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Due to the use of refined ultimate state theories as well as high strength concrete and reinforcement, resulting in longer spans and smaller depths, the serviceability criteria often limits application of modern reinforced concrete (RC) superstructures. In structural analysis, civil engineers can choose between traditional design code methods and n...
Citations
... The poor performance of this data set can be attributed to the effect of material heterogeneity on the strain localization, which is dominant for the low reinforcing ratio. This was also observed by Gribniak [26]. Gribniak [27] presented a relevant example of the random nature of concrete's mechanical performance. ...
A reliable crack width assessment is a basic part of the sustainability control of the reinforced concrete structures subjected to corrosion degradation. The uncertainty of the concrete cracking model based on a finite element method and nonlinear fracture mechanics is investigated. The parameters of numerical model, such as the finite element mesh size and amount and arrangement of reinforcement are the subject of a case study. The uncertainty of the crack width model is verified on the experimental data from the tests of reinforced concrete beams. The constitutive model of crack propagation is based on the smeared cracks. The effects of numerical discretization as well as dimensional simplification are shown.
... • Identical beam samples demonstrate very similar deformation responses. This similarity results from the bar reinforcement effect and well agree with the experimental deformation analysis principles formulated in the dissertation [55]. • The fibers improve the flexural resistance of SFRC elements with bar reinforcement in the post-cracking stage, ensuring the development of efficient composite systems, e.g., [56,57]. ...
... Unfortunately, this highly oscillated line is barely acceptable to represent the materials model. Therefore, Gribniak [55] developed the smoothing procedure, which combines stochastic modeling with a modified moving average approximation. Fig. 11b presents the smoothed stress-strain diagram averaging five inverse simulations of stochastically selected moment-curvature data points, generating individual scatterplots. ...
... Fig. 11b presents the smoothed stress-strain diagram averaging five inverse simulations of stochastically selected moment-curvature data points, generating individual scatterplots. The moving average of all five stress-strain sets described the averaged constitutive model in the studies [29,37,[54][55][56]59]. The thesis [55] describes the inverse analysis procedure in detail and presents the corresponding MATLAB code. ...
Fiber reinforcement is a promising solution to cracking problems and improving the concrete's structural performance. The residual strength of the cracked concrete can characterize the reinforcement efficiency. However, quantifying the residual performance of steel fiber-reinforced concrete (SFRC) is challenging. The existing methodologies provide empirical formulas for estimating the residual strength using test results of SFRC elements in which a predominant crack governs the mechanical resistance. For instance, the 0.5 mm crack width determines the minimum value considered in the RILEM standard formulas. Thus, the SFRC strength evolution at earlier cracking stages remains unknown. At the same time, such a crack approximation is irrelevant to structural cases when reinforcement bars stimulate the formation of multiple cracks, and the 0.1-0.2 mm crack typically corresponds to the yielding of the steel bars. This study describes an alternative approach for quantifying the average residual stresses in SFRC elements with multiple cracks. It hypothesizes the possibility of separating the mechanical resistance components, corresponding to tension stiffening and fiber bridging effects characteristic of SFRC elements with bar reinforcement, using standardized small-scale specimens to estimate the fiber contribution. The laboratory tests of the plain concrete and SFRC beams with bar reinforcement illustrate the proposed technique. The RILEM standard three-point bending tests and the numerical simulation of full-scale beams verify the analysis's adequacy. The developed model is suitable for finite element simulations (employing the smeared crack model); the capability of separating the tension stiffening and fiber bridging effects ensures its versatility.
... Fig. 10a shows that the diagram of equivalent stresses approximates the 'exact' stresses. Fig. 9b demonstrates the curvature prediction results by the layered section model [47], using this equivalent stress relationship to model the behaviour of the tensile zone of the concrete. The prediction error does not exceed 5% proving the adequacy of the proposed simplifying assumption. ...
... Numerous investigations (e.g., [47][48][49]) have proved the adequacy of this hypothesis for flexural members. • Perfectly elastic laws determine the behaviour of the reinforcement and compressive concrete. ...
... This assumption substantially simplifies analytical expressions. It is adequate for the serviceability analysis of reinforced concrete elements [47,50], though non-linear material laws are also acceptable for the simulations, using the iterative procedure described in the Ref. [30]. • The stresses in the tensile concrete follow a rectangular distribution. ...
