Analysis on the influence of the arrangement and eccentricity of non-adherent tendons on the punching resistance of prestressed flat slabs

Análise da influência do arranjo e excentricidade de cabos não aderentes na resistência à punção de lajes lisas protendidas

ABSTRACT

In conjunction with experimental studies, computational tools based on the Finite Element Method (FEA) have made it possible to analyze the phenomenon of punching and the influence of prestressing on the ultimate strength of flat slabs and thus understand this phenomenon through numerical simulations. In this study, experimental tests were simulated through three-dimensional analyses, using the constitutive models implemented in the ATENA 3D computer program, it was possible to validate the numerical results through the load-displacement and load-strain curves being compared with the experimental curves. The numerical results showed a difference in load capacity of less than 2% for the experimental models. After adequate calibration, a parametric study with eight models of prestressed slabs was implemented by varying the spacing and eccentricity of the prestressing tendons, punching resistance being evaluated with the new parameters. The punching resistant capacity of each model was also compared with the most current regulatory design predictions.

Keywords:
Flat slabs; Punching Shear; Analysis Numerical; Prestressed; Eccentricity Tendons

Keywords:
Flat slabs; Punching Shear; Analysis Numerical; Prestressed; Eccentricity Tendons

1. INTRODUCTION

The characterization of the flat slab system is due to the connection of the slab with the column, the main problem being the punching, which causes the slab to perforate through an abrupt rupture due to shear [¹]. Several structures are built with this construction system, which must take into account design criteria regarding their possible brittle failure. For VECCHIO et al. [²], this particularity may be caused due to its loading or its boundary conditions in different arrangements in the structure, also according to VIEIRA et al. [³], the maximum negative moment in a slab with uniformly distributed loading occurs around the column, this region is even more fragile when it is necessary to introduce openings, as presented in the studies by MARQUES et al. [⁴]. The formation of flexural cracks around the column can lead to a progressive collapse of the building, resulting in the loss of its bearing capacity [⁵].

Among the options to avoid the occurrence of this phenomenon in flat slabs, it is possible to mention the use of shear reinforcement, increasing the longitudinal reinforcement rate, incorporating fibers into the concrete or the application of prestressed concrete [², ⁶]. Several studies [², ⁷,⁸,⁹,¹⁰,¹¹,¹²,¹³], revealed the various benefits arising from prestressing flat slabs, whether with straight or parabolic tendons, with and without eccentricity or external prestressing.

The introduction of prestressing significantly increases the normal compressive stresses in the flat slabs, contributing to its bearing capacity, in addition to reducing concrete cracking and increasing punching resistance. Studies such as those by CLÉMENT et al. [¹³], DIAZ et al. [¹⁴] and EL-SISI et al. [¹⁵], revealed the interference caused by the eccentricity of the prestressing tendons’ layout, which results in bending moments opposite to those of external actions. CLEMENTE et al. [¹³] emphasizes that, once the prestressing forces are intercepted by the rupture surface of the drilling, vertical forces are generated contrary to the direction of loading, which can be subtracted from the shear force supported by the concrete.

Given the increase in tools using finite element methods (FEA), numerical analysis has become a powerful alternative in solving complex problems such as punching by subdividing its domain into simplified solutions, covering the behavior of reinforced and prestressed concrete structures. As highlighted by MILLIGAN et al. [¹⁶], the application of FEA is an effective strategy to predict not only capacity and failure modes, but also to analyze crack patterns and the overall behavior of concrete structures. Based on experimental data, it is possible to develop a calibrated numerical model, as observed in the studies by MARQUES et al. [¹⁷] and COSTA et al. [¹⁸], and from there, parametric studies as presented in OLIVEIRA and DELALIBERA [¹⁹], can enrich the experimental datasets, providing a more comprehensive understanding of the structural behavior and main factors influencing the strength of concrete flat slabs.

This research aims to numerically analyze the behavior of prestressed flat slabs with non-adherent tendons subjected to punching. Investigating, with the help of the ATENA 3D software, the interferences arising from the layout and eccentricity of the prestressing tendons and comparing the results obtained with the predictions presented in ACI 318 [²⁰] (ACI), next generation of Eurocode 2 [²¹] (EC2), NBR 6118 [²²] (NBR) and fib Model Code [²³] (MC).

