Maximum Crack Spacing Research Articles

Evaluation of the shrinkage crack resistance of cement-stabilized aggregate by predicting the crack spacing

Shrinkage cracks are a major issue in the manufacture of cement-stabilised aggregate (CSA) bases. This study proposes a novel mechanical method to predict the stress and crack spacing caused by shrinkage in CSA bases. Its effectiveness was found to be 71% by using field data collected from several expressways in Jiangsu Province, China. The predicted maximum crack spacing was used to evaluate the shrinkage crack resistance of CSA with different cement contents, gradations, and forming methods. The results suggest that for a specific gradation, an optimal cement content exists that leads to the best shrinkage crack resistance. The shrinkage crack resistance of a large stone base course (LSBC) filled with CSA was found to be 30% less than that of a typical gradation. Moreover, the shrinkage crack resistance of CSA specimens was improved significantly by vibration compaction forming compared with static pressure forming.

CALCULATION METHOD FOR CRACK WIDTH OF STEEL FIBER-REINFORCED LIGHTWEIGHT AGGREGATE CONCRETE BEAMS REINFORCED WITH FRP BARS CONSIDERING BOND-SLIP BEHAVIOR

Regarding the crack development of concrete beams reinforced with fiber-reinforced polymer (FRP) bars as a process wherein the FRP bars are pulled out from concrete on both sides, a differential equation of crack width of lightweight aggregate concrete beams reinforced with FRP bars considering bond-slip behavior was established. According to the crack width limits provided by the design codes, the upper limit of slip was reasonably determined and constitutive models for bond-slip relationship between FRP bars and steel fiber reinforced-lightweight aggregate concrete in ‘low slip’ stage which were suitable to the service stage of the beams were proposed and introduced. The maximum crack spacing, lmax, amplification factor of crack width, h2/h1, and residual stress of fiber reinforced-concrete in cracked sections, σfib, were specified. On this basis, a crack width model of steel fiber reinforced-lightweight aggregate concrete beams reinforced with FRP bars was proposed using iterative algorithm and its accuracy was evaluated based on measured data of maximum crack width in service stage. It is shown that within crack width limit of 0.5 mm, the proposed model generates accurate maximum crack width predictions for steel fiber-reinforced lightweight aggregate concrete beams reinforced with FRP bars.

Influence of steel corrosion to flexural behavior of coral aggregate concrete beam

To study the flexural behavior and calculation model, 8 coral aggregate concrete (CAC) beams with different types of steel were designed. The flexural behavior of CAC beam was tested. The failure mode, bearing capacity, the maximum crack width (ws) and average crack spacing (lm) were studied. A calculation model for the bearing capacity of CAC beam was proposed. The results indicated that with the steel strength increased, the cracking moment (Mcr) and ultimate moment (Mu) of CAC beam increased, and the development of the ws gradually slowed, which effectively inhibited the formation of cracks and improved the flexural behavior of CAC beam. For CAC structures in the ocean engineering, it is recommended to use organic new coated steel to extend its effective service life. In addition, considering the influence of steel corrosion, a calculation model for the Mcr, Mu, lm and ws of CAC beam was established.

Experimental Investigation and Analytical Study on the Flexural Behavior of Reinforced Recycled Aggregate Concrete Beams

The paper presents an experimental study on the flexural behavior of reinforced beams made of natural and recycled gravels under monotonic loading. 20x25x170 cm beams specimens were prepared using two reinforcement ratios and were cast from two concrete mixtures. The two concretes are respectively a mixture of natural aggregates and a concrete with 100% recycled gravels of C35/45 strength class, S4 class of workability and a constant W/C ratio. The results reported in this paper are those of experiments performed in the framework of this study beside 118 data sets taken from the literature on the flexural behavior of natural (NAC) and recycled aggregate concrete (RAC). The principal results of bending tests show that flexural capacity of recycled aggregate concrete beams is similar to the flexural capacity of natural aggregate concrete beams for the service and ultimate loading. However, cracking moment, maximum crack spacing, crack heights and deflection under serviceable load are affected by the use of recycled aggregates. Experimental results of the extensive data base were compared to load-carrying capacities and deflections calculated according to Eurocode 2 (EC2). The comparisons show that the method of deflection calculation does not correctly predict the experimental results.

