Effect of tightening zone length of reinforced concrete beams on beam capacity

Effect of tightening zone length of reinforced concrete beams on beam capacity This study investigated seismic analysis of the behavior of reinforced concrete beams with various shear spans, stirrup shapes, and tightening zone lengths using the Seismo-struct 2020 program. The load–displacement relations of 24 reinforced concrete beams with different conditions were modeled analytically. The analytical model used in the study was validated by comparing it with the experimental data from the literature. It was found that increasing the length of the tightening zone, particularly in beams with a high shear span, is essential for earthquake safety. In addition, the backbone curve of each beam was extracted, and comparison graphs were analyzed. The results obtained demonstrated that the length of the tightening zone limits the effect of stirrup shape and diameter on beam behavior.


Introduction
Currently, reinforced concrete (RC) structures are the most widely employed structural system.After every earthquake occurrence, new design strategies for RC structures have been implemented.Especially, since the 1995 Kobe earthquake, there have been significant modifications to the design of RC structures.After earthquakes, structures designed with force-based approaches become unusable.As a result, new approaches need to be developed.These new design principles, emerging from strain-based approaches, dictates that RC elements be created with a particular performance objective [1][2][3][4].
Beams are a fundamental element of the reinforced concrete structural system and thus have been investigated by numerous researchers considering new design approaches.The experimental studies are limited in terms of cost and time.In some of these studies, the shear capacity of reinforced concrete beams was analyzed, and models based on shear span were developed.Many researchers have conducted studies on the shear span, the most important parameter that determines the fracture shape of beams, and as a result, seismic code recommendations have been made [5,6].Stirrups are the most important factor in determining the shear resistance of beams.Numerous researchers investigating the effect of stirrups on behavior have proposed various seismic code modifications [7][8][9][10][11].Lateral reinforcement layouts for reinforced concrete elements are defined in seismic codes widely used worldwide.Stirrups are tightened to reduce damage in plastic hinge areas where intense damage is expected during earthquake loads.All seismic codes recommend taking various precautions in the plastic hinge areas where intense damage to beams is observed under earthquake loads.As the length of the plastic hinge region is typically expressed in terms of the section height, researchers have explained this value in terms of various parameters.Recent studies have revealed that the shear span influences the length of the plastic hinge [12,13].As seismic codes limit the plastic hinge region from exceeding two times the section height, the length of the stirrup tightening region is maintained at two times the section height.Considering the improvement in concrete quality and the advantages of concrete additives, many structures employ beams with extensive spans.In addition, the preference for short spans in conventional reinforced concrete structures has necessitated a re-evaluation of high-span beams.In recent years, computer programs [14][15][16] have enabled the analytical modeling of numerous experimental sets with various parameters.In some studies, analytical models of experimental sets are created, and the results are compared.According to the results of the analysis, analytical models accurately predicted the experimental outcomes.Thus, investigating the effect of stirrup tightening zone lengths on reinforced concrete beams with varying shear spans using analytical models and validating them with experimental models will significantly contribute to the literature.In this study, the seismic analysis of beams with different shear spans, stirrup conditions, and tightening zone lengths has been performed using the Seismo-Struct 2020 program.This study investigates the effect of the tightening zone length on the behavior of reinforced concrete beams and determines the optimal length of the tightening zone.From Fig. 1, the critical region is defined as l cr , equal to 2h.

