tag:blogger.com,1999:blog-27077940997723518102024-03-19T01:04:41.529-07:00ANÁLISIS DE ARMADURAS POR EL MÉTODO DE LOS NODOSAnonymoushttp://www.blogger.com/profile/03450060562327922078noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-2707794099772351810.post-43598233584493918582013-03-03T21:08:00.000-08:002013-03-11T22:25:23.412-07:00EL MÉTODO<div class="separator" style="clear: both; text-align: center;">
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<![endif]--><span style="font-size: 11pt; line-height: 115%;">Los
casos relacionados con cuerpos rígidos y fuerzas en equilibrio han sido el
antecedente para conocer ahora acerca de las <b>armaduras</b>, que no son otra cosa
que <b>estructuras formadas por elementos rígidos</b> unidos entre sí.</span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">En
estos casos se determinarán las <b>fuerzas externas</b> que actúan sobre la estructura
y se analizarán las <b>fuerzas internas</b> que mantienen unidas sus partes.</span></div>
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<br /></div>
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<br /></div>
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En el contenido de éste tema podrás encontrar imágenes
ilustrativas, videos, ejemplos y aplicaciones del análisis estructural. Está
diseñado con recursos de varios autores, compilado y resumido de manera que
puedas realizar el análisis de estructuras por el método de los nodos siempre
comprendiendo el objetivo final del cálculo de las fuerzas, comencemos con las
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<span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"><span style="font-size: large;"><b>Armadura:</b></span> Es un tipo de estructura de mayor
importancia en ingeniería. Proporciona soluciones tanto <b>prácticas</b> como
<b>económicas</b> a muchos problemas, principalmente en el diseño de <b>puentes y
edificios</b>. Las armaduras que a continuación vamos a analizar se tratan de
estructuras planas en dos dimensiones, pero que,<span style="mso-spacerun: yes;"> </span>varios planos unidos entre sí pueden formar
elementos tridimensionales. Una armadura consta de:</span></div>
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</span>los elementos rectos conectados entre sí por medio de <b>nodos</b> o nudos. Por
lo general, los miembros de una armadura son delgados y pueden soportar poca
carga lateral, por lo tanto, las cargas deben aplicarse sobre los nudos y no
directamente sobre los <b>miembros</b>. De esta teoría suponemos que todos los
miembros sólo son sometidos a cargas de compresión o tensión a lo largo de su
eje, y de eso se trata el análisis, de <b>encontrar las magnitudes de la tensión o
compresión de cada miembro</b>.</span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> <b>Nodos:</b>
Son las conexiones entre cada miembro. Las fuerzas que actúan sobre ellos se
reducen a un solo punto, porque son las mismas fuerzas transmitidas desde los
ejes de los miembros. A través de los nodos nunca se puede atravesar un
miembro. Las conexiones en los nudos están formadas usualmente por <b>pernos o
soldadura</b> en los extremos de los miembros unidos a una placa común llamada
<b>placa de unión</b>.</span><br />
<br />
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<br />
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<b>Apoyos:</b> Toda estructura necesariamente debe estar apoyada en
uno o más puntos, los cuales se llaman <b>puntos de apoyo</b>, y como transmiten su
carga a través de esos puntos, en el diagrama de fuerzas debemos considerar los
vectores que indiquen las <b>reacciones</b> en esos apoyos.<span style="mso-spacerun: yes;"> </span>Cada diferente tipo de apoyo generará<span style="mso-spacerun: yes;"> </span>a su vez un tipo de </div>
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<br /></div>
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<b>Reacción:</b> Son las fuerzas generadas en los apoyos, son
opuestas en dirección de las fuerzas de la estructura que actúan en ese punto,
existen tres tipos de reacciones:</div>
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Reacciones equivalentes a una fuerza con línea
de acción conocida. Generadas por apoyos tipo: <b>patines o rodamientos</b>,
balancines, superficies sin fricción, eslabones y cables cortos, collarines
sobre barras sin fricción y pernos en ranuras lisas. En las reacciones de éste
tipo hay una sola incógnita </div>
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Reacciones equivalentes a una fuerza de
dirección desconocida. Generadas por <b>pernos</b> lisos en orificios ajustados,
articulaciones y superficies rugosas. En las reacciones de este grupo
intervienen dos incógnitas.</div>
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Producidas por <b>soportes fijos</b> que impiden cualquier movimiento del cuerpo
inmovilizándolo por completo y obligándolo a reaccionar con tres fuerzas