Experimental investigation of cracking and deformations of concrete ties reinforced with multiple bars

Interpretation of test results may be inadequate even for simple test layouts. On the one hand, conventional tests, that investigate a concrete prism reinforced with a single bar in the centre, do not allow to account for the effect of variation of the diameter-to-reinforcement ratio (∅/p). This important limitation should be related to the use of simple specimens in constitutive modelling. On the other hand, a tie-test typically provides measurements of average deformations of the internal reinforcing bar and the concrete surface. The experimental evidence, however, often contradicts the general assumption of the equivalence of the mean strains of reinforcement and concrete. The strain difference is closely related to the width of the concrete cover. This paper investigates the effect of distribution of bar reinforcement on deformation and cracking behaviour of tensile elements. Special testing equipment has been developed to investigate ties reinforced with multiple bars. The test program consists of 23 ties. The number and diameter of the bars vary from 4 to 16 and from 5mm to 14mm, respectively. Two different covers (30mm and 50mm) are considered as well. The deformation analysis is based on measurements of the average reinforcement and concrete surface strains. The development of cracks was investigated using digital image correlation (DIC). The Model Code 2010 and Eurocode 2 predictions are compared with the experimental data. While the Design Codes predict that the maximum crack spacing is dependent on the ∅/p ratio, the test results indicate that the crack distances are actually much less dependent on the reinforcement characteristics.

Cracking analysis of concrete tie reinforced with two diameter bars accounting for the effect of secondary cracks

The paper presents an extension of a general crack prediction model, that has recently been proposed in co-authorship with Debernardi, to the case of a concrete tie reinforced with two types of bars with different diameters, but with the same bond characteristics, subjected to a statically applied axial force. The model, which is based on the assumptions of linear elastic σ-ε laws for both types of bars, as well as for the concrete, and on the bond law proposed in fib Model Code 2010, is used to study both the crack formation stage and the stabilized cracking stage considering the effect of internal secondary cracks. Some case studies are examined to show the influence of the diameters and of the reinforcement ratios on the cracking behaviour, even though they have not been verified experimentally because of a lack of available test results in the literature. Moreover, a parametric analysis is conducted to compare the theoretical results obtained using the general model and the calculation methods proposed in fib Model Code 2010 and Eurocode 2, and it emerges that both standards underestimate the maximum crack spacing and the maximum crack width obtained with the general model. A modified version of the fib Model Code 2010 calculation method, here called Simplified Method, which is based on an improved assessment of the average bond stress that takes into account the effect of internal secondary cracks, is also proposed for the stabilized cracking stage.

Crack Width Control in RC and Prestressed Members - The Extended Core Method

The extended cross section core method for checking crack width in prestressed and reinforced concrete members subjected to eccentric compression is presented. If the loading force is located in the core of a cross section, checking the crack width is not required. The paper refers to cases in which the force is located outside the core, but within the region of the extended core of a cross section. There are numerous examples of elements that falls under this criterion – reinforced concrete columns and prestressed concrete elements that can be considered as reinforced concrete members subjected to longitudinal compression resulting from prestressing. The assumption was made that the crack width cannot exceed the product of the maximum crack spacing according to the EC2 and the extreme tensile strain of concrete calculated in accordance with the assumption that the plane sections remain plane after the deformation. The eccentricity for which the crack width reaches the limit value is called the extended radius of the cross section's core. Formulas valid for any shape of a cross section as well as formulas and design charts derived for the rectangular and circular cross sections were presented. This method can be applied to check the width of cracks with the conservative results regardless of the amount of reinforcement.

Near Surface Mounted Composites for Flexural Strengthening of Reinforced Concrete Beams

Existing structural components require strengthening after a certain period of time due to increases in service loads, errors in design, mechanical damage, and the need to extend the service period. Externally-bonded reinforcement (EBR) and near-surface mounted (NSM) reinforcement are two preferred strengthening approach. This paper presents a NSM technique incorporating NSM composites, namely steel and carbon fiber-reinforced polymer (CFRP) bars, as reinforcement. Experimental and analytical studies carried out to explore the performance of reinforced concrete (RC) members strengthened with the NSM composites. Analytical models were developed in predicting the maximum crack spacing and width, concrete cover separation failure loads, and deflection. A four-point bending test was applied on beams strengthened with different types and ratios of NSM reinforcement. The failure characteristics, yield, and ultimate capacities, deflection, strain, and cracking behavior of the beams were evaluated based on the experimental output. The test results indicate an increase in the cracking load of 69% and an increase in the ultimate load of 92% compared with the control beam. The predicted result from the analytical model shows good agreement with the experimental result, which ensures the competent implementation of the present NSM-steel and CFRP technique.