2. SIMULATION OF NUMERICAL MODELS

The numerical analyses presented in this section form the backbone of the research, utilizing calibration processes and parametric studies conducted through the ATENA 5.9 software. This software integrates tensile (fracture) and compression (plastic) behavior, adopting constitutive models outlined in works by ČERVENKA et al. [²⁴], BRIGO et al. [⁶], and BRIGO [²⁵]. The methodology involves numerical simulations, referencing the experimental program conducted by MELGES [⁷]. Specifically, two distinct models, namely the M1 slab in reinforced concrete and the M4 slab in prestressed concrete with non-adherent tendons, were employed in this study. The subsequent discussion delves into the insights gained from these simulations, shedding light on the structural responses of these configurations in the context of flat slab systems.

The experimental slab models had dimensions of 2500 × 2500 mm² and a thickness of 160 mm, both supported by a steel plate in its central region measuring 180 mm × 180 mm × 120 mm, simulating the column. Figure 1 shows the charging scheme. This test of nine support points is composed of a set of metallic I-beams on the top face of the slab, preventing its movement while the upward load was applied incrementally by a hydraulic actuator located below the central steel plate. Reactions were measured by a load cell located between the actuator and the plate.

Figure 1
Test setup adapted from MELGES [⁷], BRIGO et al. [⁶].

For numerical modeling of slab M1, the respective MELGES [⁷] model was used, which aimed to define the boundary conditions, discretization, type of element, constitutive parameters in order to obtain the best results in a timely manner, with the respective calibration steps by BRIGO [²⁵]. Through this study, a structured mesh was determined with hexahedral elements of approximately 25 mm³, displacement increments of 0.05 mm/step per calculation step applied to a point in the center of the column (Figure 2a), fixed crack model, Newton-Raphson solution method and tolerance criteria maintained for displacement, force and residual energy of 10^–2, 10^–2 and 10^–4 respectively. The other parameters were maintained as suggested by the software described in ČERVENKA et al. [²⁴], with fracture energy according to VOS (1983) [²⁶] equal to 25f_ct^ef (N/m), tension stiffening at 0.4 and interaction limit maintained at 30 per calculation step.

Figure 2
Characteristics and boundary conditions of the numerical model M4 (a). Characteristics of the experimental model according to MELGES [⁷] (b).

The results for slab M1 showed a relationship between the numerical and experimental model at failure load (V_FEA/V_Exp) of 1.002 and displacement (D_FEA/D_Exp) of 1.111, with the first cracks appearing at a load of 0.25V.

To represent a prestressed model, the M4 model was used, with the same characteristics and dimensions applied to the M1 model. Table 1 presents the characteristics of the materials, using a 12.5 mm mesh spaced 100 mm apart in the upper bars, with an mean useful height of 12.8 mm. In the lower mesh, 8 mm bars were adopted every 100 mm. Prestressing was applied to 16 non-adherent CP-190 RB 7 type tendons. The numerical model used with its boundary conditions is represented in Figure 2a, and in Figure 2b the geometric characteristics relating to prestressing are presented.

Table 1
Property of the materials used in the prestressing model.

CONCRETE PROPERTIES			PRESTRESSING TENDON PROPERTIES				PRESTRESSING TENDON PROPERTIES
fc (MPa)	fct (MPa)	Ec (MPa)	Øp (mm)	Ap (mm2)	Vp (1%) (kN)	Ep (MPa)	Øs (mm)	fsy (MPa)	fsr (MPa)	Es (MPa)
50.92	3.87	30.46	12.7	99.9	182	208000	12.5	651.4	792.3	201541
							8	601.8	711.9	206900

• Note: _c is the strength of the concrete, _ct is the tensile strength of concrete, _c is the modulus of elasticity of concrete, Ø_p is is the diameter of the prestressing tendon, _p is the area of the tendon, _p is the vertical component of the prestressing force acting on a critical section, _p is the modulus of elasticity of the tendons, Ø_s is the steel diameter, _sy is the yield stress of steel, _sr is the failure strength of steel, and _s is the modulus of elasticity of steel.

The forces exerted on the tendons follow Table 2, referring to the re-tensioning of the tendons in the experimental model. The best representation of the test by the numerical model was divided into three loading phases: first, incremental displacements are applied to the column until the slab reaches a load of 80 kN; second, standard forces are applied according to Table 2; and in the third phase, to maintain the applied prestressing forces, master-slave node connections are activated between the anchor plate and the end of the tendon, followed by the application of an incremental displacement in the column until the slab ruptures. To represent the best results, it was necessary to assign a zero value for tension stiffening in the prestressed model.