incógnitas (dos componentes de traslación y un momento).</div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"><b>Equilibrio:</b>
Cuando las fuerzas y el par son ambos iguales a <b>cero</b> forman un sistema
equivalente nulo se dice que el cuerpo rígido está en equilibrio.</span></div>
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Descomponiendo cada fuerza y cada
momento en sus componentes rectangulares,<span style="mso-spacerun: yes;">
</span>podemos expresar las condiciones necesarias y suficientes para el
equilibrio de un cuerpo rígido por medio de las seis ecuaciones escalares
siguientes:</div>
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Las ecuaciones obtenidas pueden
usarse para determinar las fuerzas desconocidas aplicadas a cuerpos rígidos o
las reacciones desconocidas que ejercen sobre éste sus apoyos. Notamos que las
primeras tres ecuaciones expresan el hecho de que las fuerzas en X, Y y Z están
equilibradas; las otras tres ecuaciones indican que los momentos con respecto a
los tres ejes X, Y y Z también están equilibrados, o sea, <b>ni se va a mover
hacia ninguna parte y tampoco va a girar en ningún sentido</b>, el cuerpo está en
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<br /></div>
<span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">Cada caso presenta diferencias, pero la tarea
principal es <b>despejar</b> de las seis ecuaciones anteriores la <b>mayor cantidad de
variables</b> posibles, a partir del diagrama de fuerzas. </span></div>
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<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
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<w:LsdException Locked="false" Priority="68" SemiHidden="false"
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<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
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<w:LsdException Locked="false" Priority="67" SemiHidden="false"
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<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Tabla normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
mso-para-margin-top:0cm;
mso-para-margin-right:0cm;
mso-para-margin-bottom:10.0pt;
mso-para-margin-left:0cm;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-fareast-language:EN-US;}
</style>
<![endif]-->
<br />
<div class="MsoNormal" style="font-family: Verdana,sans-serif; margin-left: 18pt;">
Por lo tanto el diagrama de
fuerzas es la clave para el planteamiento correcto de las ecuaciones y el
cálculo exacto de cada fuerza en cada nudo. Veamos los siguientes ejemplos:</div>
<div class="MsoNormal" style="font-family: Verdana,sans-serif; margin-left: 18pt;">
<br /></div>
<div class="MsoNormal" style="font-family: Verdana,sans-serif; margin-left: 18pt;">
<br /></div>
<div class="MsoNormal" style="font-family: Verdana,sans-serif; margin-left: 18pt;">
<br /></div>
<div class="MsoNormal" style="font-family: Verdana,sans-serif; margin-left: 18pt;">
<!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:HyphenationZone>21</w:HyphenationZone>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>ES</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
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<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
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<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
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<w:LsdException Locked="false" Priority="22" SemiHidden="false"
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UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
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<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
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<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
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<w:LsdException Locked="false" Priority="70" SemiHidden="false"
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<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
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<b style="mso-bidi-font-weight: normal;">PROBLEMA 1. </b><span style="mso-tab-count: 1;"> </span>Usando
el método de los nudos, determine la fuerza en cada miembro de la armadura que
se muestra:</div>
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<![endif]--><span style="font-size: 11pt; line-height: 115%;">El
primer paso será representar el <b>diagrama de fuerzas</b> de la armadura completa,
dibujando <b>todos los vectores</b> que afectan a la armadura y sin olvidar las
<b>reacciones</b> en los apoyos. Es importante también colocar las medidas conocidas
de cada miembro y las magnitudes de los vectores de cada fuerza.</span><br />
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">Como
la condición para que existan las armaduras es su <b>estabilidad</b>, recordamos que
tenemos que aplicar las ecuaciones de la suma de todas las fuerzas<span style="mso-spacerun: yes;"> </span>y todos los momentos e igualarlos a <b>cero</b>.
