.

Berruecos Licona, Esteva Maraboto & García Benitez / INGE CUC, vol. 19 no. 2, pp. 85–96. July - December, 2023

Slenderness in Wall-frame Systems: Corrective factors for the Valley of Mexico

Esbeltez en Sistemas Marco Muro: Factores correctivos para el Valle de México

DOI: http://doi.org/10.17981/ingecuc.19.2.2023.07

Artículo de Investigación Científica. Fecha de Recepción: 07/02/2023. Fecha de Aceptación: 05/06/2023.

Sergio O. Berruecos Licona

UNAM. CDMX (México)

ing.berruecos@gmail.com

Luis Esteva Maraboto

UNAM. CDMX (México)

LEstevaM@iingen.unam.mx

Silvia R. García Benitez

UNAM. CDMX (México)

sgab@pumas.iingen.unam.mx

.

To cite this paper:

S. Berruecos Licona, L. Esteva Maraboto & S. García Benitez, “Slenderness in Wall-frame Systems: Corrective factors for the Valley of Mexico”, INGE CUC, vol. 18, no. 2, pp. 85–96, 2023. DOI: http://doi.org/10.17981/ingecuc.19.2.2023.07

.

Abstract

Introduction— The methodologies and procedures used in the design of buildings shown in the Mexico City Building Regulations 2017 are based on reliability and performance techniques, however, the factors applied in this standard for irregular systems are based on engineering practice.

Objective— The aim of this research is to obtain corrective factors applicable to the Mexican standards for the design of concrete structures with slenderness characteristics and with frame-wall system.

Methodology— The analysis, design and comparison of two families of concrete buildings with dual system, the first family is characterized by complying with the requirements of regularity delimited in the regulations, the second family breaks with the requirement of slenderness, both families are formed by buildings of 11, 15 and 20 levels. For each building, a sample of at least 50 buildings was created using the Montecarlo method, varying their mechanical and geometric properties, live loads, dead loads and seismic actions. The samples were evaluated by means of a reliability analysis and then compared.

Results— Recommendations are given for obtaining reliability and performance based factors associated with specific ground acceleration and different degrees of slenderness.

Conclusions— The Mexico City Building Regulations only considers the slenderness irregularity factor when the height/base ratio is greater than 4 and there is also another irregularity in the building. This study shows that buildings with slenderness ratios greater than 4 should be considered as irregular and a corrective factor should be applied according to their degree of slenderness, this in turn without having infringed any other irregularity.

Keywords— Irregular buildings; slenderness; reliability; frame-wall system; concrete frames; Opensees.

Resumen

Introducción— Las metodologías y procedimientos utilizados en el diseño de edificaciones que muestra el Reglamento de Construcciones de la Ciudad de México 2017 están basadas en técnicas de confiabilidad y desempeño, sin embargo, los factores que se aplican en esta norma para sistemas irregulares tienen fundamento en la práctica ingenieril.

Objetivo— El objetivo de esta investigación es la obtención de factores correctivos aplicables a la normatividad de mexicana para el diseño de estructuras de concreto con características de esbeltez y con sistema marco-muro.

Metodología— Se realizó el análisis, diseño y comparativa de dos familias de edificios de concreto con sistema dual, la primera familia se caracteriza por cumplir con los requisitos de regularidad delimitadas en la normativa, la segunda familia irrumpe con el requisito de esbeltez, ambas familias están formadas por edificios de 11, 15 y 20 niveles. De cada edificio se creo una muestra con un mínimo de 50 edificios mediante el método de Montecarlo variando sus propiedades mecánicas, geométricas, cargas vivas, cargas muertas y acciones sísmicas representativas. Las muestras fueron evaluadas mediante un análisis de confiabilidad y posteriormente comparadas.

Resultados— Se dan recomendaciones para la obtención de factores basados en confiabilidad y desempeño asociadas a una aceleración específica del terreno y diferentes grados de esbeltez.

