Crack Width Calculation Methods Research Articles

Full-Scale Load Testing for Evaluating Crack Performance in Precast Prestressed Concrete Communication Towers with Annular Sections

Tall prestressed concrete poles with annular cross-sections are increasingly used as communication towers. The annular section subjected to bending moments has a smaller extreme tension area, resulting in higher stress increments in the materials within this region. As slender concrete structures, their bending behavior and crack resistance performance need to be critically examined. However, large-scale tower structures have rarely been experimentally investigated. Moreover, current code-specified crack width calculation methods are designed for square sections, so their applicability to concrete members with annular sections requires further investigation. To address these issues, this study conducted full-scale static loading tests on two 30-meter-high tower structures made of prestressed high-strength concrete and evaluated the accuracy of code methods for estimating the maximum crack width. During the static loading tests, displacement, cracking moments, crack widths, and crack spacings were meticulously recorded, and a theoretical methodology for calculating the stress in the extreme tension bars was developed. Four calculation methods specified in structural codes were compared: the Concrete Design Code of China (GB50010), Eurocode 2, ACI 224R, and the Concrete Design Guideline of Japan (JGC2007). The experimental results showed that diameter significantly affects the stiffness and displacement of the structure, with reloading stiffness of the full-scale tower reducing by up to 11% after exceeding the serviceability limit state. Regarding crack width prediction, substantial deviations were observed among the results of the four methods. On average, GB50010 underestimated crack widths, while JSCE, Eurocode 2, and ACI 224R overestimated them. Eurocode 2 and ACI 224R provided relatively conservative and accurate predictions. These findings highlight the need for improved and tailored code provisions for annular sections. It is also noted that the comparison was limited to crack widths less than 0.1 mm and a relatively small amount of data. Future research should focus on developing prediction methods specifically for prestressed concrete tower structures with annular sections.

Performance study of crack width calculation methods according to Eurocodes, fib model codes and the modified tension chord model

AbstractThis article investigates the accuracy of various crack width prediction models and the newly proposed modified tension chord model (MTCM). A large number of experimental crack widths have been collected from the literature, including 203 specimens of reinforced concrete (RC) members subjected to bending and tension. The prediction models are described with upcoming new formulations and database validation. The modeling uncertainty is found by comparing the predicted crack widths against experimental data obtained using a log‐normal distribution. The results show that fib Model Code 2010 and MTCM provide the best crack width predictions of the collected databases; MTCM has the fewest mechanical simplifications of the investigated models and no empirical modifications for fitting towards experimental databases, in contrast to the approaches in Eurocode 2 and Model Code. However, the latter do predict the crack width to a reasonably good extent and are more suited for practical dimensioning than the MTCM. The findings in this article suggest that the MTCM should serve as a point of departure for further development of crack width calculation methods, and that it may have an extensive range of possible applications in the future.

Flexural behavior and crack width prediction of UHPC slabs reinforced with FRP bars

This paper aims to investigate the effects of FRP-bar configurations on the flexural behavior of the FRP-reinforced ultra-high-performance concrete (UHPC) deck slab and to propose the calculation method of crack width. Firstly, flexural tests were performed on six FRP-reinforced UHPC slab specimens with varying bar diameters, reinforcement ratios, cover thickness, and slab thicknesses. The load-deflection responses, load-FRP strain relations, and cracking behavior are measured and discussed. The results show that under service loads, the maximum crack widths of all specimens are around 0.03 mm–0.04 mm, which is significantly less than the permitted 0.5 mm in international codes for FRP-reinforced structures. At similar reinforcement ratios, a small FRP-bar diameter with a corresponding reduced bar spacing increases the ultimate capacity and energy dissipation ability. The effects of FRP-bar configurations are minor under service loads, while beyond these loads decreasing the bar diameter is beneficial for reducing the bar strain and crack width. Subsequently, by developing a practical calculation method of the stress of FRP bar embedded in UHPC slab and calibrating the bond coefficient between FRP bar and UHPC against test data, an engineer-friendly calculation method of crack width is proposed. Comparisons between predicted and experimental results indicate the proposed method is capable of producing accurate and safe predictions. The results may give guidance to designers on the appropriate FRP-bar configurations and the control of crack width for the FRP-reinforced UHPC deck slab.