Materials and methods
Similarly, the Turkey earthquake building code (TBEC-2018) accepts 2h as the length of the critical section [18].This study analyzed 24 reinforced concrete beams with various shear spans and stirrup conditions analytically, with loaddisplacement relations extracted using the Seismo-Struct program.The performance of RC beams using the material strain values in TBEC-2018 are determined.Panagiotakos and Fardis [19] proposed formulations for chord rotation capacity at yielding and "ultimate" (at 20% strength drop) strengths.The "ultimate" strength value was determined through an empirical and a semi-empirical (i.e., based on the plastic hinge length) approach derived from a large database of flexure-controlled experimental tests for RC elements.
According to TBEC-2018, the performance levels are calculated using material strain values.These calculations are depicted in equations ( 1)-( 3). ( where ε c is the shortening in the outermost concrete compression fiber, ω wc is the mechanical index of the lateral reinforcement, ε s is the unit elongation of the longitudinal reinforcement, ε su is the unit elongation at the moment of Effect of tightening zone length of reinforced concrete beams on beam capacity maximum stress of the longitudinal reinforcement, θ p is the plastic rotation of the element, f u is the maximum curvature of the section, f y is the yielding curvature of the section, L p is the plastic joint length, L s is the shear span, and d b is the longitudinal reinforcement diameter.EUROCODE-8 contains a section for assessing reinforced concrete beams, where it recommends estimating chord rotations using the given formulation in the code.This formulation is dependent on several variables, including the axial load ratio, longitudinal reinforcement ratio, transverse reinforcement ratio, and yield strength of the transverse reinforcement, as shown in Eq. ( 4). ( where γ el is the seismic element coefficient (equal to primary element is 1.5 and secondary element is 1), ϑ is the dimensionless axial load levels (N/A c f c ), h is the height of the section, w is the mechanical reinforcement ratio for compression and tension, L v is the shear span, f c is the concrete strength, f yw is the transverse steel yield strength, ρ sx is the ratio of transverse steel to parallel to the direction x of loading, α is the confinement effectiveness factor, and ρ d is the steel ratio of diagonal reinforcement.FEMA 356, the American code for the seismic rehabilitation of buildings, expresses the displacement limits of RC beams in the form of plastic rotations [20].The following equations were used to estimate the plastic capacity for the limit state that prevents collapse. ( (8)

Confirmation of the analytical model
The Seismo-Struct 2020 program was utilized to investigate the analytical results of RC beams [21].The accepted material models for TBEC-2018 were selected and modeled in the program.In addition, the results of the experiments used in the literature are compared with the program's outputs to ensure that they are accurate.Two beam samples tested in the literature are modeled in the Seismo-Struct 2020 program.The comparison of the experimental data with the analytical data is shown in Figures 2 and 3.
When the correct material models were selected, the analytical results obtained were closest to the experimental data.Examining Figures 2 and 3 reveals that the analytical models closely predict the behavior of the experimental models.In the same model, modifying the length of the tightening zone and the shear span was also considered to achieve more uniform results.

Beam properties
The properties of the 24 RC beams examined in this article are presented in Table 1.From Table 1, a/d is the shear span to depth ratio and ϕ s is the diameter of the stirrup.Within the scope of this study, the same reinforcement configuration was utilized for all models.For the longitudinal reinforcements, 4f16 is selected for both the upper and lower reinforcements.For the transverse reinforcements, 75 mm stirrup spacing in the tightening zone and 150 mm stirrup spacing in the beam spans were selected.The beam tightening zone lengths to be examined within the scope of the study are h-2h-3h.Figure 4 depicts the cross-section of the beams modeled in the Seismo-Struct 2020 program, along with the schematic loading pattern and cross-section.

Loading profile
All examined beams utilized an identical loading profile.Similar to the previous study by Lehmann and Moehle [23], increasing the amplitude of cyclic loading was applied from the beam end.
In this context, the analytically defined loading profile is shown in Figure 5. Kunnath et al. examined the effect of loading profiles on the behavior of the reinforced concrete element [24].They determined that the increasing cyclic loading more accurately reflects the   Effect of tightening zone length of reinforced concrete beams on beam capacity damage status of the RC element.In addition, when a large amount of experimental data from the literature were analyzed, it was discovered that increasing cyclic loads were utilized.

Figure 5. Schematic loading profile
While calculating the loading profile, a multiple of the yield displacement determined under monotonic loading was used.The displacement value, applied as half of the yield displacement before yielding, was applied once.It is defined as triple repetitive and increasing ductility multiples (1μ-1.5μ-2μ-3μ-4μ…)together with the yield displacement value.