Evaluation of crack width in RC ties through a numerical “range” model

Crack phenomenon in reinforced concrete (RC) ties is studied herein by means of a numerical “range model”, based on bond between steel and concrete. Since a unique definition of the crack pattern evolution is not possible for these elements, through the definition of this “range”, defined by the curves of maximum and minimum crack spacing (and consequently width), all the possible crack patterns of the considered tension member are so included. Comparisons with significant experimental results available in the technical literature prove that the proposed approach can be successfully adopted also for design purposes, since it provides a correct estimate of maximum crack width. The obtained results are compared with Codes provisions (ACI and Model Code 2010) and the effectiveness of different approaches for predicting crack width is analyzed and discussed.

비정질 강섬유로 보강된 철근콘크리트 인장부재의 균열거동

이 논문은 비정질 강섬유 및 일반 강섬유로 보강된 철근콘크리트 인장실험체를 피복두께와 철근 직경의 비에 따라 각 6개씩 제작하여 직접인장실험을 수행하고, 그 결과로부터 강섬유로 보강된 철근콘크리트 인장부재의 균열거동을 분석한 것이다. 실험 결과에 따르면 비정질 강섬유와 일반 강섬유로 보강된 콘크리트 모두 쪼갬균열의 발생과 진행을 제어하는 성능이 양호하며, 특히 비정질 강섬유로 보강된 콘크리트는 피복두께가 철근 직경의 2배 이상이면 쪼갬균열이 발생하지 않았다. 균열간격은 두가지 강섬유로 보강된 실험체 모두에서 피복두께가 두꺼워짐에 따라 증가하였으며, 현행 설계기준에서 규정하는 최대 및 평균 균열간격 식으로 계산한 것보다 비교적 작게 측정되었다. 실험으로부터 측정된 자료로부터 평균균열간격을 이용하여 최대균열 간격 및 최소균열간격을 예측할 수 있는 상관관계식을 제안하였다.

Research on Early Cracking of the CRCP in the Tunnel under Low Temperature Difference

Calculate and analysis influence of the temperature field for Continuously Reinforced Concrete Pavement design. The temperature and crack of pavement are tested, so that the temperature changing and early cracks development inside the tunnel have been got. Studies have shown that: the tunnel temperature changes slowly, the temperature difference is small. In the first two days after concrete paving, the internal temperature of the slab was significantly higher than the ambient temperature, 79% of early cracking appears in this stages; Panel temperature rise because of the cement hydration. Strain increases in process of the growth of the concrete strength and shrinkage, the cracks appears. The number of cracks in the first two days accounted for 50% of the total number in 7 days, only the number of the second day accounted for 37.59%. Crack width accounted for 60.5% of the total, which is mainly concentrated in 0.1 mm and 0.2 mm. The crack spacing is mainly concentrated in 2m to 8m, accounted for 76.8% of all. The maximum crack spacing is 84 m, the minimum is only 0.5m.

Shear Behavior of Large Reinforced Concrete Beams without Web Reinforcement

This study presents an investigation on the influence of beam depth and longitudinal reinforcement ratio on shear strength. Seven reinforced concrete beams without web reinforcement with depth varying from 500 mm to 1200 mm were tested. Maximum shear crack width, crack spacing and inclinations of shear cracks were measured and shear mechanism of concrete was discussed. In addition, other shear test data found in the literature were used to supplement the experimental data. Based on test results, the shear design methods in the GB50010 code and the ACI 318 code were examined. It was found that the size effect factor in the GB50010 shear design equations was unable to represent the reduction of shear strength for large beams due to the size effect, and that both the GB50010 method and the ACI 318 method are dangerously unconservative when applied to large beams or to beams with low longitudinal reinforcement ratio. The CSA 2004 code method developed based on the Modified Compression Field Theory was also used to analysis the test data and satisfactory results were achieved.