Various types of materials and technologies have been developed either for reinforcing or strengthening concrete structures. However, there is no uniform methodology to quantify and compare the mechanical characteristics of different reinforcement systems. Residual stiffness of flexural elements is the suggested measure of the reinforcement’s structural effectiveness, involving concrete into composite action. This manuscript proposes a new testing layout designed to form multiple cracks in a small laboratory specimen and a simplified analytical approach to quantifying the flexural stiffness of the standardised test samples. The achieved analytical solution to the stiffness problem requires neither iterative calculations nor the loading history description. That makes it acceptable for quantifying and comparing the residual stiffness of elements with various combinations of reinforcement materials. The proposed analysis procedure also enables determining the mechanical performance decay under repeated and long-term loading conditions without a loss of the calculation adequacy. Flexural tests illustrate the application of the proposed technique—the 38 specimens were mechanically loaded until failure. Several composite reinforcement schemes, including steel and glass fibre reinforced polymer (GFRP) bars, externally bonded carbon fibre (CF) sheets, and near-surface mounted (NSM) carbon fibre reinforced polymer (CFRP) strips in various combinations, are considered. The analysis reveals an exceptional efficiency of hybrid reinforcement systems, combining steel and CFRP components.
... tension-stiffening). Gausūs teoriniai ir eksperimentiniai tyrimai šioje srityje (Clark ir Speirs 1978;Clark ir Cranston 1980;Williams 1986;Wollrab et al. 1996;Polak ir Killen 1998;Kaklauskas 2001;Bischoff 2007;Gilbert 2007;Gribniak 2009;Rimkus 2017) parodė, kad tempiamojo sustandėjo įtaka elemento elgsenai labiausiai priklauso nuo armavimo procento ir betono stiprio. Nevertinant šio efekto, apskaičiuotų įlinkių paklaidos, viršijus pleišėjimo apkrovą, gali siekti iki 100 % (Gilbert ir Warner 1978;Kaklauskas 2001 ...
... Vakhshouri (2017) disertacijoje apibendrino literatūroje paskelbtus tradicinio gelžbetonio elementų analizei tinkamus tempiamojo sustandėjimo modelius trumpalaikio ir ilgalaikio apkrovimo atvejais. Nuodugni modelių tyrinėjimo evoliucija pateikta ir Lietuvos tyrėjų darbuose: Kaklauskas (2001), Gribniak (2009) ir Sokolov (2010). Apibendrinti ir papildyti trumpalaikio apkrovimo tempiamojo sustandėjimo modeliai ir jų modifikacijos (Scanlon-Murray 1974;Lin ir Scordelis 1975;Vebo ir Ghali 1977;Gilbert ir Warner 1978;Scott 1983;Damjanic ir Owen 1984;Schnobrich 1985;Massicote et al. 1990;Vecchio ir Collins 1986;Collins ir Mitchell 1987;Tamai et al. 1988;Bentz 2005; Carriera ir Chu 1986; Prakhya ir Morely 1990; Kaklauskas 1999;Foster ir Marti 2003;Beeby et al. 2005;Nayal ir Rasheed 2006;Stramandinol et al. 2008;Ng et al. 2010;Sokolov 2010;Bačinskas et al. 2012) įprasto armuoto betono elementams (su plienine armatūra) grafiškai pateikti 1.8 paveiksle. ...
... Poskyryje pateikiamas Kaklausko ir Ghaboussi (2001) pasiūlytas integralinis metodas supleišėjusio tempiamojo betono vidutinių įtempių ir vidutinių deformacijų diagramoms nustatyti iš lenkiamųjų gelžbetonių elementų eksperimentinių duomenų. Atvirkštinio uždavinio matematinis algoritmas nuodugniai aptartas Kaklausko (2001), Gribniak (2009), Girdžiaus (2011) ir kt. darbuose. ...
... 57 Besides the effect of tension stiffening, Castel et al. [11,31,32] pointed out that 58 the degradation of the moment of inertia and the irreversible deflection of the struc-59 tural member due to cracking damage have to be accounted for in the serviceability 60 analysis of existing cracked RC members. All the methods previously described are 61 dedicated to the calculation of the deflection of structural members or the curva-62 tures of cross-sections under monotonic increasing load up to failure [31]. As shown 63 in Fig. 1, the path OABC is the monotonic load-deflection envelop obtained by per-64 forming a static load test beyond the cracking load P cr . ...
... In order to cover more area of the applications of effective moment of inertia, a 313 total of 505 observations ofGilbert[60] andGribniak [29,61] are adopted to calibrate314 the model error of the effective moment of inertia. In Ref.[60], Gilbert reported 315 experimental results obtained on a total of eleven lightly reinforced concrete beams 316 (slabs). ...
