Full-scale Reinforced Concrete Columns Research Articles

Repair, flexural upgrading and seismic retrofit of RC columns with reinforced FRCC light jacket

An innovative repair, flexural upgrading and seismic retrofit solution consisting of a reinforced light jacket (i.e., 3–4 cm) made of Fibre Reinforced Cement Composites, FRCC coupled with a High-Performance steel reinforcement is proposed for existing reinforced concrete (RC) columns. The proposed solution consists in a FRCC light jacketing coupled with a High-Performance steel reinforcement that works both as anchorage system for the jacket and as additional transverse reinforcement (Reinforced FRCC light jacketing or RFRCC). The goal of the solution is to improve the columns resistance against the migration of aggressive agents and at the same time to increase its flexural capacity. The potential of the proposed solution is demonstrated on 6 full-scale RC columns experimentally tested under quasi-static cyclic loading. The RC columns under investigation are subjected to a seismic pre-damage before the application of the RFRCC jacket. Square and rectangular columns with smooth and deformed rebars are tested to assess the feasibility of the technique for the repair and flexural strengthening of existing deficient RC columns. The experimental results attest the high potential of the proposed technique in recovering and enhancing the flexural capacity, ductility and energy dissipation of seismically pre-damaged RC columns.

Experimental research on seismic behaviors of RC columns considering buckling of HRB600 longitudinal steel bars

The inelastic buckling of longitudinal bars and premature fracture that followed can always be observed in laboratory research and earthquake damage of reinforced concrete (RC) columns. The buckling deformation and accompanied fracture of HRB600 high-strength steel bars are more significant than those of conventional reinforcing bars, but the buckling properties of HRB600 reinforcement and the influence of premature fracture on the seismic performance of RC columns are far from clear. In this paper, low cyclic loading tests were conducted on six full-scale RC columns reinforced with HRB600 reinforcement by changing the slenderness ratios of longitudinal bars and the axial compression ratios of columns, and the lateral buckling displacements of longitudinal bars were measured by an identified method. Based on the lateral buckling displacements, the buckling behaviors of longitudinal bars were analyzed. It shows that cover concrete has a significant constraint effect on preventing buckling of HRB600 reinforcement. The inelastic buckling behaviors and premature fracture of HRB600 bars on the ultimate deformation capacity and ductility of RC columns were investigated according to the lateral buckling displacements and ductility coefficient. It is found that the increase of the slenderness ratio would cause larger buckling displacements making the local plastic deformation concentration and low-cycle fatigue damage of HRB600 reinforcement more serious, resulting in the premature fracture of longitudinal bars and decrease of ductility of RC columns. Furthermore, a series of individual bars accompanied by the RC columns were tested. Based on the average stress–strain curves, the effects of yield strength and slenderness ratio were discussed. Former researches of conventional longitudinal bars were involved to form a comparison group with HRB600 bars. The results indicate that the deformation capacity reserves of HRB600 reinforcement after 85% peak load were significantly lower compared with conventional bars. It is suggested to limit the application of RC columns reinforced with HRB600 longitudinal bars in high seismic intensity areas and improve the limitation on the slenderness ratio of high-strength steel bars.

Cyclic behaviour of as-built and strengthened existing reinforced concrete columns previously damaged by fire

A structure, during its life, may be subjected to multiple hazards. These hazards are sometimes combined over a short period of time, or in some cases occur many years apart, with the first hazard influencing the structural response under a second hazard. A reinforced concrete (RC) structure previously damaged by fire and then exposed to seismic loading is one such example. To assess such structures, the effects of fire on the cyclic performance of RC elements needs to be better understood. Moreover, it is also important to develop and validate strengthening methods that can reinstate or improve the seismic performance of fire-damaged RC elements. This paper presents the results of a novel experimental campaign where six full-scale RC columns with detailing representing existing Mediterranean buildings designed to old seismic codes are subjected to fire and then cyclic loading. Four RC columns were damaged after exposure to 30 or 90 min of the ISO 834 standard fire curve in a furnace and then tested under uniaxial cyclic lateral loading up to failure. Two of these columns were repaired and strengthened post-fire with Carbon Fibre Reinforced Polymer (CFRP) wrapping. The strengthening method aimed to increase the concrete strength through confinement, and to increase the displacement ductility and energy dissipation capacity under seismic loading. Two additional control columns, one as-built and another strengthened, were cyclically tested for comparison with the fire-damaged columns. It was found that the 30 min fire exposure resulted in few concrete cracks, whilst cover spalling and general cracking was observed in the 90 min fire exposure. A significant decrease in the displacement ductility and dissipated energy of the columns was observed following fire exposure, even for the 30 min fire. The columns that had post-fire repair and CFRP strengthening, showed better cyclic performance than the control column without fire exposure. It was also found that post-fire strengthened columns may reach similar seismic performance than similarly strengthened columns without previous fire damage.

