Continuously Reinforced Concrete Research Articles

Moment redistribution in continuous reinforced concrete beams: Experimental study and analytical investigation

This paper presents the results of experimental and analytical studies carried out on continuous reinforced concrete (RC) beams to determine moment redistribution in statically indeterminate RC structures. For this purpose, continuous RC beams were produced with varying tensile reinforcement ratio at the intermediate support, which are shown as the parameters that affect moment redistribution the most in the literature. One of the main goals of this study is to check if the formulations in the design code provisions and in the literature give a safe estimate, and in order to perform this check, a dataset consisting of the experimental results of 141 beams in the literature has been used for validation and the moment redistribution ratios of this dataset have been estimated with all these formulations. The obtained results have been compared using various statistical indices such as the mean value (MV), standard deviation (SD), coefficient of variation (COV), the root mean square error (RMSE), mean absolute percentage error (MAPE). In particular, the formulations in the literature that take into account many parameters affecting the moment redistribution have been found to give better results than the formulations in the design code provisions. The results of this study confirm that elastic moment redistribution, which occurs in the process from the moment when the concrete cracks until the tensile reinforcement yields and constitutes a significant part of the total moment redistribution, is also important. Moreover, the properties of continuous RC beams related to their general behaviors, such as load-displacement relationships, ductility and moment-curvature relationships have been also investigated in detail.

Restoration of two-span RC beams with severely corroded reinforcement using C-FRCM composites

The feasibility and viability of using carbon fabric-reinforced cementitious matrix (C-FRCM) composites for restoration of continuous reinforced concrete (RC) beams with severely corroded reinforcement were examined. Five large-scale dual-span RC beams were fabricated and tested. One beam was not corroded to serve as a control. Four beams were subjected to accelerated corrosion that corresponded to a tensile steel cross-sectional loss of 40% in either the sagging or the hogging region. Such a steel cross-sectional loss would cause a comparable reduction in the yield load of bare steel reinforcing bars. Two of the corroded beams were repaired with C-FRCM composites. An analytical model was formulated and utilized to design the number of C-FRCM layers required to fully restore the original load capacity. Experimental results verified the redistribution of moments between the sagging and hogging regions due to yielding of the tensile steel at critical sections. Both sagging and hogging sections contributed to the load-bearing capacity, and hence, the reduction in the load capacity caused by corrosion in one of the critical sections was smaller than the tension steel cross-sectional loss caused by corrosion. It was possible to predict the load capacity of the tested beams with reasonable accuracy considering the residual cross-sectional area of the corroded tension steel bars while keeping their yield strength and Young’s modulus unaltered in addition to implementing other conventional assumptions adopted by international codes and guidelines. As predicted analytically and verified experimentally, rehabilitation of corroded continuous beams with appropriate number of C-FRCM composite layers fully restored their original load capacity. Research findings would assist practitioners in conducting a proper analysis of continuous RC beams with corroded reinforcement before and after repair with C-FRCM composites.

GFRP continuous RC beams having web openings and externally strengthened with CFRP composites

With the enormous development of modern buildings, it is highly required to accommodate web openings in continuous reinforced concrete (RC) beams for passing utility service equipment. A wide range of studies had been conducted with regard to this subject. wtCurrent study examined numerically the major effect of the large rectangular web openings in (GFRP) reinforced concrete continuous beams under concentrated loads. Moreover, it investigated the effects of different CFRP strengthening schemes that would retrieve the ultimate capacity of the solid beam. Based on that, the main parameters that had been utilized here are the opening size, opening location and the strengthening scheme. Results showed that openings reduced the ultimate load capacity of the beams and increased the overall deflections. Furthermore, using CFRP sheets to strengthen continuous RC beams including opening retrieved (70%) of the ultimate capacity of continuous RC solid beams especially beams with openings near the external support or midspan. Likewise, using CFRP composites retrieved (48%) of the ultimate capacity of continuous RC solid beams with openings near the interior support. Furthermore, the optimum location for constructing web openings was near the external supports, which was subjected to the lowest values of shear forces and sagging moments and leaded to accommodate greater ultimate loads (85.18 kN) than other beams of other openings location.

