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Design of FRP-wrapped reinforced concrete columns for enhancing axial load carrying capacity
Abstract
The paper proposed a design method and an experimental programme to evaluate the axial load strength of rectangular and square reinforced compression members confined with GFRP (glass fibre reinforced polymer plates) jackets and steel hoops. Three square and three rectangular columns were tested under axial compression up to failure. The test results clearly showed the efficiency of the jackets in enhancing the ultimate strain and strength of the columns. The design method was calibrated using data from the tests. Closed-form equations are proposed for calculating the axial load strength of columns confined with FRP jackets.
... To account for the increased axial strength the assumption (6) entails, it was decided not to include the contribution of longitudinal reinforcement in calculating the ultimate axial strength. In other models, for the calculation of the contribution of the longitudinal bars usually the yield stress of longitudinal reinforcement is assumed [40], [41], while in [30] the measured strains of the steel bars were introduced in the design model. ...
... The design model proposed in [40] aims at the calculation of the axial strength of FRP-and steelconfined columns with rectangular and square section. The nominal compressive strength in terms of axial force is determined from (29). ...
... More details about the model may be found in [40]. ...
Basic assumptions made in available design models aimed at estimation of the axial strength of axially loaded reinforced concrete columns wrapped with fiber reinforced polymer jackets are discussed. The performance of representative available design models is assessed based on their ability to accurately predict the axial strength of 101 specimens from the literature. A simple design model is proposed and described in detail, which has resulted from a combination of Eurocode provisions in such a way that the predictions are good and also safe.
... A three dimensional Finite difference model FDM which was used in different previous studies [e.g. [25][26][27][28], were constructed and used to predict the structural response of the FRP confined RC columns. ...
... The FDM is used to relate the column deflections (d x & d y ) and curvatures (/ x & / y ) at the different segments across the longitudinal direction of the column; i.e. for any two adjacent segments the following expressions can be applied: Table 1 Details of columns used in FDM validation [17,[23][24][25][26][27]. [23], [24], [17], [25], [26] and [27] respectively. ...
... The FDM is used to relate the column deflections (d x & d y ) and curvatures (/ x & / y ) at the different segments across the longitudinal direction of the column; i.e. for any two adjacent segments the following expressions can be applied: Table 1 Details of columns used in FDM validation [17,[23][24][25][26][27]. [23], [24], [17], [25], [26] and [27] respectively. P, means partially confined with FRP width 65 mm and spacing 105 mm. ...
... A practical (owing to the easy application) empirical model evaluated against a number of test data was proposed by Roussakis et al. (2008). More detailed models that were formulated to take into account the confining effect of both FRP sheets and steel stirrups were proposed by Wang et al. (2007), and by Pellegrino et al. (2010). It is noted that the model of Wang et al. (2007) does not include provisions for FRP strips. ...
... More detailed models that were formulated to take into account the confining effect of both FRP sheets and steel stirrups were proposed by Wang et al. (2007), and by Pellegrino et al. (2010). It is noted that the model of Wang et al. (2007) does not include provisions for FRP strips. The model of Pellegrino et al. (2010) is based on the recommendations of the Italian Research Council (CNR), 2004, and takes into account the contribution of fibers spirally installed at an angle a with respect to the member cross-by multiplying the lateral effective confining pressure with the coefficient K : ...
... Analytical predictions according to the model ofWang et al. (2007). ...
A series of concrete specimens partially confined by by carbon fiber reinforced polymers (CFRP) have been tested in the Laboratory of NED University of Engineering & Technology, in Karachi, Pakistan. The specimens examined had circular and square cross-sections and height between 300mm and 600mm. Unreinforced specimens, reinforced concrete specimens, as well as specimens strengthened with different layouts of CFRP confinement, aiming at the reduction of the FRP material used, have been tested. The aim of this work is to offer a methodology to predict the increase of the compressive strength of the specimens for the various layouts tested. EN code provisions, and models found in the literature are applied to reproduce the experimental results. A modified model is proposed that predicts more accurately the specimens's strength for the FRP layouts reported in this research.
... So, Wang and Hsu [1] model conservatively predicted the compressive strength. In case of the analytical model proposed by Wang and Hsu [1], there was somewhat a good agreement between the predicted calculation and the corresponding experimental results. Actually, the accuracy of available analytical models for FRP-confined rectangular RC columns should be verified with additional test results reflecting the effects of different design parameters for the general applications in predicting the compressive strength of FRPconfined rectangular RC columns. ...
... P an = f cc ′ A c + A s f yl (1) f cc ′ = α 1 α 2 (f co ′ + k 1 Acc area of concrete core enclosed by the center lines of the perimeter hoop (mm 2 ) ...
In this paper an investigation on the behavior of short rectangular reinforced concrete columns wrapped with fiber reinforced polymer (FRP) sheets under axial compression loading was conducted. This study aims at experimentally evaluating the performance of these strengthened columns by using a new promising FRP material (Basalt fiber reinforced polymer (BFRP)) sheets. Moreover, it aims to investigate the limit of the cross-sectional aspect ratio parameter which has been the subject of controversial for the last two decades. Hence, eight RC columns with aspect ratios (1.0, 1.5, 2.0 and 2.5) were tested .The behavior of columns in the axial and transverse directions was analyzed. After that, some existing confinement models for rectangular RC columns were used to predict the nominal compressive strength of rectangular RC BFRP-confined columns sheets. From this research, it can be concluded that, using BFRP sheets in confining of RC columns increases the carrying capacity and ductility. Also, the limit of the aspect ratio at which the gained strength becomes insignificant is 2.0. Finally, the model of Wang and Hsu [1] has a good agreement to predict the nominal compressive strength of rectangular RC columns strengthened with BFRP sheets. Index Terms-Reinforced concrete columns, aspect ratio, FRP, Basalt fiber reinforced polymer (BFRP), full wrapping. _____________________________________________________________________________________________________
... The database included the test results of 326 FRP-confined square and rectangular URC concrete specimens (Abbasnia and Ziaadiny, 2015;Abbasnia et al., 2012Abbasnia et al., , 2013Al-Salloum, 2007;Chen and Ozbakkaloglu, 2016;Hantouch, 2004;Hany et al., 2015;Ilki and Kumbasar, 2003;Ilki et al., 2008;Isleem, 2015;Lam and Teng, 2003;Ozbakkaloglu, 2013a;Ozbakkaloglu and Oehlers, 2008;Parvin and Wang, 2001;Pessiki et al., 2001;Rochette and Labossiere, 2000;Rousakis et al., 2007;Shehata et al., 2002;Suter and Pinzelli, 2001;Tao et al., 2008;Wang and Wu, 2008;Wang et al., 2012aWang et al., , 2016Wu and Wei, 2010). Due to the limited data available in the literature for RC columns, test data for only 130 specimens could be extracted (Anselm, 2005;Harajli et al., 2006;Ilki et al., 2008;Isleem, 2015;Paula, 2003;Tastani et al., 2006;Toutanji et al., 2010;Wang and Hsu, 2008;Wang et al., 2012a). Table 1 provides a summary of the compiled test database and Figure 1 shows details of the internal longitudinal and hoop steel reinforcement of the RC specimens. ...
... This approach is similar to that reported in some other studies (e.g. Isleem et al. (2018b); Maalej et al., 2003;Wang and Hsu, 2008) where the effect of steel confinement in the shorter and longer sides of a rectangular crosssection reinforced by different arrangements of steel hoops (refer to Figure 1) is considered. ...
Composite materials such as Fiber Reinforced Polymer (FRP) offered several advantages compared to conventional materials. High specific modulus and strength and corrosion resistance also made FRP suitable for use as construction materials in structural engineering. Strengthening of reinforced concrete (RC) columns with FRP requires appropriate design methods. However, the available design guides are based on models from tests on unreinforced concrete prisms (i.e., the width, b or depth, h, of cross-sections = 100-200 mm; aspect ratio, h/b, 1.0-2.0; height of specimens = 300-500 mm). The available models might not be reliable in predicting the strength and ductility of FRP-confined RC columns of large scale as found in practice.
Based on results from recent test programs to investigate the influence of aspect ratio and size of cross-sections, hoop reinforcement ratio, thickness of FRP wraps, nature of loading (i.e., monotonic and cyclic), and different configurations of FRP anchors on the axial strength and compressive behavior of FRP-confined rectangular RC columns of larger size (i.e., the sections depth = 200-600 mm; aspect ratio varied between 2.0 and 4.0; height of specimens = 600-1000 mm), significant issues related to the parameter effects have been clarified: (1) Confinement of these columns by FRP wraps provides an increase in axial strength but with a very low rate compared to the axial strain, resulting in post-peak stress-strain responses. (2) Anchoring the externally-bonded jacket using additional FRP anchors increases the confinement to the concrete core, resulting in a significant strength enhancement. (3) An increase of the hoop steel reinforcement ratio or the number of FRP layers influences the shape of stress-strain envelope curves under monotonic compression by enhancing the axial stress and strain capacities. (4) The presence of internal steel bars also influences the plastic strains and the shapes of the unloading and reloading paths, (5) The overall trends of the second and third branches of the stress-strain responses are largely influenced by the increase of aspect ratio.
Therefore, based on experimental observations and a comprehensive database of FRP-confined concrete columns with different geometric and material properties from recent test programs and relative tests compiled from the available literature published between 2000 and the current year, the main objectives of the dissertation address the existing research gabs through a series of scientific chapters.
