Optimal dimensioning for the corner combined footings

Lopez-Chavarria, Sandra,Luevanos-Rojas, Arnulfo,Medina-Elizondo, Manuel Techno-Press 2017 Advances in computational design Vol.2 No.2

This paper shows optimal dimensioning for the corner combined footings to obtain the most economical contact surface on the soil (optimal area), due to an axial load, moment around of the axis "X" and moment around of the axis "Y" applied to each column. The proposed model considers soil real pressure, i.e., the pressure varies linearly. The classical model is developed by trial and error, i.e., a dimension is proposed, and after, using the equation of the biaxial bending is obtained the stress acting on each vertex of the corner combined footing, which must meet the conditions following: 1) Minimum stress should be equal or greater than zero, because the soil is not withstand tensile. 2) Maximum stress must be equal or less than the allowable capacity that can be capable of withstand the soil. Numerical examples are presented to illustrate the validity of the optimization techniques to obtain the minimum area of corner combined footings under an axial load and moments in two directions applied to each column.

A new model for T-shaped combined footings part II: Mathematical model for design

Luevanos-Rojas, Arnulfo,Lopez-Chavarria, Sandra,Medina-Elizondo, Manuel Techno-Press 2018 Geomechanics & engineering Vol.14 No.1

The first part shows the optimal contact surface for T-shaped combined footings to obtain the most economical dimensioning on the soil (optimal area). This paper presents the second part of a new model for T-shaped combined footings, this part shows a the mathematical model for design of such foundations subject to axial load and moments in two directions to each column considering the soil real pressure acting on the contact surface of the footing with one or two property lines restricted, the pressure is presented in terms of an axial load, moment around the axis "X" and moment around the axis "Y" to each column, and the methodology is developed using the principle that the derived of the moment is the shear force. The classic model considers an axial load and a moment around the axis "X" (transverse axis) applied to each column, i.e., the resultant force from the applied loads is located on the axis "Y" (longitudinal axis), and its position must match with the geometric center of the footing, and when the axial load and moments in two directions are presented, the maximum pressure and uniform applied throughout the contact surface of the footing is considered the same. To illustrate the validity of the new model, a numerical example is presented to obtain the design for T-shaped combined footings subjected to an axial load and moments in two directions applied to each column. The mathematical approach suggested in this paper produces results that have a tangible accuracy for all problems.

Optimal design for the reinforced concrete circular isolated footings

Lopez-Chavarria, Sandra,Luevanos-Rojas, Arnulfo,Medina-Elizondo, Manuel,Sandoval-Rivas, Ricardo,Velazquez-Santillan, Francisco Techno-Press 2019 Advances in computational design Vol.4 No.3

In this paper is presented the minimum cost (optimal design) for reinforced concrete circular isolated footings based on an analytic model. This model considers a load and two moments in directions of the X and Y axes, and the pressure has a variation linear, these are the effects that act on the footing. The minimum cost (optimal design) and the Maple program are shown in Flowcharts. Two numerical experiments are shown to obtain the minimum cost design of the two materials that are used for a circular footing supporting an axial load and moments in two directions in accordance to the code of the ACI (American Concrete Institute), and it is compared against the current design (uniform pressure). Also, the same examples are developed through the normal procedure to verify the minimum cost (optimal design) presented in this document, i.e., the equations of moment, bending shear and punching shear are used to check the thickness, and after, the steel areas of the footing are obtained, and it is compared against the current design (uniform pressure). Results section show that the optimal design is more accurate and more economical than to any other model. Therefore, it is concluded that the optimized design model presented in this paper should be used to obtain the minimum cost design for the circular isolated footings.

A new model for T-shaped combined footings part I: Optimal dimensioning

Luevanos-Rojas, Arnulfo,Lopez-Chavarria, Sandra,Medina-Elizondo, Manuel Techno-Press 2018 Geomechanics & engineering Vol.14 No.1