Conclusiones— El reglamento de Construcciones de la Ciudad de México contempla únicamente el factor de irregularidad por esbeltez cuando la relación altura/base es mayor a 4 y además se cuente con otra irregularidad en la edificación. Este estudio muestra que los edificios con relaciones de esbeltez mayores que 4 deben ser consideradas como irregulares y debe aplicarse un factor correctivo de acuerdo con su grado de esbeltez, esto a su vez sin haber infringido alguna otra irregularidad.

Palabras clave— Edificios irregulares; esbeltez; confiabilidiad; sistema marco muro; marco de concreto; Opensees

I. Introduction

The Mexico City Building Regulations and its Complementary Technical Standards (RCCDMX and NTC respectively [1]-[2], in their Spanish acronyms) have been for years the basis for the design of buildings in the metropolis. These regulations go through reviews and updates when major events occur. The RCCDMX17 and its NTC17 (regulations published after the September 19th, 2017, seismic event that strongly shakes Mexico City) are based on reliability and performance of structures, however, the factors related to irregularities in buildings applied in seismic design spectrum so far are based on engineering criteria [1]-[2]. In this research corrective factors are proposed for seismic design spectrum specifically for buildings with slenderness irregularity. Two families of buildings (11, 15 and 20 levels) with frame-wall system were analyzed [1]-[2]. The first family conforms the regulations marked by the NTC17 to be considered regular while the second family does not satisfy slenderness condition (height-base ratio greater than or equal to 4.0) [1]-[2].

The modelled buildings are founded at Lake zone (potent deposits of highly compressible clay strata often covered superficially by alluvial soils, dried materials and artificial fill materials) and defined with irregularity factor equal to 1.0. For prototypes with same number of levels their fundamental period must be similar (for meaningful comparisons between them (regular building is the reference and through an iterative process the sections of the irregular building are set to get the closest fundamental period).

The software SIB (Simulation of Buildings) [5] was used for obtaining the numerical framework that considers the uncertainties for live load, dead load, dimensions of the cross sections, coverings, area of the reinforcing steel and the spacing of the stirrups. A step-by-step nonlinear analysis was performed for each 3D model (of distributed plasticity) using the Opensees program [6]. The input seismic records were obtained for different return periods using the hybrid method developed by UNAM and UPAEP researchers [7]. For each orthogonal directions on seismic inputs, the minimum Secant Stiffness Reduction Index (IRRS) and the reliability (according to the minimum value of the intensity required to produce collapse) [4] of each building were obtained. A mathematical equalization of the reliability functions of the systems that share the same number of levels and fundamental period was performed. Comparing the Cornell beta (β) of a regular system with its irregular simile a corrective factor to be applied to the ordinates of the design spectrum stablished by the RCCDMX, is obtained.

II. Description of the models

The analyzed objects are two reinforced concrete set of buildings with wall-frame system. These buildings are set in the iconic SCT site (Secretariat of Communications and Transportation) (Zone III or Lake). The first set are structures with a square base of 18 × 18 m and height-base ratio less than 4, this family is defined by the NTC17-Seism as regular buildings (Fig. 1). For the second set, the base is of 9 × 9 m with height-base ratios greater than 4, catalogued as irregular (Fig. 2). Both families were designed with a ductility factor Q = 2 and a correction factor of irregularity equal to 1. The soil-structure effects were considered by translational and rotational stiffnesses, and damping coefficients (as specified in the NTC17-Seism) [8]. The whole set of buildings were designed with f’c 250 kg/cm2 and fy = 4 200 kg/cm2, in Table 1, Table 2 and Table 3 their cross-sections and fundamental periods are shown.

Fig. 1. 3D view of a family of “Regular buildings”.
Source: Authors.
Fig. 2. 3D family view of “Irregular buildings”.
Source: Authors.
Table 1.
Cross sections in Regular Buildings.

