A Theoretical Study on Fiber-Reinforced Polymer Application in Reinforced Concrete Structures

1. Introduction

Fiber-reinforced polymer composites applied to masonry infill walls in reinforced concrete structures and the effects of this application on reinforced concrete (RC) frame system behavior have been discussed comprehensively in our previous articles. In the study presented here, the contribution of carbon fiber-reinforced polymer fabric (CFRP) applied to masonry infill walls of an existing low-rise RC structure to seismic behavior was examined theoretically. The nonlinear incremental pushover analysis method was employed in the theoretical study to determine seismic performance. The reinforced concrete structure system was comparatively evaluated in two different conditions in terms of the seismic performance it exhibits: bare and reinforced masonry infill walls. It was concluded that the proposed strengthening method provided significant contributions to building performance. Research on experimental and theoretical examination of reinforced concrete frames with masonry infills has continued from the 1960s to the present. The experimental studies conducted by Polyakov in the 1960s were extremely important in understanding the behavior of plane reinforced concrete frames with masonry infills. Experimental studies conducted by Klinger and Bertero (1976), Bertero and Brokken (1983), Zarnic and Tomazevic (1988), and Mander and Nair (1993) enabled the determination of rigidity and strength of reinforced concrete frames with masonry infills. It is known that the use of masonry infills in appropriate locations within the frame will increase the overall structural strength and rigidity of the building. Dhanasekar and Page (1986), Mosalam (1996), Shing et al. (1994) modeled the behavior of frames with masonry infills under horizontal effects using the finite element method. A disadvantage of the finite element method is that it is quite time-consuming when solving multi-story structures. In such structures, it is more appropriate to use macro models from which global behavior can be found. Holmes (1961) modeled masonry infills with pendulum bars representing 1/3 of the width of the diagonal length of the masonry infill. Stafford Smith (1962) and Stafford Smith & Carter (1968) modeled the width of pendulum bars representing masonry infills based on the horizontal rigidity parameter of the infilled frame. Mainstone (1971) later supported this model with empirical relationships in the rigidity relationship. Wood (1978) performed nonlinear analyses to determine the failure load and failure mode of frames with masonry infills containing window openings. Saneinejad and Hobbs (1995) proposed a method for calculating and designing steel frames with concrete or brick walls under horizontal loads. As a result of examining calculations performed with the nonlinear finite element method alongside experimental studies, it was concluded that masonry infills can be modeled with diagonal bars if their mechanical properties are known. Negro and Verzeletti (1996) examined a full-scale actual structure using pseudo-dynamic test technique under ground acceleration of PGA=0.3g. The effect of masonry infills on the general system behavior was explained in terms of energy. In the frame experiment with masonry infills on all floors, it was noted that horizontal displacement and rotations in the structure were considerably smaller compared to the other two samples. Garevski et al. (2003) tested 1/3 scale masonry infill and CFRP-reinforced masonry infill specimens on a shaking table. It tested them sequentially under increasingly larger amplitudes from the Izmit acceleration record ranging from PGA=0.023g to PGA=0.45g. In shaking table experiments, at the maximum acceleration level of PGA=0.45g, the maximum horizontal peak displacement that occurred in the bare masonry infill specimen was 168 mm, while this value decreased to 87 mm in the specimen reinforced with CFRP. Sofronie (2004) expressed the contribution of masonry walls' internal friction to structural energy consumption with the statement: "If masonry walls are reinforced with polymer materials, they fully assume the active damping function during seismic motion." Friction generated along the surfaces between masonry infill and frame columns and beams as well as along joints in the masonry infill provides additional damping to the structure. For this reason, masonry infills serve as sources of damping and energy dissipation in addition to increasing system strength and rigidity. Increased structural damping means reduced seismic demand, consequently reducing the earthquake loads acting on the structure. Priestly (2005) expressed the importance of energy consumed by masonry infills with the statement: "Without masonry infills, friction forces in the building system would remain at negligible levels." Hashemi and Mosallam (2006) performed shaking table tests on 3/4 scale reinforced concrete frames with masonry infills. The study noted that masonry infills increased building rigidity by a factor of 4, reduced the natural vibration period by 50%, increased equivalent viscous damping ratio to 5-12% levels, and significantly increased dissipated energy. Ozkaynak et al. (2016) proposed an analytical model called "Wall" in which masonry infills can be represented with horizontally oriented spring-type elements. In the model in question, masonry infills are defined by a three-segment capacity curve established based on maximum shear strength, initial rigidity, ductility ratio, and other structural parameters. The study stated that the proposed "Wall" model has the capability to represent the contribution of both bare and reinforced walls to RC frame behavior. The comprehensive experimental and analytical studies completed by Ozkaynak (2010) emphasize that masonry infills in reinforced concrete structures can be strengthened using the braced diagonal strengthening method with CFRP fabrics, and that this application would provide significant contributions to building seismic performance.

