Cracking Analysis of FRP-Reinforced Concrete Flexural Members

The paper is dedicated to the cracking analysis of FRP (Fiber-Reinforced Polymer)-reinforced concrete elements. A general nonlinear calculation procedure, based on the slip and bond stresses, is described and adopted for the prediction of the crack width and crack spacing in FRP-reinforced concrete beams. An analytical expression of the bond-slip law is estimated using the corresponding experimental results available in the literature. A numerical investigation is carried out and the influence of the mechanical and geometrical parameters of the material (bond-slip law, reinforcement ratio, concrete strength, diameter of rebars, etc.) on the crack formation is investigated. Referring to glass-FRP-reinforced concrete beams, a comparison between the theoretical predictions and experimental results is made. The results obtained are presented and discussed.     

Environmental Effects on the Mechanical Properties of Glass-FRP and Aramid-FRP Rebars

In the paper, the experimental results on the effect of temperature and moisture on the mechanical properties of FRP (Fiber-Reinforced Polymer) reinforcements are presented. FRP rebars made from glass and aramid fibers were subjected to cyclic thermal actions at temperatures ranging between 20 and 70°C, typical of natural hot-climate environments. Tensile tests were also carried out on FRP rebars. The effect of moisture was investigated by cyclic wetting and drying the FRP rebars under laboratory conditions before their testing in tension. Finally, the elastic modulus and tensile strength of the FRP rebars exposed to these cyclic actions were compared with those obtained for unexposed ones, in order to evaluate the mechanical damage caused by environmental conditions.     

Effect of shear stiffness and concrete wedge cone failure on fracture of a fiber-reinforced plastic rod at an intersection with a concrete crack

Experimental results of model speciments in which FRP rods fractured due to local deformation at a crack intersection in a concrete member were analyzed by a 3D nonlinear finite element method in which orthogonal anisotropy of the FRP rod was considered. The analytical results indicated that accurate prediction of shear modulus of the FRP rod and size of concrete wedge cone failure around the FRP rod was significant to predict deformation and fracture of the FRP rod. FRP rods as reinforcement in concrete members, the small shear modulus, because of the orthogonal anisotropy and the wedge cone failure, may prevent the FRP rod from fracturing at a very low tensile stress due to the local deformation at the crack intersection.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Published in Mekhanika Kompozitnykh Materialov, Vol. 21, No. 2, pp. 158–166, March–April, 1996.     

An analytical study on the bond behaviour between an externally bonded FRP and concrete in the case of continuous beams

One of the greatest challenges in structural engineering nowadays is the strengthening, upgrading, and retrofitting of existing structures. The use of fibre-reinforced polymers (FRPs) bonded to the tension face of a structural member is an attractive technique in this field of application. The strengthening of reinforced concrete structures by means of an externally bonded reinforcement (EBR) is achieved by gluing a FRP laminate to the concrete substrate. For an efficient utilization of the FRP EBR systems, an effective stress transfer is required between the FRP and concrete. The paper discusses the bond behaviour between a FRP and concrete in the case of flexural strengthening of continuous beams. With respect to this type of beams, only a few studies have been reported, though continuous members often occur in concrete constructions. The structural behaviour of statically indeterminate elements is typically characterized by redistributions of the internal forces. These distributions are related to the nonlinear deformations of the beams and has also a distinct influence on the bond behaviour between the FRP and concrete. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 389–402, May–June, 2008.     

Load-deflection analysis of concrete elements reinforced with FRP rebars

The behavior of fiber reinforced plastic (FRP) concrete elements under service conditions is analyzed. Taking into account the real constitutive law of materials and local bond-slip law which adequately describes the interaction between the FRP reinforcement and concrete, a numerical procedure is proposed for obtaining moment-curvature relationships for a cracked beam element. Using the moment-curvature laws, the load-deflection analysis of FRP concrete beams is carried out. To study the influence of geometric and mechanical parameters, a numerical investigation was carried out and the results obtained were compared with those from other methods and Codes. The results of the experimental investigation are described and compared with those of the proposed procedure; the comparison shows good agreement between the theoretical and experimental results.     