Table 2
Forces recorded in re-stressing in the experimental model M4 of MELGES [7].

	DIRECTION X				DIRECTION Y
RE-STRESS	5	6	7	8	5	6	7	8
	128.77	129.61	133.21	130.61	128.65	132.29	127.48	131.94

From the numerical results, the load-displacement and load-strain curves were compared with the experimental model. In the curves of Figure 3a it is possible to notice the moment at which prestressing is applied, represented by the increasing straight line without variations in displacement, justified by the simultaneous application of the prestressing force in all tendons. Comparing the end point of prestressing, the good convergence of the numerical model can be seen, reaching 218.74 kN compared to 221.30 kN in the experimental model. The numerical response showed significant accuracy in representing the test curve, with a V_FEA/V_Exp ratio of 1.016, and D_FEA/D_Exp of 1.063, values that are sufficiently accurate. A good convergence was found for the concrete strain at position E₂₅, As shown in Figure 3b, a small variation in strain was observed when prestressing was applied at the beginning of loading. In Figure 3c, the strain of a tension bar, position E₆, and in Figure 3d of a compressed bar, E₁₈, can be observed. Both numerical curves managed to follow the same orientation as the experimental curve.

Figure 3
Experimental-numerical comparison of the M4 model for, Load-displacement (a), Load-strain of concrete (b), Load-strain in tension bar (c), Load-strain in compressed bar (d).

The crack overview is also shown in Figure 4. Better crack control was observed due to prestressing, with the first crack appearing at 0.45V. The numerical model showed cracks following the upper bars towards the edge of the model. Close to the rupture (Figures 4a and c), inclined and tangential cracks were identified in the thickness of the slab around the column, typical of the formation of a punching cone, as predicted.

Figure 4
Cracking pattern in model M4 and comparison with the experimental model by MELGES [⁷] (b).

3. PARAMETRIC STUDY

The objective of this parametric study was to investigate how the arrangement of central prestressing tendons with different spacing and eccentricity can affect the punching resistance of flat slabs. To this end, the models developed maintained the same characteristics according to the calibration of the M4 model, thus, materials, geometry, longitudinal reinforcement rate, forces applied to the prestressing tendons maintained as Table 2, as well as monitoring points and boundary conditions were maintained, varying only the parameter analyzed.

Eight models were evaluated, which were separated into two series. For the two series analyzed, the central prestressing tendons were changed as shown in Figure 5, in the center of the slab, with variations of 5 cm, 10 cm, 15 cm and 20 cm. In the Series A models, the eccentricity with parabolic curvature of the M4 model tendons was maintained, as shown in Figure 1b. In the EC Series models, the prestressing cables were made straight, without curvature, not exerting forces due to the eccentricity in the geometric center of the slab.

Figure 5
Configuration of the tendons for the new models.

The models are defined by the nomenclature: series-spacing. Thus, the Series model with 10 cm spacing such as A-10 and EC-10.

3.1. Comparison between series A and EC results

With the results achieved with the two series, it was possible to evaluate the degree of interference caused by spacing and eccentricity in the prestressing tendons. In Table 3, the maximum load (V) obtained for each model of the two series analyzed is presented.

Table 3
Maximum capacity of each A and EC series model.

MODELS	V (kN)	$\frac{V}{M^4}$	DISPLACEMENT (mm)
A–5	788.12	1.00	8.89
A–10	785.06	1.00	8.79
A–15	753.17	0.96	7.85
A–20	690.83	0.88	6.31
EC–5	665.06	0.85	9.28
EC–10	619.18	0.79	7.99
EC–15	638.85	0.81	8.63
EC–20	600.96	0.76	7.19

The load-displacement curves of the four Series A slab models are presented in Figure 6a, as well as the experimental model. In the analysis of the models in this series, it was possible to observe that the greater space between the tendons had a strong influence on punching resistance. Furthermore, it is possible to note that the A-5 model showed an increase in resistance in relation to the experimental model, which can be justified by the fact that the contact surface of the column with the slab coincides with two prestressing tendons, differing from the other models.

Figure 6
Load-displacement curves, Series A (a), Series EC (b).

When analyzing the EC Series results, it is possible to evaluate the degree of interference caused by the eccentricity of the prestressing tendons. The load-displacement curves of the four EC Series slab models are presented in Figure 6b, the experimental curve was kept for comparison purposes. Load-displacement results revealed a significant reduction in punching resistance when keeping the prestressing tendons straight without eccentricity.