Applicability of Existing Crack Controlling Criteria for Structures with Large Concrete Cover Thickness

Abstract Widely used crack width calculation models and allowable crack width limits have changed from time to time and differ from region to region. It can be identified that some crack width calculation models consist with limitations for parameters like cover thickness. The current Norwegian requirement for cover thickness is larger than these limitations. The applicability of existing crack width calculation models and the allowable crack width limits must be verified for structures with large cover thickness. The background of crack width calculation models in Eurocode, Model Code 2010, Japanese code, American code and British code have been examined. By comparing the experimental crack widths with the predictions of the aforementioned models, the existing codes can be identified as requiring modification. Considering the durability aspect, it can be identified a long-term study proving that the allowable crack width can be increased with the increase in cover thickness. When considering the aesthetic aspect, the authors suggest categorizing the structures based on their prestige level and deciding the allowable crack widths accordingly. The paper proposes potential solutions for future research on how to improve both crack width calculation methods and allowable crack width limits to be used effectively in structures with large cover thickness.

The analysis of crack width in flexural concrete members reinforced with polymer composite bars

Introduction. Rebars, made of fiber-reinforced polymers (FRP), have a number of distinguishing characteristics and disadvantages along with well-known strengths, such as high tensile strength, low specific density, high corrosion resistance, and low thermal conductivity. One of its principal strengths is the modulus of elasticity which is relatively low compared to steel. As a result, elements, having FRP reinforcement, feature higher deformability. In this regard, the requirements of serviceabi-lity limit states, applicable to structures, may become the main obstacle to the use of FRP as the reinforcement for concrete members. It is assumed that cracking patterns of members, having FRP reinforcement, may differ from those of traditional reinforced concrete structures.
 Materials and methods. Experimental studies were carried with regard for and in compliance with the provisions of National State Standard 8829-94. Tested samples represented concrete beams that were 1,810 mm long and had a cross section of 120 × 220 mm. Their tensile side was reinforced with two bars. Steel, glass fiber-reinforced polymer (GFRP) and basalt fiber-reinforced polymer (BFRP) bars were used to reinforce the beams. The value of the reinforcement ratio varied. Crack width calculation methods, applied according to Construction rules and regulations 63.13330.2012 and 295.1325800.2017 (Russia) and ACI 440.1R-06 (USA) were analyzed.
 Results. The results of the theoretical and experimental studies of the crack resistance of flexural members having FRP reinforcement are obtained. Discrepancies between the calculation methods are identified.
 Conclusions. Сracking patterns, typical for members having FRP reinforcement, are specified. They contest the applicabi-lity of methods, prescribed in the Construction Rules and Regulations. The methods, prescribed by Construction Rules and Regulations 63.13330.2012 and 295.1325800.2017, differ in respect of crack width calculations, and it leads to diverging calculation results.

Analytical Calculation Model for Predicting Cracking Behavior of Reinforced Concrete Ties

This paper formulates an analytical calculation model for predicting the cracking behavior of reinforced concrete ties to provide more consistent crack width calculation methods for large-scale concrete structures in which large bar diameters and covers are used. The calculation model was derived based on the physical behavior of reinforced concrete ties reported from experiments and finite-element analyses in the literature. The derivations led to a second order differential equation for the slip that accounts for the three-dimensional effects of internal cracking by using a proper bond-slip law. The second order differential equation for the slip was solved completely analytically, resulting in a closed-form solution in the case of lightly loaded members and in a non-closed-form solution in the case of heavily loaded members. Finally, the paper provides a solution strategy to facilitate a practical and applicable method for predicting the complete cracking response. Comparison with experimental and finite-element results in the literature demonstrated the ability of the calculation model to predict crack widths and crack spacing consistently and on the conservative side regardless of the bar diameter and cover.

Calculation Method of Early-Age Crack Width in Reinforced Concrete Bridge through a Nonlinear FEA Model

A prestressed concrete (PC) box girder with the total length of three span 130 m was constructed by the method of cast-in-place layer by layer with full framing, and the cracking of the top slab in the box room was found during the construction. Cracking is one of the main distresses for a reinforced concrete (RC) bridge, which also reduces the safety and service life of the structure. The existing calculation methods of crack width, which are used to evaluate the crack width induced by the external loads, are not suitable to calculate the early-age crack width. To evaluate the early-age crack width, a calculation method of early-age crack width was presented. The finite element analysis (FEA) model of the PC box girder being built was used to analyze two affecting parameters of early-age cracking by ABAQUS 2017 program. Through the nonlinear FEA model of the PC box girder, the calculation formula of early-age crack width was used to evaluate the crack width. The validity of the nonlinear FEA method has been verified by comparing the simulation results with the measured results.