A finite element model for hygrothermal analysis of masonry walls with FRP reinforcement

Modeling of moisture migration and heat transfer in fiber reinforced polymer (FRP) composite upgraded masonry structures is of great importance, since the interfacial adhesive between the reinforcing FRP laminate and the host masonry is prone to moisture damages. In this paper, a generic theoretical formulation was first developed to model moisture and heat transport in a layered structure consisting of distinct materials. This formulation was based on the framework of the hygrothermal model presented by Philip and De Vries for a monolithic porous medium. Finite element implementation of the formulation was subsequently used to model moisture and heat transport in an FRP reinforced masonry block. Analytical results were then compared with experimental data to validate the model. Parametric studies were then performed for a concrete block with a reinforcing FRP laminate partially covering one surface. The results showed that changing temperature gradient affects the moisture distribution considerably. This effect was found particularly significant at the concrete/FRP interface where a drastic change in local temperature gradient is present.     

FRP-strengthened reinforced concrete beams: a review and the assessment of cracking and deflection models

A review of some cracking and deflection models used for a structural analysis of FRP-strengthened reinforced concrete beams is presented, and, with reference to short-term deflections, a comparison between model predictions and experimental results is made. By using predictions provided by a nonlinear model derived from a cracking analysis, founded on slip and bond stresses, and experimental results for 63 FRP-strengthened beams, a modification of the well-known semi-empirical Branson’s formula to compute beam deflections is proposed. Finally, the efficiency of the modification is evaluated by comparison with experimental results.     

Load-deflection analysis of concrete elements reinforced with FRP rebars

The behavior of fiber reinforced plastic (FRP) concrete elements under service conditions is analyzed. Taking into account the real constitutive law of materials and local bond-slip law which adequately describes the interaction between the FRP reinforcement and concrete, a numerical procedure is proposed for obtaining moment-curvature relationships for a cracked beam element. Using the moment-curvature laws, the load-deflection analysis of FRP concrete beams is carried out. To study the influence of geometric and mechanical parameters, a numerical investigation was carried out and the results obtained were compared with those from other methods and Codes. The results of the experimental investigation are described and compared with those of the proposed procedure; the comparison shows good agreement between the theoretical and experimental results.Department of Materials Science, University of Lecce, Via per Arnesano, 73100 Lecce, Italy. Published in Mekhanika Kompozitnykh Materialov, Vol. 35, No. 2, pp. 163–172, March–April, 1999.     

Finite-element modeling of the interaction of reinforcement with concrete matrix

A finite-element model of a reinforced concrete beam with rebars modeled by a 3-D deformable body has been developed. An analysis of the stress-strain state of the beam allowed us to determine the stress distribution on cross sections of the rebars and the location of zones with cracks in concrete. It is found that the break of bond between the reinforcement and concrete goes outside the areas of intensely cracked concrete matrix. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 309–316, May–June, 2008.     

Tensile Characterization of FRP Rods for Reinforced Concrete Structures

The application of FRP rods as an internal or external reinforcement in new or damaged concrete structures is based on the development of design equations that take into account the mechanical properties of FRP material systems.The measurement of mechanical characteristics of FRP requires a special anchoring and protocol, since it is well known that these characteristics depend on the direction and content of fibers. In this study, an effective tensile test method is described for the mechanical characterization of FRP rods. Twelve types of glass and carbon FRP specimens with different sizes and surface characteristics were tested to validate the procedure proposed. In all, 79 tensile tests were performed, and the results obtained are discussed in this paper. Recommendations are given for specimen preparation and test setup in order to facilitate the further investigation and standardization of the FRP rods used in civil engineering.     