Building

Floor

Column dimensions (m)

Beam dimensions (m)

Thickness slab (m)

Wall thickness (m)

Regular Building 1

1-6

0.75 × 0.75

0.32 × 0.60

0.15

0.48

7-11

0.60 × 0.60

0.30 × 0.60

0.15

0.30

Regular Building 2

1-5

0.60 × 0.60

0.45 × 0.60

0.15

0.45

6-10

0.55 × 0.55

0.45 × 0.60

0.15

0.40

11-15

0.50 × 0.50

0.40 × 0.50

0.15

0.30

Regular Building 3

1-7

1.05 × 1.05

0.80 × 1.00

0.15

0.45

8-14

0.85 × 0.85

0.60 × 0.85

0.15

0.40

15-20

0.75 × 0.75

0.65 × 0.75

0.15

0.30
Source: Authors.
Table 2.
Cross Sections in Irregular Buildings.

Building

Floor

Column dimensions (m)

Beam dimensions (m)

Thickness slab (m)

Wall thickness (m)

Irregular Building 1

1-6

0.50 × 0.50

0.35 × 0.48

0.10

0.35

7-11

0.45 × 0.45

0.35 × 0.45

0.10

0.35

Irregular Building 2

1-5

0.55 × 0.55

0.35 × 0.55

0.10

0.35

6-10

0.50 × 0.50

0.35 × 0.50

0.10

0.35

11-15

0.45 × 0.45

0.35 × 0.45

0.10

0.35

Irregular Building 3

1-7

0.85 × 0.85

0.60 × 0.85

0.10

0.40

8-14

0.80 × 0.80

0.50 × 0.80

0.10

0.40

15-20

0.65 × 0.65

0.45 × 0.65

0.10

0.40
Source: Authors.
Table 3.
Periods of studied systems.

Mode

Regular Building 1 (sec)

Regular Building 2 (sec)

Regular Building 3 (sec)

Irregular Building 1 (sec)

Irregular Building 2 (sec)

Irregular Building 3 (sec)

1

0.921

1.083

1.25

1.003

1.157

1.303

2

0.921

1.083

1.25

1.003

1.157

1.303

3

0.608

0.624

0.734

0.659

0.695

0.516

4

0.231

0.256

0.347

0.269

0.296

0.321

5

0.231

0.256

0.347

0.269

0.296

0.321

6

0.156

0.157

0.215

0.183

0.186

0.166

7

0.108

0.118

0.167

0.123

0.131

0.151

8

0.108

0.118

0.167

0.123

0.131

0.151

9

0.074

0.075

0.106

0.085

0.085

0.096

10

0.064

0.071

0.101

0.073

0.077

0.096

11

0.064

0.071

0.101

0.073

0.077

0.095

12

0.043

0.048

0.071

0.05

0.052

0.069
Source: Authors.

III. Building modeling

Traditional structural modeling does not explicitly express the uncertainties associated with human error in construction, design, material qualities, etc. In this investigation these uncertainties were considered through Montecarlo simulations (program “Simulation of buildings” [5]). Variations in live loads are simulated using the traditional load intensity model [9], and the contributions of studies at UNAM (Mexico) [10], while the conditions of dead loads follow ANSI recommendations [11]. Cross sections and reinforcing steel are set according with U of A research (Canada) guidelines [12]-[13], and UNAM investigations [14], and mechanical properties of concrete [15], [16].

More than 50 conditions were simulated under Montecarlo for each building. In the simulations (Opensees running) has DispBeamColumn elements with 5 discretizations in beams and 3 in columns (fiber type sections are under Navier-Bernoulli hypothesis). The model calibrated by UNAM and UFPS (Colombia) [17], was used for reinforced concrete walls using TRUSS2 type elements and ConcretewBeta material [18], the beam and column materials used in Opensees were Concrete01 for the unconfined concrete, Concrete02 for the confined concrete and Steel02 for the reinforcing steel. The soil-structure interaction was modeled using a ZeroLength element with a master node with the equaldof command.