Sería conveniente comenzar por un nodo donde sólo exista <b>una incógnita</b>; la ecuación
del momento en el nodo <b>C</b> nos podría dar el valor del vector que genera la
reacción en el apoyo <b>E</b>. Porque automáticamente se eliminan las fuerzas Cx y Cy,
puesto que no provocan ningún giro en <b>C</b></span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Enseguida
podemos darnos cuenta de que la sumatoria de fuerzas en X implica <b>un</b> solo
vector, por lo que su ecuación tendrá <b>una sola incógnita</b>. Y será fácil su
deducción:</span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Una
vez que conocemos la magnitud en la reacción del nodo <b>E</b>, nos damos cuenta de
que la ecuación que incluye a las fuerzas en el sentido vertical (Y) sólo
tendrá <b>una</b> incógnita, por lo que procedemos a resolverla para encontrar el
vector generado por la reacción vertical en el nodo <b>C</b>.</span></div>
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</div>
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Y entonces, ahora sí procedemos a
calcular las fuerzas en cada nodo.<br />
<br />
Comencemos con el nodo <b style="mso-bidi-font-weight: normal;">A</b>.</div>
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<br /></div>
<span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">En primer lugar vamos a dibujar el <b>diagrama de fuerzas</b>
que conocemos que intervienen en este nodo, dejando con líneas punteadas los
vectores de los miembros que todavía no conocemos.</span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">Enseguida
hacemos un <b>polígono de fuerzas en equilibrio</b>, es decir, un polígono con los
vectores involucrados en el nodo, acomodados de <b>punta a cola</b>, de tal manera que
se cierre el polígono. Sólo existe una combinación para equilibrar triángulos.</span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Con
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por lo tanto es el <b>mismo</b> ángulo de inclinación de los vectores. La función
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conocemos el valor del vector que está aplicado verticalmente en <b style="mso-bidi-font-weight: normal;">A</b>, y tenemos el ángulo</span><b style="font-family: Verdana,sans-serif;"><span style="font-size: 11pt; line-height: 115%;"></span></b><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">, podemos fácilmente conocer<span style="mso-spacerun: yes;"> </span>la magnitud de cualquiera de los otros dos
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Ahora,
mediante la <b>observación</b> únicamente, deduciremos el sentido de los vectores
recién encontrados. El vector <b style="mso-bidi-font-weight: normal;">F</b></span><b style="font-family: Verdana,sans-serif;"><span style="font-size: 8pt; line-height: 115%;">AB</span></b><span style="font-family: Verdana,sans-serif; font-size: 8pt; line-height: 115%;"> </span><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">se
dirige hacia la derecha, si lo trasladáramos al diagrama de fuerzas (en la
línea punteada) podemos darnos cuenta de que “<b>tira</b>” del nodo <b style="mso-bidi-font-weight: normal;">A</b>, por lo tanto deducimos que el
miembro está en <b>tensión</b>.</span></div>
<div style="font-family: Verdana,sans-serif; text-align: justify;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghyGojhLq-I8-3ssChrEIuL6cCq5KgqLlo30kvxmtDwzqFYsIQBj5OTF_F9C6UoQZjodRkzZOigMpAwpR4z3CX3FF-xxa7CIF492vXLyvVMvUaCk7y2IRVCpWGaUjjpMNIhF9SvLEyX5_N/s1600/Imagenes+para+trabajo+final+7-sss.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghyGojhLq-I8-3ssChrEIuL6cCq5KgqLlo30kvxmtDwzqFYsIQBj5OTF_F9C6UoQZjodRkzZOigMpAwpR4z3CX3FF-xxa7CIF492vXLyvVMvUaCk7y2IRVCpWGaUjjpMNIhF9SvLEyX5_N/s1600/Imagenes+para+trabajo+final+7-sss.jpg" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
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table.MsoNormalTable
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mso-para-margin-right:0cm;
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mso-para-margin-left:0cm;
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mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-fareast-language:EN-US;}
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Así
mismo si trasladamos el vector del polígono en equilibrio al diagrama de
fuerzas, podemos ver que el vector <b style="mso-bidi-font-weight: normal;">F</b></span><b style="font-family: Verdana,sans-serif;"><span style="font-size: 8pt; line-height: 115%;">AD</span></b><span style="font-family: Verdana,sans-serif; font-size: 8pt; line-height: 115%;"> </span><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">“presiona”
al nodo, por lo que deducimos que está en <b>compresión</b>.</span></div>
<div style="font-family: Verdana,sans-serif; text-align: justify;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbemXpSW6JW_SCez3uVyoCa8fe0u5GKQzJQEVlaWhjm047OL3UVIOXOXXJRBaSWNZBe22g7QXPv8DRYJ-h3cR0jfi9r-dIhAzXIakw9qUxKzP1zmjlzOzAlZiG-uRaqgu_OvrQ5YuE7E1n/s1600/Imagenes+para+trabajo+final+8-sss.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbemXpSW6JW_SCez3uVyoCa8fe0u5GKQzJQEVlaWhjm047OL3UVIOXOXXJRBaSWNZBe22g7QXPv8DRYJ-h3cR0jfi9r-dIhAzXIakw9qUxKzP1zmjlzOzAlZiG-uRaqgu_OvrQ5YuE7E1n/s1600/Imagenes+para+trabajo+final+8-sss.jpg" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div style="font-family: Verdana,sans-serif; text-align: justify;">