Rational prediction of moment redistribution in continuous concrete beams reinforced with FRP bars

In continuous fiber reinforced polymer (FRP) reinforced concrete (RC) beams, moment redistribution is typically not allowed in the design owing to the lack of ductility of FRP bars. However, this simplification cannot be justified as moment redistribution depends primarily upon the difference in stiffness along the beam length. This study aims at improving the current state-of-the-art redistribution quantification in continuous FRP RC beams. Redistribution behavior against neutral axis depth (c/d) of continuous FRP RC beams are numerically assessed, focusing on the impact of ρr1/ρr2 (ρr1, ρr2= tensile reinforcement ratios at positive, negative moment zones). It is shown that continuous FRP RC beams may experience marked positive or negative redistribution of moments, depending on ρr1/ρr2. However, the importance of ρr1/ρr2 is neglected in c/d-based code models (EC2, BSI and CSA). A modified BSI model is proposed to estimate the moment redistribution in continuous FRP RC beams. By introducing ρr1/ρr2, the proposed simplified model accounts for the structural characteristic and demonstrates a rational prediction of moment redistribution in these beams.

AC layer fatigue damage analysis and reflective cracking control of CRC + AC composite pavement

The current continuous reinforced concrete composite asphalt pavement (CRC + AC) design method in China does not consider the effect of the asphalt concrete (AC) layer on the longitudinal reinforcement rate of the continuous reinforced concrete (CRC) layer. To address such issues, a finite element model of CRC + AC using continuum damage mechanics theory and finite element method was established. The most unfavorable working condition and the location of the greatest damage by comparing the damage distribution under different working conditions were determined. To resolve the limitations of traditional design methods of CRC + AC composite pavement, criteria for the microcrack width of the CRC layer under different AC layer thicknesses were proposed, based on the combined effects of AC layer thickness and CRC layer microcrack width on the damage of the AC layer. The results suggest that the left lane vehicles braking and the right lane vehicles driving at a constant speed are the most unfavorable working conditions, with the greatest degree of damage found on the lane divider of AC layer. meanwhile, the microcrack width should be below 0.64 mm to mitigate the risk of Top-Down cracking and reflective cracking. Additionally, the CRC plate crack width control standards are provided for AC layer thicknesses ranging from 4 cm to 14 cm.

Partially restrained seismic isolation system to retrofit a continuous girder RC bridge

The present paper proposes a partially restrained seismic isolation (PRSI) system to retrofit existing continuous girder reinforced concrete (RC) bridges. It involves a pure-friction system with a self-centring force provided by the stiffness of the deck and the frictional forces generated at the area of contact acting as an energy dissipation mechanism. The advantage is that the very small height of the system allows its application to existing bridges. The dynamic response until the collapse of an existing bridge subjected to seismic accelerations was assessed through a detailed 3D numerical model. This numerical model employed an explicit integration scheme that avoids numerical convergence drawbacks as a result of the strength and stiffness degradation of concrete structures. It was able to identify collapse mechanisms such as the development of cracks in the concrete elements. The seismic response of the original bridge was compared with that resulting from structural rehabilitation through implementation of a P-F type isolator in combination with the PRSI technique, which provided the system with a restitutive mechanism minimizing residual deformations. In addition, a classic structural reinforcement was incorporated by means of steel jacketing of the column. Both structural rehabilitation strategies were compared under the same seismic actions, assessing their efficiency and highlighting their benefits.

Moment redistribution capacity of continuous RC beams with High-Strength steel reinforcement

Moment redistribution (MR), a nonlinear behavior occurring in continuous reinforced concrete (RC) beams, is related to the redistributed section's ductility and the stiffness distribution along the whole beam. The use of high-strength steel (HSS) reinforcement could affect the redistributed section’s ductility and can delay or even prevent the formation of plastic hinge after another. The lack of research regarding the influence of those phenomena on MR is one of the reasons that hinder design engineers from using HSS. This paper conducts a broad-range parametric study through finite element (FE) method to check if the design provisions on MR are still applicable to beams with HSS reinforcement of yield strength of more than 600 MPa. The critical sections' yield state (whether the plastic hinge is formed) at the ultimate limit state (ULS) and its influences on MR are investigated. The study demonstrations that the MR capacity decreases with the increase in yield strength of reinforcement, especially when the midspan section cannot yield at ULS due to the use of HSS reinforcement. Besides, the yield state is influenced by the coupling effect of multi-parameters and significantly affects the influence degree of each parameter on MR. A new method considering the yield state is proposed to estimate the MR capacity of the continuous beams. This method's reasonable accuracy is proved. It is recommended to reduce the specified MR by about 6% for every 100 MPa increase in yield strength of reinforcement.

