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

• Proceedings of the Korean Geotechical Society Conference
• /
• 2010.09a
• /
• pp.3-25
• /
• 2010

The paper deals with two bearing capacity problems of shallow footing under combined loading. The first is a FEM study of shallow strip footing on two-layer clay deposits subjected to a vertical, horizontal and moment combined loading, while the second is a centrifuge study of shallow rectangular footing on dry sand under double eccentricity. The FEM results revealed that the existence of top soft layer sensitively affects more on horizontal and moment capacity than vertical capacity for cases of footing on soft clay overlying stiff clay. Practical design charts are presented to evaluate bearing capacities of footing for various combinations of the ratio of the depth of the upper layer to the footing width and the ratio of undrained strength of the upper layer to that of the lower. The centrifuge tests indicated that current design practice of calculating failure load of rectangular surface footing under double eccentricity underestimates the centrifuge loading test data. This trend is more marked when the eccentricity becomes larger. The decreasing trend in failure load with an increase of double eccentricity is rather uniquely expressed by a single curve, using a newly defined resultant eccentricity and the diagonal length of the footing base.

• Geomechanics and Engineering
• /
• v.30 no.6
• /
• pp.525-538
• /
• 2022

This paper presents a more general model for T-shaped combined footings that support two columns aligned on a longitudinal axis and each column provides an axial load and two orthogonal moments. This model can be applied to the following conditions: (1) without restrictions on its sides, (2) a restricted side and (3) two opposite sides restricted. This model considers the linear soil pressure. The recently published works have been developed for a restricted side and for two opposite sides restricted by Luévanos-Rojas et al. (2018a, b). The current model considers the uniform pressure distribution because the position of the resultant force coincides with the center of gravity of the surface of the footing in contact with the soil in direction of the longitudinal axis where the columns are located. This paper shows three numerical examples. Example 1 is for a T-shaped combined footing with a limited side (one column is located on the property boundary). Example 2 is for a T-shaped combined footing with two limited opposite sides (the two columns are located on the property boundary). Example 3 is for a T-shaped combined footing with two limited opposite sides, one column is located in the center of the width of the upper flange (b₁/2=L₁), and other column is located at a distance half the width of the strip from the free end of the footing (b₂/2=b-L₁-L). The main advantage of this work over other works is that this model can be applied to T-shaped combined footings without restrictions on its sides, a restricted side and two opposite sides restricted. It also shows the deficiencies of the current model over the new model.

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

• Geomechanics and Engineering
• /
• v.4 no.4
• /
• pp.263-279
• /
• 2012

The present paper deals with the analysis of combined footings resting on geosynthetic reinforced granular fill overlying stone column improved poor soil. An attempt has been made to study the influence of inclusion of geosynthetic layer on the deflection of the footing. The footing has been idealized as a beam having finite flexural rigidity. Granular fill layer has been represented by Pasternak shear layer and stone columns and poor soil have been represented by nonlinear Winkler springs. Nonlinear behavior of granular fill layer, stone columns and the poor soil has been considered by means of hyperbolic stress strain relationships. Governing differential equations for the soil-foundation system have been derived and solution has been obtained employing finite difference scheme by means of iterative Gauss Elimination method. Results of a detailed parametric study have been presented, for a footing supporting typically five columns, in non-dimensional form in respect of deflection with and without geosynthetic inclusion. Geosynthetic layer has been found to significantly reduce the deflection of the footing which has been quantified by means of parametric study.

• Geomechanics and Engineering
• /
• v.14 no.1
• /
• pp.61-69
• /
• 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
• /
• v.16 no.6
• /
• pp.691-704
• /
• 2019

This study simulates the responses of large-scale bridge piers under pseudo-dynamic tests to investigate the performance of four types of numerical models that consider the nonlinear behavior of the pier and the rocking behavior of the footing. In the models, beam-column elements with plastic hinges are used for the pier, two types of foundation models (rotational spring and distributed spring models) are adopted for the footing behavior, and two types of viscous damping models (Rayleigh and dashpot models) are applied for energy dissipation. Results show that the nonlinear pier model combined with the distributed spring-dashpot foundation model can reasonably capture the behavior of the piers in the tests. Although the commonly used rotational spring foundation model adopts a nonlinear moment-rotation property that reflects the effect of footing uplift, it cannot suitably simulate the hysteretic moment-rotation response of the footing in the dynamic analysis once the footing uplifts. In addition, the piers are susceptible to cracking damage under strong seismic loading and the induced plastic response can provide contribution to earthquake energy dissipation.

• Steel and Composite Structures
• /
• v.30 no.2
• /
• pp.109-121
• /
• 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
• /
• v.14 no.1
• /
• pp.51-60
• /
• 2018

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.

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