A. Seismic inputs

The buildings are analyzed under the two simultaneous orthogonal seismic components representative of soils in SCT site. The intensity measure was taken as (1):

Where

Sax (T), Say (T) = Pseudo-accelerations of the response spectrum associated with the fundamental period of the structure in the X and Y direction respectively.

The analyses of UNAM studies [19], were used to obtain the seismic hazard in the site, where the accelerations associated with the fundamental period of each building under study were obtained for different return periods (Table 4 and Table 5).

Table 4.
Accelerations associated with the fundamental period of regular structures.

Return period

Regular

Building 1

Regular

Building 2

Regular

Building 3

(years)

Acceleration

Acceleration

Acceleration

250

206.5

271.3

335.0

500

234.7

308.7

385.0

1000

261.5

350.7

433.5

2500

305.3

411.6

511.0

5000

339.9

458.4

575.0
Source: Authors.
Table 5.
Accelerations associated with the fundamental period of irregular structures.

Return

period

Irregular

Building 1

Irregular

Building 2

Irregular

Building 3

(years)

Acceleration

Acceleration

Acceleration

250

241.1

295.8

345.65

500

274.3

337.4

394.40

1000

307.5

391.2

446.99

2500

359.9

455.5

526.58

5000

399.1

506.6

592.86
Source: Authors.

For considering extreme earthquakes, a minimum of 10 pairs of records were simulated for each return period shown in Table 4 and Table 5, obtaining 50 pairs of accelerograms for each structural system [20]. The average response spectrum obtained for each pair of simulations in the X and Y directions with (1) are shown in Fig. 3.

Fig. 3. Spectrum used in regular and irregular buildings.
Source: Authors.

IV. Results

A. Secant Stiffness Reduction Index

The “Secant stiffness reduction index” was obtained [4]. This index has the advantage of being a global indicator that generalizes the stiffness reduction of the system by taking the secant stiffness of a nonlinear dynamic analysis. IRRS = 0 can be interpreted as the initial stiffness of the structure did not reduced and IRRS = 1 means that the structure failed. This index is expressed as (2):

Where

K0 = Initial system stiffness.

KS = Secant stiffness of the system.

Both K0 and KS were determined for each simulated building using hysteresis curves derived from nonlinear dynamic analyses. Each simulated building underwent a nonlinear analysis with a low-intensity earthquake to obtain its initial stiffness (K0), and subsequently, it was evaluated with medium and high-intensity earthquakes to obtain its secant stiffness (KS) by means of the following expression (3):

Where

δa = Maximum displacement at the roof center of masses.

Vb = Basal shear associated with the maximum displacement at the roof center of masses.

B. Step-by-step nonlinear dynamic analysis

The parameter K0 is obtained from nonlinear analyses for low intensity earthquakes where the structure remains in the linear range. Analogously, Ks results of analyses with intermediate and high magnitude earthquakes where the structure is in the nonlinear range. Each analysis (for K0 and Ks) was developed in 3D and with simultaneous earthquakes obtaining 2 hysteresis curves, one corresponding to the X direction and the other corresponding to the Y direction. The resulted IRRS are for each quadrant and the largest one is selected to represent the greatest degradation of stiffness of the system (global view). Some responses for X and Y directions are shown in Fig. 4.

Fig. 4. Global responses of the systems.
Source: Authors.

C. Reliability criteria

To obtain the reliability functions, the seismic capacity of the structural systems is expressed by the minimum collapse intensity (YC) [4] and the safety margin (Zm) (4):

Where

ln YC = ZF = Natural logarithm of the minimum value of the intensity required to produce collapse.

ln y = ZF = Natural logarithm of the seismic intensity.

The beta index (β) [21], as a reliability measurement parameter, is set by (5):

Where

E(ln YC) = E(ZF) = Expected value of the natural logarithm of minimum value of the intensity required to produce collapse.

σz(ln YC) = σz(ZF) = Standard deviation of the natural logarithm of the minimum value of the intensity required to produce collapse.