Another relevant aspect is the resistance gains at the end of the prestressing application, which are different for each Series. The EC Series models presented resistance gains of just 20 kN, in contrast, the Series A models presented resistance gains of more than 130 kN. The difference in resistance gains at the end of applying the Series prestressing demonstrates the strong influence caused by the eccentricity of the tendons.

In models from both Series, it is possible to observe a decrease in the models’ resistance as the spacing between the prestressing tendons increases. However, it can be seen that this reduction was less significant in the EC Series, at just 9% between the EC-5 and EC-20 models, compared to 14% between the A-5 and A-20 models. Greater resistance was also observed in the EC-15 model compared to the EC-10. This variation can be justified due to the greater proximity of the 5x,y tendons to the weakest point for rupture, at the end of the column.

The eight models showed similar behavior in relation to concrete strain, with a difference between the curves at the moment close to rupture. It was also observed that when centered prestressing is applied, there is greater stability in the concrete. In Figures 7a and 7b it is possible to notice that the increase in the spacing between the tendons, in addition to reducing resistance, generated a reduction in the capacity to withstand strains. A reduction in maximum strain is observed in models with greater spacing in addition to anticipation of rupture, indicating a more fragile rupture.

Figure 7
Concrete load-strain curves, Series A (a), Series EC (b).

Regarding the analysis of the load-strain curves in the tensile steel, illustrated in Figures 8a and b of the eight models, it is possible to notice a similar behavior in both series up to a value close to 600 kN, which, in turn, does not demonstrate interference with the steel when changing the eccentricity of tendons. This behavior can also be justified, as the values are close to the yield stress of the bars. The strain of the models begins to differ from this value, with the models with smaller spacing (A-5 and EC-5) showing greater stability in strain. When analyzing the evolution of the curves of the lower compressed bars (Figures 8c and d), a good convergence of results is observed, as well as the degree of interference caused by the spacing between the prestressing tendons.

Figure 8
Tensile steel load-strain curves, Series A (a), Series EC (b) and Load-strain in compressed bar Series A (c), Series EC (d).

In Table 4, the maximum force that each tendon reached at the moment of rupture is verified, in both directions (x and y), in each of the four models of each series. For Series A models, the interference of the eccentricity of the tendons with the resistance gains of the models is noticeable. Analyzing each model individually, it is noted that slab A-10 was the one that provided the greatest increase in forces for the model’s resistance. As for the A-5 slab, even though it was the one that resisted the ultimate load the most, the tendons suffered less stress than the reference model A-10. This same logic was not observed for the EC Series, with the EC-5 model being the one that presented the greatest stresses suffered by the tendons. In models with eccentricity, A-15 and A-20, it is possible to notice that the maximum resistance reached by the strands follows a tendency to reduce as there is an increase in spacing, a characteristic also observed, but not as noticeable in models with prestressing. centered. Considering only the central cables 5, 6 and 7, these presented greater variations in the efforts resisted by the Series A cables of up to 4.2 kN in the x direction, and up to 5.0 kN in the y direction, while when compared to the models from the EC Series, greater stability is observed, with variations close to 1.0 kN proving how eccentricity affects the results.

Table 4
Comparison between Series A and Series EC of the prestressing force of tendons at rupture.

	DIRECTION X				DIRECTION Y
TENDON MODEL	5	6	7	8	5	6	7	8
A-5	136.41	136.27	140.93	135.02	138.23	141.86	137.18	137.77
A-10	137.28	137.94	141.41	135.63	139.13	142.61	137.52	138.17
A-15	135.73	136.21	139.41	134.08	137.38	140.59	135.13	136.45
A-20	133.76	134.09	137.19	132.85	135.07	138.11	132.50	134.99
EC-5	132.89	133.75	137.45	133.39	134.88	133.75	133.83	136.33
EC-10	132.24	133.03	136.64	132.79	133.97	133.03	132.71	135.46
EC-15	132.95	133.63	137.16	132.98	134.88	133.63	133.39	135.76
EC-20	131.91	132.51	136.04	132.29	133.54	132.51	131.90	134.80

The cracking patterns are discernible in Figures 9 and 10, reflecting a remarkable consistency with the crack progression observed in the numerical calibration model, M4 (or A-10), as addressed in the study by Melges [⁶]. Regardless of the presence or absence of eccentricity in the tendons, both models showed that the evolution of the radial cracks was in line with the orientation of the upper flexural bars. It is especially noteworthy that the A-5 and EC-5 models, characterized by the proximity of the prestressing tendons, demonstrated a substantially greater capacity to resist deformations compared to the other models. Furthermore, these models stood out as they presented the greatest manifestations and distribution of cracks on the surface of the slab, attributed to the concentration of prestressing tendons in the central region adjacent to the column, giving them greater resilience in the face of considerable deformations.