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Ahora continuaremos con el <b>nodo D:</b></div>
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<br /></div>
<span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">En primer lugar vamos a dibujar el <b>diagrama de fuerzas</b>
que conocemos que intervienen en este nodo, dejando con líneas punteadas los
vectores de los miembros que todavía no conocemos, pero la ventaja es que ahora
sí conocemos una de las fuerzas de los miembros, la que fue calculada en el
nodo <b>A</b>: <b>F</b></span><span style="font-family: Verdana,sans-serif; font-size: 8pt; line-height: 115%;"><b>AD</b> </span><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">=
2,500 lb en compresión. Quedan dos fuerzas sin determinar, por lo que las
dejamos como líneas punteadas.</span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Enseguida
dibujamos el <b>polígono de fuerzas</b> en equilibrio para el nodo <b>D</b>, donde inciden
<b>tres</b> vectores, uno de ellos conocido, recordemos que la condición de equilibrio
se cumple si los vectores se acomodan de <b>punta a cola</b>.</span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Con
las medidas de los miembros podemos obtener los ángulos internos del triángulo,
y con la ley de los senos, podremos encontrar las magnitudes de los vectores
que faltan.</span></div>
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<span id="goog_1935781500"></span><span id="goog_1935781501"></span><br />
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<div style="font-family: Verdana,sans-serif; text-align: justify;">
<span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">Ahora,
mediante la <b>observación</b> únicamente, deduciremos el sentido de los vectores
recién encontrados. El vector <b style="mso-bidi-font-weight: normal;">F</b></span><b style="font-family: Verdana,sans-serif;"><span style="font-size: 8pt; line-height: 115%;">DB</span></b><span style="font-family: Verdana,sans-serif; font-size: 8pt; line-height: 115%;"> </span><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">se
dirige hacia arriba a la derecha, si lo trasladáramos al diagrama de fuerzas
(en la línea punteada) podemos darnos cuenta de que “tira” del nodo <b style="mso-bidi-font-weight: normal;">A</b>, por lo tanto deducimos que el miembro
está en <b>tensión</b>.</span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Así
mismo si trasladamos el vector del polígono en equilibrio al diagrama de
fuerzas, podemos ver que el vector <b style="mso-bidi-font-weight: normal;">F</b></span><b style="font-family: Verdana,sans-serif;"><span style="font-size: 8pt; line-height: 115%;">ED</span></b><span style="font-family: Verdana,sans-serif; font-size: 8pt; line-height: 115%;"> </span><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">“presiona”
al nodo, por lo que deducimos que está en <b>compresión</b>.</span></div>
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<br />
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Ahora continuaremos con el <b>nodo
B</b>:</div>
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<br /></div>
<span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">En primer lugar vamos a dibujar el <b>diagrama de fuerzas</b>
que conocemos que intervienen en este nodo, dejando con líneas punteadas los
vectores de los miembros que todavía no conocemos, pero la ventaja es que ahora
ya conocemos <b>tres</b> de las fuerzas involucradas, las que fueron calculadas en el
nodo <b>A</b> y en el nodo <b>D</b>. Quedan dos fuerzas sin determinar, por lo que las
dejamos como líneas punteadas.</span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Es
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evitar confusiones.</span></div>
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mso-para-margin-right:0cm;
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mso-para-margin-left:0cm;
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Enseguida
dibujamos los <b>vectores faltantes</b>, suponiendo arbitrariamente que los miembros
están en tensión, esto es, que están “tirando” del nodo <b>B</b>.</span><br />
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</div>
<div class="separator" style="clear: both; text-align: center;">
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mso-fareast-language:EN-US;}
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Las
fuerzas que no son horizontales o verticales (es decir, <b>todas las inclinadas</b>)
deberán descomponerse en sus dos componentes X y Y, utilizando las funciones
seno, coseno y tangente. Primero que nada, se deducirán los ángulos de los
vectores inclinados.</span></div>
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Ahora se dibujan dos vectores
rectangulares en vez de cada uno de los vectores inclinados, de esa manera
