• Coupled systems mechanics
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• v.6 no.4
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• pp.417-437
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• 2017

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.

• Coupled systems mechanics
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• v.11 no.3
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• pp.233-257
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• 2022

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.

• Structural Engineering and Mechanics
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• v.52 no.4
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• pp.767-786
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• 2014

This paper presents the design of reinforced concrete circular footings subjected to axial load and bending in two directions using a new model. The new model considers the soil real pressure acting on contact surface of the circular footings and these are different, with a linear variation in the contact area, these pressures are presented in terms of the axial load, moments around the axis "X" and the axis "Y". The classical model takes into account only the maximum pressure of the soil for design of footings and it is considered uniform at all points of contact area. Also, a comparison is presented in terms of the materials used (steel and concrete) between the two models shown in table, being greater the classical model with respect the new model. Therefore, the new model is the most appropriate, since it is more economic and also is adjusted to real conditions.

• Steel and Composite Structures
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• v.30 no.2
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• pp.109-121
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• 2019

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.

• Geomechanics and Engineering
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• v.14 no.1
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• pp.61-69
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• 2018

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.

• Earthquakes and Structures
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• v.8 no.5
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• pp.1255-1276
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• 2015

The importance of considering soil-structure interaction effect in the analysis and design of RC frame buildings is increasingly recognized but still not penetrated to the grass root level owing to various complexities involved. It is well established fact that the soil-structure interaction effect considerably influence the design of multi-storey buildings subjected to lateral seismic loads. The shear walls are often provided in such buildings to increase the lateral stability to resist seismic lateral loads. In the present work, the linear soil-structure analysis of a G+5 storey RC shear wall building frame resting on isolated column footings and supported by deformable soil is presented. The finite element modelling and analysis is carried out using ANSYS software under normal loads as well as under seismic loads. Various load combinations are considered as per IS-1893 (Part-1):2002. The interaction analysis is carried out with and without shear wall to investigate the effect of inclusion of shear wall on the total and differential settlements in the footings due to deformations in the soil mass. The frame and soil mass both are considered to behave in linear elastic manner. It is observed that the soil-structure interaction effect causes significant total and differential settlements in the footings. Maximum total settlement in footings occurs under vertical loads and inner footings settle more than outer footings creating a saucer shaped settlement profile of the footings. Each combination of seismic loads causes maximum differential settlement in one or more footings. Presence of shear wall decreases pulling/pushing effect of seismic forces on footings resulting in more stability to the structures.

• Structural Engineering and Mechanics
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• v.56 no.5
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• pp.745-765
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• 2015

This paper presents the design of reinforced concrete combined footings of trapezoidal form subjected to axial load and moments in two directions to each column using a new model to consider soil real pressure acting on the contact surface of the footing; such pressure is presented in terms of an axial load, moment around the axis "X" and moment around the axis "Y" to each column. The classical model considers an axial load and moment around the axis "X" (transverse axis) applied to each column, and when the moments in two directions are taken into account, the maximum pressure throughout the contact surface of the footing is considered the same. The main part of this research is that the proposed model considers soil real pressure and the classical model takes into account the maximum pressure, and also is considered uniform. We conclude that the proposed model is more suited to the real conditions and is more economical.

• Journal of the Korean Society of Safety
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• v.21 no.1 s.73
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• pp.105-113
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• 2006

The footing of a bridge is a very essential part that support the whole load induced by the bridge itself and the traffic as well. However, once a bridge is built, the footing is buried under soil so the footing is invisible from outside. Therefore, the safety or condition of the footing is very difficult to estimate. Not only the length of the imbedded part of the footings but also the type of footings are unknown once the design record is gone. Some nondestructive techniques can be used to evaluate invisible part of the footings but the results have not been successful yet. Using GPR (Ground Penetrating Radar), which has been used for the nondestructive evaluation in military purposes, the condition assessment of the footings have been successfully conducted in this research. The field evaluation and laboratory tests have been conducted to find effective factors in the condition assessment of the footings. The equipment and basic theory of the GPR has been presented. The field test results show that the GPR can be successfully used for the safety evaluation of the footings. More test results and field data are needed for more precise evaluation of the footings.

• Advances in Computational Design
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• v.3 no.1
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• pp.49-69
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• 2018

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.

• Advances in concrete construction
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• v.16 no.1
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• pp.21-34
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• 2023

This work presents a complete optimal model for trapezoidal combined footings that support a concentric load and moments around of the "X" and "Y" axes in each column to obtain the minimum area and the minimum cost. The model presented in this article considers a pressure diagram that has a linear variation (real pressure) and the equations are not limited to some cases. The classic model takes into account a concentric load and the moment around of the "X" axis (transverse axis) that is applied due to each column, i.e., the resultant force is located at the geometric center of the footing on the "Y" axis (longitudinal axis), and when the concentric load and moments around of the "X" and "Y" axes act on the footing is considered the uniform pressure applied on the contact surface of the footing, and it is the maximum pressure. Four numerical problems are presented to find the optimal design of a trapezoidal combined footing under a concentric load and moments around of the "X" and "Y" axes due to the columns: Case 1 not limited in the direction of the Y axis; Case 2 limited in the direction of the Y axis in column 1; Case 3 limited in the direction of the Y axis in column 2; Case 4 limited in the direction of the Y axis in columns 1 an 2. The complete optimal design in terms of cost optimization for the trapezoidal combined footings can be used for the rectangular combined footings considering the uniform width of the footing in the transversal direction, and also for different reinforced concrete design codes, simply by modifying the resisting capacity equations for moment, for bending shear, and for the punching shear, according to each of the codes.