界面弧形裂纹对混凝土开裂强度的影响研究

混凝土由于水分蒸发、干缩、泌水以及骨料与砂浆变形不一致等原因会导致骨料与砂浆的界面层中产生弧形裂纹,从而对混凝土开裂强度产生很大影响.从细观角度将混凝土视作由粗骨料和水泥砂浆组成的两相复合材料,并将界面层视为粗骨料与水泥砂浆的接触层进行分析.首先基于相互作用直推估计(interaction direct derivative, IDD)法,考虑混凝土中骨料颗粒的相互作用,将施加在混凝土表征体积元的远场外荷载等效为无限大基体中含单一骨料的等效外荷载.然后,将等效外荷载转化为最大和最小主应力,基于断裂力学理论得到界面层中弧形裂纹的应力强度因子,并根据复合型裂纹幂准则判断弧形裂纹是否发生开裂,进而来研究混凝土开裂强度的变化规律.通过与数值模拟结果的比较,验证了界面弧形裂纹应力强度因子解析解的有效性,参数分析结果表明,当裂纹与最大主应力垂直或与最小主应力呈45°夹角时,骨料周围弧形裂纹最易发生开裂破坏.随着裂纹长度增加,混凝土受拉和受压开裂强度先减小后增大,且均存在最不利的裂纹长度.混凝土开裂强度随着骨料体积分数的增加而增大,随着骨料粒径的增大而减小.在裂纹长度较小时,增大骨料的弹性模量有利于提高混凝土开裂强度.骨料周围承受同号应力可以提高混凝土的开裂强度,反之,异号应力会降低开裂强度.     

Model for cover cracking due to corrosion expansion and uniform stresses at infinity

The mechanical model of the cover layer cracking in reinforced concrete structures due to corrosion expansion of reinforcement and uniform stress at infinity is established in this paper. The principle of superposition and the series expansion technique of the theory of complex potential established by Muskhelishvili are applied. The complex stress potentials are assumed to be in the form of Taylor and Laurent series expansions, and the unknown coefficients are determined by the boundary conditions and the stress state at infinity. Finally the analytical solution for hoop stresses in concrete is derived. Referring to the previous studies in the literature, the equation for time of concrete cracking due to corrosion expansion of reinforcement and uniform stresses at infinity is established. It is found that the change of stress state at infinity may accelerate or decelerate the initiation of crack. In addition, compared with the case without corrosion, the existence of corrosion products can alter the location of cracking. Further analyses indicate that the effect of the ratio between reinforced bar and concrete on the cracking is insignificant, and that the possibility of cover layer cracking increases with increasing penetration of corrosion.     

Bond of FRP Reinforcement in Concrete - a Challenge

The bond of ordinary steel reinforcement in concrete depends on many factors, such as the pullout resistance, the geometry of a concrete member, the placement of a bar in the member cross section, the cover splitting, the confinement caused by concrete and the surrounding reinforcement, the order of bond-crack appearance, and the bond-stress distribution along the bond length. The bond of FRP reinforcement depends on even a greater number of factors. Moreover, the types of FRP bars are numerous. Their surface is weaker than that of steel bars and may fracture by bond forces. The surface of FRP bars is softer and does not create as high local stress concentrations in bond contact points to concrete as the harder steel bars do. This fact often delays the appearance of cover splitting cracks along the bars. However, the load necessary for developing the crack pattern of ultimate splitting failure in concrete is then very dependent on whether the bar surface is glossy or rough. The FRP reinforcement can also be used for external shear and/or flexural strengthening of existing members. For this application, FRP bars are placed in grooves cut on the surface of the member to be strengthened and are fixed there with a cement mortar or epoxy paste. In such an application, the performance of bond between the FRP rod and the mortar or resin and then between the mortar or resin and concrete is critical for the effectiveness of the technique. The presence of two interfaces increases the number of parameters needed to characterize the global joint behavior and introduces new possible failure modes. The fundament for the bond resistance estimation should be an accepted bond philosophy linked to appropriate models. A system of bond tests should provide necessary coefficients for the models.     

Experimental Study on the Flexural Ductility of BFRP Bar Concrete Beams With Bamboo Fiber and Steel Wire Mesh北大核心CSCD

To study the effects of bamboo fiber and steel wire mesh on the flexural ductility of basalt fiber reinforced polymer（BFRP）bar concrete beams, 7 BFRP bar concrete beams with bamboo fiber and steel wire mesh were tested with different bamboo fiber lengths (0 mm, 30 mm and 45 mm) and different steel wire mesh layout ranges (0, 1/2 maximum bending moment point layout and full beam length layout). The flexural failure tests of the 7 beams were carried out, and the initial crack loads, the crack developments, the ultimate loads and the deformations were detected. The effects of the fiber length and the wire mesh layout range on the crack resistance and the deformation resistance of the specimens were analyzed based on the test data. With the function model, the equivalent yield points of the 7 test beams were obtained, and their ductility coefficients were calculated. The results show that, the addition of bamboo fiber and steel wire mesh increases the cracking loads of BFRP bar concrete beams by 12%~68%, decreases the crack spacings and the crack length development speed, reduces the test beam deformation under the same load, and increases the ductility coefficient by 1.58%~31.75%. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