(1) In chapter 2, based on results of 456 tests, a modified confinement pressure model was provided. The model considers the effects of size and aspect ratio of cross-section, curvature of section corners, and internal hoops reinforcement. Predictive expressions for bilinear and postpeak softening stress-strain curves under monotonic compression were provided. Based on the proposed model and compiled database, the lightly and heavily FRP-confined thresholds were also provided. The comparisons finally show that the model significantly improved the strength and strain results compared to those of existing models.
(2) In chapter 3, key solutions to increase the effectiveness of FRP confinement provided to columns with an aspect ratio of greater than 2.0. One of these is by modifying a rectangular cross-section to an elliptical or oval cross-section. Based on a regression analysis of limited test results, a new confinement model was, as a result, presented for the strength and strain capacities of strengthening existing and designing new structural columns. The other part of chapter 3 presents a stress-strain model for FRP-confined rectangular RC columns with a combination of FRP wraps and FRP anchors. The proposed model can be considered an extension of the main research gabs addressed in chapter 2 but with limited applicability to the parameters considered in these tests, in which 80 RC columns with aspect ratio of from 1.5 to 4.0 and sections depth up to 600 mm were regressed. All expressions were finally validated using the same database used in the model calibration, showing better correlations as compared with the existing models.
(3) In chapter 4, based on limited tests, a new model considering cyclic axial compression for FRP-confined rectangular RC columns having post-peak softening behaviors was proposed. The model mainly considers the effect of internal steel stirrups on the plastic strains and shapes of reloading and unloading stress-strain curves and well predicts the results compared with underestimated predictions by the existing models of FRP-confined plain concrete.
(4) In chapter 5, the research addresses a research gab based on limited tests on 26 large-scale columns with internal longitudinal and lateral FRP reinforcement. An analytical framework for predicting an axial stress-strain response under monotonic compression was provided. The geometric and mechanical parameters affecting the model response were also considered. Existing models for steel-confined columns and for columns confined by circular FRP hoops do not give accurate predictions for the test results. On contrary, good agreement between the experimental results and the model predictions was finally obtained.
Keywords: FRP-confined; RC columns; rectangular sections; axial compression; cyclic response.
... Αναλυτική περιγραφή των μοντέλων που εξετάστηκαν γίνεται στις εργασίες των Ι. Παπαρίζου (2016) και Ε. Μηλιώκα (2016). Η πειραματική βάση δεδομένων που χρησιμοποιήθηκε για την αξιολόγηση των αναλυτικών προσομοιωμάτων αποτελείται από 101 δοκίμια (εκ των οποίων τα 86 από οπλισμένο και τα 15 από άοπλο σκυρόδεμα): Rodrigues and Silva (2001), Chaallal and Shahawy (2000), Cole and Belarbi (2001), Esfahani and Kianoush (2005) Roussakis and Karabinis (2008), Carey and Harries (2005), Bai et al. (2012), Chastre and Silva (2010), Wang and Hsu (2008), Bournas et al. (2007) και Wang et al. (2012). Τα δοκίμια που περιελήφθησαν στην βάση ήταν ανέπαφα, δηλαδή δεν είχαν υποστεί βλάβες λόγω προγενέστερης δοκιμής. ...
... Η μορφή της διατομής των δοκιμίων ποικίλει: Περιλαμβάνονται 42 δοκίμια με κυκλική, 38 με τετραγωνική και 21 με ορθογωνική διατομή. Ο εγκάρσιος οπλισμός στα 86 δοκίμια οπλισμένου σκυροδέματος είχε τάση διαρροής που κυμαινόταν από 200 μέχρι 600 MPa, ενώ το πλήθος των στρώσεων FRP που εφαρμόστηκε στα 101 δοκίμια κυμαινόταν από 1 έως και 5 στρώσεις (με εξαίρεση την έρευνα των Wang and Hsu, 2008, όπου εφαρμόστηκαν έως και 6 στρώσεις FRP). Η επιλογή των δοκιμίων της βάσης έγινε έτσι ώστε να καλύπτεται ευρύ πεδίο τεχνικών και μηχανικών χαρακτηριστικών (π.χ. ...
... The database included the test results of 326 FRP-confined square and rectangular URC concrete specimens (Abbasnia and Ziaadiny, 2015;Abbasnia et al., 2012Abbasnia et al., , 2013Al-Salloum, 2007;Chen and Ozbakkaloglu, 2016;Hantouch, 2004;Hany et al., 2015;Ilki and Kumbasar, 2003;Ilki et al., 2008;Isleem, 2015;Lam and Teng, 2003;Ozbakkaloglu, 2013a;Ozbakkaloglu and Oehlers, 2008;Parvin and Wang, 2001;Pessiki et al., 2001;Rochette and Labossiere, 2000;Rousakis et al., 2007;Shehata et al., 2002;Suter and Pinzelli, 2001;Tao et al., 2008;Wang and Wu, 2008;Wang et al., 2012aWang et al., , 2016Wu and Wei, 2010). Due to the limited data available in the literature for RC columns, test data for only 130 specimens could be extracted (Anselm, 2005;Harajli et al., 2006;Ilki et al., 2008;Isleem, 2015;Paula, 2003;Tastani et al., 2006;Toutanji et al., 2010;Wang and Hsu, 2008;Wang et al., 2012a). Table 1 provides a summary of the compiled test database and Figure 1 shows details of the internal longitudinal and hoop steel reinforcement of the RC specimens. ...
... This approach is similar to that reported in some other studies (e.g. Isleem et al. (2018b); Maalej et al., 2003;Wang and Hsu, 2008) where the effect of steel confinement in the shorter and longer sides of a rectangular crosssection reinforced by different arrangements of steel hoops (refer to Figure 1) is considered. ...
Abstract: In this paper, a new confinement model is introduced to accurately estimate the strength of FRP-confined unreinforced and reinforced concrete (RC) columns of rectangular cross-sections using 456 test data compiled from 30 studies available in the technical literature. The test database covers unconfined concrete strength varying from approximately 10 to 80 MPa. The width of the cross-section ranged between 90 and 400 mm, and its depth ranged between 100 and 500 mm. The effects of column parameters: (1) aspect ratio and size of cross-sections, (2) effective rupture strain of FRP wrap, (3) corner radius, and (4) internal hoop steel reinforcement were accounted for in the model. Based on the same database the thresholds of lightly and heavily-confined concrete have also been proposed to ensure that the columns have a sufficient level of FRP confinement. It was finally shown that the model predictions were in good agreement with the test results.
Keywords: Concrete Columns, Composite materials; Stress, Modelling.
... There are two application modes of FRP, one is used in the reinforcement of existing buildings, and the other is directly used in newly built structure. Most research of FRP mainly focuses on the maintenance and reinforcement, results show that the load-carrying capacity and ductility of FRP reinforced concrete are obviously improved, and the service life and durability of concrete structure are prolonged (Wu et al., 2006;Kader et al., 2006;Abbasnia and Ziaadiny, 2010;Jumaat et al., 2010;Yung-Chih and Hsu, 2008;Jiang et al., 2007). *Corresponding author. ...
... In order to further study the performance of PVC-FRP confined concrete column, the determination of stressstrain model is the key issue to analyze the behavior of PVC-FRP confined concrete column. Scholars have done much research and proposed many stress-strain models for FRP confined concrete column (Yung-Chih and Hsu, 2008;Jiang et al., 2007;Feng and Ditao, 2009). ...
The design of PVC-FRP confined concrete members requires accurate evaluation of the performance enhancement due to the confinement provided by PVC-FRP tube. Based on the static equilibrium condition and the yield criteria of concrete and PVC-FRP tube, this paper presents a calculating model of the load-carrying capacity of PVC-FRP confined concrete column, the influences of the hoop spacing of FRP strips and equivalent confinement effect coefficient on load-carrying capacity were well considered. According to the ingression of experimental data, a calculating formula of the ultimate axial strain is also put forward. For this last case, a bilinear stress-strain model of PVC-FRP confined concrete column in axial and lateral directions is established. The comparison between experimental and numerical results indicates that the model provides satisfactory predictions of the stress-strain response of the columns.
... The extensive experimental studies demonstrate that the strengthened of RC column specimens shows the load-displacement capacity. It is governed by the significant influential parameters like the compressive strength, cross-section area, aspect ratio of the column specimens, different radius, the number of wrap layers, the orientation of FRP wrap, ratio and orientation of longitudinal reinforcement, and the nature of loading [6][7][8][9][10][11]. The performance of fully FRP wrapped columns were investigated by many researchers [12,13]. ...