Modeling in Seismo-Struct
The selection of material models is one of the key parameters affecting the behavior of the RC beam.The Managetto-Pinto model was used to describe the behavior of the reinforcement [25].For the behavior of concrete, the model representing the nonlinear behavior defined by Mander et al. was used [26].
Images of the models defined in the program are shown in Figure 6.
In the validation models produced for comparison with the experimental results, the A1 parameter was set to 19.55.The same value was used in all beam models to reduce the strength of the Managetto-Pinto model close to the real behavior.The tightening zone and the beam span region, which influence the beam behavior, are defined as separate sections and is designed with 75 mm spacing between the stirrups in the tightening zone and 150 mm spacing between the stirrups in the beam span.As these two beam regions are defined as two different sections in the program, the verification beams also consider these design factors.Keeping the stirrup spacing constant was shown to reflect the behavior correctly.Thus, the analytical model reflects the effect of the tightening zone as reflected by two different models.The view of the beam modeled in the program is shown in Figure 7.

Analytical results
Figure 8 depicts the analytical results of a seismic analysis conducted under increased amplitude cyclic loading simulated from earthquake loads.Considering the load-displacement curves of the beams, the performance levels calculated according to TBEC-2018, FEMA356, and EUROCODE were calculated with the aid of 1-8 relations and marked.In addition, the displacement demand corresponding to a 20% reduction in lateral load carrying capacity is plotted on the curve for control purposes.

Backbone curves
Using the backbone curve, the available ductility of the beam considering its post-failure response to cyclic loads can be evaluated more precisely.In this study, the backbone curves were obtained according to the FEMA356 code. Figure 9 depicts the schematic backbone curve and sample beams backbone curve.The backbone curves have been combined on the same graphs to compare the results of all beams examined within the scope of the study.
The combined backbone curves prepared in this context are shown in Figure 10.

Proposed model for tightening zone length
Analytical models have revealed a correlation between the length of the tightening zone and the shear span ratio.In this context, the length of the tightening zone should be expressed as a function of the shear span ratio.The proposed formula is shown in Equation 9.
L cr = 1,7+0,16 (a/d) where l cr is the beam tightening zone length.Five analytical models with varying shear spans were developed to verify the proposed equation.The properties of confirmation beams with varying shear spans are shown in Table 2.
The analytical results of the confirmation models are shown in Figure 11.
Based on the results, the length of the tightening zone calculated according to the proposed equation yields results consistent with all seismic codes.In addition, the displacement capacities calculated according to all seismic codes for the proposed tightening zone length remained within the safe zone.

Conclusion
This study investigated the effect of the length of the tightening zone on the beam capacity.The results of the study are listed as follows: -As the length of the tightening zone increases (especially 3h), the displacement capacity also increases.However, the increase in lateral load capacity is more limited.-Considering the lateral load and displacement capacity, the influence of the diameter and shape of the stirrup is minimal.As the length of the tightening zone increases for beams with a 10 mm stirrup diameter, the lateral load capacity increases significantly.Therefore, the increase in stirrup diameter and length of the tightening zone contributes significantly to the beam capacity.
-The highest and lowest displacement capacity estimate for all beams was made by TBEC-2018 and FEMA356, respectively.
-In all seismic codes, when the length of the tightening zone is 2h, the displacement capacity of beams with a high shear span ratio is calculated to be higher than the true value.In beams with a tightening zone length of 3h, all seismic codes produce results closer to the actual displacement capacity.
-According to the results of the limited number of analytical models, it would be preferable to increase the tightening zone length to 3h, particularly in beams with high shear spans.
-It was observed that the proposed equation within the scope of the study yields safe results for all seismic codes.In this context, it is believed that all seismic codes would be more accurate in expressing the length of the tightening zone depending on the shear opening.

Figure 1 .
Figure 1.Transverse reinforcement in critical regions of beams for EUROCODE

Figure 4 .
Figure 4. Schematic loading layout and section of the beams

Figure 7 .
Figure 7. Screenshot of the model made in the Seismo-struct 2020 program