An Efficient Method for Optimizing HPC-FRP Retrofit Systems of Flexural Strengthened One-Way Continuous Slabs Based on ACI 440.2R.

An innovative retrofit system consisting of fiber-reinforced polymers (FRP) and high-performance concrete (HPC) considering the difficulty of the accessibility and installation of FRP on the underside of reinforced concrete (RC) slabs was found to be efficient in the flexural strengthening of existing RC slabs. It is important to note that continuous slabs using the FRP-HPC retrofit systems are less effective in exploiting FRP tensile strength and can cause sudden failure once excessively enhanced flexural strength exceeds shear strength. A design method to ensure ductile failure mode was also proposed for strengthened continuous RC slabs in the previous literature. Thus, it is necessary to optimize retrofit systems in terms of mechanical performance aspects to improve the efficiency of retrofitted slabs in serviceability. This study proposes a design method for optimizing the strength of materials and inducing ductile failure of continuous slab retrofitting FRP-HPC systems. The proposed approach demonstrated its effectiveness for strengthening a continuous RC slab with various FRP-HPC retrofit systems through a case study. The results show that the design factored load in the serviceability limit state does not change appreciably from a decrease in carbon fiber-reinforced polymers (CFRP) of 38%; the design factored load decreased only by 9% and the ultimate failure load by 13% while reducing CFRP by 20% and HPC by 25%.

Flexural Behavior of Two-Span Continuous CFRP RC Beams.

This paper investigates the feasibility of replacing steel bars with carbon-fiber-reinforced polymer (CFRP) bars in continuous reinforced concrete (RC) beams. A numerical model is introduced. Model predictions are compared with the experimental results that are available in the literature. A comprehensive numerical investigation is then performed on two-span CFRP/steel RC beams with ρb2 = 0.61–3.03% and ρb1/ρb2 = 1.5, where ρb1 and ρb2 are tensile bar ratios (ratios of tensile bar area to effective cross-sectional area of beams) over positive and negative moment regions, respectively. The study shows that replacing steel bars with CFRP bars greatly improves the crack mode at a low bar ratio. The ultimate load of CFRP RC beams is 89% higher at ρb2 = 0.61% but 7.2% lower at ρb2 = 3.03% than that of steel RC beams. In addition, CFRP RC beams exhibit around 13% greater ultimate deflection compared to steel RC beams. The difference of moment redistribution between CFRP and steel RC beams diminishes as ρb2 increases. ACI 318-19 appears to be conservative, and it leads to more accurate predictions of moment redistribution in CFRP RC beams than that in steel RC beams.

Numerical Analysis of Reflective Cracking of Continuous Reinforced Composite Pavement under Multifactor Coupling

The occurrence and expansion of reflective cracking is a typical problem associated with the composite pavement that has a proven impact on the life of the continuous reinforced composite pavement. The current research studies a 3D finite element model to preset cracks at the top of the continuously reinforced concrete (CRC) layer’s transverse crack and at the bottom of the asphalt concrete (AC) layer based on the theory of linear elastic fracture mechanics in order to explore the factors responsible for the reflective cracking formation mechanism and expansion law. Considering the main stress parameters that affect the formation of reflective cracking (layer bottom tensile stress and vertical shear stress), the most unfavorable load position and the most unfavorable point of the corresponding stress parameter are determined that are then used to calculate the stress intensity factor of the crack tip under the coupling effect of multiple factors based upon the position and point above the crack, by using the confinement integral. The variance analysis of the stress intensity factor of the crack tip under the multifactor coupling effect is conducted via an orthogonal test in order to determine the main factors affecting the formation and development of reflective cracking. Meanwhile, the analysis of single-factor sensitivity is carried out on all these factors, which reveal the real contribution in the formation and expansion of reflective cracking in the continuous reinforced composite pavement. The results show that the most unfavorable load position for reflective cracking is when the load is on the side of the CRC layer’s lateral crack, while the most unfavorable point of the stress parameter is concentrated within the range of the wheel track. At the same time, analysis of multifactor variance and that of single-factor sensitivity show that the cracking mode of reflective cracking in the continuous reinforced composite pavement is a mixed one, dominated by K2 (slip type), supplemented by K1 (open type), and participated by K3 (tear type), whereas the AC layer’s preset-crack depth ratio, instantaneous temperature drop, and CRC-transverse-crack load transfer capacity are the main factors that affect the formation and development of the reflective cracking. Moreover, a better bonding state between the AC layer and the CRC layer improves the stress intensity factor of the preset crack tip on the bottom of the AC layer.