Reinforced concrete (RC) columns, jacketing of FRPs has become a standard strengthened technique in the present times. The current research scenario focuses on the fact that strengthened and rehabilitation of RC columns by CFRP and GFRP are more effective. Additionally, the present research also highlights a new class of natural composites of BFRP (Basalt Fiber Reinforced Polymer) bonded with adhesive to column specimens as an alternate confinement material. Generally, it is advisable to use RC columns instead of CFRP and GFRP confinement material. The experimental study was strengthened by partially and fully wrapped square RC columns using GFRP and BFRP uni - directional and bi-directional. The behavior of stress-strain curves and failure modes were observed. The experimental results show that the substantial increment in ultimate load-displacement capacity, ultimate stress-ultimate axial and lateral strains lead to BFRP and GFRP failure. The fully warped square reinforced concrete (RC) column performs better in getting stress-strain behavior and displacement limit as compared to the partially covered system. It is a fact that the strengthened obtained by partial wrapping with BFRP and GFRP is a preferable and cost-effective alternative as compared to the fully wrapped. The test results show that the CNR-DT-R1 model is more reliable than Lam & Tang and provides reasonable and precise calculations for the ultimate axial stress of partially and fully wrapped RC columns. HIGHLIGHTS Now days strengthening and rehabilitation of RC columns by CFRP and GFRP is more effective, but the natural composite BFRP is also an alternative confinement material The experimental study was strengthened by partially and fully wrapped square RC columns using GFRP and BFRP Uni - directional and bi-directional The behaviour of stress-strain curves and failure modes were observed. The experimental results show that the substantial increment in ultimate load-displacement capacity, stress, axial and lateral strains lead to BFRP and GFRP failure The study has been performed to verify the experimental data's reliability and accuracy with the theoretical models such as CNR-DT R1 and Lam & Teng model GRAPHICAL ABSTRACT
... The combined effects of chloride and freeze-thaw erosion on the RC columns have not been fully studied. Furthermore, although the stress-strain models [34][35][36][37][38][39][40] and strength calculation methods [41][42][43] of FRP confined concrete columns under compressive loading have been widely studied and the relevant specification has been proposed [44], the strength models of FRP strengthened RC columns considered the damage factors of environmental erosion, especially under combined environmental conditions, have not received much attention. The analytical model for ultimate load capacity prediction of FRP strengthened RC column subjected to combined corrosion and freeze-thaw erosion is desperately needed to provide the foundation for a mechanism-based rational design. ...
The compression test of glass fiber-reinforced polymer (GFRP) partially strengthened corroded reinforced concrete (RC) columns subjected to freeze-thaw cycling was conducted in this study. A total of 45 small-scale RC columns were prepared. The columns were firstly subjected to accelerated corrosion conditioning to obtain the target level of steel loss, and then partially strengthened with 2-ply GFRP strips; finally, the strengthened RC columns were subjected to different freeze-thaw cycles. The main parameters in this experiment were reinforcement corrosion degree (0, 10%, and 20%) and number of freeze-thaw cycles (0, 25, 50, and 75). The compressive behaviors of columns were evaluated in terms of failure mode, load capacity, load-displacement response, stiffness, and ductility. Results showed that GFRP partially strengthening could significantly improve the load capacity, stiffness, and ductility of corrosion-damaged RC columns, while the ultimate load capacity and stiffness of strengthened columns decreased with the increase of freeze-thaw cycles. Moreover, a design-oriented calculation method for the ultimate load capacity of GFRP partially strengthened corroded RC columns subjected to freeze-thaw cycles was proposed and validated by the experimental results.
... Therefore, Type B specimens are used in the following interpretations for simplicity. According to the design method developed by Wang and Hsu (2008), the concrete in the entire cross section can be divided into three regions as follows under the dual confinements from steel hoops and FRP strips (as shown in Fig. 14): the ineffectively confined region (area = A 1 ), the effectively confined zone exerted by FRP strips (area = A 2 ), and the dually effective-confined region by steel hoops and FRP strips (area = A 3 ). Therefore, the load capacity of a partially FRP-wrapped RC column consists of the total axial force carried by the internal longitudinal steel reinforcement (N us ) and concrete (N uc ), which can be determined by the following formula: ...
This study first presents an experimental investigation on the compressive behavior of carbon fiber-reinforced polymer (CFRP)-confined square seawater-sea sand concrete (SSC) columns with embedded epoxy-coated reinforcement (ECR). Thirty-three columns were tested to explore the influence of several parameters, including clear spacing ratios, FRP wrapping schemes, FRP volumetric ratios, and internal steel reinforcement ratios. Test results reveal that the location of CFRP strips with respect to the steel hoops has a significant impact on the mechanical behavior of specimens, especially for the deformation capacity. Furthermore, more obvious improvements of strength and ductility are detected for the reinforced columns with smaller clear spacing ratios and higher volumetric ratios of FRP wraps. In specific, the maximum enhancements of load capacity and ductility index for the reinforced SSC specimens with two-layer CFRP strips are 11.8% and 92.9%, respectively, while the improvements increase to 15.6% and 189.2% when the thickness of CFRP jackets doubles. A regression based stress-strain model is developed to evaluate the ultimate conditions of FRP partially wrapped concrete columns, and a better agreement can be achieved by the developed model compared with other existing models. Finally, a simple expression is also proposed based on the experimental observations, which can accurately predict the load capacity of plain and reinforced concrete columns wrapped with FRP strips.
... Wang and Hsu conducted a theoretical study and suggested a closed-form design equation to evaluate the axial load strength of the RC columns confined with FRP. The values from the prediction of the equations calibrate the experimental results [28]. Colomb et al. tested eight short columns subjected to axial load to study the shear failure of RC columns. ...
The ductility and strength of reinforced concrete (RC) columns could be noticeably improved by replacing steel bars with polymeric bars. Despite the previous research on RC columns, most of those studies focused only on the lateral load capacity of this structural member and were mainly costly experimental studies. However, this paper is concentrated on the previously occurred damages to the reinforced columns in the previous earthquakes. Subsequently, finite element analysis has been performed to examine 24 models including the various shapes of RC columns. In employing the plastic behavior of steel, carbon fiber-reinforced polymer (CFRP), and glass fiber reinforced polymer (GFRP) bars, the bilinear hardening has been considered. To capture both compressive and tensile behavior of the concrete, the concrete damage plasticity model has been implemented. Furthermore, the optimization technique is used for CFRP models to compare with other models. In this paper, the parameters of energy, seismic factor, stiffness, and ductility have been computed using the method proposed by the authors. This suggested method is considered to compare the results from each parameter. Finite element results of steel bars are compared with carbon and glass models. The results show the stiffness of models is improved by CFRP bars, while the energy absorption and ductility factor are enhanced with steel bars. Moreover, GFRP bars can enhance the seismic factor. The reduction of column stiffness to almost half would occur in some rectangular cross-section columns.
... The specimens considered had, in general, steel reinforcement and were wrapped with FRP fabric extending to the whole height of the column: thirteen specimens with glass FRP fabric (GFRP), and the rest with carbon FRP fabric (CFRP). The test data is taken from the following publications: Bai et al. (2012), Bournas et al. (2007), Carey and Harries (2005), Chaallal and Shahawy (2000), Chastre and Silva (2010), Cole and Belarbi (2001), De Luca et al. (2011), De Paula and Da Silva (2002, Esfahani and Kianoush (2005), Feng et al. (2002), Harajli et al. (2006), Ilki et al. (2008), Li et al. (2003), Matthys et al. (2006), Rodriguez and Silva (2001), Roussakis and Karabinis (2008), Tastani et al. (2006), Wang and Hsu (2008), and Wang et al. (2012). The range of the test parameters in the database included are grouped in Table 1. ...
The enhancement of the axial strength of plain concrete columns wrapped with fibre-reinforced polymer (FRP) fabrics has been extensively investigated, both analytically and experimentally. Respective research on reinforced concrete (RC) columns strengthened with FRP is significantly more limited. This paper deals with axially loaded RC columns fully wrapped with carbon and glass FRP, with circular, square, and rectangular cross-section. A simple design model is proposed and described in detail, which has resulted from a combination of Eurocode provisions in such a way that the predictions are good and also safe. Furthermore, three models from the literature, selected among others because of their good agreement with experimental data, are also presented and some of their aspects are discussed. All models are applied to 95 specimens tested in the literature. The criteria for selecting the models presented here were their simplicity in application, combined with their accuracy in predicting the strength of test data available in the literature.
... Confinement of concrete with fiber-reinforced polymer (FRP) has been one of the widely used methods for retrofitting existing concrete members [1]. This is mainly because i) FRP enhances load carrying capacities of the concrete by providing confinement to the lateral dilation of the concrete and ii) it improves the ductility of the concrete, which is highly important for earthquake-resistant design of structures [2][3][4]. Accurate predicting the mechanical behavior of FRP-confined concrete is needed to reliably design and model structural members manufactured with this composite system [5]. ...
The accurate design‐oriented model for concrete confined with fiber‐reinforced polymer (FRP) is important to provide safe design of this composite system. In this paper, the response surface model (RSM) is coupled with support vector regression (SVR) for developing a novel hybrid model, namely RSM‐SVR, with the aim of predicting the ultimate condition of FRP‐confined concrete. Predictions obtained by the proposed model were compared with those by six empirical models and two data‐driven models of RSM and SVR for database containing 780‐test column results with circular cross section. Statistical analysis reveals that the proposed RSM‐SVR model predicts the compressive strength and corresponding axial strain of the concrete confined with FRPs more accurately in comparison with the existing models. The results also show that RSM‐SVR and SVR models provide stable predictions of strength and strain enhancement ratios for lateral confining ratio of >1 while the other models exhibit chaotic model error. The high accuracy and stable predictions by the proposed model are achieved based on its high flexibility and robustness in capturing the effect of lateral confining pressure as the interaction between the concrete core and FRP jacket in comparison with the existing models.
... Although the upgrading of RC columns using FRP-wrapped sheets is a cost-effective strengthening technique [1,5], numerous studies have been developed. However, the majority of these studies investigated RC columns having a circular cross section. ...