Seismic behaviour of full-scale lightly reinforced concrete columns under high axial loads

Failure of lightly reinforced concrete (RC) columns has been the primary cause of the seismic collapse of aged or under-designed structures. Moreover, the columns in medium to high-rise buildings are often subject to high axial compression, further increasing their seismic vulnerability. Many past studies experimentally investigated the seismic behavior of lightly RC columns based on scaled specimens with cross-sections less than 500 mm and subject to a low to moderate axial load ratio (ALR) of less than 0.3. However, the size effects are recognized to influence the RC column behavior significantly. This study aimed to provide new insights into the influence of critical conditions, including high ALR and light transverse reinforcement, on the seismic behavior of full-scale RC columns. Based on the test results of a series of full-scale columns under displacement reversals, the increase of ALR led to brittle failure modes with decreased displacement ductility, but the shear strength, stiffness, energy dissipation, and plastic hinge length could be enhanced. While the ALR adversely impacted the drift capacity of flexure-dominant columns, it had an insignificant influence on the drift capacity of flexural-shear- and shear-dominant columns. Furthermore, the ratios of the displacement components were slightly affected by the ALR but were dependent on the transverse reinforcement ratio. In addition to the experimental results, predictions by analytical/empirical models from design codes and the literature were presented and discussed. It was found that the ACI shear model became less conservative when the ALR of the column was increased from 0.1 to 0.58. Moreover, the influence of the displacement ductility and aspect ratio on the ratio of the experimental and predicted shear strengths of the tested full-scale columns generally followed the trend of the data of the thirty-two shear-critical columns collected from previous studies.

Seismic performance of PVA textile cementitious composites used as permanent formwork in full-scale circular RC columns

The strength, stiffness and ductility capacity of structural systems must be protected under seismic effects. In the presence of lateral reinforcement, the confinement effect provides these critical properties to reinforced concrete (RC) structures. Textile reinforced cementitious composites (TRCC) have very good tensile, flexural and long-term performance. The effect of confinement will occur in RC columns by using these multilayer composites as permanent formwork. In addition, thanks to the permanent formworks, the service life will be extended against the drawbacks of structural defects. In this study, TRCC circular permanent formworks were manufactured by using a newly developed PPR (Pull-Pour-Roll) technique and machine. A cementitious mortar was designed and 4 & 6 layers of PVA textile were selected for the production of composite permanent formworks. The most important feature of permanent formworks is that they are hollow, thin sectioned and three-dimensional structural elements. Four full-scale circular column specimens were tested in the laboratory under the combination of constant axial load and reversed cyclic lateral load. Two of the columns were constructed as permanent formwork, while others were reference specimens built by temporary formworks. Composite formwork columns and one of the reference specimens include insufficient lateral reinforcement whereas the other reference column has adequate lateral reinforcement. This study was conducted to evaluate the effects of TRCC permanent and conventional temporary formworks in RC columns on key parameters of confinement. These parameters are respectively the hysteretic response, strength, displacement ductility, stiffness degradation, energy absorption capacity, damping ratio, residual displacement, crack pattern and failure mechanism. Extensive experimental studies have shown that the lateral load capacities, ductility, initial stiffness and energy dissipation in composite formwork columns have increased considerably compared to conventional columns. Thus, the TRCC permanent formwork increases the efficiency of confinement. Consequently, there is a great potential for use of TRCC permanent formworks as an alternative for conventional formworks in the RC columns.