재료 특성 변화에 따른 철근콘크리트 휨부재의 간접균열제어 방법 연구

철근콘크리트 부재의 균열은 필수불가결한 현상이다. 따라서 효과적으로 균열폭을 측정하기 위한 많은 경험식이 제시되었고, 또한 간편한 적용성 때문에 철근 간격과 직경의 제어를 통한 간접균열제어법이 제시되고 널리 사용되고 있다. EC2에서는 최대균열간격과 평균변형률의 곱으로 설계 균열폭을 산정한다. 이 연구에서는 재료 특성에 따른 최대철근간격과 최대철근직경을 산정하였다. 특히 인장증강효과 모델과 최대균열간격에 따른 영향을 분석하였고, 이를 콘크리트구조설계기준에서 제시한 값과 비교하였다. 해석 결과 인장증강효과 모델에 따라 큰 차이가 발생하였고, 2차식 형태의 인장증강효과 모델과 Part II의 최대균열간격을 사용함으로써 과소평가되었다. 따라서 2차식 형태의 인장증강효과 모델을 사용함으로써 합리적인 간접균열제어가 가능하다. 또한 이를 통해 휨부재의 사용성 검증에 일관성을 확보할 수 있을 것으로 판단된다. 이와 함께 균열제어를 위한 두 가지 모델을 제안하였다.

Evaluation of mechanical properties of ceramic coatings on a metal substrate

Nanoindentation and tensile tests were performed for TiN coatings on a stainless steel substrate to investigate the indentation induced deformation behavior of the coatings and the adhesion of the coating–substrate interface. Load–displacement curves show the transition of plastic deformation state from coating only to coating–substrate composite in a penetration depth of 1/10 of the coating thickness, which is approximately two times smaller than that of metal coatings. We employed two specimens with different interface characteristics for the evaluation of the adhesion. The tensile test can clearly detect the difference by the analysis of statistics of extremes for the maximum crack spacing, while the indentation results show no difference, suggesting that the tensile test is superior in detecting the adhesion of the coating–substrate interface.

Prediction of the critical particle size for toughening a glassy polymer

A bilayer specimen composed of a thin polystyrene (PS) film on a polycarbonate (PC) mini-bar was prepared for tensile test. It was observed by scanning electron microscopy that periodic cracks appeared in the PS film when the specimen was deformed in tension. From the maximum crack spacing in the PS, the ultimate shear stress at the PS/PC interface was estimated to be 49 MPa using the periodic cracking method. Based on the deformation mechanism operative in the glassy polymer and the measured crack spacing in the PS film, a new methodology was proposed and applied to predict the critical particle size for toughening a PS/PC polymer blend.

Adhesion assessment of DLC films on PET using a simple tensile tester: Comparison of different theories

The adhesion of Diamond-Like Carbon (DLC) films on Poly(ethyleneterephthalate) (PET) sheet has been characterised by tensile testing, using simple equipment. Three theoretical analyses of the tensile test are described, and their validity has been studied by calculating in three different ways the adhesion of the same samples (DLC on PET). The theoretically predicted adhesion from the longitudinal strain required for coating debonding did not appear to be an appropriate indicator for coatings on polymers. An approach consisting of measuring either the minimum or the maximum crack spacing led to results which were more consistent with the literature. The adhesion of DLC films on PET has been increased by a factor of 1.8 when a 5 min argon plasma treatment is applied prior to deposition. Although quantitative results have to be considered with caution, this method is a simple and quick means of obtaining semi-quantitative results.

TENSION CRACKING BEHAVIOR OF REINFORCED CONCRETE BEAM BRIDGES

Studies were carried out to investigate the cracking properties of the tension zones of actual RC bridges. Crack spacings and crack widths of three different types of RC bridges were measured and statistically examined. Experiments using RC specimens were also carried out to evaluate the influences of tension and drying.The spacing and the width in bending zone of actual RC bridges comform well to logarithmic normal distribution. A relation W0.95 (95% fractile in the distribution of crack width)=aL+b was observed. Where a and b are coefficients and L is crack spacing. And according to the drying of concrete, both a and b increased. A formula giving the maximum crack spacing and maximum crack width of actual RC bridge was proposed.

New Formulas for Maximum Crack Width and Crack Spacing in Reinforced Concrete Flexural Members

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Cracking and Bond Slip in Concrete Beams

Based on an assumed model of crack formation, expressions are developed for maximum crack spacing and crack width in reinforced concrete beams in pure flexure. Both the maximum crack width at the tension surface of the member and the maximum crack width at the surface of the reinforcement are considered, and the former and an upper bound on the latter are related to the crack spacing through a slip modulus between the concrete and the steel. Various physical parameters involved in the expressions are evaluated by use of elastic finite element analysis and through statistical analysis of crack measurements available in the literature. These data are then used to provide approximate expressions which make it possible to predict maximum crack width at the surface of the reinforcement and at the tension surface of flexural members.