Finite element (FE) simulation of confined RC columns is a complex task, as it involves the precise representation of a concrete material model that could express the volumetric change of concrete under a triaxial state of stress. The problem of confining RC columns using fiber-reinforced polymer (FRP) is more complex. This is due to the passive nature of FRP containment. Recently, the concrete damage plasticity (CDP) model available in an FE software product (ABAQUS) has been widely used to represent RC columns subjected to axial loading. The present paper aims to calibrate the concrete dilatancy angle and viscoplastic regularization parameters in the CDP model for the applications of square RC columns confined with FRP sheets. Ten experimental FRP-confined RC column specimens are incorporated in the calibration. In addition, a parametric study is investigated, including 96 cases, to obtain the influence of various design variables on the ratio between the confined to unconfined concrete compressive strength (fcc/fc). Four design variables are considered (i.e., the corner radius, concrete compressive strength, FRP reinforcement ratio, and cross-sectional size of columns). The study also focuses on assessing the reliability of four design codes: ACI-440, ECP-208, CSA-S806 and FIB-Bulletin-14. The numerical results show that a viscoplastic regularization with a fixed value equal to 0.0005 could provide accurate behavior. Nevertheless, the dilation angle cannot be considered a fixed value and should be related to the confinement degree coefficient Cd, which depends on the cross-sectional geometrical and FRP properties. Among the four considered design codes, ACI-440 and ECP-208 provide more accurate behavior than CSA-S806 and FIB-Bulletin-14.
... Schematic Designs for FRP Wrapped Concrete Columns[1]. ...
In this paper, the FRP wrapped concrete column is investigated. . According to the research results of Shan et al. (2020) [2], Li et al. (2006) [3], and Deb et al. (2010) [4], this paper analyzes the variables that need to be controlled in the design of columns from these three perspectives: the shape of the cross-section, fiber orientation and bonding between the concrete column and FRP confinement. Impact tests and compressive tests are performed on different specimen. The setting of different samples follows the principle of controlling variables. The results indicate that FRP-wrapped columns with a circular cross-section are better than that with square or rectangular columns and basalt FRP is the optimal FRP material for strengthening the concrete column under the impact. Fiber orientation and types of bonding layers have a great impact on the mechanical properties of FRP wrapped concrete columns.
... To estimate the effectiveness of this strengthening technique, numerous investigations have been carried out concerning columns with or without internal steel reinforcement having circular cross sections (for example [4,[17][18][19][20][21][22]). Significant research has also been done for square/rectangular reinforced concrete (RC) or plain concrete columns under monotonic axial loading [1,[23][24][25][26][27][28][29][30] among others. Similar work has been carried out for FRP-confined concrete columns under cyclic axial loading for circular specimens [31][32][33][34][35][36][37] and rectangular ones [2,3,28,35,[38][39][40][41][42][43][44][45][46][47][48], with or without transverse and longitudinal steel reinforcement. ...
This paper utilizes the advanced potential of pseudodynamic three-dimensional finite-element modeling to study the axial mechanical behavior of square and rectangular reinforced concrete columns, confined with fiber reinforced polymer (FRP) jackets and continuous composite ropes in seismic applications. The rigorous and versatile Riedel-Hiermaier-Thoma (RHT) material model for concrete is suitably calibrated/modified to reproduce the variable behavior of characteristic retrofitted columns with deficient internal steel reinforcement detailing, suffering nonuniform local concrete cracking and crushing or bulging and bar buckling. Similarly, the 3D FRP jacket or rope confinement models may account for damage distribution, local fracture initiation and different interfacial bonding conditions. The satisfactory accuracy of the reproduced experimental stress-strain envelope behavior enables the analytical investigation of several critical design parameters that are difficult to measure reliably during experiments. Additional parametric analyses are conducted to assess the effects of steel quality. The significant variation of the field of developed strains on the FRP jacket at the ultimate and of the developed strains and deformations on steel cages among different columns are thoroughly investigated. This advanced analytical insight may be directly utilized to address missing critical parameters and allow for more reliable FRP retrofit design of seismic resistant reinforced concrete (RC) columns. Further, it allows for arbitrary 3D seismic analysis of columns (loading, unloading, cyclic or loading rate effects or preloading) or addresses predamages.
... Wang et al [11] studied the axial load strength of rectangular and square RC compression members confined with GFRP jackets and steel hoops, and noticed that the FRP jackets provided excellent confinement in rectangular and square reinforced concrete columns, increasing both the ultimate strength and strain. ...
This paper presents results of an experimental program undertaken to investigate the behavior of short rectangular reinforced concrete columns that have been strengthened with carbon fiber-reinforced polymer (CFRP) sheets under axial compression. The effects of cross-sectional aspect ratio and strengthening system of the confinement were investigated experimentally through the tests of 12 reinforced concrete (R.C) columns. The behavior of columns in the axial and transverse directions was analyzed. From the experimental results, it is found that the aspect ratio between depth and width (t/b) of the cross-section plays a significant role on the efficiency of the applied strengthening system .Whenever aspect ratio increases; gained nominal strength clearly decreases so that in aspect ratio more than 2.5, the strength enhancement of confined rectangular column is insignificant. For the same amount of used fiber, it is found that the case of full wrapping is more effective than that of partial wrapping. Despite of this, partial wrapping strengthening system still gives a significant efficiency for rectangular columns.
... The wrapping of RC columns by FRP is another technique for strengthening and ductility enhancement. Several researchers have examined the use of FRP jackets to reinforced RC columns [42][43][44][45][46][47][48][49][50][51][52]. As an alternative to above two methodologies, the FRP composites presented it as an attractive option. ...
In civil and structural engineering, building structures with vigorous stability and strength utilizing economical materials is challenging. Stability of structures during their lifespan is a very demanding endeavor in civil engineering systems. Recent trends are highly focused on high strength materials, strong corrosion-resistance in structural elements, slender structure development, broad span provision, and load reduction. in order to achieve these conditions, composite materials have proved to be a successful aspirant. The fiber-reinforced polymer (FRP) possesses novel properties that encourage the researchers to strengthen or restore the structural degradation of the reinforced concrete (RC) columns via confinement. The present study highlighting the different aspects of (FRP) confined (RC) column having different aspect ratios, the axial load, and the high temperature under extensive literature review. The FRP confinement is much more effective in the case of circular columns than sharp-edged rectangular columns. The variation of the cross-sectional aspect ratio (section depth to width ratios) of RC columns plays a vital role in the evaluation of the efficiency of strengthening techniques. In spite of the clear and proven advantages of utilizing FRPs over conventional materials, awareness of the behavior of such composite materials after exposure to high temperature is noticeable and requires more research.
... This was attributed to the fact that jacketing provides a uniform confining stress around the circular concrete core. Wang and Hsu (2008) observed that the GFRP jackets were effective in preventing premature buckling of the longitudinal reinforcing bars in the columns. They conducted experiments on square and rectangular columns wrapped with multiple layers of GFRP. ...
A new composition of precursors was identified using china clay, quartz and calcium carbonate to fabricate the microfiltration membrane. The membrane was fabricated by pressing method and sintered at 1000°C. Various characteristics of membrane such as porosity, average pore size, water permeability and chemical resistance were evaluated. Energy Dispersive X-ray analysis (EDX) was conducted to identify the elements present in the membrane. The porosity, water permeability and pore size of membrane are found to be 37%, 2.88 × 10−3 L/m2.h.Pa and 555 nm respectively. Corrosion resistance test indicates that the membrane can be subjected to acid and alkali based cleaning procedure.
... Studies have found that there is no significant gain in the confined ultimate strength, particularly for columns with a cross-sectional aspect ratio of 2·0, as generally shown in Figures 2(a) and 2(b). More clearly, from the existing literature (Abbasnia and Ziaadiny, 2015;Abbasnia et al., 2012Abbasnia et al., , 2013Al-Salloum, 2007;Anselm, 2005;Chen and Ozbakkaloglu, 2016;Hantouch, 2004;Hany et al., 2015;Harajli et al., 2006;Ilki and Kumbasar, 2003;Ilki et al., 2008;Isleem et al., 2018aIsleem et al., , 2018bLam and Teng, 2004;Ozbakkaloglu and Oehlers, 2008;Ozbakkaloglu, 2013aOzbakkaloglu, , 2013bParvin and Wang, 2001;Paula, 2003;Pessiki et al., 2001;Rochette and Labossiere, 2000;Rousakis et al., 2007;Shehata et al., 2002;Suter and Pinzelli, 2001;Tao et al., 2008;Tastani et al., 2006;Toutanji et al., 2010;Wang and Hsu, 2008;Wang and Wu, 2008;Wang et al., 2012aWang et al., , 2012bWang et al., , 2016Wu and Wei, 2010), in total, almost 500 test results are assembled in Figure 2 from studies published between 2000 and the current year, with the majority of these results being for rectangular columns with limited aspect ratio varying between 1 and 2, whereas much fewer are for rectangular columns with a larger variation in their aspect ratios. It is evident from Figures 1(a) and 1(b) that, with respect to f 0 c , ...
Much work has been published in recent years on the strength benefits of confining rectangular reinforced concrete columns less than 300 mm across and with an aspect ratio less than 3 with fibre-reinforced polymer wraps and anchors. However, there has been little published research on the effects of polymer confinement on larger, flatter columns. This paper provides a new strength-prediction model with a wider scope than those in the existing literature. Test results provided by two independent researchers for 44 specimens were used as a basis for the model expressions. The test database included columns with aspect ratios ranging from 1·5 to 4·0 and depths of section varying from 100 mm to 600 mm. The key parameters influencing the confined strength, including aspect ratio, number of polymer layers, hoop steel reinforcement and cross-sectional area, and configuration of polymer anchors, were all accounted for. For a sufficient amount of polymer confinement, the threshold values of the lightly and heavily confined columns were proposed to be 0·125 and 0·25, respectively. Finally, the accuracy of the proposed model was verified by comparing its predictions with the database, together with the predictions of other existing models.