Maximum Likelihood Estimation of Parameters for Advanced Continuously Reinforced Concrete Pavement (CRCP) Punchout Calibration Model

Pavement performance prediction is the essential part of the pavement design, which is very important for highway agencies for the purpose of budget allocating. This study introduces a model of local calibration for punchout, which is the major structural distress of continuously reinforced concrete pavement (CRCP). It is assumed that the number of equivalent single axle loads’ (ESALs) leads to punchout follows a Weibull distribution. The parameters of Weibull distribution were estimated by maximum likelihood estimation (MLE). Additionally, an approach of estimating the initial value of the parameters was also presented before applying the Newton method for solving the likelihood equations. The regression result was found to fit the performance-monitoring data from LTPP very well. The proposed calibration model is capable of describing the punchout and can be employed to predict the failure rate and reliability of CRCP in the pavement design and the arrangement of rehabilitation activities.

Efficiency of EB CFRP composites for flexural strengthening of continuous RC beams: A comparative study with NSM CFRP rods

This paper presents an experimental study of the use of carbon fiber-reinforced polymer (CFRP) composites to strengthen two-span reinforced concrete (RC) beams. Six large-scale beams were strengthened in hogging and sagging regions according to the external bonding (EB) technique and then statically tested to investigate the impact of the CFRP position , CFRP form , CFRP layers , and weight of carbon fibers on the flexural performance of continuous beams. The experimental results of the strengthened beams were carefully studied in terms of load-carrying capacity, failure modes, cracking patterns, moment redistribution, and reinforcement strain and compared with the results of an unstrengthened control beam. The efficiency of the EB technique in strengthening continuous RC beams was assessed through a comparative study with the near surface mounted (NSM) technique. For this purpose, another two beam specimens strengthened with NSM-CFRP bars were considered.Based on the experimental results, a general improvement in the flexural performance of strengthened beams was observed. By applying the EB-CFRP composites, the yield and ultimate load capacity could be improved up to 59.1% and 49.8% respectively. . The results also showed that increasing the carbon fiber weight was found to be effective in improving the strength capacity of beams and it may use as an alternative to multiple sheet layers… Comparisons regarding the global flexural performance allow confirming the higher efficiency of the NSM system in comparison to the EB one.

Numerical analysis of the shear behavior of FRP-strengthened continuous RC beams having web openings

Web openings are usually constructed in continuous reinforced concrete (RC) beams to accommodate the utility pipes and cables. This paper investigates numerically shear strengthening of continuous RC beams having web openings with FRP layers. The finite element analysis software ABAQUS/standard was used to construct non-linear finite element model (FEM) to analyze continuous RC beams having web openings strengthened with different schemes of fiber reinforced polymers (FRP) layers. The FEM was verified using the available experimental studies of both FRP-strengthened simply supported and continuous RC beams with/without openings found in literature before conducting the numerical investigation. The numerical investigation was carried out using the validated numerical FEM to investigate the impacts of crucial parameters such as opening location, opening area and strengthening configuration on the shear behavior of continuous RC beams strengthened with FRP layers. Three different locations were suggested along the length of the RC beam to construct the web openings. On the other hand, the effects of five different opening area on the load capacity and failure patterns were investigated. Moreover, two different FRP strengthening configurations were considered either strengthening above and below the opening or strengthening the whole RC beam height. Results showed that continuous RC beams containing openings at zone II group was the most affected among analyzed locations. The reduction in load capacities of this group ranged from 7.3 to 66.1% compared to the solid beam. The ultimate loads of specimens strengthened over the whole RC beam height exhibited the highest values among analyzed specimens.