Axial test of full-scale columns strengthened with jacket section

This study examines the effect of different arrangements of transverse reinforcement in the jacket section on the axial performance of full-scale reinforced-concrete columns strengthened with a seismic section enlargement approach. For the jacket section with seismic details, overlapped channel-shape bars and prefabricated bar units were designed as the closed peripheral hoops, and V-ties or segmented cross-ties were used for the supplementary transverse reinforcement. For the compressive tests of full-scale strengthened columns with a 750 mm square section, a steel loading frame with a 40 000 kN capacity hydraulic jack was specially devised. Test results showed that the strengthened columns without supplementary V-ties in the jacket section possessed lower ductility capacity when compared with that of the existing non-seismic column. At the same level of transverse reinforcement index, the axial ductility ratio obtained from the present full-scale columns was typically lower than that compiled from the scaled-down column specimens with a square section of 200–300 mm. However, the strengthened column with prefabricated bar unit hoops including supplementary V-ties exhibited good ductility, which was comparable to the axial ductility ratios obtained in scaled-down columns, although a size effect potentially induced a more rapid decreasing rate at the descending branch of the stress–strain relationship of the concrete.

External steel ties and CFRP jacketing effects on seismic performance and failure mechanisms of substandard rectangular RC columns

One of the feasible retrofitting techniques for existing reinforced concrete (RC) structures is to use Fiber Reinforced Polymers (FRPs). On the other hand, the efficiency of the FRP jacketing strategy in rectangular RC columns is less than square and circular cross-section. For this purpose, the seismic retrofit of five full-scale substandard rectangular RC columns is evaluated both numerically and experimentally in terms of load–displacement performance, failure mechanism and autopsy after the test. Besides, the study introduces an enhanced strategy employing carbon fiber reinforced polymers (CFRPs) as well as external steel ties to retrofit the full-scale RC columns with rectangular cross-section loaded through the weak direction. The findings demonstrate that the CFRP jackets and external steel ties considerably usefulness in comparison to the used retrofitting strategy specifically concerning ductility and energy dissipation capacity. Regarding the analytical work, the non-elastic performance of the retrofitted and reference specimens was established by using realistic material models employing Seismostruct as a finite element platform. Lastly, the analytical forecasting carried out employing the FRP retrofitting design methods presented by the Turkish Seismic Design Code (TSDC), ACI 440.2R and Eurocode 8 Part 3 are compared with experimental results.

Seismic behavior of corroded reinforced concrete column joints under low-cyclic repeated loading

To investigate the influence of corroded steel bars on seismic performance of reinforced concrete (RC) columns, eight full-scale RC columns were designed and fabricated, which were composed of one uncorroded RC column, three RC columns with longitudinal reinforcement corrosion and four stirrup-corroded RC columns. The electrochemical test was conducted to accelerate the corrosion of steel bars in RC columns, and the low-cyclic repeated loading tests on RC columns with corrosion-damaged steel bars were carried out. The seismic behavior indicators, including the hysteretic curves, skeleton curves, displacement ductility coefficient, stiffness degradation curves and energy dissipation capacity of corroded RC columns and uncorroded columns, were compared and discussed. The experimental results show that with the increase in steel bars corrosion degree, the pinch phenomenon of the hysteretic curve gradually increases, and the energy dissipation capacity, stiffness and plastic deformation capacity of specimen reduce significantly. The ductility and energy dissipation coefficient decreased by 20% and 36%, respectively, when the stirrups corrosion ratio of specimen reaches 15.2%, and a shear failure surface was formed in the plastic hinge zone at the foot of the columns, which leads to the change of failure mode from ductile bending failure to shear failure with poor ductility under the ultimate load for corroded columns. The influence of stirrup corrosion on the failure mode of specimens is remarkable, but the effect of longitudinal reinforcement corrosion is negligible for specimens with the corrosion ratio within 14.7%. The adverse effects caused by over 15.2% stirrup corrosion should be considered in seismic design of structures in seismic zone.

Prediction of Seismic Performance Levels of Corroded Reinforced Concrete Columns as a Function of Crack Width