... Wang et al. [6] did designing methods and experimental test on the behavior of concrete columns retrofitted by GFRP wraps. He examined three square and three rectangular columns under compressive axial loads to find out the enhancing of load capacity. ...
A new analytical technique was established to analyze concrete columns strengthened by FRP Systems. The technique used finite element ABAQUS software coupled with MATLAB considering the actual behavior of materials including the concrete's damage-plasticity model. The analytical results were evaluated against experimental results of twenty two concrete axially loaded columns divided into eight different groups from A to H. The analytical study was extended to include additional fourteen columns for verification. The analytical results showed a comparable agreement with the laboratory's results. The proposed new technique will provide the engineers with means to analyze damaged columns retrofitted by FRP systems.
... Moreover, compared with traditional retrofit techniques, FRP composites are more practical to construct with minimal changes to the appearance of the structure, and more importantly, they do not increase the stiffness of the structure and hence will not alter the structural dynamic response, which is a significant characteristic for seismic retrofit [8]. A large number of experimental and numerical studies have been reported in the literature on the monotonic behavior of FRP-confined concrete columns (e.g., [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]). The experimental and numerical results have demonstrated that the use of FRP composites as a confining material can enhance the strength and ductility of the concrete column. ...
This paper presents results of an experimental program in which basalt and carbon fiber-reinforced polymer (FRP) sheets are used as confining jackets to enhance the seismic performance of square reinforced concrete (RC) columns with inadequate transverse reinforcement. Crack patterns, failure modes, lateral hysteresis loops, displacement ductility, energy dissipation capacity and stiffness degradations of one unretrofitted column and five retrofitted columns are presented and discussed. The effects of the amount and type of FRP sheets on the seismic behavior of the retrofitted columns are also examined. Experimental results indicate that the unretrofitted column has poor ductility with brittle shear failure, while the FRP jackets are useful in enhancing the seismic resistance of the retrofitted columns and result in more stable hysteresis loops with improved energy dissipation capacity and lower stiffness degradations. The columns retrofitted with BFRP sheets have equivalent or even superior seismic performance compared to counterparts that are retrofitted with the same number of layers of carbon FRP (CFRP) sheets, and the material costs of the former are only 20% that of the latter. It has been demonstrated that the BFRP composites have promising potential for use as an alternative to conventional FRPs for seismic retrofit of square RC columns.
... However, most of the studies are based on circular cross-sections [20e25] and cannot be applied directly for square columns due to the fact that unlike circular columns, the lateral stress in square columns is not uniform over the perimeter. More concentration of stress are observed at the corners of the square column while the lateral stress is less pronounced on the flat edges [26,27]. In addition, the detailing of longitudinal and transverse reinforcement steel affect the stress distribution in square column which is different compared to circular column [28]. ...
... Wang and Hsu [26] investigated the axial load strength of rectangular and square reinforced compression members confined with GFRP jackets and steel ties. A total of six columns were prepared for testing (set 2). ...
Recently, the need to increase the strength of reinforced concrete members has become a subject that civil engineers are interested in tackling. Of the many proposed solutions, fiber-reinforced polymer (FRP) materials have attracted attention due to their superior properties, such as high strength-to-weight ratio, high energy absorption and excellent corrosion resistance. FRP wrapping of concrete columns is done to enhance the ultimate strength due to the confinement effect, which is normally induced by steel ties. The existence of the two confinement systems changes the nature of the problem, thus necessitating specialized nonlinear analysis to obtain the column’s ultimate capacity. Existing research focused on a single confinement system. Furthermore, very limited research on rectangular sections was found in the literature. In this work, a model to estimate the combined behavior of the two systems in rectangular columns is proposed. The calculation of the effective lateral pressure is based on the Lam and Teng model and the Mander model for FRP wraps and steel ties, respectively. The model then generates stress-strain diagrams for both the concrete core and the cover. The model was developed for the analysis in extreme load events, where all possible contributions to the column’s ultimate capacity should be accounted for without any margin of safety. The model was validated against experiments, and the results obtained showed good agreement with almost all of the available experimental data.
... where lc is the lateral confinement pressure exerted by the CFRP strips; frp is the tensile strength of FRP in the hoop direction; frp is the FRP volumetric ratio to concrete for the column wrapped with CFRP strips (Figure 1) and can be determined by the following equation: Silva [32] Lei-Ming Wang, Yu-Fei Wu [40] Yung-Chih Wang and Hsu [47] Hadi [48] Wonsiri Punurai et al. [49] Yaqub and Bailey [13] Marc Quiertant and Jean-Luc Clement [50] Thong M. Pham et al. [51] Guoqiang Li et al. [52] Nadeem A. Siddiqui et al. [53] Sushil S. Sharma et al. [54] Present study ...
In an attempt to mitigate the high cost of FRP composite strengthening, an experimental investigation was carried out that sought to achieve efficient and most favorable FRP strengthening using CFRP composite strips. 50 mm wide CFRP composite strips were used in two different spacings (20 mm and 40 mm) to confine columns. The test results of the column confined with smaller spacing (20 mm) showed significant restraint of axial deformation of the column and enhanced the strength capacity to a maximum of 99.20% compared to that of reference column. In contrast, the column confined by strips with larger spacing (40 mm) failed by crushing of concrete alone, which occurred even before the CFRP strips reached their ultimate strain. In addition, the embodied energy that exists in the CFRP strips could not be utilized effectively. The stress and strength enhancement ratio of this present study was compared with the previous research that has been conducted on columns confined with full wrapping. From the obtained results, it is recommended that CFRP strips with a spacing of 20 mm be used to improve the strength capacity of the RC column; in addition, this wrapping technique provides economic benefits compared to a column confined with full wrapping.
... Some researchers resolved this problem by means of superimpose the confining stresses attributed to internal steel stirrups and external FRP jackets (Harajli 2006;Debaiky el tal. 2007), or accumulating the contributions of internal steel stirrups and external FRP jackets to load capacity of the columns (Li et al. 2003;Lin and Liao 2004;Maalej et al. 2003;Wang and Hsu 2008). ...
Based on the experimental data presented in part I of these companion papers, a semi-empirical model is proposed for axial stress-strain curves of reinforced high-strength concrete square columns confined by aramid fiber reinforced polymer (FRP) jackets. Additionally, a three-dimensional finite element model is developed to simulate the mechanical behaviors of the columns. In the finite element model, both material nonlinear and contact nonlinear are taken into account. Moreover, the influence of contact nonlinear (i.e., the end friction on the contact surface between test machines and specimens) is investigated deeply. Predictions from both the semi-empirical model and the finite element model agree with the experimental results, and it is also demonstrated that the friction coefficient of end friction notably affect the properties of columns when it ranges from 0.00 to 0.25.
... Haskett et al. (2009) observed that there is an increase in the torsional capacity and ductility of FRP retrofitted beams. In the study of Wang and Hsua (2008), columns were tested, with a total of 6 different sequences, under axial pressure force until they suffered damage. It could be seen that the bearing forces of FRP retrofitted columns increased. ...
Due to design codes and regulations and the variety of building plans in Turkey, it is very often seen that band-type windows are left for ventilation and lightening of the basements of buildings which are used for various purposes such as workplaces and storage. Therefore when the necessary support measures cannot be given, short columns are subjected to very high shear forces and so damage occurs. One of the precautions to avoid the damage of short column mechanisms in buildings where band-type windows are in the basement is to strengthen the short columns with fiber reinforced polymer (FRP). In this study, the effect of the FRP retrofitting process of the short columns around band-windowed structures, which are found especially in basement areas, is analyzed in accordance with Turkish Seismic Code 2007 (TSC 2007). Three different models which are bare frame, frame with short columns and retrofitted short columns with FRP, are created and analyzed according to TSC 2007 performance analysis methods to understand the effects of band windows in basements and the effect of FRP retrofitting.
... Yet, this longitudinal strain cannot be tolerated in practical application. According to Wang & Hsu [9] for example, the column's compression is restricted to 1% in the ultimate limit state. The achieved increases of loadbearing capacity of the TRC of series D and CFRP-reinforcement with the same stiffness of series E1 under axial compression of 1.0% were opposed. ...
The increase of the load carrying capacity of columns being reinforced with Textile Reinforced Concrete (TRC) is partly achieved by the additional concrete cover. But then it is also decisively caused by the confinement effect of the textile reinforcement. The confinement is thereby producing a three axial state of stress within the concrete core of the column. The effectiveness of such a confinement is especially dependent on the geometry of the concrete column to be strengthened. At rectangular ones with sharp edges without fillets the TRC strengthening can only augment the load carrying concrete share, not create a confinement effect which can be achieved at the round counterparts.
Within the study we tested columns with all possible cross sections from square to circle with different fillet radiuses. Thus the influence of the fillet radius onto the local bearing capacity of the reinforcing textile was recorded. Furthermore the impact of different fibre materials and reinforcement degrees of the TRC strengthening layer has been examined. The first results show a considerable disproportionate increase of the confinement effect with rising fillet radius, as well as a growth of the confinement effect with augmenting level of reinforcement in the TRC strengthening layer.
... Diese Längsverformungen sind in der Praxis jedoch nicht tolerierbar. Nach [11] wird die Stauchung Bild 12. Einfluss der Kernbetonfestigkeit und der Lagenanzahl auf die Tragfähigkeitssteigerung (Vergleich für das CFHT-Textil anhand der Geometrie 6) Fig. 12. Impact of the core concrete strength and the number of layers onto the increase of load bearing capacity (comparison for the CFHT textile with geometry 6) Bild 13. Vergleich zwischen Textilbeton-und CFK-Verstärkung Fig. 13. ...