Flexural capacity of continuous reinforced concrete beams strengthened or repaired by CFRP/GFRP sheets

The flexural strengthening of reinforced concrete (RC) beams by bonding external composite materials has proved to be an effective and convenient technique. Several works, focus on mechanical behaviour of continuous reinforced concrete beam with two spans strengthened by composite materials, were reported in literature. This paper presents the flexural capacity of continuous RC beams with three spans strengthened or repaired by bonding carbon or glass fibre reinforced polymer (CFRP or GFRP) sheets. Experimental program consists of eight continuous RC beams strengthened by CFRP or GFRP sheets and one beam of reference. The dimension is the same for all beams with a length 9 m and a section 15x25 (cm). Experimental tests with monotonic loading were carried out by varying damaged level of the beams, composite material type and strengthening thickness. Five failure modes of strengthening beams were observed. The results show that the ultimate bending moment of the beam can be improved between 14.8 and 26.6% in case of the beams by bonding CFRP sheets and between 7.2 and 11.8% by bonding GFRP sheets. The beam, which was pre-damaged under pre-loading level 100% of the failure load, can be repaired as strengthened continuous RC beam. The optimal strengthening thickness in the positive and negative bending moment region was obtained. The variation of the strain in the positive and negative bending moment was analysed.

Assessment of California’s Continuously Reinforced Concrete Pavement Practice and Performance

Around 2009, the California Department of Transportation (Caltrans) adopted continuously reinforced concrete pavement (CRCP) as the preferred pavement type for high-volume truck corridors across the state. Over the last decade, Caltrans has constructed more than a dozen CRCP projects in different climates and exposure to different truck volumes. Caltrans was interested in assessing early CRCP performance and identifying potential areas where design, materials, plans, and specifications, and/or construction practices warranted improvement. This project included a review of national CRCP practice, documentation of Caltrans’ statewide practice, and condition assessment of select CRCP projects statewide. For the most part, Caltrans’ CRCP practice is similar to national guidance and other state highway agency practice. A condition assessment of 14 CRCP projects revealed a wide range of performance with various degrees of distresses (i.e., transverse, cluster, and Y-cracking, and punchouts). However, pavements with average transverse crack spacing below Caltrans’ desired lower limit of 3 ft appeared to have acceptable performance. Excessive map cracking, a high percentage of cluster cracking, and initial development of punchouts was evident in sections that appeared to be performing poorly. General recommendations are provided to advance Caltrans’ CRCP practice.

Moment Redistribution in Continuous RC Beams Top Strengthened with Steel and CFRP Plates

It is common practice to retrofit continuous reinforced concrete (RC) beams by fiber reinforced polymer (FRP) or steel plates. This can cause a significant amount of moment redistribution (MR) which results in an efficient and economic design when taken into consideration. There is lack in research regarding MR in continuous RC beams when strengthening plates are applied only at the top side at the hogging regions. The main purpose of this paper is to assess MR in continuous RC beams top strengthened with steel and/or carbon fiber reinforced polymer (CFRP) plates. In this respect, a nonlinear finite element model was developed using ABAQUS 6.14 and validated using experimental research program. The model was found capable of stimulating the behavior of such beams and hence assessing the percentage of MR which can be achieved using steel and CFRP strengthening. A parametric study is conducted to investigate the effect of various parameters, different from those investigated in the experimental program, on the MR in continuous RC beams. Parameters related to the concrete compressive strength, reinforcement ratio, beam thickness and thickness of strengthening plates were considered in this study. The results showed that significant amounts of MR can be achieved using either steel or CFRP plates and that MR is enhanced with the change in concrete compressive strength. Moreover, it was found out that the change in steel bars reinforcement ratio or in thickness of the strengthening plates has different effect on the beams strengthened with steel plates than those strengthened with CFRP plates.

Investigation of Factors Affecting Distresses on Continuously Reinforced Concrete Pavement using Ground Penetrating Radar

The utilization of continuously reinforced concrete pavement (CRCP) has been widely used throughout the United States during the construction of interstate highways since the 1930s. The essential design criterion of CRCP is to manage the crack type, size, and spacing that forms to reduce the distress; thus, identification of the factors affecting the location and extent of the cracks and distresses provides a prediction for the service life of CRCP pavements. In this paper, the influence that reinforcement placement and concrete cover has on the distresses of CRCPs is investigated using ground penetrating radar (GPR) and eddy current technology at six major interstate and state highway locations in Georgia. It was concluded that pavement having inefficient concrete cover depth and pavement thickness results in increased clusters of single transverse cracks and/or punchouts. A result of this study is the recommendation that longitudinal reinforcement be placed at one-third of the depth of the slab from the top surface of the pavement. Furthermore, a distress factor (DF) was established as a good indicator of the performances of pavements relative to each other. Ideal pavement with no crack acquires a DF of 0. In this study, pavements in good, fair, and poor conditions received DFs of “0.03 and 0.05,” “0.97 and 0.98,” and “3.23 and 3.33,” respectively.

