• Structural Engineering and Mechanics
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• v.15 no.2
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• pp.159-180
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• 2003

In this paper spacing and width of flexural cracks in reinforced concrete beams are determined using two-dimensional finite element analysis. At early loading stages on the beam the primary crack spacing is based on the slip length, which is the development length required to resist the steel stress increment that occurs at a cracked section on the formation of the first flexural crack. A semi-empirical formula is presented in this paper for the determination of the slip length for a given beam. At higher load levels, the crack spacing is based on critical crack spacing, which is defined as the particular crack spacing that would produce a concrete tensile stress equal to the flexural strength of concrete. The resulting crack width is calculated as the relative difference in extensions of steel reinforcement and adjacent concrete evaluated at the cracked section. Finally a comparative study is undertaken, which indicates that the spacing and width of cracks calculated by this method agree well with values measured by other investigators.

• International Journal of Highway Engineering
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• v.18 no.2
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• pp.43-49
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• 2016

PURPOSES : The field application and performance of continuously reinforced concrete pavement (CRCP), constructed by using the mechanical tube-feeding method, are evaluated in this study. METHODS: The location of the rebar was evaluated by using the MIRA system. The early-age CRCP performance was evaluated via visual survey, in which the crack spacing and crack width were examined. RESULTS: The location of longitudinal reinforcing bars was evaluated via MIRA testing and the results showed that the longitudinal rebars all lie within a given tolerance limit (${\pm}2.5cm$) of the target elevation. In addition, owing to the low temperature when the concrete was pured, the crack spacing in the Dae-Gu direction is slightly wider than that of the Gwang-Ju direction. Almost all of the crack spacings lay within the range of 1.0 m~3.0 m. A crack width of <0.3 mm was measured at the pavement surface. However, as revealed by the field survey, the crack spacing was not correlated with the crack width. CONCLUSIONS : In CRCP constructed by using the mechanical tube-feeding method, almost all of the longitudinal reinforcing bars lay within the tolerance limit (2.5 cm) of the target elevation. The concrete-placing temperature affects the crack spacing, owing to variations in the zero-stress temperature. Crack survey results show that there is no correlation between the crack spacing and crack width in CRCP.

• Proceedings of the Korea Concrete Institute Conference
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• 2002.05a
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• pp.227-232
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• 2002

This paper describes a calculation of an average crack spacing and the maximum crack width for the high-strength concrete tensile and flexural members. Based on the uniform bond stress distribution of the average steel and concrete strains over the transfer length, the crack spacing and the crack width are proposed to utilize influence of the concrete strength and the cover thickness. This analytical results presented in this paper indicate that the proposed equations can be more effectively estimated the maximum crack width and the average crack spacing of the reinforced concrete flexural and tensile members.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.38 no.2
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• pp.193-202
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• 2018

This paper proposed a crack spacing calculation formulation which is an important parameter for calculating the crack width, that is the main factor for verification of serviceability limit states and durability performance evaluation of reinforced concrete members. The basic equation of average crack spacing is derived by considering the bond characteristics which is the governing equation for the analysis of cracking behavior in reinforced concrete members. In order to consider the effect of the cover thickness and concrete compressive strength, the crack spacing measured in 124 direct tensile tests performed by several researchers was analyzed and each coefficient was proposed. And, correlation analysis was performed from 80 specimen data where the maximum and average crack spacing were simultaneously measured, and a correlation coefficient that can easily predict the maximum crack spacing from the average crack spacing was proposed. The results of the proposed average crack spacing equation and maximum crack spacing correlation were compared with those current design code specification. The comparisons of proposed equations and the Korean design codes show that the proposed formulation for the average crack spacing and the maximum crack spacing improves the accuracy and reliability of prediction compared to the corresponding provisions of the Korean Concrete Structural Design Code and Korean Highway Bridge Design Code (Limit States Design).

• International Journal of Highway Engineering
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• v.18 no.3
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• pp.75-86
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• 2016

PURPOSES : The purpose of this study is to investigate characteristics of crack spacing and crack width and their relationship in continuously reinforced concrete pavement (CRCP) based on the data obtained from long-term field observations. METHODS : The crack spacings and crack widths are measured periodically over 10 years at two different CRCP sections: one with asphalt bond breaker beneath concrete slab, and the other with bonded lean concrete base beneath concrete slab. The effects of steel ratio, type of underlying layer, terminal treatment method, and seasonal temperature change on the crack characteristics are evaluated by analyzing the measured data. RESULTS : The CRCP with lean concrete base shows smaller crack spacings than those of the CRCP with asphalt bond breaker. As the steel ratio increases, both the crack spacing and crack width tend to decrease. The crack width becomes larger as the crack age increases, but once the crack age is over a certain value the crack width tends to converge. When the terminal anchor lug system is not used and the expansion joints are employed at the terminals, the crack spacings and crack widths increase near the terminal sections. The crack spacing and crack width seem to be proportional each other, but not necessarily linearly, and their relationship is more distinguished in the summer when the crack widths become smaller. CONCLUSIONS : The steel ratio, underlying layer type, terminal treatment method, and seasonal temperature change affect the characteristics of cracks and the crack spacing and crack width are related to each other.