Die Tragfähigkeitserhöhung von Stützen, die mit textilbewehrtem Beton (TRC) verstärkt wurden, wird zum einen durch den zusätzlichen Betonmantel erreicht. Zum anderen wird sie aber entscheidend durch die Umschnürungswirkung der textilen Bewehrung bewirkt, was insbesondere im Lasteinleitungsbereich von Stützen von großer Bedeutung ist. Die Umschnürung erzeugt dabei einen günstig wirkenden dreiaxialen Spannungszustand im Kern der Stütze. Die Wirksamkeit einer solchen Umschnürung ist insbesondere abhängig von der Geometrie der zu verstärkenden Betonstütze. Mit Hilfe von Versuchen an Stützenköpfen mit Querschnitten vom Quadrat bis hin zum Kreis mit unterschiedlichen Ausrundungsradien wird der Einfluss des Ausrundungsradius auf die Wirksamkeit der Bewehrungstextilien erfasst. Des Weiteren wurde der Einfluss verschiedener Fasermaterialien und Bewehrungsgrade der TRC-Verstärkungsschicht untersucht und mit üblichen CFK-Sheet-Verstärkungen verglichen. Ein Berechnungsmodell für die Traglaststeigerung durch die TRC-Verstärkung wird vorgestellt.
... To the best of the writer's knowledge, a comprehensive study shows that the load carrying capacity of the wrapped RC columns is governed by the major influencing parameters such as the concrete compressive strength, the aspect ratio of the cross-sectional area of the specimens, the number of wrap layers, modulus and Poisson's ratio of the wrapping sheet, fiber orientation, longitudinal steel reinforcement ratio and their orientation, and the type of loading [6][7][8][9][10][11][12]. ...
In Kapitel 7 werden die Nachweiskonzepte im Grenzzustand der Tragfähigkeit (GZT) behandelt. Ausgehend von den Prinzipien des Sicherheitskonzepts werden zunächst die Herleitung von Bemessungswerten des Bauteilwiderstandes und von Teilsicherheitsbeiwerten für Bauteile aus Carbonbeton erläutert. Danach wird auf die Ermittlung der Robustheitsbewehrung zur Sicherstellung eines duktilen Bauteilverhaltens eingegangen. Den Kern des Kapitels bilden die Nachweise für Biegung mit Längskraft, Querkraft, Torsion, Durchstanzen und zur Stabilität. Bei den Nachweisen wird unterscheiden zwischen Bauteilen, die vollständig aus Carbonbeton hergestellt werden und Bauteilen aus Stahlbeton, die mit Carbonbeton verstärkt werden. Abschließend werden beispielhafte Bemessungshilfen für die Biegebemessung von Carbonbetonneubauteilen vorgestellt.
This current research scenario focuses on strengthening and rehabilitation of RC columns by CFRP and GFRP. The ongoing study reveals a new class of natural composites made of basalt fiber reinforced polymer (BFRP) bonded to concrete specimens with epoxy resin as an alternative confinement material. The experimental study was conducted for strengthening by partially and fully wrapped square RC columns using BFRP unidirectional and bidirectional. The behavior of stress-strain curves and failure modes was observed. The experimental results show a substantial increment in the ultimate load-displacement capacity and ultimate stress-ultimate axial and lateral strains of BFRP failure. The fully wrapped square reinforced concrete (RC) column gives a better stress-strain behavior and displacement limit than the partially covered system. However, the strengthening with partial wrapped with BFRP is a promising and economical alternative compared to the fully wrapped. The test results exhibit that the CNR-DT-R1 model is more reliable compare to the Lam-Teng model.KeywordsReinforced concreteRC columnCFRP and GFRPWrapping
A complete reorganization about the behavior of rectangular RC columns confined with FRP sheet is very important to predict the axial compressive strength values of the strengthened rectangular RC columns. That is because the process of strengthening RC rectangular column depending on several parameters that role this type of strengthening. These parameters include the characteristics of the used fiber, the grade of concrete and the geometry of the cross section including the rectangularity aspect ratio, corner radius, and size of specimens. Besides that, using a wide scope of experimental data may affect positively to generalize a model that considers the whole parameters affect the value of the axial strength. So, in this paper a review about parameters that affect the axial compressive strength values of rectangular RC columns was conducted. After that, based on the test results regarding FRP-confined rectangular RC columns available in the literature or conducted by the author, some existing confinement models for rectangular RC columns were assessed. Further, a new model is proposed through regression analysis of the database. A new model is proposed through regression analysis of the database. The proposed model was found to be in good agreement with the test results in the database. Finally, based on the results conclusions were drawn.
This paper investigates the crucial design parameters for the prediction of the ultimate axial compressive deformation of reinforced concrete columns externally confined with fiber reinforced polymer (FRP) materials. Numerous test results of available columns with a square and rectangular section under cyclic axial loading were gathered in an advanced database. Herein, the database is enriched with necessary design parameters in order to address the unique tensile strain field variation of the FRP jacket. Since there is a lack of consequent recording of the FRP strain field in existing experiments, three dimensional pseudodynamic finite element analyses results from several characteristic cases of tested columns are utilized to address this gap. Therefore, a hybrid experimental–analytical database is formed, including several critical FRP strains, steel strains and deformations. A modified model is proposed to predict the ultimate axial strain for reinforced concrete columns externally confined with FRP materials. The proposed model aims to address indirectly the effects of the internal steel cage, concrete section shape and of their interaction with the external FRP jacket on the critical tensile strain of the FRP jacket at failure of the column. The predictive performance of the model over the available tests of (reinforced concrete) RC columns under cyclic compression is remarkably improved when compared against the performance of other existing models. It provides predictions with average ratio (AR) of 0.96 and average absolute error (AAE) of 36.5% and therefore may contribute to safer seismic resistant redesign.
The compressive response of confined concrete greatly depends on the mechanical properties of the confining material. Based on these materials, various stress–strain models have been proposed in the past. Among these materials, the use of fiber reinforced–polymer (FRP) composites is now considered a promising solution to improve the overall behavior of confined concrete. New materials are being developed and used in seismic strengthening/retrofitting applications. Without experimental evidence, applicability of existing stress–strain models to new confining materials with different mechanical properties remains questionable. In this paper, existing stress–strain models which were mostly developed for steel and other FRPs with high elastic modulus and low rupture strain were assessed in predicting the ultimate condition of concrete confined by polyethylene terephthalate (PET) FRP, which is a newly developed material with low elastic modulus and large rupture strain (LRS). The ultimate strength was predicted well by some of these models; however, the ultimate strain could not be well predicted. Regarding the prediction of ultimate strain, some of those models which considered the axial strain capacity of FRP performed relatively better. Considering this discrepancy, a new simple stress–strain model is proposed for PET FRP–confined concrete, which not only considers the ultimate conditions but also the control points in the course of stress–strain path. Based on these control and ultimate points, stress–strain curves were generated using a well-known base curve. Finally, the proposed model was verified in predicting the ultimate condition of existing test data of PET FRP–confined concrete.
Use of fiber-reinforced polymers (FRPs) as internal confining reinforcement in combination with longitudinal steel bars in concrete compression members provides significantly improved strength, ductility, and durability. To date, only a few experimental studies have been carried out to establish the compressive behaviour of concrete columns longitudinally reinforced with steel bars and confined with FRP ties. This paper provides a confinement model with several expressions for predicting the axial stress-strain response of hybrid-reinforced (i.e. longitudinal steel bars combined with FRP ties) square concrete columns under axial compression loading. The model considers the influences of several test parameters such as configuration, size, volumetric ratio, spacing, and type of ties (pultruded FRP bar ties and close-type wound rectangular-sectioned ties). The proposed model well predicted the peak and ultimate strength and strains over existing models. The overall accuracy of the model was also assessed against selected test stress-strain responses.
The main objective of the research reported in this paper was to predict the effectiveness of carbon-fibre-reinforced-polymer composite wrapping on a prototype reinforced concrete column with a large aspect ratio and without any shape modification under combined loading. Six rectangular columns with aspect ratio greater than 2 were cast, strengthened with composite wrapping without chamfering the corners, and tested up to collapse under axial, lateral and combined axial and lateral loadings. The load–deflection behaviour, failure load, modes of failure, increase in capacity and post-peak behaviour were obtained. The test results demonstrated that the load-carrying capacity of composite-strengthened columns with aspect ratios greater than 2 was enhanced by 38, 27 and 29% under axial, lateral and combined axial and lateral loading, respectively compared with the corresponding control columns. The confining effect of the wrapping was achieved before the concrete reached its crushing strain.
The load carrying capacity of reinforced concrete columns (RC) shall be enhanced by providing lateral confinement using fiber reinforced polymer (FRP). As per ACI 440.2R-08 [1], external strengthening using FRP composites is more effective for circular columns than rectangular columns having an aspect ratio greater than 2.0. The main objective is to develop column interaction diagrams for RC rectangular columns having an aspect ratio greater than 2.0 externally strengthened using FRP composites without any shape modification and subjected to combined axial load (Pn) and bending moment (Mn) due to lateral loading. Tests are conducted and semi-empirical equations developed for FRP strengthened RC rectangular columns with large aspect ratio. Pn–Mn interactions diagrams are developed using the semi-empirical solutions and validated with 3D finite element analysis. The column interaction diagrams are developed by varying the unconfined compressive strength of concrete, yield strength of steel, percentage of steel reinforcement and thickness of FRP composite. These diagrams shall be used for the design of FRP strengthened RC rectangular columns with large aspect ratio.
