Strain Efficiency Factor Research Articles

Axial behavior of basalt FRP-confined reinforced concrete columns with square sections of different corner radii

Axial compressive tests were conducted on fourteen BFRP-confined square reinforced concrete (RC) columns, involving variations of the corner radius and FRP layers. The test results demonstrate thatthe Basalt-FRP confinement leads to strength improvement, such as 109% gain at a corner radius ratio of 0.6, and also improves the ductility of the RC column. The stress–strain response has a bilinear type, and the difference in confinement level is mainly reflected in the inelastic range. Furthermore, the observation of the distribution of hoop strain values shows that the confinement pressure uniformity increases with thecornerradius. Finally, a prediction equation for the strain efficiency factor is proposed to improve the accuracy of existing square section strength models. A modified strength model of Wu and Zhou shows good agreement with the experimental results.

Review of the key parameters of the international calculation guidelines for non-circular RC columns confined with CFRP composites. Comparison with medium and large-scale tests

Several international guides offer recommendations for the calculation and design of reinforcements with fibre reinforced polymer (FRP) composites. To strengthen axially-loaded columns, the guides adopt design stress–strain models based on extensive research into small-scale specimens of plain concrete confined with FRP. However, through this type of testing, it is difficult to accurately predict the behaviour of existing full-scale reinforced concrete (RC) columns confined with FRP composites.This paper presents a review of the formulation proposed by four international guides. The study compiles the available test results on medium and large-scale rectangular RC columns confined with carbon FRP composites subjected to axial compression concentric load.The predictions of the axial strength and the ultimate strain of the FRP-confined concrete are compared to the experimental results. The minimum confinement ratio (CR) recommended in the guides to guarantee sufficient confinement level is also analysed, alongside the estimation of the effective strain in the CFRP jacket at failure. The results obtained have proven uneven.The best predictions of the concrete strength improvement have been obtained with the ACI and fib guides. In general, to comply with the minimum CR proposed by the guides fails to prevent a softening stress–strain response, frequent in the rectangular tests analysed. The more restrictive CR criteria (from the CNR and fib guide) have shown themselves to be more suitable.The ultimate strain of the confined concrete is underestimated by the guides and the errors obtained are much higher than in the prediction of the strength enhancement ratio.Despite the widespread dispersion of the results, the mean value of strain efficiency factor obtained in the tests is similar to the value of 0.55 recommended by ACI. This parameter is not easy to determine for rectangular columns, but its estimation is essential for the calculation.

Effect of ultra-high lateral strain capability on the performance of damaged concrete strengthening with PET-FRP: Test and modeling

The lateral confinement of fiber-reinforced polymer (FRP) has a significant impact on the deformability, strength, and energy dissipation of core concrete, especially for damaged concrete. To address the performance of damaged concrete strengthened with the large rupture strain of FRP (LRS-FRP), the effects of damage degree, confinement stiffness, and loading rate were analyzed. Results show that the strain efficiency factor of LRS-FRP made of recycled polyethylene terephthalate (PET) can be stabilized at a high value of 0.87 even with a high damage degree when used for strengthening cylinders, which is larger than other FRP (BFRP and CFRP) and agrees with PET confined undamaged concrete reported in existing papers. The test results indicated that the increased initial damage degree result in a slight decrease in ultimate strain and ultimate strength. The loading rates will improve the initial compressive strength of core concrete, this result in the increase of the reflection point stress of LRS-FRP confined concrete from the elastic stage to the enhancement stage. But, the tangent modulus of the enhancement stage is hardly affected by loading rates even though the core concrete is under different initial damage conditions. One strength model with good performance after evaluation and a continuous integrable and derivable model are incorporated into this new work, which predicts the performance of damaged concrete strengthening with LRS-FRP.