tendremos en el diagrama de fuerzas <b>solamente fuerzas verticales y
horizontales</b>, por lo que ya podemos aplicar las ecuaciones del equilibrio. </div>
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Comenzamos con la sumatoria de
fuerzas en Y, de donde podemos deducir la magnitud del vector F<span style="font-size: 8.0pt; line-height: 115%;">BE</span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">Inmediatamente
nos damos cuenta de que el miembro está en compresión, porque fue
arbitrariamente <b>dibujado en tensión, y el resultado fue negativo</b>, por lo tanto
el miembro está en <b>compresión</b>.</span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Ahora
continuamos con la ecuación donde sumamos todas las fuerzas en <b>X</b>, de ahí
deduciremos la magnitud del vector <b>F</b></span><span style="font-family: Verdana,sans-serif; font-size: 8pt; line-height: 115%;"><b>BC</b>.</span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">También
podemos observar que este miembro sí está en <b>tensión</b>, pues el resultado
obtenido es de signo positivo. Vamos bien.</span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Ahora
vamos a calcular los vectores del nodo <b>E</b>. Dibujemos el diagrama de fuerzas de
los vectores que inciden en <b>C</b>, de los cuales conocemos 3, sólo existe una
incógnita, la cual es <b>F</b></span><span style="font-family: Verdana,sans-serif; font-size: 8pt; line-height: 115%;"><b>EC</b>, </span><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">la cual también será incluida en el diagrama de
fuerzas, la supondremos arbitrariamente a tensión,<span style="mso-spacerun: yes;"> </span>el resultado nos comprobará si fue buena la
suposición.</span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Como
los vectores <b>F</b></span><span style="font-family: Verdana,sans-serif; font-size: 8pt; line-height: 115%;"><b>BE</b> </span><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">y <b>F</b></span><span style="font-family: Verdana,sans-serif; font-size: 8pt; line-height: 115%;"><b>DE</b> </span><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">y la reacción <b>E</b></span><span style="font-family: Verdana,sans-serif; font-size: 8pt; line-height: 115%;"> </span><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">“presionan” al nodo <b>E</b>, podemos pasarlos del otro lado
del nodo, lo cual nos facilitará la comprensión del diagrama de fuerzas y no lo
afecta para nada.</span></div>
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<![endif]--><span style="font-size: 11pt; line-height: 115%;">Dibujamos
el vector desconocido <b>F</b></span><b><span style="font-size: 8pt; line-height: 115%;">EC</span></b><span style="font-size: 11pt; line-height: 115%;">, suponiendo arbitrariamente que está en tensión.</span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">Calculamos
los ángulos con las medidas de los miembros y la función tangente.</span></div>
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<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Tabla normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
mso-para-margin-top:0cm;
mso-para-margin-right:0cm;
mso-para-margin-bottom:10.0pt;
mso-para-margin-left:0cm;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-fareast-language:EN-US;}
</style>
<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Con la
aplicación de la ecuación de la sumatoria de las fuerzas en <b>X</b>, podemos deducir
la magnitud de <b>F</b></span><span style="font-family: Verdana,sans-serif; font-size: 8pt; line-height: 115%;"><b>EC</b>. </span><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">La cual resulta negativa, lo que quiere decir que la
fuerza realmente está en compresión, al contrario de cómo fue supuesta antes de
hacer el cálculo.</span></div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGUO9zwcD57B69LUbpBao5HwK6yrP1rcAPcku3tMzwSu67iB4is3sRMdoer2RWvOBjwyODYrFlslogD95gN_RITosIPVL63S2rBdR5s5YxrDHvzDVOBPqAeUTvbVZ_eKU6IZ1tvPa3qOVe/s1600/Mas+imagenes+para+el+trabajo+final+16.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGUO9zwcD57B69LUbpBao5HwK6yrP1rcAPcku3tMzwSu67iB4is3sRMdoer2RWvOBjwyODYrFlslogD95gN_RITosIPVL63S2rBdR5s5YxrDHvzDVOBPqAeUTvbVZ_eKU6IZ1tvPa3qOVe/s1600/Mas+imagenes+para+el+trabajo+final+16.jpg" width="320" /></a></div>
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<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
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resultados de la ecuación (que debe resultar cero).</span></div>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">Ya por
último resta el nodo C; con los valores obtenidos en los otros nodos para los
vectores F</span><span style="font-family: Verdana,sans-serif; font-size: 8pt; line-height: 115%;">BC </span><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;">y F</span><span style="font-family: Verdana,sans-serif; font-size: 8pt; line-height: 115%;">EC,</span><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> y los valores de las reacciones obtenidas al