Due to its efficiency, Fiber Reinforced Polymers (FRP) jacketing has become a common practice for confining concrete columns that need increased axial strength, axial ductility or shear capacities. The presence of confining lateral steel in columns, when externally retrofitted with FRP, changes the mechanism of concrete behavior. The interaction between lateral and longitudinal steel and FRP jacketing redistributes stress concentrations in concrete and yields more complex effective confined area compared to that of plain concrete confined with either FRP or lateral steel alone. Square columns confined with lateral steel and FRP are not well-addressed in the literature compared to circular columns. Therefore, this research focuses on square columns confined with lateral steel and FRP sheets through reviewing existing models in the literature and benchmarking their performance against experimental cases of square columns using axial stress-strain diagrams. Moreover, statistical analysis conducted for theoretical peak strength and ultimate strain obtained from the available models highlight their comparative performance which can be further improved. Therefore, this paper proposes a new model that overcomes shortcomings found in the reviewed models and predicts peak strength and ultimate strain more accurately.
Semi-empirical solutions are proposed to predict the axial and lateral capacities of reinforced concrete (RC) rectangular columns having aspect ratio greater than 2.0 strengthened using fiber reinforced polymer (FRP) composites without any shape modification and subjected to axial, lateral and combined axial and lateral loading. 3D finite element models are generated for the analysis of FRP strengthened RC columns. Semi-empirical solutions and finite element models are validated with the test results. Column interaction diagram between axial capacity Pn and bending moment Mn is generated using the proposed semi-empirical solutions and compared with Pn - Mn interaction diagram generated as per ACI 440.2R-08 [1] procedure. From this study, it is concluded that the proposed semi-empirical solutions shall be used for the design of RC rectangular columns having aspect ratio greater than 2.0 strengthened with FRP composites and without any shape modification.
Fibre-reinforced polymer (FRP) jacketing is an effective confinement tool for reinforced concrete (RC) columns. To avoid the excessive stress concentration in square-shaped columns, a jacketing technique with rounded column edges needs to be practiced. The load-carrying capacity of RC square short columns wrapped with glass FRP (GFRP) on axial loading was investigated. The efficiency of confinement offered by improved jacketing schemes with different corner radii of the column, number of layers of FRP and various vertical distribution methods of jacketing are compared. The experimental study was conducted on 31 columns of size 140 mm x 140 mm x 1200 mm with one, two and three layers of FRP distributed over one-fourth, one-third and full length of the column. The corner radii of the columns were 0,12.5, 25 and 37.5 mm. Specimens were loaded to the failure modes in concentric uniaxial compression, and the behaviour of the specimens was analysed. An analytical model for the ultimate load-carrying capacity of RC square columns confined by GFRP is proposed from the test results.
Concrete structures in marine areas frequently suffer from sulfate attack, which causes structural performance deterioration. External bonding of fiber reinforced polymer (FRP) is an effective method to improve the mechanical performance of these concrete structures. Thus, this paper presents a study of mechanical performance of FRP-confined sulfate-attacked concrete columns. An accelerated corrosion test by sulfate solution in a high-temperature dry–wet cycle was introduced to simulate the external sulfate corrosion environment. Thirty circular columns with a diameter of 150 mm and a height of 300 mm were subjected to sulfate exposure for a range of time periods and then confined with FRP jackets. All the columns were axially loaded to failure. Both the strength deterioration of the unconfined concrete after sulfate corrosion and the stress–strain relationship of the FRP-confined sulfate corroded concrete were recorded. Two damage indexes, i.e., the concrete strength deterioration rate and the rate of change in ultrasonic velocity of concrete, were carefully defined to quantitatively characterize the mechanical damage to the concrete due to sulfate attack. High correlation between these two damage indexes is detected and modeled. The effect of sulfate-induced damage on the ultimate strength, strain capacity, initial elastic modulus, and strain-hardening modulus of FRP confined concrete columns is quantified in terms of the two above damage indexes. On this base, a stress–strain relationship model is finally developed. A comparative analysis of the test results indicates that the model can provide reasonably accurate predictions. As the rate of change in ultrasonic velocity of concrete by sulfate attack can be measured easily using an ultrasonic non-destructive testing method, the proposed stress–strain relation model is of great significance to the design and life-cycle assessment of FRP strengthened sulfate-corroded concrete columns.
The purpose of this experimental investigation is to study the behavior of short columns produced from High Performance Concrete. In this investigation HPC was manufactured by usual ingredients such as cement, fine aggregate, coarse aggregate, water and mineral admixtures such as silica fume and fly ash at various replacement levels and the Super PIasticizer used was CERAPLAST-300. The water binder ratio (w/b) adopted is 0.30. The concrete used in this investigation was proportioned to target a mean strength of 60 MPa. Specimens such as cubes, cylinders and prism beams were cast and tested for various mixes viz. Seven mixes M1 to M7 are cast with 0%, 5%, 7.5% and 10% replacement of SF and another set of specimens with 0%, 5%, 7.5% and 10% replacement of SF along with 10% constant replacement of fly ash to study the mechanical properties such as compressive strength, split tensile strength and flexural strength at different ages of concrete such as 3,7,28,56 and 90 days. The result shows that the optimum replacement of silica fume is 7.5%. If 10% of fly ash is added the optimum replacement of silica fume is 5%. Totally 7 Columns were cast for mixes Ml to M7. The column specimens were tested in 1000 kN loading frame at 28 days. From this, Load - Mid height deflection (P -δ) curves were drawn and compared. The same failed columns were rehabilitated with GFRP sheets with one or two layers and again tested in 1000 kN loading frame. The results were then compared with the initial results.
The purpose of this experimental investigation is to study the behavior of short columns produced from High Performance Concrete (HPC). In this investigation HPC was manufactured by usual ingredients such as cement, fine aggregate, coarse aggregate, water and mineral admixtures such as Silica Fume (SF) and Fly ash at various replacement levels and the Super Plasticizer used was CERAPLAST-300. The water binder ratio (w/b) adopted is 0.30. The concrete used in this investigation was proportioned to target a mean strength of 60 MPa. Specimens such as cubes, cylinders and prism beams were cast and tested for various mixes viz. Seven mixes M1 to M7 are cast with 0%, 5%, 7.5% and 10% replacement of SF and another set of specimens with 0%, 5%, 7.5% and 10% replacement of SF along with 10% constant replacement of Fly ash to study the mechanical properties such as compressive strength, split tensile strength and flexural strength at different ages of concrete such as 3, 7, 28, 56 and 90 days. The result shows that the optimum replacement of silica fume is 7.5%. If 10% of Fly ash is added the optimum replacement of silica fume is 5%. Totally 7 columns were cast for mixes M1 to M7. The column specimens were tested in 1000kN loading frame at 28 days. From this, Load-Mid height deflection (P-Δ) curves were drawn and compared. The same failed columns were rehabilitated with GFRP sheets with one or two layers and again tested in 1000kN loading frame. The results were then compared with the initial results.
Fibre reinforced polymer composites have played a dominant role for a long time in a variety of applications for their high specific strength and modulus. Although glass and other synthetic fibre-reinforced plastics possess high specific strength, their fields of applications are very limited because of their inherent higher cost of production. In this connection, this project aims at using natural local fibres, which are abundantly available in India. Natural fibres are not only strong and lightweight but are relatively very cheap. In our present investigation we used jute as a natural fibre and E-Glass as glass fibre. Cementitious material known as FLOGROUT 60 was used for wrapping NFRP sheet, where as epoxy resin and hardener(Araldite AY 103 and HY 951 )were used for wrapping GFRP sheet. Cylinders and prisms were casted for finding the compressive strength, split tensile strength, modulus of elasticity and flexural strength. R.C Beams were also casted. The beams were strengthened by wrapping with Natural Fibre Reinforced Polymer composite(NFRP) and Glass Fibre Reinforced Polymer composite (GFRP) on tension side and along U-shaped and tested under static loading condition. The greatest advantage is the ultimate load carrying capacity is increased in case of beams with minimal addition of dead load to the structures. The test results indicate that there is a considerable increase in the ultimate load carrying capacity and reduced deformation due to confinement with NFRP and GFRP. Also the performance of beams wrapped with GFRP was slightly higher than the beams wrapped with NFRP.
This paper presents a new, efficient, and economic confinement technique for square reinforced concrete (RC) columns with unbonded glass fiber-reinforced polymer (GFRP) wrapping and lightweight concrete elements at the side faces. Three confined columns with different reinforcement ratios were tested under concentric axial force. The force-deformation responses show a distinctly increased load-carrying capacity at plastic deformations up to 4% average axial strain. This confinement technique is a considerable improvement for square columns with a large side-to-corner radius. Only a slight change in column geometry has to be accepted because of the use of unbonded lightweight concrete panels. DOI: 10.1061/(ASCE)CC.1943-5614.0000310. (C) 2012 American Society of Civil Engineers.
Although retrofitting and strengthening reinforced concrete (RC) columns by wrapping fiber reinforced polymer (FRP) composites have become a popular technique in civil engineering, the study on reinforced high-strength concrete (HSC) columns is still not sufficient. The objective of these companion papers is to investigate the mechanical properties of reinforced HSC square columns confined by aramid FRP (AFRP) jackets under concentric compressive loading. In the part I of these companion papers, an experiment was conducted on 54 confined RC specimens and nine unconfined plain specimens, the considered parameters were the concrete strength, the thickness of AFRP jackets, and the form of AFRP wrapping. The experimental process and results are presented in detail. Subsequently, some discussions on the confinement effect, failure modes, strength, and ductility of the columns are carried out.