Abstract An experimental study was conducted for the prediction of the seismic performance levels of corroded reinforced concrete (RC) columns as a function of the initial corrosion crack widths. A full-scale accelerated-corrosion pool was used to corrode 25 full-scale RC columns. The initial crack widths at different levels of corrosion were measured for three different concrete strength levels: 9, 27, and 37 MPa. The seismic performance levels of corroded RC columns under combined cyclic lateral-displacement excursions at two different axial-load ratios (0.20 and 0.40) were measured. The corrosion levels obtained for the initially measured corrosion crack widths were used for establishing a correlation with the lateral-displacement capacities of the RC columns according to an energy-based method. Three empirical models were developed. The first was for predicting the cross-sectional area reduction of reinforcement bars according to the initial corrosion crack widths. The second model was for predicting the percentage of energy capacity of RC columns as a function of the drift ratio and corrosion levels. The third model was for predicting the seismic performance levels of RC columns as a function of the initial corrosion crack widths and was used for an in situ structural assessment. The experimental test results showed that above a 2% drift ratio, all uncorroded RC columns (regardless of the concrete strength levels) exhibited a sudden reduction in energy capacity, and their total energy capacity was consumed. In the case of corrosion, the energy capacity of concrete with high strength levels was prematurely exhausted above a 1.4% drift ratio because of the effects of the corrosion products under the high strength levels of the concrete.

Investigation of Structural Behavior of Full-Scale Reinforced Concrete Columns Subjected to Corrosion under Monotonic Loading Effect: Suggestions for Corrosion Studies

Korozyona maruz kalmış betonarme yapıların sismik performanslarının tahmin edilmesi korozyona uğramamış yapılara göre daha zordur. Gerçekleştirilen bu deneysel çalışma ile birlikte korozyona maruz kalmış betonarme elemanları üzerine yapılacak olan çalışmalara ışık tutulması amaçlanmıştır. Beş adet tam ölçekli betonarme kolonu hızlandırılmış korozyon yöntemi kullanılarak farklı korozyon oranları için paslandırılmıştır. Paslandırılmış betonarme kolonları sabit eksenel yük altında monotonik yüklemeye tabi tutularak, akma ve nihai yükleri, süneklik oranları ve enerji yutma kapasiteleri deneysel olarak elde edilmiştir. Betonarme kolonlarındaki gerçek korozyon oranları yükleme deneylerinden sonra betonarme kolonlarının kırılarak ve gömülü olan tüm betonarme donatılarının çıkartılması ile elde edilmiştir. Yapılan deneysel çalışma sonucunda, monotonik yüklemenin tersinir-tekrarlanır yüklemeye göre zayıf yönleri göz önüne alınan deprem indeksleri açısından değerlendirilmiştir. Elde edilen deneysel sonuçlar doğrultusunda ileriki korozyon çalışmaları için önemli önerilerde bulunulmuştur. Gerçekleştirilen bu çalışma kapsamında, paslanmış betonarme kolonlarının monotonik yükleme etkisi altında süneklik oranları ve enerji yutma kapasiteleri artan korozyon oranına bağlı olarak azalmıştır. Monotonik yükleme etkisi altında pasın belirli oranlarına kadar sağlamış olduğu sargı etkisi ve buna bağlı olarak deprem indekslerindeki artışlar net bir şekilde görülememiştir. Tek doğrultuda göçme modu kabulü ile yapılacak olan sismik değerlendirmelerde kullanılmak üzere paslanmış betonarme kolonların süneklik ve enerji yutma kapasitelerinin tahmin edilebilmesi için iki ampirik model geliştirilmiştir.

Seismic behavior of strengthened square reinforced concrete columns under combined loadings

This paper presents an experimental study examining the seismic behavior of square reinforced concrete (RC) columns subjected to combined loadings. In this study, nine full-scale square RC columns were made with the same structural properties. Five of them were strengthened with high-performance ferrocement laminate and bonded steel plates in order to investigate the effects of strengthening on the seismic behavior of RC columns under combined loadings. Finally, the failure mode, hysteretic load-displacement response, bearing capacity, energy dissipation, ductility and plastic hinge characteristics were recorded and analyzed. The results show that combined loadings reduced the bearing capacity and changed the failure modes and deformation characteristics. Strengthened RC columns had significantly improved bearing capacity and different failure modes under the same combined loadings in contrast to the non-strengthened RC columns. The vertical eccentricity had little effect on the mechanical properties of columns, while the horizontal eccentricity significantly weakened the mechanical properties of columns. The mechanical properties of uniaxial compression-bending-shear-torsion columns were the worst. The tri-linear model calculation parameters under different failure modes and combined loadings were fixed and validated by experimental results.

Comparative Analysis of Existing RC Columns Jacketed with CFRP or FRCC.

