<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1405-7743</journal-id>
<journal-title><![CDATA[Ingeniería, investigación y tecnología]]></journal-title>
<abbrev-journal-title><![CDATA[Ing. invest. y tecnol.]]></abbrev-journal-title>
<issn>1405-7743</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Facultad de Ingeniería]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1405-77432023000200004</article-id>
<article-id pub-id-type="doi">10.22201/fi.25940732e.2023.24.2.012</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Área óptima para zapatas combinadas rectangulares asumiendo que la superficie de contacto con el suelo trabaja parcialmente a compresión]]></article-title>
<article-title xml:lang="en"><![CDATA[Optimal area for rectangular combined footings assuming that the contact surface with the soil works partially to compression]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Montes-Paramo]]></surname>
<given-names><![CDATA[Pablo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Luevanos-Rojas]]></surname>
<given-names><![CDATA[Arnulfo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[López-Chavarría]]></surname>
<given-names><![CDATA[Sandra]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Medina-Elizondo]]></surname>
<given-names><![CDATA[Manuel]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Sandoval-Rivas]]></surname>
<given-names><![CDATA[Ricardo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma de Coahuila Facultad de Contaduría y Administración ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Autónoma de Coahuila Facultad de Contaduría y Administración ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Autónoma de Coahuila Facultad de Contaduría y Administración ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad Autónoma de Coahuila Facultad de Contaduría y Administración ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af5">
<institution><![CDATA[,Universidad Autónoma de Coahuila Facultad de Contaduría y Administración ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2023</year>
</pub-date>
<volume>24</volume>
<numero>2</numero>
<fpage>0</fpage>
<lpage>0</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1405-77432023000200004&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1405-77432023000200004&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1405-77432023000200004&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Este documento presenta un modelo matemático para obtener el área mínima de la superficie de contacto con el suelo (el suelo se considera elástico) para zapatas combinadas rectangulares rígidas asumiendo que la superficie de contacto trabaja parcialmente a compresión, es decir, una parte del área de contacto de la zapata está sujeta a compresión y en la otra parte de la zapata no hay presión (presión cero). Algunos documentos presentan el costo mínimo (el costo mínimo depende del área de contacto de la zapata con el suelo) para diseño de zapatas combinadas rectangulares (Velázquez et al., 2018), pero se considera el área de la zapata con el suelo trabajando completamente en compresión, y otros documentos muestran las ecuaciones para las dimensiones de la zapata combinada rectangular trabajando parcialmente a compresión, pero el momento sobre el eje transversal no se considera (Luévanos, 2016). La metodología se desarrolla para los cinco casos posibles de zapatas sometidas a flexión biaxial y cuatro casos posibles de zapatas sometidas a flexión uniaxial (dos en dirección transversal y dos en dirección longitudinal de la zapata), tomando en cuenta las propiedades geométricas que se generan del diagrama de presiones producidas por el suelo sobre la zapata. Ejemplos numéricos se muestran para encontrar el área mínima de zapatas combinadas rectangulares bajo flexión biaxial y uniaxial. El modelo propuesto presenta una reducción significativa en el área mínima de contacto en el suelo, respecto al modelo propuesto por otros autores, si la fuerza resultante se encuentra fuera del núcleo central.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This paper presents a mathematical model to obtain the minimum area of the contact surface with soil (the soil is considered elastic) for rigid rectangular combined footings assuming that the contact surface works partially to compression, i.e., a part of the contact area of the footing is subject to compression and the other there is not pressure (pressure zero). Some papers present the minimum cost (the minimum cost depends on the contact area of the footing with the soil) for design of rectangular combined footings (Velázquez et al., 2018), but the footing area with the soil working completely in compression is considered, and other papers show the equations for the dimensions of the rectangular combined footing partially working to compression, but the moment on the transverse axis is not considered (Luévanos, 2016). The methodology is developed for the five possible cases of footings subjected to biaxial bending, and four possible cases of footings subjected to uniaxial bending (two in the transverse direction and two in the longitudinal direction of the footing), taking into account the geometric properties generated from the diagram of pressures produced by the soil on the footing. Numerical examples are shown to find the minimum area of rectangular combined footings under biaxial and uniaxial bending. The proposed model presents a significant reduction in the minimum contact area on the soil with respect to the model proposed by other authors, if the resultant force is located outside the central nucleus.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Área mínima]]></kwd>
<kwd lng="es"><![CDATA[zapatas rectangulares combinadas]]></kwd>
<kwd lng="es"><![CDATA[flexión biaxial]]></kwd>
<kwd lng="es"><![CDATA[flexión uniaxial]]></kwd>
<kwd lng="es"><![CDATA[area trabaja parcialmente bajo compresión]]></kwd>
<kwd lng="en"><![CDATA[Minimum area]]></kwd>
<kwd lng="en"><![CDATA[rectangular combined footings]]></kwd>
<kwd lng="en"><![CDATA[biaxial bending]]></kwd>
<kwd lng="en"><![CDATA[uniaxial bending]]></kwd>
<kwd lng="en"><![CDATA[area works partially under compression]]></kwd>
</kwd-group>
</article-meta>
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