Figure 9
Detail of crack patterns on A Series models.

Figure 10
Detail of crack patterns on EC Series models.

In Figures 9a, b, and c, and Figures 10a, b, and c, it is possible to observe the formation of tangential cracks around the column on the surface, as well as inclined cracks in the thickness of the slab (Figures 9c, f, and i, and Figures 10c, f, and i), typical of punching cone configuration. Such visual illustrations highlight how the spacing of the tendons influences not only the load capacity of the slab but also the concentration of cracks, highlighting the crucial role of the eccentricity of the parabolic prestressing tendons in improving punching resistance.

Furthermore, it is important to highlight that the formation of tangential cracks around the column on the surface, together with the inclined cracks in the thickness of the slab, as observed in Figures 9 and 10, are significant indicators of the phenomenon known as punching shear. These cracking patterns not only reflect the distribution of stresses in the structure but also provide valuable insights into the effectiveness of sizing and positioning of prestressing tendons. Therefore, when analyzing the figures presented, it becomes evident how the spacing of the tendons not only influences the load capacity of the slab but also plays a crucial role in the distribution and concentration of cracks, contributing to greater structural robustness and punching resistance.

4. NORMATIVE COMPARISON

With the numerical results of Series A and EC, presented previously, it is possible to make a comparison of the punching resistance pressures in accordance with the design standards, ACI 318 [²⁰] (ACI), next generation of Eurocode 2, FprEC2 [²¹] (EC2), NBR 6118 [²²] (NBR) and fib Model Code [²³] (MC) levels II and III (LoA II and LoA III) of approximation. The safety parameters provided for in the project codes were assigned as 1.0. To facilitate understanding, the ultimate load results (V), predicted by the normative codes, are compared with the numerical models (V_FEA) using the V_FEA/V_Code relationship. This comparison making it possible to observe how each standard can predict the breaking load for each model of the two series analyzed.

4.1. Comparison of project code estimates for the EC series

In this section, the estimates obtained numerically for the four Series A models are presented in Table 5 by the V_FEA/V_Code relationship, and also presented the mean values, standard deviation (S.D.) and coefficient of variation (C.V.) for each design standard and in Figure 11 it is possible monitor the evolution of each model’s normative predictions.

Table 5
Comparison of theoretical load predictions with Series A numerical models.

DIMODELS	VFEA (kN)	$\frac{V_{FEA}}{V_{ACI}}$	$\frac{V_{FEA}}{V_{EC2}}$	$\frac{V_{FEA}}{V_{NBR}}$	$\frac{V_{FEA}}{V_{MCII}}$	$\frac{V_{FEA}}{V_{\mathrm{}MCIII}}$
A-5	788.12	1.53	1.16	1.39	1.23	1.21
A-10	785.06	1.55	1.15	1.38	1.22	1.21
A-15	753.17	1.51	1.11	1.37	1.17	1.16
A-20	690.83	1.39	1.12	1.26	1.07	1.06
Mean		1.5	1.14	1.35	1.17	1.16
S.D.		0.06	0.02	0.05	0.06	0.06
D.V.		4.26	1.92	3.93	5.19	5.19

Figure 11
Evolution of the breaking load for the A Series according to design codes.

From the predictions of the calculations, the mean results that best represented the numerical predictions were represented, respectively, by the EC2 predictions followed by the MC in its level III and II (LoA III and LoA II) approximation respectively. Both numerical results presented mean increase rates below 1.23, above normative predictions. More conservative results are observed for the ACI and NBR forecasts, with rates corresponding to 50% and 35% respectively of numerical estimates.

The results obtained by EC2 represented the best mean, with indices varying from 1.11 to 1.16, and the lowest variational coefficient, 1.92%. For MC, at both levels of approximation they presented good mean results, however it is worth noting the higher variational coefficient rates, indicating greater variation in results compared to mean predictions. With the results presented in Table 5, it can be seen from the standard deviation indices and the mean that EC2 and MC, at both levels of approximation, managed to predict more satisfactory results and close to numerical models.