• Journal of the Korea Concrete Institute
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• v.23 no.1
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• pp.87-98
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• 2011

Crack formations are inevitable in reinforced concrete structures. To estimate crack widths, empirical formulae are used widely and indirect crack controling methods of limiting bar spacing and bar diameter are also used due to their simplicity. In EC2, the characteristic crack width is calculated by multiplying maximum crack spacing and average strain. In this study, limit values of maximum bar spacing and bar diameter are examined as the material characteristics are varied. Two models of tension stiffening effect and maximum crack spacing and their effects are evaluated. The obtained results are compared with the values obtained using KCI method. The results showed that a significant difference is found when two tension stiffening effect are employed, and an under-estimation is found when 2nd order tension stiffening effect and maximum crack spacing limit from Part II were implemented. Therefore, a rational indirect crack control method attained using the tension stiffening effect of 2nd order form is needed. Also, a consistency in serviceabiliy analysis in flexural members needs to be secured. In order to achieve these goals, two crack controling models are suggested.

• Proceedings of the Korea Concrete Institute Conference
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• 2000.10a
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• pp.105-108
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• 2000

With exact analysis of cracks in RC beam, present or past stress states can be traced. For analysis of Flexural cracks, experiments are carried out focusing on variation of crack widths and crack spacing due to stress, beam properties. The crack width expectation formulas of each code are compared and initial crack spacing expectation formula is proposed.

• Magazine of the Korea Concrete Institute
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• v.9 no.4
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• pp.207-214
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• 1997

This study was performed to verify the effect of axial force due to restraint on the mechanical behavior and the average crack spacing of the reinforced concrett. ilexural menlbers. For. this purpose, the flexural sttvngt.h and rigidity werc experimentally investigated undcl. axially rcstmined and unr.est.rainrd conditions. Furthermore , the average crack spacing was also checkcd for the axilly restrained contlit.ion. Thc test results showd that the flexual strength and rigidity of t,he restrained beam were higher. than those of the unrestrained beam. The major. factors affecting on the average crack spacing were steeel stress, axial force, cicumference of reinforcing bar and effective tension arm of concrete. However. the concrete compressive strength was minor effect. Including thesc factors, a prediction equation for the average crack spacing of the restrained member was proposed.

• Structural Engineering and Mechanics
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• v.83 no.4
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• pp.495-513
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• 2022

This paper aims to study the fracture mechanism of rocks under the 'u'shape cutters considering the effects of crack (pre-existing crack) distances, crack spacing and crack inclination angles. The effects of loading rates on the rock fragmentation underneath these cutters have been also studied. For this purpose, nine experimental samples with dimensions of 5 cm×10 cm×10 cm consisting of the non-persistent cracks were prepared. The first three specimens' sets had one non-persistent crack (pre-existing crack) with a length of 2 cm and angularity of 0°, 45°, and 90°. The spacing between the crack and the "u" shape cutter was 2 cm. The second three specimens" set had one non-persistent crack with a length of 2 cm and angularity of 0°, 45°, and 90° but the spacing between pre-existing crack and the "u" shape cutter was 4 cm. The third three specimens'set has two non-persistent cracks with lengths of 2 cm and angularity of 0°, 45° and 90°. The spacing between the upper crack and the "u" shape cutter was 2 cm and the spacing between the lower crack and the upper crack was 2 cm. The samples were tested under a loading rate of 0.005 mm/s. concurrent with the experimental investigation. The numerical simulations were performed on the modeled samples with non-persistent cracks using PFC2D. These models were tested under three different loading rates of 0.005 mm/s, 0.01 mm/sec and 0.02 mm/sec. These results show that the crack number, crack spacing, crack angularity, and loading rate has important effects on the crack growth mechanism in the rocks underneath the "u" shape cutters. In addition, the failure modes and the fracture patterns in the experimental tests and numerical simulations are similar to one another showing the validity and accuracy of the current study.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.5
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• pp.98-105
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• 2018

Cracks in RC members occurred as a result of material and structural factors. The crack width and a crack location are very difficult to examine. A direct crack control method and indirect crack control method to control a crack are presented in the KHBDC (LSD) and KSCDC (2012). In the KSCDC text, cracks are controlled by steel spacing indirectly under a service load. On the other hand, in the KSCDC appendix, cracks are controlled by a crack width directly under a sustained load. In particular, the loading state considered is different. On the other hand, cracks are controlled under a combination of service load and an effective elastic modulus is used in KHBDC. Therefore, in this study, an effective elastic modulus that can reflect the ratio of the sustained load and live load was applied, and a maximum steel spacing was calculated through a design crack width. A variable interpretation was carried out, and a rational crack control method was assessed. As a result, a steel spacing through the design crack width in the KSCDC was smaller than that from the design crack width in the KHBDC, which leads to a conservative design. In addition, the maximum steel spacing suggested in this study has a consistency eliminating the difference between direct crack control and indirect crack control.