Experimental investigation on the compressive behaviour of FRP-confined rectangular concrete columns

This paper presents a comprehensive experimental study on the behaviour of FRP-confined concrete in square and rectangular columns and focuses on some issues that might be addressed with a view to improving the predictive models. For this purpose, 31 prismatic concrete specimens with a height of 600 mm and low- and medium-strength concrete (20–35 MPa) were tested under centred compression. The parameters studied were the aspect ratio between the sides of the section (1, 1.5 and 2), the radius of curvature of the corners (20, 25 and 30 mm) and the number of carbon FRP layers applied. The experimental results included stress–strain curves of specimens and detailed information about the confined concrete strength and the axial and lateral strain achieved on the FRP jacket during the tests. The stress–strain response and ultimate condition are analysed, showing that FRP jacketing is an efficient technique for increasing the strength and strain capacity, but that confinement efficiency decreases as the aspect ratio of the section increases. In spite of such decrease, significant strength improvement was achieved for low-strength concrete in rectangular sections with aspect ratios of 1.5 (strength gain up to 81%), and even 2 (up to 36%). The axial strength of the tests was compared with the design criteria of four international guidelines, resulting in predictions that did not properly fit for rectangular sections. A predictive equation is proposed to assess the axial compressive strength of the FRP-confined concrete, which includes a better adjustment for the strain efficiency factor and the shape factor for rectangular columns.

A reliability-based approach and code calibration of FRP-Confined rectangular RC columns subjected to concentric loading

This study aims to present an approach to investigate the reliability levels of reinforced concrete (RC) columns confined by Fiber Reinforced Polymers (FRP) subjected to concentric loading. First, the statistical properties of random variables such as model error, FRP strain efficiency factor (FSE factor) and axial resistance of columns are investigated. Then in respect to the existing correlation between variables and extensive collected database, an appropriate probabilistic model for model error, FSE factor and compressive resistance of RC column is proposed. In addition, the effects of live-to-dead load ratio, reinforcement ratio and the confinement levels on the reliability of FRP-confined columns are studied through a reliability analysis. Furthermore, based on existing studies, reliability indices for various levels of confinement are calculated. Finally, a calibration analysis on safety factors of ACI 440.2R-17 guideline and shape factor of rectangular cross-section is presented.

Strengthening of Low-Strength Concrete Columns with Fibre Reinforced Polymers. Full-Scale Tests

Confinement of columns with externally bonded fibre reinforced polymers (FRP) sheets is an easy and effective way of enhancing the load carrying and strain capacity of reinforced concrete (RC) columns. Many experimental studies have been conducted on cylindrical small-scale un-reinforced concrete specimens externally confined with FRP. It is widely accepted that confinement of square or rectangular columns is less efficient than the confinement of circular columns. The theoretical models for rectangular sections are mostly based on approaches for circular columns modified by a shape factor, but the different models do not give similar results. This paper presents an experimental program on large-scale square and rectangular RC columns externally strengthened with carbon FRP sheets and subjected to axial load. The main variables were the side-aspect ratio of the cross-section, the radius of curvature of the corners and the amount of FRP reinforcement. The results show that the FRP confinement can increase the strength and strain capacity of rectangular concrete columns with low strength concrete. The FRP hoop ultimate strain was much lower than the material ultimate tensile strain obtained from flat coupon tests and the strain efficiency factor achieved in the tests was less than the value usually recommended by design guides.

Design-oriented model for circular F-STC stub columns subjected to axial compression

A fiber-reinforced polymer (FRP)-steel composite tubed concrete (F-STC) column is formed by wrapping FRP sheets around a steel tubed concrete column (STC). Both the strength and deformability of the core concrete are improved by the FRP-steel composite tube and the steel tube is prevented from corrosion. A number of studies have been conducted on the prediction of stress-strain behavior of FRP-confined concrete columns and steel tube-confined concrete columns. However, few models focus on the concrete under combined confinement of FRP and steel tube. This paper presents an analytical study on the design-oriented model for F-STC columns. To determine the confining stress, the stress distribution of steel tube was firstly analyzed and the equivalent stress was obtained. In addition, a strain efficiency factor was proposed for the prediction of rupture strain of FRP. Then the peak condition and ultimate condition of F-STC columns were investigated and related predicting models for the load bearing capacity and deformation were proposed. Finally, design-oriented models were proposed for F-STC columns with different types of axial load-strain curves and generally coincided well with the existing test results.

