 formulas since curvature of symmetrically reinforced sections is expected to be equal zero. In fact, more aggregates are typically found in the bottom half than in the top half of cast elements (Jeong, et al., 2015). In addition, the stiffness of the top section can be reduced during the casting as a result of surface tamping and bleeding (Hobbs, 1974;Hoshino, 1989). ...
Drying shrinkage of concrete can induce significant additional deflection and cracking in RC structures and lead to undesirable serviceability problems. Flexural reinforcement in RC structures resists shrinkage strains/stresses and contributes to higher deflections due to induced curvatures. It is generally accepted, without more justification, that drying shrinkage develops uniformly throughout a section while member curvature is caused by the asymmetric reinforcement. To investigate this issue, this research examines the behaviour of six doubly-reinforced concrete beams with the same ratio of tension and compression reinforcement, as well as singly-reinforced smaller elements. Manufactured and recycled tyre steel fibres are used in some of the mixes to examine their effect in controlling shrinkage cracking. Shrinkage was measured for a period of four months along the entire length of the specimens at the level of the top and bottom reinforcement. The experimental shrinkage curvatures are compared with the predictions of Eurocode and Model Code 2010. Results show that concrete shrinkage strains are higher at the top of the section for all reinforcement configurations. This contradicts the current design code predictions. The addition of the steel fibres had a minor effect on total shrinkage but contributed to crack width control under flexural loads.
The effects of shrinkage variation within the beam depth and bending creep on the time-dependent flexural behavior of reinforced concrete (RC) beams were examined via two sets of experiments and numerical analyses. Each test set included four types of experiments: axial creep, beam shrinkage, bending creep, and time-dependent RC beam bending tests. The variations in beam shrinkage and bending creep strain were determined using the American Concrete Institute’s shrinkage and creep prediction models, respectively. Time-dependent finite-element beam equilibrium equations were presented using an incremental form of the age-dependent constitutive equation. The mathematical creep model of the constitutive equation accounted for the aging effects of the elastic modulus and the creep development under a multi-sequential loading condition with a single creep curve. The resulting finite-element formulation captured the mechanical and non-mechanical phenomena of the aging effect of concrete at an early age, shrinkage variations within the beam depth, and bending creep. Comparisons between the age-dependent responses of the measured and predicted results of the RC beam test specimens illustrated the significant effects of shrinkage variation and bending creep on the time-dependent behaviors of RC flexural members.
The durability and functionality of concrete overlay repairs are highly dependent on the extent of cracking and crack widths, which are difficult to predict. This article presents an experimental and analytical investigation on restrained shrinkage of overlays made with rapid hardening mortar mixes reinforced with recycled fibres. The investigated parameters include cement type (calcium sulfoaluminate cement-CSA and calcium aluminate cement-RSC), overlay depth, bond condition and fibre dosage. Sixteen composite prisms were tested to determine shrinkage strains and cracking development over time. Both plain (RSC) and fibre reinforced (FRSC) overlaid prisms made of calcium aluminate cement developed multiple cracks in less than 16 h due to their high shrinkage values, but 60% lower crack widths developed in FRSC. An effective analytical model is derived to estimate the crack spacing of concrete overlays. As concrete crack width predictive models are shown to be deficient in predicting the crack width of materials with flexural hardening properties, a semi-empirical approach is adopted to quantify the effect of fibres in such matrices. The predicted crack widths are in a good agreement with the experimentally measured values. The suggested model is expected to make a contribution towards safer and more sustainable solutions for concrete repairs.
This article presents FE numerical studies on restrained shrinkage of plain and fibre reinforced rapid hardening mortars. Moisture diffusivity analysis is coupled with structural analysis to calculate the evolution of hygral stresses, strains and cracking over time. The numerical results are validated against results from analytical models and compared to measured experimental values. Parametric studies are carried out to examine the effect of the interface stiffness, moisture content of the substrate layer and overlay depth on restrained shrinkage strain and stresses of overlays. Fibre inclusion is shown to reduce the risk of deterioration by slowing down the evolution of local slippage and controlling crack widths. It is also found that the uniform shrinkage strain distribution that is assumed in analytical models underestimates the hygral tensile stresses of overlays compared to real non-linear strain distribution. A modification to account for this effect is proposed through shrinkage amplification factor. This approach is expected to provide a better estimation of the risk of cracking in overlays.