Based on the load predictions that the standards employ in prestressed flat slabs, stability is noted among all estimates provided by MC, which is justified by the verification taking into account all prestressing forces that are in the range of support (b_s) referring to 3 times the radius of the zero-bending moment plus the width of the column. Stability was also observed in EC2 for the A-5, A-10 and A-15 series, due to the update of the European standard considering all prestressing forces being within the bs range referring to 6 times the useful height of the slab plus the pillar width. Stability in the results was also observed between the estimates predicted by the ACI, indicating that the design standard only considers the prestressing forces exerted in a region, and the rupture estimate for flat slabs does not take into account the distance between the tendons. For the EC2 update, it was noticeable that the reduction of its control perimeter affected, above all, the eccentricity point that coincides with the prestressing tendons, thus being the main contributing factor to the improvement in the approximation of results.

4.2. Comparison of project code estimates for the EC Series

To better understand how normative codes deal with the effect of eccentricity in prestressing tendons, Table 6 presents the design estimates of the four EC Series models, and the V_FEA/V_Code relationship, as well as their respective D.P. and C.V.. In Figure 12 it is possible to follow the evolution of the normative predictions of each model.

Table 6
Comparison of theoretical load predictions with Series EC numerical models.

MODELS	VFEA (kN)	$\frac{V_{FEA}}{V_{ACI}}$	$\frac{V_{FEA}}{V_{EC2}}$	$\frac{V_{FEA}}{V_{NBR}}$	$\frac{V_{FEA}}{V_{MCII}}$	$\frac{V_{FEA}}{V_{MCIII}}$
EC-5	665.06	1.36	1.22	1.30	1.55	1.47
EC-10	619.18	1.27	1.14	1.21	1.45	1.37
EC-15	638.85	1.31	1.17	1.25	1.49	1.41
EC-20	600.96	1.23	1.16	1.18	1.40	1.33
Mean		1.29	1.17	1.24	1.47	1.39
S.D.		0.05	0.03	0.05	0.06	0.05
D.V.		3.77	2.69	3.77	3.77	3.77

Figure 12
Evolution of the breaking load for the E Series according to design codes.

For the normative predictions of the EC Series, the predictions revealed mean results closer to those of the numerical models using the equations from the update of the European standard EC2, with an mean estimate 17% higher. For the update of the Brazilian NBR standard, a more conservative trend is noted in the results. From the variational coefficient (Table 6), more stable results are observed, not exceeding 3.77%.

From the results, it is noted that the MC was the one that presented the greatest interference in the results with estimates of up to 55% higher than the numerical models. This can be justified by the fact that MC presents an approach to predictions based on the prestressing moment based on the eccentricity in the prestressing tendons in the support range (b_s).

The normative predictions of the EC Series also showed stability in the ACI and MC results, indicating that these normative codes lack a parameter capable of assisting in predictions taking into account the spacing between the prestressing tendons. It was observed that the American standard was the one with the smallest variations between the two series, which is justified by the fact that the ACI does not assign in its formulations any additional parameter due to the eccentricity of the tendons, except for the vertical force due to prestressing which becomes be disregarded in models without eccentricity.

5. CONCLUSIONS

The results of the numerical analyzes showed a good agreement with the experimental data, so that the modeling correctly predicted the punching failure in concrete slabs. Given that the results are in agreement, a parametric study of new structural models was presented to better understand the effects caused by variations in spacing and eccentricity in prestressing tendons.

In the numerical models presented for Series A, the influence of the spacing between the prestressing tendons on shear resistance was evaluated. In the models analyzed, there was a reduction in the punching-resistant capacity of the slabs, as well as in the strain of the concrete.

From the EC Series models, they were evaluated for interference caused by the increase in eccentricity in prestressing tendons. According to the models presented, it is possible to conclude that the eccentricity of the tendons is necessary due to its great influence on the punching resistance, as it does not exert a contrary vertical force due to the eccentricity.

Based on the predictions of the design codes, it can be concluded that the design standards predicted more conservative results. When considering the prestressing force in a domain range, the design standards represented stability between some models, which indicates the need for a relevant parameter capable of improving results due to a small change in the distance between the tendons. Regarding eccentricity, it may be that the fib Model Code [²³] presents more sensitive parameters due to the lack of eccentricity interfering with the results. It can be concluded that design codes act to promote safety in both situations.

6. ACKNOWLEDGMENTS

This research was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-Brasil (CAPES)-Finance Code 001.

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Publication Dates

• Publication in this collection
  09 Sept 2024
• Date of issue
  2024

History

• Received
  03 May 2024
• Accepted
  10 July 2024