Effect of aggressive marine environment on strain efficiency factor of FRP-confined concrete

In order to find effective confining pressure in concrete members externally wrapped with Fiber Reinforced Polymer (FRP) jackets, different values of the so-called strain efficiency factor have been suggested by several researchers. In this paper, the durability of Carbon Fiber Reinforced Polymer (CFRP) and Glass Fiber Reinforced Polymer (GFRP) sheets in aggressive marine environment is assessed, and the effect of such environments on the strain efficiency factor in compressive members is investigated. A set of 3D finite element analyses (FEA) are performed to find the strain efficiency factor. The strain efficiency factor of GFRP jackets is lower than that of CFRP jackets in different environmental conditions. Furthermore, the strain efficiency factor decreases as the exposure time increases, which is more evident in GFRP-wrapped concrete. After 3000 and 9000 h of marine exposure, the strain efficiency factors decrease by 11% and 43%, respectively, in GFRP jackets. In CFRP-wrapped members, the reduction is about 18% and 25%, respectively.

Strain distribution of basalt FRP-wrapped concrete cylinders

This paper presents the results of an experimental study on the distribution of strain on a unidirectional basalt fiber-reinforced polymer (FRP) wrapped around concrete cylinders. A total of 12 cylinders (150 mm x 300 mm) were wrapped with 2, 4, and 6 layers of basalt FRP (BFRP) and the distribution of hoop strain under axial compression load was studied using multiple strain gauges. The new aspect of this study is the use of BFRPs as a new construction material for wrapping concrete elements with a focus on the distribution of hoop strain towards refining design strain of the wrap. Also, the effect of number of BFRP layers on the premature rupture of the wrap with respect to flat coupon test was evaluated in the form of a strain efficiency factor. It was concluded that the maximum hoop strain was not necessarily associated with the ruptured areas of the wrap. Also, an analysis of variances showed that the difference between hoop strains in the overlap and non-overlap regions was non-significant and an average hoop strain can represent the overall dilation of the specimens. The average strain efficiency factor was found ranging from 0.61 to 0.86. The test data was added to a large database of concrete cylinders wrapped with unidirectional FRPs and after statistical evaluations a refined strain efficiency factor of 0.70 was proposed instead of the current factor of 0.55 in ACI 440.2R-17 for design applications.

CFRP retrofit of concrete circular columns: Evaluation of design guidelines

Carbon fiber reinforced polymer (CFRP) composite external wrapping has become an increasing popular strengthening and confining method for deteriorated or damaged concrete structures. The benefits are high strength-to-weight ratio, corrosion resistance, economy of labor and space savings. This study involved a non-linear theoretical modeling of axially loaded concrete columns with external CFRP laminate application. One-layer and two-layer application, and hoop versus inclined application, were considered. The theoretical of representative confined columns were contrasted against corresponding values from design guidelines. It was found that the guidelines significantly under-predict the strength, maximum stress and strain in CFRP confined columns. The extra CFRP layer was helpful in enhancing the column performance. The numerical model axial capacities were in line with published literature. The failure tensile strain in CFRP was quite a bit larger than the manufacturer suggested value. Inclined CFRP application was not as effective as the hoop application. An optimum value of the CFRP confining strength can be recommended to increase the accuracy of the design guidelines. The strain efficiency factor from ACI, which accounts for premature failure of the CFRP jacket, does not take into account the FRP contributions.