Experimental and theoretical investigation of crack width calculation methods for RC ties

This paper theoretically and experimentally investigates the semi‐empirical formulas recommended by Eurocode 2 (EC2), fib Model Code 2010 (MC2010), and Eurocode 2 with the German National Annex (DIN) for calculating crack widths in reinforced concrete. It is shown that the formulas can be derived from the principles for the idealized behavior of RC ties. However, instead of explicitly solving the resulting differential equations, the use of simplifications leads to inconsistent formulas. An experimental study was carried out involving the testing of eight RC ties to discover the modeling uncertainty of the formulas. It was found that EC2 substantially overestimated the crack widths for the RC ties. MC2010 and DIN seemed to predict the crack widths better, but gave rather a large number of nonconservative crack width predictions. These experimental results, combined with the theoretical study, suggest that a more consistent calculation model should be formulated by explicitly solving the resulting differential equation.

Research for different crack width calculation methods of concrete-lined steel pressure pipe

Based on a certain threshold to ensure the durability of structure, the concrete-lined steel pressure pipes used in the structure of large hydropower station widely are allowed to exist in concrete cracking under the action of a certain hydraulic pressure. According to the 1:2 large scale experiment model and the measured data of Three Gorges Hydro-power Station, the existing different methods for calculating crack width were compared and improvements and crack control measures were raised.

Empirical calculation method of residual flexural tensile strength fR,1 of SFRC

An empirical calculation method is proposed in the article for the calculation of residual flexural tensile strength of steel fibre reinforced concrete. The method was developed analyzing factors which have an influence on residual tensile strength, and using the experimental results of 446 specimens. Assuming that the residual flexural tensile strength depends on three functions the relevant variables and constants were deduced, and so the optional functions were established. The proposed calculation method is suitable for the SFRC, where fibre content varies from 15 to 80 kg/m 3 as well as mean compressive strength varies from 25 to 60 MPa. Only circular cross-section hooked end steel fibre is available however, traditionally vibrated as well as self-compacting concrete is suitable for this method. The residual flexural tensile strength ( f R, 1 ) is used in various crack width calculation methods, and it should be determined experimentally according to standards. Therefore, the proposed calculation method has a great practical benefit. DOI: http://dx.doi.org/10.5755/j01.mech.21.4.9551

Experimental Study of Bending Properties of CFRP Bars Concrete Beam and Crack Analysis

A test of the flexural behavior of concrete beam strengthened with sand-coated screwed CFRP bars was carried out to analyze the bending performance and cracking development process under staged loading, and different stage of crack distribution was plotted. Based on the test results, this paper discussed the crack mechanism and cracking feature of CFRP bars concrete beam under the load, and influencing factors of crack width and crack spacing were analyzed. Finally, calculation method of crack width was presented.

Analysis of Crack Width Calculation of Steel Fibre and Ordinary Reinforced Concrete Flexural Members

It is known that steel fibre can reduce the crack width of reinforced concrete flexural members however generally accepted crack width calculation method does not exist yet. The residual tensile strength which is used for crack width calculations should be obtained from tests. Three crack width calculation methods of steel fibre and ordinary reinforced concrete flexural members are discussed in this paper. All these methods have been derived using Eurocode 2 provisions, which are intended to the members without the fibre. Experimental cracking results of small cross section flexural members reinforced with steel fibre and ordinary reinforcement are also discussed. A scatter of the residual tensile strength which is obtained from three point bending test and its influence to the crack width is also reviewed briefly. Calculated crack widths are compared to the experimental results. It is determined that due to lack of the specimens the large deviations of residual flexural tensile strength can be obtained and it can cause the significant errors of calculated crack widths. DOI: http://dx.doi.org/10.5755/j01.sace.6.1.6336

Calculation Method of Crack Width of Steel Fiber Reinforced High-Strength Concrete Beams under Fatigue Load

Based on the fatigue test, 8 steel fiber reinforced high-strength concrete beams are studied, the influencing factors of crack width are discussed in the paper, and the calculation method of crack width under fatigue load is investigated. Based on the analysis of test results, the formulas are put forward. The results show that adding steel fiber into the high-strength concrete beams can prevent the development of the fatigue crack, fatigue crack widths are decreased by 26.0%~121.0% and the calculated values have good agreement with test date.

Crack Width Calculation Methods of Reinforced Concrete Bridges and Application of Box Girder Bridge

AbstractCrack width calculation is an important part of concrete structure design. Due to many factors, the calculation formulas for crack width of concrete beam in various national standards are d...