An improved closed-form solution to interfacial stresses in rc beams strengthened with a composite plate

The strengthening of concrete structures in situ with externally bonded fiber-reinforced plastic (FRP) composite sheets is increasingly being used for the repair and rehabilitation of existing structures. However, debonding along the FRP-concrete interface can lead to premature failure of the structures. The interfacial stresses have played a significant role in understanding this premature debonding failure of such repaired structures. In this paper, an improved theoretical analysis of the interfacial stresses is presented for a simply supported concrete beam bonded with a FRP plate. The shear strains of the adherends have been included in the present theoretical analysis by assuming a parabolic distribution of shear stress across their thickness. Contrary to some existing studies, the assumption that both adherends have the same curvature is not used in the present investigation. The results of this numerical study are beneficial for understanding the mechanical behavior of material interfaces and for the design of hybrid FRP-reinforced concrete structures.     

Bond-slip behavior of CFRP plate-concrete interface

The paper deals with evaluation of the bond performance between a CFRP plate and concrete with respect to various compressive strengths of concrete and bond lengths of the CFRP plate as parameters. To consider stress conditions in the tensile zone of reinforced concrete (RC) structures, double-lap axial tension tests were conducted for eight specimens with CFRP plates bonded to concrete prisms. In addition, a simple linear bond-slip model for the CFRP plate/concrete joints, developed from the bond tests, was used. To verify the model proposed, a total of seven RC beams were strengthened with CFRP plates and tested in flexure employing various bond lengths, strengthening methods, and numbers of CFRP plates. A nonlinear finite-element analysis, with the bond–slip model incorporated in the DIANA program, was performed for the strengthened RC beams. Also, the results of flexural test and analytical predictions are found to be in close agreement in terms of yield and ultimate loads and ductility.     

A model for predicting the shear bearing capacity of FRP-strengthened beams

The shear failure of reinforced concrete beams needs more attention than the bending failure since no or only small warning precedes the failure. For this reason, it is of utmost importance to understand the shear bearing capacity and also to be able to undertake significant rehabilitation work if necessary. In this paper, a design model for the shear strengthening of concrete beams by using fiber-reinforced polymers (FRP) is presented, and the limitations of the truss model analogy are highlighted. The fracture mechanics approach is used in analyzing the bond behavior between the FRP composites and concrete. The fracture energy of concrete and the axial rigidity of the FRP are considered to be the most important parameters. The effective strain in the FRP when the debonding occurs is determined. The limitations of the anchorage length over the cross section are analyzed. A simple iterative design method for the shear debonding is finally proposed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 357–372, May–June, 2008.     

纤维增强聚合物加固木柱的非线性稳定性分析

考虑加固层中纤维增强聚合物布（FRP布）拉伸与压缩时的不同弹性模量,基于梁大挠度变形假定,首先建立了FRP加固细长木梁大挠度弯曲的一般数学模型,给出了考虑梁弯曲二阶效应的非线性控制方程．其次,研究了FRP布加固细长简支木柱的非线性稳定性问题,得到了FRP加固简支木柱的临界载荷公式．理论证明了其过屈曲解的存在性,并利用摄动法,得到了临界载荷附近过屈曲状态的渐近解析解．进行了参数分析,结果表明:FRP加固层对临界载荷有显著的影响,而对其无量纲过屈曲状态影响较小．     

Modeling and Simulation of Multiple Cracking in Textile Reinforced Concrete Tension Specimen using Fracture Mechanics Approaches

This paper concerns with the finite element simulation of textile reinforced concrete (TRC) behavior under tension loading by using discrete cracking concept and fracture mechanics approaches. 3D Finite-Element models are formulated on the meso-scale by simulating all the heterogeneous structural components, the matrix, the fibers, and the fracture mechanisms in both fiber-matrix interface, and the discrete cracks of the matrix. The presented numerical simulation in this study allows for better understanding of the stress distribution and the interaction between all damage mechanisms and the corresponding energy dissipations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)