In this investigation, the combined confinement effect of spacing of lateral ties, volume fraction of polyolefin fibres and fibre reinforced polymer(FRP) wraps was studied both experimentally and analytically from the point of deformability characteristics of concrete for seismic resistance. Low modulus synthetic fibers such as polyolefin based fibers, it is shown that polyolefin fibers with sufficient tensile strength can successfully enhance the mechanical properties of concrete. The mechanism of delaying and arresting the progressive internal cracking by the fibres can be made use in passive confinement of concrete. In this study the confinement effectiveness of GFRP wraps of single and double layer and polyolefin fibres of volume fractions 0.7% and 0.9% in addition to lateral ties of spacing 145mm and 75mm on concrete prisms of size 150 x150 x300 mm were investigated. Such concrete is termed as FRP confined fiber reinforced concrete (FRPCFRC). This paper presents an analytical model(profile) for predicting the constitutive behaviour of FRPCFRC based on the experimental and analytical results. A total of thirty nine prisms of size 150 x150 x300 mm were cast and tested under strain control rate of loading. The results of the testing demonstrate the behavioral differences between FRP confined concrete and FRP confined FRC and the ability of the synthetic macro fiber to be used as secondary reinforcement in performance based seismic resistance applications.
External confinement of concrete by means of high-strength fiber composites can significantly enhance its strength and ductility as well as result in large energy absorption capacity. The confinement mechanism may include fiber-wrapping of existing columns as a retrofitting measure or encasement of concrete in a fiber reinforced plastic (FRP) tube for new construction. Proper design of such hybrid columns, however, requires an accurate estimate of the performance enhancement. Current design methods use simple extension of the models developed for conventional reinforced concrete columns. Results from a series of uniaxial compression tests on concrete-filled FRP tubes are compared with the available confinement models in the literature. The present study indicates that these models generally result in overestimating the strength and unsafe design. The study also shows a unique characteristic of confinement with fiber composites in that, unlike steel, FRP curtails the dilation tendency of concrete, as it reverses the direction of volumetric strains. This paper provides a framework for better understanding of the behavior of fiber-wrapped or FRP-encased concrete columns.
An analytical method for evaluating the short-term axial load deformation behavior of rectangular and square reinforced compression members confined with glass fiber-reinforced polymer plates (GFRP) jackets and steel hoops is proposed in this paper. Three square and three rectangular columns were tested under axial tension/compression up to failure. The results clearly showed the efficiency of the jackets in enhancing the ultimate strain and strength of the columns. The jackets were also very effective in preventing longitudinal bar buckling from occurring. The analytical model was calibrated using data from the tests. Closed-form equations are proposed for evaluating the short-term load-deformation behavior of columns confined with FRP jackets.
Fibre reinforced composite materials are becoming more frequently used in civil engineering structures. One of the most practical applications of these new materials concerns the strengthening of reinforced concrete columns by means of confinement with fibre composite sheets. In the literature, various theoretical models have been proposed to describe the behaviour of confined concrete columns. These models can be grouped into three families: empirical, nonlinear elastic, and elastoplastic. The last two classes are considered in this paper. Comparisons of numerical predictions with experiments show that the nonlinear elastic approach is not very suitable for fibre composite confinement. The elastoplastic formulation gives predictions that agree quite well with experimentally determined axial load–deformation curves.
A stress‐strain model is developed for concrete subjected to uniaxial compressive loading and confined by transverse reinforcement. The concrete section may contain any general type of confining steel: either spiral or circular hoops; or rectangular hoops with or without supplementary cross ties. These cross ties can have either equal or unequal confining stresses along each of the transverse axes. A single equation is used for the stress‐strain equation. The model allows for cyclic loading and includes the effect of strain rate. The influence of various types of confinement is taken into account by defining an effective lateral confining stress, which is dependent on the configuration of the transverse and longitudinal reinforcement. An energy balance approach is used to predict the longitudinal compressive strain in the concrete corresponding to first fracture of the transverse reinforcement by equating the strain energy capacity of the transverse reinforcement to the strain energy stored in the concrete as a result of the confinement.
This paper presents results of testing eccentrically loaded columns externally wrapped with two types of materials. Six cylindrical (205 mm diameter and 925 mm height) plain columns were cast and tested. Half of the columns were wrapped with GFRP and the other half with CFRP. All columns were tested by applying an axial load at 50 mm eccentricity. In each group (GFRP or CFRP wrapped) of columns, one column did not have any vertical straps, one had vertical straps made of one layer of wrapping material and one column had vertical straps made of three layers of wrapping material. All columns were horizontally wrapped with three layers of material (GFRP or CFRP). A steel reinforced column was also cast and tested to serve as a reference column. Based on testing the columns it can be concluded that considerable gain in strength and ductility are obtained when reinforcing the columns with CFRP (vertical straps and horizontally wrapped).
Due to the aging of the infrastructures in the US, repair and rehabilitation of damaged steel reinforced concrete structures using fiber reinforced plastics (FRP) are increasingly becoming a topic of interest in the infrastructure community. In this study, a finite element analysis using ANSYS® was utilized to conduct a parametric analysis. Experiments were also conducted to justify the finite element analysis results. A reasonable agreement was found between the finite element analysis and the test results. The effect of the thickness, stiffness, and fiber orientation of the FRP layers as well as the interfacial bonding between the FRP wraps and the concrete on the strength and stiffness of the repaired columns was evaluated using the finite element modeling.
The results of an analytical study on the behaviour of reinforced concrete T-beams retrofitted with carbon fibre reinforced polymer (CFRP) plates for flexure and glass fibre reinforced polymer (GFRP) plates for shear are discussed in this paper. A test series comprising four 5 m long simply supported beams were tested under monotonic load to verify the analytical model. Particular emphasis was given to the performance of predicted model building upon discrete element analytical methodology incorporating the dual effects of flexure and shear in beams. The effects of curtailed longitudinal CFRP plates bonded to the soffit of test beams were also analysed to examine the prediction accuracy of the model. An important conclusion in this paper is that the predicted model can be used to accurately predict the behaviour of load versus displacement and FRP plate bond stresses.
Thus study has two parts. The first describes experiments and the second presents a model to accurately predict the compressive strength of concrete columns confined by composite materials. FRP is wrapped around concrete columns and RC columns to determine the difference between their behaviors under uniaxial compression. Experimental results indicate that the FRP confinements of the two specimen types are similar. Accordingly, a method for analyzing the behavior of an FRP-wrapped concrete column can be used also to analyze that of an FRP-wrapped RC column.When an RC column takes a uniaxial load, the concrete is first shear-fractured. Then, the steel is buckled and finally the FRP breaks. Confinement using FRP is a good ideal because FRP can be wrapped all around an RC column. Its stress–strain plot is bilinear.This study presents a theoretical stress–strain model. Some comparisons between experimental stress and the stress predicted using a model indicate that the present model is good to predict the fracture stress of FRP-wrapped concrete column.
An investigation on the performance of reinforced concrete beam-column joints under cyclic loading is reported. Joints have been cast with adequate and deficient bond of reinforcements at the beam-column joint. FRP sheets and strips have been applied on the joints in different configurations. The columns are subjected to an axial force while the beams are subjected to a cyclic load with controlled displacement. The amplitude of displacement is increased monotonically using a dynamic actuator. The hysteretic curves of the specimens have been plotted. The energy dissipation capacity of various FRP configurations has been compared. In addition, the control specimens have been reused after testing as damaged specimens that are candidates for rehabilitation. The rehabilitation has been carried out using FRP and their performance has been compared with that of the undamaged specimens.
The practical application of composite materials for retrofitting of reinforced concrete bridge T-sectional girders was investigated. Carbon and glass fibre-reinforced polymers (CFRP and GFRP) saturated in an epoxy resin matrix were used to enhance the service load-carrying capacity of the bridge. Three 5-m-long simply supported beams were tested under monotonic and cyclic loads for comparison to a beam subjected to more than 106 cycles in the service load range. The results show that an FRP-strengthened T-beam subjected to fatigue loading demonstrated excellent behaviour that can be expected from well-detailed retrofit schemes incorporating carbon and glass fibre laminates.
In this study, the performance of axially loaded, small-scale, and fiber-reinforced polymer (FRP) wrapped concrete columns with various wrap angle configurations, wrap thicknesses, and concrete strengths was investigated through nonlinear finite element analysis. Three different wrap thicknesses, wrap ply angle configurations of 0°, ±15°, and 0°/±15°/0° with respect to the circumferential direction, and concrete strength values ranging from 3 ksi to 6 ksi were considered. An existing experimental study on FRP-confined circular columns in the literature was utilized to validate numerical analysis models. The finite element analysis results showed substantial increase in the axial compressive strength and ductility of the FRP-confined concrete cylinders as compared to the unconfined cylinders. The increase in wrap thickness also resulted in enhancement of axial strength and ductility of the concrete columns. The gain in axial compressive strength in FRP-wrapped concrete columns was observed to be higher for lower strength concrete and the highest in the columns wrapped with the 0° ply angle configuration.
Introduction Axially Loaded Short Columns Eccentrically Loaded Short Columns with Uniaxial Bending Eccentrically Loaded Short Columns with Biaxial Bending Slender Columns References
Design manual for Tyfo fibrwrap system – Rev
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Design manual for Tyfo fibrwrap system - Rev. 1. California
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