principio del problema podemos dibujar el diagrama de fuerzas en el nodo C. No
olvidemos anotar las medidas conocidas de los miembros.</span></div>
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<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Tabla normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
mso-para-margin-top:0cm;
mso-para-margin-right:0cm;
mso-para-margin-bottom:10.0pt;
mso-para-margin-left:0cm;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-fareast-language:EN-US;}
</style>
<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Recordemos
que los vectores que inciden en compresión al nodo, deben pasarse del otro lado
del nodo, en la misma línea de acción, para evitar confusiones.</span></div>
<div class="MsoNormal" style="font-family: Verdana,sans-serif; margin-left: 18pt;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYK0CTlB8HLwBmMWkHVANDIJ9Xw_CKW28q-IH-2ma-jHB_K5ISYHsmCHfbIwfWbwQ9rtPKkEDy8ShXwUSibcF_w_XU8WVJSq9uXNc8ioM8Oc_IhMId74VSd7bdACwjNl4rJ11A26K-m3-o/s1600/Imagenes+para+trabajo+final+26.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYK0CTlB8HLwBmMWkHVANDIJ9Xw_CKW28q-IH-2ma-jHB_K5ISYHsmCHfbIwfWbwQ9rtPKkEDy8ShXwUSibcF_w_XU8WVJSq9uXNc8ioM8Oc_IhMId74VSd7bdACwjNl4rJ11A26K-m3-o/s1600/Imagenes+para+trabajo+final+26.jpg" width="400" /></a></div>
<div class="MsoNormal" style="font-family: Verdana,sans-serif; margin-left: 18pt;">
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<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:HyphenationZone>21</w:HyphenationZone>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>ES</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="267">
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<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
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<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
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<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
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<w:LsdException Locked="false" Priority="10" SemiHidden="false"
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<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
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<w:LsdException Locked="false" Priority="62" SemiHidden="false"
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<w:LsdException Locked="false" Priority="63" SemiHidden="false"
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<w:LsdException Locked="false" Priority="65" SemiHidden="false"
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UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
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<w:LsdException Locked="false" Priority="65" SemiHidden="false"
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<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
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<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
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<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
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<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
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<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
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<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
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<w:LsdException Locked="false" Priority="70" SemiHidden="false"
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<w:LsdException Locked="false" Priority="71" SemiHidden="false"
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<w:LsdException Locked="false" Priority="72" SemiHidden="false"
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<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
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<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
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<w:LsdException Locked="false" Priority="65" SemiHidden="false"
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<w:LsdException Locked="false" Priority="66" SemiHidden="false"
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<w:LsdException Locked="false" Priority="67" SemiHidden="false"
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<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
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<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
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<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
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<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
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<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
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<w:LsdException Locked="false" Priority="70" SemiHidden="false"
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<w:LsdException Locked="false" Priority="62" SemiHidden="false"
