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Featured Application: This study is a practical tool for Structural Engineers to obtain the minimum contact area with the ground for rectangular isolated footings with an eccentric column. This manuscript aims to present a novel model to find the optimal area of a rectangular isolated footing with an eccentric column, taking into account that the footing is partially supported; that is, one part of the contact surface is compressed and the other part has zero pressure. The methodology is developed by integration and can also be verified using the geometric properties of a triangular-based pyramid to determine the axial load, the moments in the X and Y axes in terms of the available allowable soil pressure, the footing sides, the greatest distance on one of its sides in the X-direction where it crosses the neutral axis, the greatest distance on one of its sides in the Y-direction where it crosses the neutral axis, and the coordinates at the base of the footing. Four types of numerical problems are shown to find the optimal area of a rectangular footing with an eccentric column subjected to biaxial bending: (1) the column in the center of the footing; (2) the column on the edge of the footing in the X-direction; (3) the column on the edge of the footing in the Y-direction; and (4) the column in the corner of the footing. A comparison is presented of the new model against a model proposed by another author. The new model presents a reduction of up to 42.37% for the column in the center of the footing and up to 40.32% for the column in the corner of the footing compared to the model by the other authors. Therefore, the new model will be of great help to professionals in foundation design. [ABSTRACT FROM AUTHOR]

This paper presents a comparative study for minimum areas in contact with the ground of RIF (rectangular isolated footings) y CIF (circular isolated footings) that work totally CM (Current model) or partially NM (New model) under compression. Methodology is described using the equations developed by the same author for RIF y CIF. Main findings: RIF under uniaxial bending have less area than CIF in the CM and in the NM; NM presents less area than CM for RIF y CIF under biaxial bending in all cases; NM for CIF shows less area than RIF, when the moments are equals and the relation of the axial load divided by the moment is 0.75 or greater, when the smallest moment divided by the largest moment is between 0.50 and 0.75, and the axial load is greater than the largest moment. Therefore, it is recommended to carry out a previous study to choose the type of footing. [ABSTRACT FROM AUTHOR]

This paper presents a general model for the design to obtain the thickness and reinforcing steel areas of rectangular footings that support from 1 to "n" columns aligned on a longitudinal axis. The pressure diagram is considered linear. Some recently published papers are restricted to certain types of footings as the rectangular isolated footings, and rectangular combined footings that support two columns. The first part of this paper shows the minimum soil area that supports 1 to "n" columns aligned on a longitudinal axis. Three numerical examples are presented for design of rectangular footings subjected to an axial load and two orthogonal moments in each column that supports one, two and three columns. The main advantage of this document over other documents is: this model can be applied for one or more columns supported on a rectangular footing (unrestricted on its sides, one side restricted and two opposite sides restricted). [ABSTRACT FROM AUTHOR]

This paper presents a general model for the design to obtain the thickness and reinforcing steel areas of rectangular footings that support from 1 to "n" columns aligned on a longitudinal axis. The pressure diagram is considered linear. Some recently published papers are restricted to certain types of footings as the rectangular isolated footings, and rectangular combined footings that support two columns. The first part of this paper shows the minimum soil area that supports 1 to "n" columns aligned on a longitudinal axis. Three numerical examples are presented for design of rectangular footings subjected to an axial load and two orthogonal moments in each column that supports one, two and three columns. The main advantage of this document over other documents is: this model can be applied for one or more columns supported on a rectangular footing (unrestricted on its sides, one side restricted and two opposite sides restricted). [ABSTRACT FROM AUTHOR]

This paper shows a general model of rectangular footings to obtain the soil minimum contact area (optimal surface) that support from 1 to n columns aligned on a longitudinal axis. The proposed model considers that the soil pressure varies linearly. The recently published models have been presented individually to obtain the soil contact area for rectangular isolated footings, rectangular combined footings that support two columns, these models present the equations, but it is not guaranteed to be the minimum area. The present research complies with the models mentioned above (Luévanos-Rojas 2013, 2016) and can be applied to footings that support 3 or more columns, and also the minimum area is guaranteed. Also, numerical problems are shown the soil minimum contact surface for rectangular isolated footings, and rectangular combined footings that support two and three columns (unrestricted on its sides, one side restricted and two opposite sides restricted). [ABSTRACT FROM AUTHOR]

Beams are classified according to its cross section: prismatic beam whose cross section is constant along its entire length and non-prismatic beam whose cross section is not constant along its entire length. This paper shows a model for non-prismatic T-section beams with straight haunches under uniformly distributed load. Bending and shear deformations are considered to obtain the fixed-end moments and carry-over and stiffness factors, which are the main parts of this research. The superposition method is used to solve these types of beams, and the conjugate beam method by an exact integration is used to find the deformations at any location in the beams. The superposition method consists in splitting a statically indeterminate problem into separate statically determinate problems; that is, the slope or deflection at any point on the beam is equal to the resultant of the slopes or deflections at that point caused by each of the loads acting separately. The traditional model does not consider shear deformations; other authors consider the bending and shear deformations; thorough tables are presented but are limited to some parameters. Also a comparison of the proposed model against the traditional model is shown in Tables 1 and 2, and the main differences are presented in the parameters, d = 0.20L. For the fixed-end moments, in some cases the traditional model is greater and in others, the proposed model is greater, and for the carryover and stiffness factors in all cases, the traditional model is greater. The proposed model is more suitable and exact for structural engineering analysis and also is adapted to the real conditions, since the shear forces and bending moments act at any structure type and thus the bending and shear deformations are presented. A significant advantage is that the fixed-end moments and carryover and stiffness factors are calculated for every T-section using their mathematical equations. [ABSTRACT FROM AUTHOR]

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 tenns 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. [ABSTRACT FROM AUTHOR]

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. Tire 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. [ABSTRACT FROM AUTHOR]

This paper proposes a method for analysis of statically indeterminate beams, considering the shear deformations, which is an extension to the moment-distribution method, which is used to analyze all kinds of continuous beams. This methodology considers the shear deformation and flexure. The traditional method takes into account only the flexure deformation and without taking into account the shear deformation, this is how it usually develops structural analysis of statically indeterminate beams. It also makes a comparison between the proposed method and the traditional method, the differences between both methods are greater, especially members of short length as can be seen in the results tables of the problems considered in the traditional method not all values are on the side of safety. Therefore, the usual practice, without to consider the shear deformations in clear short between its supports, will not be a recommended solution and it is proposed the use of considering shear deformations and also is more attached to reality. [ABSTRACT FROM AUTHOR]