Reinforced concrete (RC) columns typical of existing structures often exhibit premature failures during seismic events (i.e., longitudinal bars buckling and shear interaction mechanisms) due to the poor quality concrete and the absence of proper seismic details in the potential plastic hinge region. The Fiber Reinforced Polymers (FRP) externally bonded reinforcement is known to be a valid technique to improve the shear capacity or the ductility of existing RC columns. However, few experimental tests have proven its effectiveness in the case of columns affected by shear interaction mechanisms. In this work, the behavior of existing RC columns with border line behavior between flexure and shear have been investigated in the case of poor quality concrete and light FRP strengthening with local jacketing and medium quality concrete and strong FRP strengthening with local jacketing, in order to highlight the effect of concrete strength on the effectiveness of the retrofit intervention. As an alternative to FRP jacketing; the effectiveness of the Fiber Reinforced Cementitious Composite (FRCC) jacketing for the seismic strengthening of columns with highly deteriorated concrete cover or columns already damaged by an earthquake is also evaluated. Six full-scale RC columns have been tested under cyclic loading: one was used as a control specimen; four were strengthened in the potential plastic hinge region with carbon FRP (CFRP); and one was fully jacketed with FRCC. The comparison between poor and medium quality concrete columns showed that the CFRP local jacketing is more effective in the case of poor quality concrete. The FRCC jacketing appears to be a sound repair strategy and a suitable alternative to the FRP jacketing in case of poor quality; however, more experimental research is needed for improving this retrofit technique.

Eccentric Behavior of Full-Scale Reinforced Concrete Columns with Glass Fiber-Reinforced Polymer Bars and Ties

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A Highly Accurate Algorithm for Nonlinear Numerical Simulation of RC Columns Under Biaxial Bending Moment and Axial Loading Applying Rotary Oblique Fiber-Element Discretization

A highly accurate nonlinear analytical algorithm to simulate the behavior of reinforced concrete (RC) columns under monotonic biaxial bending moment and axial loading is proposed. In the proposed algorithm, the nonlinear behavior of confined and unconfined concrete elements as well as steel elements is considered, and the column is discretized into two macro-elements located between the pseudo-plastic hinges at critical sections and the inflection point. The critical sections of the column are discretized into a number of rotary oblique fiber elements (ROFEs) and the neutral axis (N.A.) position of each section in each step of loading is searched automatically using a proposed “4-rotations and 2-translations” search model. The ROFEs remain always parallel to the N.A. of the sections and make a uniform stress distribution along each ROFE in each section. Consequently, the variations of stress across each fiber are quite small which increase the accuracy of the calculation, while the number of elements (fibers) is relatively small compared to those of the fixed rectangular finite element (FRFE). This research shows that there is a better agreement between the simulated results using ROFE discretization and experimental results performed in the full-scale RC columns than when the FRFE discretization model is employed. The application of the component effect combination method is also compared with the proposed simultaneous direct method.

Global and Local Cumulative Damage Models for Reinforced Concrete Structures Subjected to Monotonic, Cyclic, or Fatigue Loading

This paper deals with both global and local versions of an energetic analytical model to quantify the damage caused to reinforced concrete (RC) structures under monotonic, cyclic, or fatigue loading. The proposed model closely represents the damage to structures, and presents a damage index (DI) formulation for the RC members. The model is based on the cumulative energy absorbed by the structure. The data required to apply the model can be obtained either from numerical simulation or from experimental test. A computer program has been developed to simulate numerically the response of RC members under cyclic loading. In the program, the non-linear behavior of the materials and the structure involved are taken into account. The proposed numerical simulation model was verified by comparison with practical tests undertaken by other researchers on over 20 full-scale RC columns. The comparison demonstrates that the model provides a realistic estimation of the damage of the RC structural members. The comparison between values of the proposed DI calculated based on experimental test data and numerical simulation results shows that to calculate DI, it is not necessary to perform expensive experimental tests, employing a non-linear structural numerical simulation program is sufficient. The proposed DI is also compared to a damage model proposed by Meyer.

Experimental Performance Assessment of Nearly Full-Scale Reinforced Concrete Columns with Partially Debonded Longitudinal Reinforcement

AbstractThis paper presents an experimental study investigating the effect of partial debonding of longitudinal reinforcement at the location of the plastic hinge on the performance of reinforced c...