Let Z = ln y, we define as the natural logarithm of the random variable Y associated with a value of IRRS = u for a building under study. A sample of pairs of random values is required to estimate the mean and standard deviation of Z(u). It is known that at the instant of failure where IRRS = 1, the values of Z(ZF = lnYc) show the intensity at which buildings fail. However, it is not possible to obtain the minimum intensity at which they would fail (ZF). Therefore, examples from the sample that exhibit failure behavior should not be included in estimating E[Z(u)] and σ[Z(u)] through a least squares regression.

If the sample includes cases where it equals 1.0, those statistical moments E[Z(u)]│α1] and σ[Z(u)]│α2] and the corresponding parameters {α1, α2} should be determined using a maximum likelihood criterion (6) [20].

Where m is the number of pairs of values (zi, ui) for ui < 1.0, and n is the number of pairs of values for uj = 1. fZ and FZ are the normal density function and cumulative distribution function respectively. The maximum likelihood criterion is used because values of u = 1 can be reached for different intensity values, and to apply the least squares fitting criterion, it is necessary to work with the minimum values of intensity that lead to u = 1.

Fig. 5 compares the reliability functions obtained for regular and irregular buildings.

Fig. 5. Comparison of reliability functions for studied systems.

Source: Authors.

V. Corrective factors

For the determination of the corrective factors, the following assumptions were made:

  1. Both families (regular and irregular) are founded on the same site.
  2. The family of regular buildings shares the same floor plan dimensions.
  3. The family of irregular buildings shares the same floor plan dimensions.
  4. Each regular building will be associated with an irregular one with the same height.
  5. The comparative buildings share the same number of levels with the same mezzanine heights.
  6. The comparative buildings share the same arrangement of beams, columns, and walls.
  7. The comparative buildings share a similar fundamental period.
  8. The comparative buildings comply with the stipulations of the RCCDMX and its NTC.
  9. The comparative buildings are designed with irregularity factors equal to 1.0.
  10. The comparative buildings will share the β of the regular system (βRegular Building) associated to a representative acceleration of 250 years defined in the RCCDMX17 and its NTC17 [1]-[2].

A graphical representation of the comparative reliability equations of a regular building versus an irregular building is shown in Fig. 6.

Fig. 6. Comparison of reliability equations for regular and irregular buildings.
Source: Authors.

The reliability equations of a regular building and an irregular building are expressed as (7)-(8):

Same level of reliability between irregular and regular buildings, involves (9):

The equality shown in (9) defines the same level of reliability for the regular system as for the irregular system. We use the equation of the irregular system evaluated at Y3 that equals the reliability of the regular system, as shown below (10):

Clearing Y3 from (10):

The acceleration Y1 is taken as a reference for regular systems, the difference that has with Y3 for irregular systems is (12):

The addition of δY1Y3 to the acceleration Y2 represents the acceleration at which the irregular building must be designed (13).

The corrective factor of the ordinates of the design spectrum of accelerations for the slender irregular system will be given by (14):

The properties of the simulated cases are summarized in Table 6.

Table 6.
Reliability equations for each system.

Building

βRegular building

βIrregular building

1

β = –9.578ln(Y) + 55.959

β = –2.033ln(Y) + 15.165

2

β = –6.325ln(Y) + 39.413

β = –1.838ln(Y) + 13.496

3

β = –2.457ln(Y) + 17.698

β = –1.527ln(Y) + 11.300
Source: Authors.

Applying the equations above to the reliability functions of each building, the corrective factors that affect the ordinates of the design spectrum are show in Fig. 7.

Fig. 7. Corrective factors for slenderness.
Source: Authors.

Fig. 7 shows the corrective factors applicable in the design spectrum to match the reliability levels of a slender system and a regular system, these factors increase when the slenderness ratio is greater than 4.0. Finally, the inverse of these corrective factors are the irregularity factors (Fig. 8) applicable in RCCDMX17 and its NTC17 [1]-[2].

Fig. 8. Irregularity factors for slenderness.
Source: Authors.