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<w:LsdException Locked="false" Priority="70" SemiHidden="false"
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<w:LsdException Locked="false" Priority="71" SemiHidden="false"
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<w:LsdException Locked="false" Priority="72" SemiHidden="false"
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<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
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<w:LsdException Locked="false" Priority="61" SemiHidden="false"
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<w:LsdException Locked="false" Priority="62" SemiHidden="false"
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<w:LsdException Locked="false" Priority="63" SemiHidden="false"
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<w:LsdException Locked="false" Priority="64" SemiHidden="false"
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<w:LsdException Locked="false" Priority="65" SemiHidden="false"
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<w:LsdException Locked="false" Priority="66" SemiHidden="false"
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<w:LsdException Locked="false" Priority="67" SemiHidden="false"
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<w:LsdException Locked="false" Priority="68" SemiHidden="false"
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<w:LsdException Locked="false" Priority="70" SemiHidden="false"
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<w:LsdException Locked="false" Priority="71" SemiHidden="false"
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<w:LsdException Locked="false" Priority="72" SemiHidden="false"
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<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
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UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Tabla normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
mso-para-margin-top:0cm;
mso-para-margin-right:0cm;
mso-para-margin-bottom:10.0pt;
mso-para-margin-left:0cm;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-fareast-language:EN-US;}
</style>
<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Enseguida
se proceden a calcular los ángulos de inclinación de los miembros inclinados
(no horizontales ni verticales).</span></div>
<div class="MsoNormal" style="font-family: Verdana,sans-serif; margin-left: 18pt;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQ0NNrTRSU05REu25JmahxAljzS9nPbbLwt5UJ2qpuiQurI1BcYOFsr8GIP0DauRQW8vvY5WhW75bDnSzghxIq_okOdt5RCmBcaujQPg2nSZJbv5ndu76wejRHnoi5pDLqFrr3nVUWYn0y/s1600/Imagenes+para+trabajo+final+27.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQ0NNrTRSU05REu25JmahxAljzS9nPbbLwt5UJ2qpuiQurI1BcYOFsr8GIP0DauRQW8vvY5WhW75bDnSzghxIq_okOdt5RCmBcaujQPg2nSZJbv5ndu76wejRHnoi5pDLqFrr3nVUWYn0y/s1600/Imagenes+para+trabajo+final+27.jpg" width="320" /></a></div>
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<w:TrackFormatting/>
<w:HyphenationZone>21</w:HyphenationZone>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>ES</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
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<![endif]--><span style="font-family: Verdana,sans-serif; font-size: 11pt; line-height: 115%;"> Ahora
se procede a aplicar la ecuación de las fuerzas en X, como conocemos todos los
valores, simplemente nos sirve de comprobación.</span></div>
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mismo hacemos con la ecuación de las fuerzas en Y. También para comprobar.</span></div>
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Anonymoushttp://www.blogger.com/profile/03450060562327922078noreply@blogger.com1tag:blogger.com,1999:blog-2707794099772351810.post-69167145230612426662013-03-03T15:45:00.001-08:002013-03-03T15:45:50.130-08:00BIENVENIDOS<span style="font-family: Verdana, sans-serif;">BIENVENIDOS:</span><br />
<br />
<span style="font-family: Verdana, sans-serif;">ESTE TUTORIAL PRETENDE ACOMPAÑARTE DURANTE EL PROCESO DE ANÁLISIS ESTRUCTURAL DE ARMADURAS POR EL MÉTODO DE LOS NODOS, ES UNA EXCELENTE OPORTUNIDAD PARA ENTENDER ESTE TEMA BÁSICO EN LA ESTÁTICA.</span><br />
<br />
<span style="font-family: Verdana, sans-serif;">AQUÍ ENCONTRARÁS LA TEORÍA RESUMIDA Y EXPLICADA DE MANERA SENCILLA, ENTENDIBLE, EL PROCEDIMIENTO, PASO A PASO Y POR ÚLTIMO ENCONTRARÁS UN EJEMPLO TÍPICO DE ARMADURAS EN 2D.</span><br />
<br />
<span style="font-family: Verdana, sans-serif;">SE HAN RECOPILADO LOS MEJORES RECURSOS AUDIOVISUALES PARA EL APRENDIZAJE DEL MÉTODO DE LOS NODOS PARA EL ANÁLISIS DE ESTRUCTURAS, Y LOS PUEDE ENCONTRAR EN LOS LINKS DEL DOCUMENTO, JUSTO DONDE SIRVEN DE EJEMPLO O ILUSTRACIÓN DEL CONTENIDO.</span><br />
<br />
<span style="font-family: Verdana, sans-serif;">ESPERO QUE DISFRUTES EL PROCESO DE APRENDIZAJE, Y RECUERDA VISITAR LAS PÁGINAS DE REFERENCIA, PARA ENCONTRAR MÁS INFORMACIÓN Y OTROS PUNTOS DE VISTA.<span style="background-color: #6aa84f;"></span> </span>Anonymoushttp://www.blogger.com/profile/03450060562327922078noreply@blogger.com0