Influence of geometry and fiber properties on rupture strain of cylindrical FRP jackets under internal ICE pressure

This paper presents an study on the rupture strain of cylindrical fiber-reinforced polymer (FRP) jackets under internal ice pressure. A total of 45 cylindrical FRP jackets were prepared using three unidirectional carbon, glass, and basalt fabrics in three different internal diameters, namely 60, 114, and 216 mm, and one-, two-, and three-plies. Three jackets for each combination were typically tested and the average hoop rupture strains were obtained and compared to the rupture strain of flat coupons in the form of a strain efficiency factor. It was found that the strain efficiency factor ranged from 0.53 to 1.05 with an average of 0.77. A new analytical model was also developed based on the bi-axial state of stress in a cylindrical FRP jacket to obtain the rupture strain and strain efficiency factor of the FRP jacket using a closed-form solution. The model engaged four major parameters, namely: diameter, thickness, axial/transverse strength ratio, and Poisson’s ratio of the FRP jacket. The two latter parameters were eliminated after a parametric study to propose a simplified formula. The analytical and simplified models predicted the experimental strain efficiency factors with an average error of −3.4% and −4.6%, respectively.

Providing a model for estimating the compressive strength of square and rectangular columns confined with a variety of fibre-reinforced polymer sheets

One of the most common ways of strengthening the columns is the confinement of the reinforced concrete columns. So far, several experiments have been conducted on concrete columns confined with fibre-reinforced polymer sheets and the results show that the use of fibre-reinforced polymer sheets increases the compressive strength of the concrete columns effectively. Different models in order to determine the compressive strength of the fibre-reinforced-polymer-confined concrete columns are provided in the previous researches. In this study, a wide range of experimental data for square and rectangular columns confined with a variety of fibre-reinforced polymer sheets has been collected. In order to increase the accuracy in the existing models, a modified model for predicting the compressive strength of square and rectangular columns confined with different fibre-reinforced sheets has been proposed by using the collected data. In the current study, the fibre-reinforced polymer strain efficiency factor and the section shape factor are composed and considered as a unique factor. Considering the fibre-reinforced polymer hoop strain concentration at the affected area including the corners area and the surrounding area of them, this factor has been adopted as a fibre-reinforced polymer averaged hoop strain factor for the whole circumference of the section. Based on the published experimental data, a comparison between the analytical results obtained with the present model and the results of the other models, shows considerably better results of the proposed model described in this study. Moreover, application of the proposed model for behaviour prediction of concrete-filled fibre-reinforced polymer tubes is evaluated in this study and the results show that the proposed model is more accurate than the other models.

An experimental investigation of the behaviour of heat-damaged RC columns confined with CFRP fabrics using photogrammetry

This paper describes an experimental study of the behaviour of unheated and heat-damaged reinforced concrete (RC) circular columns wrapped with carbon fibre reinforced polymer (CFRP) fabric. The purpose of the study was to measure the hoop and axial strain variation over the surfaces of unheated and heat-damaged CFRP-confined RC columns using an innovative digital image correlation technique (DICT), which is a photogrammetric technique. Eighteen large-scale (O 204 mm × 750 mm) identical columns were fabricated and tested, of which 12 were heated and cooled under 30 % of maximum load at ambient temperature then wrapped with CFRP fabrics after air cooling. The variables considered in these tests included unheated and heat-damaged columns, number of layers of CFRP sheet, level of heat exposure, and strain variation. It was found that the use of CFRP fabric increases both the compressive strength and the ductility of both unheated and heat-damaged columns. The DICT system was successfully used to determine the variation of both axial and hoop strain distributions along the heights of the columns. Strain gauge data from gauges installed on the concrete/CFRP surfaces at mid-height were consistent with the data taken using photogrammetry at those locations, provided the gauges did not debond. The failure strain of columns confined by CFRP does not occur at the ultimate tensile strains determined from coupon tensile tests defined by the strain efficiency factor.

Probabilistic assessment of FRP-confined reinforced concrete columns

This paper presents a reliability study on reinforced concrete (RC) columns retrofitted by Fibre Reinforced Polymers (FRP) confinement. First, variability of the compressive resistance of FRP-confined RC columns considering uncertainty in the model error, material properties, section dimensions, FRP strain efficiency factor and minimum load eccentricity as well as any existing correlation among random variables was studied. Then, reliability of FRP-confined RC columns designed based on the ACI 440 and the fib bulletin 14 guidelines was investigated. Results showed that in order to achieve the target reliability used in design of conventional RC columns, resistance reduction factors of these guidelines require modification. For the design of FRP-confined RC columns, a resistance reduction factor of 0.85 for the ACI 440 guideline and a partial safety factor of 1.45 for the fib bulletin 14 are suggested.