The foundations are classified into shallow and deep, which have important differences: in terms of geometry, the behavior of the soil, its structural functionality, and its constructive systems. The shallow foundations may be of various types according to their function; isolated footings, combined footings, strip footings, and slabs foundation. The isolated footings are of the type rectangular, square and circular. The combined footing may be rectangular, trapezoidal or T-shaped in plan. This paper presents a new model for T-shaped combined footings to obtain the most economical contact surface on the soil (optimal dimensioning) to support an axial load and moment in two directions to each column. The new model considers the soil real pressure, i.e., the pressure varies linearly. The classical model uses the technique of test and error, i.e., a dimension is proposed, and subsequently, the equation of the biaxial bending is used to obtain the stresses acting on each vertex of the T-shaped combined footing, which must meet the conditions following: The minimum stress should be equal or greater than zero, and maximum stress must be equal or less than the allowable capacity that can withstand the soil. To illustrate the validity of the new model, numerical examples are presented to obtain the minimum area of the contact surface on the soil for T-shaped combined footings subjected to an axial load and moments in two directions applied to each column.

Numerical experimentation for the optimal design for reinforced concrete rectangular combined footings

Velazquez-Santilla, Francisco,Luevanos-Rojas, Arnulfo,Lopez-Chavarria, Sandra,Medina-Elizondo, Manuel,Sandoval-Rivas, Ricardo Techno-Press 2018 Advances in computational design Vol.3 No.1

This paper shows an optimal design for reinforced concrete rectangular combined footings based on a criterion of minimum cost. The classical design method for reinforced concrete rectangular combined footings is: First, a dimension is proposed that should comply with the allowable stresses (Minimum stress should be equal or greater than zero, and maximum stress must be equal or less than the allowable capacity withstand by the soil); subsequently, the effective depth is obtained due to the maximum moment and this effective depth is checked against the bending shear and the punching shear until, it complies with these conditions, and then the steel reinforcement is obtained, but this is not guaranteed that obtained cost is a minimum cost. A numerical experimentation shows the model capability to estimate the minimum cost design of the materials used for a rectangular combined footing that supports two columns under an axial load and moments in two directions at each column in accordance to the building code requirements for structural concrete and commentary (ACI 318S-14). Numerical experimentation is developed by modifying the values of the rectangular combined footing to from "d" (Effective depth), "b" (Short dimension), "a" (Greater dimension), "${\rho}_{P1}$" (Ratio of reinforcement steel under column 1), "${\rho}_{P2}$" (Ratio of reinforcement steel under column 2), "${\rho}_{yLB}$" (Ratio of longitudinal reinforcement steel in the bottom), "${\rho}_{yLT}$" (Ratio of longitudinal reinforcement steel at the top). Results show that the optimal design is more economical and more precise with respect to the classical design. Therefore, the optimal design presented in this paper should be used to obtain the minimum cost design for reinforced concrete rectangular combined footings.

A comparative study for design of boundary combined footings of trapezoidal and rectangular forms using new models

Luevanos-Rojas, Arnulfo,Barquero-Cabrero, Jose Daniel,Lopez-Chavarria, Sandra,Medina-Elizondo, Manuel Techno-Press 2017 Coupled systems mechanics Vol.6 No.4

This paper shows a comparative study for design of reinforced concrete boundary combined footings of trapezoidal and rectangular forms supporting two columns and each column transmits an axial load and a moment around of the axis X (transverse axis of the footing) and other moment around of the axis Y (longitudinal axis of the footing) to foundation to obtain the most economical combined footing. The real soil pressure acting on the contact surface of the footings is assumed as a linear variation. Methodology used to obtain the dimensions of the footings for the two models consider that the axis X of the footing is located in the same position of the resultant, i.e., the dimensions is obtained from the position of the resultant. The main part of this research is to present the differences between the two models. Results show that the trapezoidal combined footing is more economical compared to the rectangular combined footing. Therefore, the new model for the design of trapezoidal combined footings should be used, and complies with real conditions.

Deflections and rotations in rectangular beams with straight haunches under uniformly distributed load considering the shear deformations

José Daniel Barquero-Cabrero,Arnulfo Luévanos-Rojas,Sandra López-Chavarría,Manuel Medina-Elizondo,Francisco Velázquez-Santillán,Ricardo Sandoval-Rivas 국제구조공학회 2018 Smart Structures and Systems, An International Jou Vol.22 No.6

This paper presents a model of the elastic curve for rectangular beams with straight haunches under uniformly distributed load and moments in the ends considering the bending and shear deformations (Timoshenko Theory) to obtain the deflections and rotations on the beam, which is the main part of this research. The traditional model of the elastic curve for rectangular beams under uniformly distributed load considers only the bending deformations (Euler-Bernoulli Theory). Also, a comparison is made between the proposed and traditional model of simply supported beams with respect to the rotations in two supports and the maximum deflection of the beam. Also, another comparison is made for beams fixed at both ends with respect to the moments and reactions in the support A, and the maximum deflection of the beam. Results show that the proposed model is greater for simply supported beams in the maximum deflection and the traditional model is greater for beams fixed at both ends in the maximum deflection. Then, the proposed model is more appropriate and safe with respect the traditional model for structural analysis, because the shear forces and bending moments are present in any type of structure and the bending and shear deformations appear.