VI. Conclusions

Reliability based corrective factors applicable to the seismic design spectrum marked in the RCCDMX17 and its NTC17 [1]-[2], were obtained for buildings designed with Q = 2 and classified as slender with wall-frame system founded in zone III of the lake.

NTC17-Seism specifies that to satisfies the condition of “regular building” the ratio of the height to the smallest dimension of its base must not be greater than 4, thus an irregular building is assigned an irregularity factor of 0.8, which coincides with 0.83 calculated for a slenderness of 4.28. However, the 0.8 factor specified in the regulation does not apply unless there is another irregularity in the building. Therefore, it would not meet the reliability requirements specified in this study.

Since as of 2017 the design spectrums are performed through the SASID software [3] and since this only provides the irregularity factors of 1.0, 0.8 and 0.7, the following proposal is made in the use of this tool:

To take in consideration the irregularity factor, the following conditions are recommended:

A. Irregular structure

A structure will be considered irregular slender if it satisfies the requirement where: “The ratio of its height to the smallest dimension of its base is greater than 4.0 and less than 6.0” (it is not necessary not to satisfy another requirement described in section 5.0 of the NTC17S).

B. Very irregular structure

A structure will be considered very irregular if it does not satisfy two or more of the requirements described in section 5.0 of NTC17-seismic [1]-[2], or if the ratio of its height to the dimension of its base is greater than 6.0 and less than 8.0 (Table 7).

Table 7.
Irregularity factors suggested for SASID tool.

Structure classification

Relation (H/B)

Irregularity factor

Regular

(H/B) < 4

1.0

Irregular

4 (H/B) < 6

0.8

Very Irregular

6 (H/B) < 8

0.7
Source: Authors.

In case of using the equations of the NTC17-Seism [1]-[2], to obtain the design spectrum, it is recommended to use the values from the Fig. 8.

Acknowledgments

Thanks to the Consejo Nacional de Ciencia y Tecnología (CONACYT), for the financial support provided to the first author during the completion of this research.

Declarations Conflicts of interests and competing interests

References

[1] Normas Técnicas Complementarias para el Diseño y Construcción de Cimentaciones, Gob. CDMX, Gaceta No. 220 Bis, 15 dic. 2017, pp. 10-43. Recuperado de https://www.smig.org.mx/archivos/NTC2017/normas-tecnicas-complementarias-reglamento-construcciones-cdmx-2017.pdf

[2] Normas Técnicas Complementarias para el Diseño y Construcción de Estructuras de Concreto, Gob. CDMX, Gaceta No. 220 Bis, 15 dic. 2017, pp. 372–566. Recuperado de https://www.smig.org.mx/archivos/NTC2017/normas-tecnicas-complementarias-reglamento-construcciones-cdmx-2017.pdf

[3] Normas Técnicas Complementarias para el Diseño por sismo, Gob. CDMX, Gaceta No. 220 Bis, 15 dic. 2017, pp. 44–83. Recuperado de https://www.isc.cdmx.gob.mx/servicios/servicio/normas-tecnicas-complementarias-y-sasid

[4] L. Esteva & O. J. Díaz-López, “Seismic reliability functions for complex systems based on a secant-stiffness reduction index,” in Reliability and Optimization of Structural Systems: Assessment, Design, and Life-Cycle Performance, D. Frangopol, M. Kawatani & C. Kim, Eds., LDN, UK: Taylor & Francis e-Library, 2007, pp. 83–92. https://doi.org/10.1201/b16819-11

[5] J. G. Rangel & L. Esteva. Reference Manual of Simulation of Buildings (version 1.0). VER, MX: UV, 2015.