Under in-service conditions, beams and slabs in reinforced concrete structures are almost always cracked, as the tensile strength of the concrete is low. Due to the irreversible reduction in overall stiffness resulting from cracking and the residual deflection after unloading, the structural response is load path dependent. In this paper, an existing average moment of inertia model and Monte Carlo simulation (MCS) are adopted to take into account the effect of historical cracking damage on the reliability of serviceability calculations for reinforced concrete (RC) members. The suitability of the average moment of inertia model for reliability analysis is verified by considering experimental tests on a total of eleven reinforced concrete beams. The errors associated with both the effective and average moment of inertia predicted by the model are calibrated using the experimental data. By using the proposed approach to account for the various sources of uncertainty in reinforced concrete beams, the quantitative loss in the short-term and long-term serviceability reliability of a cracked reinforced concrete beam was calculated. The results confirm that the effect of historical cracking damage on short-term serviceability reliability should be taken into account when the deflection induced by historical loading is larger than the deflection limitation. Light historical damage has no influence on the short-term serviceability reliability, although it affects the probability density distribution of the deflection. However, in the long-term serviceability reliability analysis, even when the historical damage is light, the long-term serviceability reliability index is decreased as the cracking damage to the stiffness affects the time-dependent deflection. Additionally, the later a damaging load is applied to a reinforced concrete beam, the less is the influence of cracking damage on the long-term serviceability reliability.
... Based on the proposed model in Eqs. (30) and (31), when the reinforcement ratio is approaching the minimum ratio, the tensile reinforcement will immediately yield after cracking leading to a fully degraded effective moment of inertia equal to cracked moment of inertia I cr , which is not captured by Bischoff's model. Additionally, the two approaches are derived differently. ...
... Eight beams were tested under a four-point loading scheme by Gribaniak et al. [20,31]. The experimental program consisted of two series of beams. ...
... The experimental program consisted of two series of beams. In the first series (S-1 and S-2), the tensile reinforcement comprise of four /10 mm bars, whereas the beams of the second series (S-3 and S-4) had two /14 mm bars [31]. Practically, the reinforcement ratio for the beams of both series was the same, i.e. about 0.40%. ...
Tension stiffening affects the strain distribution along the tensile reinforcement in a cracked reinforced concrete beam and in the tensile concrete between cracks. It also affects the overall stiffness and hence the deflection of the beam. In this paper, the results of experiments on eleven reinforced concrete beams with reinforcement ratios between 0.56% and 0.88% are reported. The overall strain in the reinforcement and the load-deflection response under both monotonic loading and cycles of loading and unloading were measured for each beam. Based on the experimental results, a model of the effective strain in the reinforcement is presented and is used to assess the effective moment of inertia of reinforced concrete beams subjected to in-service monotonic loading. Measurements from the test beams were used to calibrate a model of the steel-concrete interface damage caused by cycles of loading and unloading. The comparisons between predicted and measured overall stiffness and load-deflection responses show the validity of the present model.
... In reality, a small tension stiffening effect persists even at the yield point; however, this assumption is not expected to introduce significant error at service load levels and is adopted here. The effect of restrained shrinkage on the increase of interfacial damage [22][23][24] may be taken into account by superimposing a fictitious tensile stress in the bare reinforcement in addition to the reinforcement stress caused by the external loading. The determination of this fictitious reinforcement stress r s,sh is considered in Section 3.4. ...
... The deleterious effect of shrinkage on the time-dependent decay in tension stiffening has been the subject of a limited number of studies in the literature (e.g. [22][23][24]). When concrete is restrained, it develops shrinkage-induced tensile stresses which encourage the formation and extension of cracks over time. ...
The instantaneous stiffness of a reinforced concrete (RC) beam deteriorates with time and this fact may have important consequences for the long-term in-service behavior of RC structures, particularly those that are subjected to repeated loads, vibrations or dynamic effects. There are two main causes of the time-dependent deterioration of instantaneous stiffness. The first is the formation of new primary cracks, both within and outside of the original cracked region of the beam. The second is the propagation of fine cone-shaped cracks that originate at the steel-concrete interface and are mainly confined within the cover concrete. These cover-controlled cracks facilitate a reduction in bond that is manifested in a decay of tension stiffening within the cracked region of the beam. The formation and propagation of both primary cracks and cover-controlled cracks are driven by the combined effects of shrinkage-induced tensile stress in the concrete and a reduction of the concrete's tensile strength under sustained stress (creep rupture). This paper presents an analytical model for the estimation of the instantaneous stiffness of RC beams with a particular focus on time effects. The model is shown to agree well with recent experimental results.