2. Analytical Study

Within the scope of the study presented here, the objective was to determine the seismic behavior of a three-dimensional reinforced concrete structural system both when strengthened with fiber-reinforced polymer fabrics and in bare condition without strengthening. For this purpose, both structures were subjected to nonlinear incremental pushover analysis. For the incremental pushover method to be applicable, the structure must have no torsional irregularity, the number of building stories excluding basement must not exceed 8, and the ratio of effective mass corresponding to the computed dominant vibration mode to the total building mass must be at least 0.70. In the incremental equivalent seismic load method, nonlinear static analysis is performed under the effect of equivalent seismic loads that are proportional to the dominant vibration mode shape and incrementally increased in one direction up to the seismic demand limit. The relationship established between the response strength corresponding to each target displacement is defined as the capacity curve. The capacity curve provides important information about the general seismic performance level of the structure. The load-bearing system of the RC structure examined in the study is shown in Figure 1. The building's load-bearing system consists of plane reinforced concrete frames. In all frames arranged in the long direction, columns bend about their weak axes. All building stories have a height of 4.20 m, and the total structure height is 12.6 meters. In two main directions, the distances between column axes are 6 meters. Column and beam cross-sections remain constant throughout the structure height, and two types of columns and beams exist. External columns have 30×60 cm sections, while internal columns have 30×70 cm section dimensions. External beams are 30×80 cm, while internal beams are 30×50 cm. Longitudinal reinforcement ratios vary between 1.0% and 2.0% depending on the dimensions of column elements. In creating the analytical model, the RC structural system was idealized using frame elements and analyses were performed in SAP2000 software. In all analyses, it was assumed that floor slabs behave as infinitely rigid in their own plane. XTRACT software was used to determine the moment-curvature relationships of reinforced concrete column and beam elements. Plastic hinge properties were assigned externally to relevant locations. Cracked bending rigidities were defined for the sections of reinforced concrete elements between hinges. The dimensions of ribbed beams show differences between each other in terms of moment-curvature relationships depending on whether they are at mid-span or in support regions. Transverse and longitudinal reinforcement quality was S220, and the realized concrete strength was determined as 18 MPa. Since there was no transverse reinforcement confinement, confinement effects in concrete were not considered. The method of application of the fiber-reinforced polymer fabrics proposed for strengthening the reinforced concrete structure is shown in Figure 2. The fiber-reinforced polymer application shown in Figure 2 was examined in detail in the study by Ozkaynak (2010). The floor plan of the reinforced concrete structure is shown in Figure 3. The openings containing masonry infill walls strengthened with fiber-reinforced polymer application are indicated in orange color on the building floor plan. For representing strengthened masonry infills in the strengthened structure, the "Wall" spring model proposed in the study by Ozkaynak (2016) was used. Five input parameters are required from external sources to develop this model. According to the Ozkaynak (2016) study, input parameters for a masonry infill of known dimensions were determined as maximum shear strength (Vmax) and ductility of the masonry infill (µ=8). The inclusion of the masonry infill in the analytical model and its working principle are shown schematically in Figure 4. Incremental pushover analysis was performed within the scope of FEMA440. In accordance with FEMA440, the performance point was determined on the spectral acceleration and spectral displacement curve defined by the capacity spectrum method, and pushover analysis was performed for the reinforced concrete structure both with and without masonry infills based on target performance points. The reinforced concrete structure is located in the 2nd degree seismic zone and on Z1 type soil. For Z1 type soil as defined in the Seismic Regulation (TDY-07), Ta=0.10 sec and Tb=0.30 sec are defined. In determining the performance point, service earthquake with 50% probability of exceedance in 50 years will be used. Column, beam, and floor loads were calculated separately for normal stories and roof story. In pushover analysis, G+0.3Q vertical loads were taken as basis. The load analyses performed were evaluated according to the general dimensions of the structure, and total building weights for the 1st and 2nd normal stories were 9,584.00 kN and the weight for the 3rd story was 5,670 kN, resulting in a total building weight of 24,840 kN. As a result of free vibration analysis performed on the analytical model of the reinforced concrete structure, the first natural vibration period of the structure was calculated as 1.78 sec. The seismic demand curve determined considering the above-mentioned soil properties, seismicity, and 5% viscous damping was placed in the same environment as the capacity curve in spectral format (Sa-Sd), and the performance point was calculated. The elastic demand curve and capacity curve initial rigidities were intersected, with Sd displacement corresponding to the displacement that would be reached under inelastic behavior through the equal displacement approach. As a result of calculations in both directions, performance points for bare condition were determined as Sdx=0.38 and Sdy=0.26. The corresponding physical displacements are δx=490 mm and δy=343 mm. In the strengthened condition, the spectral curve determined for 10% damping ratio was used as the seismic demand curve. Performance points in the strengthened condition were calculated as Sdx=0.06, Sdy=0.08, and corresponding physical displacements as δx=70 mm and δy=100 mm. In the strengthened condition, displacement demand decreased by a factor of 7 in the long direction and by a factor of 3 in the short direction.

Bare Condition, Strengthened Condition

When the same frames in bare and strengthened condition are compared, the plastic hinge distributions were examined and colored damage distributions are given in Figure 6. In the strengthened system, plastic hinges did not form at many sections, and the plastic hinges that formed remained near the immediate occupancy (IO) performance level.

3. Conclusions

1. In the three-dimensional structural system, existing seismic safety was increased by confining an adequate number of masonry infills in two directions with CFRP. Relative story drifts and column and beam end plastic rotations were evaluated according to FEMA 356, and the structure's performance level was shown to have improved. 2. With the proposed strengthening method in the existing structure, displacement reduction of 7 times in the long direction and 3 times in the short direction was achieved. Capacity curves showed that approximately 5 times strength increase in the long direction and 4 times strength increase in the short direction was provided for the strengthened condition. 3. In the strengthened condition, the performance of the structure in the long direction improved from the collapse prevention (CP) performance level to the immediate occupancy (IO) performance level. Plastic hinges did not form at many sections in the strengthened condition. Assoc. Prof. Hasan Özkaynak / Beykent University Faculty of Engineering Department of Civil Engineering

4. References

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