Nonlinear Numerical Simulation of Reinforced Concrete Columns Under Cyclic Biaxial Bending Moment and Axial Loading

A nonlinear finite element algorithm is proposed to analyze the reinforced concrete (RC) columns subjected to cyclic biaxial bending moment and axial loading. In the proposed algorithm, the following parameters are considered: uniaxial behavior of concrete and steel elements, the pseudo-plastic hinge produced in the critical sections, and global behavior of the columns. In the proposed numerical simulation, the column is discretized into two macro-elements located between the pseudo-plastic hinges at critical sections and the inflection point. The critical sections are discretized into fixed rectangular finite elements. The basic equilibrium is justified over a critical hypothetical cross section assuming the kinematics Navier’s hypothesis with an average curvature. The method used qualifies as a “strain plane control process” that requires the resolution of a quasi-static simultaneous equation system using a triple iteration process over the strains in each section. To reach equilibrium, three main strain parameters (the strains in the extreme compressive point, the strains in the extreme tensile point and the strains in another corner of the section) are used as the three main variables. The proposed algorithm has been validated by the results of tests carried out on full-scale RC columns. The application of the components effects combination method is also compared with the proposed simultaneous direct method. The results obtained show the necessity of applying SDM for the post-elastic phase, which occurs frequently during earthquake loading.

Nonlinear numerical simulation of RC columns subjected to cyclic oriented lateral force and axial loading

A nonlinear Finite Element (FE) algorithm is proposed to analyze the Reinforced Concrete (RC) columns subjected to Cyclic Loading (CL), Cyclic Oriented Lateral Force and Axial Loading (COLFAL), Monotonic Loading (ML) or Oriented Pushover Force and Axial Loading (OPFAL) in any direction. In the proposed algorithm, the following parameters are considered: uniaxial behavior of concrete and steel elements, the pseudo-plastic hinge produced in the critical sections, and global behavior of RC columns. In the proposed numerical simulation, the column is discretized into two Macro-Elements (ME) located between the pseudo-plastic hinges at critical sections and the inflection point. The critical sections are discretized into Fixed Rectangular Finite Elements (FRFE) in general cases of CL, COLFAL or ML and are discretized into Variable Oblique Finite Elements (VOFE) in the particular cases of ML or OPFAL. For pushover particular case, a fairly fast converging and properly accurate nonlinear simulation method is proposed to assess the behavior of RC columns. The proposed algorithm has been validated by the results of tests carried out on full-scale RC columns.

Experimental Research on Full-Scale Reinforced Concrete Columns with Strong Confinement under Concentric Compression

To investigate the axial compressive behavior of reinforced concrete columns with strong confinement, a total of five full-scale reinforced concrete columns with stirrup characteristic values in the range 0.22~0.47 and section dimension 600mm×600mm were tested under concentric compression loading. The test results indicated that all specimens failed in a similar way. The longitudinal bars buckled in compression; the peripheral stirrups bowed out and several stirrups fractured; the cover concrete in the mid-height section of specimens spalled seriously; however, the core concrete of specimens was not crushed. The axial compressive bearing capacity and deformation ability of reinforced concrete columns could be improved by strong confinement. When specimens reached the ultimate bearing capacity, the longitudinal reinforcement yielded and provided axial bearing capacity for specimens; the transverse reinforcement reached tensile yield strength and provided effective confinement for the core concrete.

Bond Strength of Lap-Spliced Bars in Concrete Confined with Composite Jackets

The effectiveness of fiber-reinforced polymer (FRP) and textile-reinforced mortar (TRM) jackets was investigated experimentally and analytically in this study to confine old-type reinforced concrete (RC) columns with limited capacity because of bond failure at lap-splice regions. The local bond strength between lap-spliced bars and concrete was measured experimentally along the lap-splice region of six full-scale RC columns subjected to cyclic uniaxial flexure under constant axial load. The bond strength of the two column specimens tested without retrofitting was found to be in good agreement with the predictions given by two existing bond models. These models were modified to account for the contribution of composite material jacketing to the bond resistance between lap-spliced bars and concrete. The effectiveness of FRP and TRM jackets against splitting at lap splices was quantified as a function of jacket properties and geometry as well as in terms of the jacket effective strain, which was found to depend on the ratio of lap-splice length to bar diameter. Consequently, simple equations for calculating the bond strength of lap splices in members confined with composite materials (FRP or TRM) are proposed.