Modeling for the strap combined footings Part I: Optimal dimensioning

Gabriel Aguilera-Mancilla,Arnulfo Luévanos-Rojas,Sandra López-Chavarría,Manuel Medina-Elizondo 국제구조공학회 2019 Steel and Composite Structures, An International J Vol.30 No.2

This paper presents a new model for the strap combined footings to obtain the most economical contact surface on the soil (optimal dimensioning) to support an axial load and moment in two directions to each column. The new model considers the soil real pressure, i.e., the pressure varies linearly. Research presented in this paper shows that can be applied to the T-shaped combined footings and the rectangular combined footings. The classical model uses the technique of test and error, i.e., a dimension is proposed, and subsequently, the equation of the biaxial bending is used to obtain the stresses acting on each vertex of the strap combined footing, which must meet the conditions following: The minimum stress should be equal or greater than zero, and maximum stress must be equal or less than the allowable capacity that can withstand the soil. Numerical examples are presented to obtain the optimal area of the contact surface on the soil for the strap combined footings subjected to an axial load and moments in two directions applied to each column. Appendix shows the Tables 4 and 5 for the strap combined footings, the Table 6 for the T-shaped combined footings, and the Table 7 for the rectangular combined footings.

Modeling for the strap combined footings Part II: Mathematical model for design

Juan Antonio Yáñez-Palafox,Arnulfo Luévanos-Rojas,Sandra López-Chavarría,Manuel Medina-Elizondo 국제구조공학회 2019 Steel and Composite Structures, An International J Vol.30 No.2

This paper presents the second part of the modeling for the strap combined footings, this part shows a mathematical model for design of strap combined footings subject to axial load and moments in two directions to each column considering the soil real pressure acting on the contact surface of the footing for one and/or two property lines of sides opposite restricted, the pressure is presented in terms of an axial load, moment around the axis “X” and moment around the axis “Y” to each column, and the methodology is developed using the principle that the derived of the moment is the shear force. The first part shows the optimal contact surface for the strap combined footings to obtain the most economical dimensioning on the soil (optimal area). The classic model considers an axial load and a moment around the axis “X” (transverse axis) applied to each column, i.e., the resultant force from the applied loads is located on the axis “Y” (longitudinal axis), and its position must match with the geometric center of the footing, and when the axial load and moments in two directions are presented, the maximum pressure and uniform applied throughout the contact surface of the footing is considered the same. A numerical example is presented to obtain the design of strap combined footings subject to an axial load and moments in two directions applied to each column. The mathematical approach suggested in this paper produces results that have a tangible accuracy for all problems and it can also be used for rectangular and T-shaped combined footings.

A comparative study between trapezoidal combined footings and T-shaped combined footings

Garcia-Galvan, Marylu,Luevanos-Rojas, Arnulfo,Lopez-Chavarria, Sandra,Medina-Elizondo, Manuel,Rivera-Mendoza, Jose Benito Techno-Press 2022 Coupled systems mechanics Vol.11 No.3

This work presents a comparative study between two different models: trapezoidal and T-shaped combined footings. The comparative study between trapezoidal and T-shaped combined footings presented in this paper generatesresultsthat have an unparalleled accuracy for all foundation engineering problems. The main part of this research is to obtain the optimal area, reinforcing steel, and thickness of the trapezoidal and T-shaped combined footings using the new models. The comparison is made for two trapezoidal combined footings and two T-shaped combined footings ofreinforced concrete subjected to the same load.Themain findings are: themodelfortrapezoidal combined footings can be used for rectangular and triangular, and the T-shaped combined footings can be used for rectangular. The structure of the paper is asfollowsfirst a very complete state of the art with extensive referencesthat describesthe methodology used for the different models clearly, presents different numerical examples, results and at the end conclusions.