Assessment of the flexural behavior of continuous RC beams strengthened with NSM-FRP bars, experimental and analytical study

This paper deals with strengthening statically indeterminate reinforced concrete (RC) beams with carbon and glass Fiber Reinforced Polymers (FRP) rods by using the Near Surface Mounted (NSM) technique. The test program consisted of six two-span beams; one control beam, which had exploited for comparison purposes, and five others initially strengthened in flexure with NSM-FRP rods in both hogging and sagging regions. The main test parameters were type, ratio and length of the FRP bars as well as characteristics of the filling material. The study presents and discusses their impacts on the global flexural behavior of continuous RC beam that mainly includes investigating the overall capacity, failure mode, moment redistribution and ductility state.All NSM-FRP strengthened beams displayed higher overall capacity than the control beam; the test results showed that implementing the NSM technique in an appropriate way could significantly improve the yielding capacity and load-carrying capacity of RC beams without large decrease in the ductility index or the moment redistribution degree despite the non-conventional failure mode. The beam failure was primary affected by the strengthening length; terminating the FRP bars before the zero moment point caused to change the failure mode from pull out of the FRP bars to premature peeling off of the concrete cover. On the other hand, moment redistribution and ductility of the NSM-FRP beams were negatively affected by: (I) Increasing the FRP reinforcement, (II) Decreasing the FRP length or (III) Using mortar as a filling material instead of epoxy-resin. Adopting a nonlinear analysis of the cross-sections could accurately quantify the moment–curvature and the ultimate load of the NSM-FRP continuous beams.

Residual properties of three-span continuous reinforced concrete slabs subjected to different compartment fires

This paper presents an experimental study on the post-fire residual behavior of continuous reinforced concrete (RC) slabs. The mechanical performance of five post-fire continuous RC slabs is investigated, including load-deflection curves, concrete and reinforcement strains, cracking patterns, and failure modes. The results indicate that the residual material properties of heated compartments and concrete spalling significantly affect the ultimate load and failure mode of the fire-damaged continuous RC slabs. The deflection failure criterion is suitable for determining the ultimate state of each span in fire-damaged continuous RC slabs. Apart from the flexural failure mode, punching shear failure also occurred in the fire-damaged continuous slab, particularly in the span with considerable explosive concrete spalling. Compared with the edge spans, the middle span in the continuous slab tends to exhibit better ductility performance owing to continuity at both supports of the span. In addition, several theoretical methods are used to estimate the residual performance of the tested slabs. The reinforcement strain difference and ACI methods are proposed to help predict the residual limit loads of the post fire continuous RC slabs.

Experimental and analytical investigation of continuous RC beams strengthened by SMA strands under cyclic loading

Shape Memory Alloys (SMAs) are a new type of alloy that are capable of strengthening reinforced concrete structures. This study aims to investigate the behavior of continuous reinforced concrete (RC) beams strengthened by SMA strands. The superelastic behavior of Nitinol to recover the deformation of concrete beams under cyclic loading is discussed. We present the experimental results of research to determine the effects of reinforcement ratio and two types of normal and high strength concrete (NSC, HSC) in eight strengthened or non-strengthened continuous beams. The results indicate that SMA strands demonstrate acceptable superelasticity. High strength concrete beams strengthened by Nitinol strands show more ability to recover flexural cracks. However, the recovering capacity of midspan deflection and flexural crack width in SMA-NSC beams is more than their corresponding HSC beams. A better distribution of cracks is observed on both normal and high strength concrete beams strengthened by Nitinol strands. In addition, comparison between experimental deflection and predicted values based on the moment-area method exhibits a good agreement up to yielding of the steel reinforcements. Because of the superelasticity of SMAs, energy absorption capacity and residual stiffness of SMA RC beams increased significantly. Besides, the moment–curvature response leads to more ductile behavior of RC beams strengthened by SMA strands.