[6] OpenSees. (3.3.0, 2021). PEER. [Online]. Available: http://opensees.berkeley.edu

[7] L. Esteva & E. Ismael, “A maximum likelihood approach to system reliability with respect to seismic collapse,” presented at 11th WG7.5 Working Conference, IFIP, BFF, CA, 2-5 Nov. 2003. https://doi.org/10.1201/9781003078876

[8] A. Vásquez, “Funciones de daño acumulado para edificios de concreto reforzado”, Tesis de Maestría, Instut. Ing., UNAM, CDMX, MX, 2010. Disponible en https://repositorio.unam.mx/contenidos/73622

[9] J-C. Pier & A. Cornell, “Spatial and temporal variability of live loads”, J. Struct. Div. ASCE, vol. 99, no. 5, pp. 903–922, May. 1973. https://doi.org/10.1061/JSDEAG.0003512

[10] J. Soriano, “Análisis teórico de cargas vivas en edificios”, Tesis de Maestría, Fac. Ing., UNAM, CDMX, MX, 1996. Recuperado de 132.248.9.195/ppt1997/0234028/Index.html

[11] American National Standard A58, Minimum Design Loads in Buildings and Other Structures, ANSI, Jun. 1980. Available from https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nbsspecialpublication577.pdf

[12] S. Mirza & J. MacGregor, “Variability of mechanical properties of reforcing bars”, J. Struct. Div. ASCE, vol. 105, no. 5, pp. 921–937, May. 1979. https://doi.org/10.1061/JSDEAG.0005146

[13] S. Mirza & J. MacGregor, “Variations in dimensions of reinforced concrete members”, J. Struct. Div. ASCE, vol. 105, no. 4, pp. 751–766, Apr. 1979. https://doi.org/10.1061/JSDEAG.0005132

[14] M. Rodríguez y J. Botero, “Comportamiento sísmico de estructuras considerando las propiedades mecánicas de aceros de refuerzo mexicanos”, Rev. Ing. Sismic., no. 49, pp. 39–50, Ene. 1995. https://doi.org/10.18867/RIS.49.268

[15] C. Mendoza, “Evaluación de la resistencia del concreto en la estructura por medio del ensayo de corazones”, IMCYC, vol. III, no. 34, pp. 611–611, 1991. Disponible en http://www.imcyc.com/revistacyt/jul11/anteriores.html

[16] R. Meli y C. Mendoza, “Reglas de verificación del concreto”, Revista de Ingeniería, vol. LXI, pp. 19–24, Dic. 1991.

[17] A. Vásquez y R. Gallardo, “Respuesta no lineal de estructuras con muros de concreto reforzado”, INGE CUC, vol. 14, no. 2, pp. 55–61, Jun. 2018. https://doi.org/10.17981/ingecuc.14.2.2018.05

[18] N. Stevens, S. Uzumeri, M. Collins & G. Will, “Constitutive Model for Reinforced Concrete Finite Element Analysis”, ACI Struct. J., vol. 88, no. 1, pp. 49–59, Jan. 1991. https://doi.org/10.14359/3105

[19] Esteva, O. Díaz-López & J. García-Pérez, “Reliability functions for earthquake resistant design,” Reliab. Eng. Syst. Saf., vol. 73, no. 3, pp. 239–262 Sep. 2001. https://doi.org/10.1016/S0951-8320(01)00045-X

[20] E. Ismael & L. Esteva, “A hybrid method for simulating strong ground motions records,” presented at First European Conference on Earthquake Engineering and Seismology, ECEES, GE, CH, 3-8 Sept. 2006. Available: https://www.preventionweb.net/quick/38670

[21] C. Cornell, “A Probability-Based Structural Code”, ACI J. Proc., vol. 66, no. 12, pp. 974–985, Jan. 1969. https://doi.org/10.14359/7446

Sergio O. Berruecos Licona. UNAM (CDMX, México).

Luis Esteva Maraboto. UNAM (CDMX, México).

Silvia R. García Benitez. UNAM (CDMX, México).

.
© The author; licensee Universidad de la Costa - CUC.
INGE CUC vol. 19 no. 2, pp. 85-96. July - December, 2023
Barranquilla. ISSN 0122-6517 Impreso, ISSN 2382-4700 Online
.