Probabilistic Design Models for Ultimate Strength and Strain of FRP-Confined Concrete

AbstractThis paper presents a probabilistic procedure for deriving design models for the ultimate strength and strain of fiber–reinforced-polymer (FRP)-confined concrete. First, a large database of axial compression tests performed on circular FRP-confined concrete specimens is collected for calibrating an ultimate strength model, based on the Drucker-Prager criterion, and an ultimate strain model, based on the ultimate dilation rate. The database is also employed for deriving a probabilistic model for the FRP strain efficiency factor. The calibrated models, though simple, show superior performance over some of the models in the literature. Then, using the Central Limit Theorem and considering uncertainty in the mechanical properties of the concrete and FRP material as well as their correlation, analytical probabilistic design models for the ultimate strength and strain of FRP-confined concrete are derived. These models can be used in the design and reliability analysis of FRP-confined columns.

Behaviour of FRP confined concrete in square columns

A significant amount of research has been conducted on FRP-confined circular columns, but much less is known about rectangular/square columns in which the effectiveness of confinement is much reduced. This paper presents the results of experimental investigations on low strength square concrete columns confined with FRP. Axial compression tests were performed on ten intermediate size columns. The tests results indicate that FRP composites can significantly improve the bearing capacity and ductility of square section reinforced concrete columns with rounded corners. The strength enhancement ratio is greater the lower the concrete strength and also increases with the stiffness of the jacket. The confined concrete behaviour was predicted according to the more accepted theoretical models and compared with experimental results. There are two key parameters which critically influence the fitting of the models: the strain efficiency factor and the effect of confinement in non-circular sections.

A Rational Approach toward Strain Efficiency Factor of Fiber-Reinforced Polymer-Wrapped Concrete Columns

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Analytical model for the effective strain in FRP-wrapped circular RC columns

The available models for predicting the ultimate capacity and stress–strain relationships of confined concrete rely on an assumed FRP ultimate strain value. It is commonly assumed that FRP fails when hoop strain in the jacket reaches its ultimate tensile strain determined according to flat coupon tests. However, experimental results of FRP confined concrete showed that in most cases, FRP experimental ultimate tensile strain is clearly not reached at the rupture of the FRP jacket. The discrepancies may include the shape and conditions of concrete substrate as well as defects or stress concentrations in FRP jackets (in particular, the multiaxial stress state in FRP wrapping due to the transfer of loads through the bond with concrete). The present paper covers only issues related to this latter aspect. Since the average absolute error of all confinement models showed a remarkable decrease when the effective FRP hoop strain (smaller than ultimate flat coupon strain) was inserted in the equations, an analytical model to directly evaluate the FRP strain efficiency factor as the strain ratio between the effective FRP hoop strain at failure and the flat coupon test outcomes has been formulated. Multiaxial failure criteria have been adopted (i.e. 3D Tsai–Hill criterion for FRP) in the model considering axial, circumferential and radial stresses. Results of theoretical analyses and experimental tests (experimental data available in literature) have been compared showing a good agreement.

Concrete confined by FRP systems: Confinement efficiency and design strength models

This paper presents a large database including results from compression tests performed on over 450 concrete cylinders externally wrapped with Fiber Reinforced Polymer materials. The collected results were first employed to perform a statistical evaluation of the FRP strain efficiency factor; in particular, the influence of the type of fiber and the strength of the unconfined concrete were considered. New relationships for estimating the compression strength of the FRP confined concrete were then developed through best-fit analyses. Finally, a procedure available in the literature was applied by the Authors for the statistical determination of the FRP confined concrete strength to use for design purposes.