... In more detail, concrete shrinkage is rigorously modelled by inserting it explicitly into 2D-PARC general algorithm as a prescribed deformation. The effectiveness of the proposed procedure is verified herein through the modelling of two experimental programs [13,14] on RC shrunk beams with low reinforcement ratio tested to short-term bending. These elements are highly sensitive to shrinkage effects, especially in presence of a non-symmetric arrangement of steel reinforcement in the element cross-section. ...
... he effectiveness of the above described procedure, as well as of its correct implementation into a commercial finite element (FE) code (ABAQUS), are verified herein through comparisons with detailed test data on shrunk RC beams subjected to short-term bending. The first considered experimental program (carried out by Gribniak, [13]) mainly focuses on the effects of concrete shrinkage on beam deflection and first cracking moment in case of different amounts of top reinforcement, while the second one (by Sato et al. [14]) compares the flexural behavior of RC beams subjected or not to shrinkage prior to loading. ...
... Four RC beams tested by Gribniak [13] -respectively named S1, S1R, S2, S2R -and subjected to four-point bending are first analyzed. The considered specimens were characterized by the same geometry, with a rectangular cross-section (300 mm deep and 280 mm wide) and a total length equal to 3280 mm, with a net span of 3000 mm. ...
Shrinkage effects on short-term behavior of reinforced concrete elements are often neglected both
in design code provisions and in numerical simulations. However, it is known that their influence on
serviceability performance can be significant, especially in case of lightly-reinforced beams. As a matter of fact,
the restraint provided by the reinforcement on concrete determines a reduction of the cracking load of the
structural element, as well as an increase of its deflection. This paper deals with the modeling of early-age
shrinkage effects in the field of smeared crack approaches. To this aim, an existing non-linear constitutive
relation for cracked reinforced concrete elements is extended herein to include early-age concrete shrinkage.
Careful verifications of the model are carried out by comparing numerical results with significant experimental
data reported in technical literature, providing a good agreement both in terms of global and local behavior.
... The shrinkage measurements at the 200 mm base were performed using the surface-glued steel gauge studs. A detailed explanation of the measurement technique is presented in [18]. The variation of shrinkage strain with time is shown in Figure 2. ...
The increasing application of high-performance materials in civil engineering led to the development of reinforced concrete (RC) structures with reduced cross sections and increased spans. In such structures serviceability limit state often becomes the governing condition of the design. Present study investigates the deformation behaviour of high-strength RC ties reinforced with high-grade bars. Experimental investigation was carried out measuring the postcracking stiffness of the specimens at high strain levels. It was found that, despite the reduction in stiffness, a considerable part of the average tensile stresses were carried by the concrete at the advanced loading stages, thus effectively stiffening the RC member.
... The model will enable deflection checking in the design stage by simple numerical methods, and the deflection checking would deem to satisfy the codified requirements. The inverse technique for deformation analysis developed by Kaklauskas and Ghaboussi (2001) and subsequently modified by Gribniak (2009) and is employed for derivation of tension-stiffening relationships from the moment-curvature diagrams calculated based on GB 50010-2010 formulations. To confirm the applicability of the proposed model, it is adopted in structural analysis of concrete beams with the use of the nonlinear finite element software ATENA. ...
... The present research employs the inverse technique which was modified by Gribniak (2009) and . The flowchart in Figure 2 illustrates the analysis procedures algorithmically. ...
... Conversely, if |(κth,j/κcode,j) -1| > Δ, i.e. convergence condition is not met, the analysis is repeated with the secant modulus adjusted by the hybrid Newton-Raphson and bisection procedure (Gribniak 2009;Gribniak et al. 2012) until convergence is attained or the iteration number reaches its limit N, which is set at 100 or other values to suit the numerical procedures. Then the analysis proceeds to the next increment step until the final loading step is reached. ...
A generalised stress-strain tension-stiffening relationship conforming to the Chinese Code for Design of Concrete Structures GB 50010-2010 is proposed. Based on the provisions in GB 50010-2010 for rigidity and curvature calculations of reinforced concrete flexural members, tension-stiffening relationships were derived from moment-curvature relations by means of the inverse technique for deformation analysis. A parameterized stress block for tension-stiffening was suggested. The proposed tension-stiffening model was applied to nonlinear finite element analysis of reinforced concrete beams. Good agreement between the analysis results based on the proposed model and those based on the codified formulas in GB 50010-2010 was achieved. The proposed model will be able to serve as a design aid for serviceability evaluation of concrete beams in general.
