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z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="B">R</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">cm</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="3968" left="174" top="254.25" width="70.5" height="12" align-x="187.5" align-y="264" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Radios internos: </text> </region> <region region-id="4470" left="264" top="255" width="48.75" height="16.5" align-x="282" align-y="264" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="A">r</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>5.5</ml:real> <ml:id xml:space="preserve">cm</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="4473" left="342" top="255" width="47.25" height="16.5" align-x="358.5" align-y="264" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="B">r</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>3.5</ml:real> <ml:id xml:space="preserve">cm</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="3769" left="6" top="302.25" width="179.25" height="12" align-x="27.75" align-y="312" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="11"> Resolución: </f> </text> </region> <region region-id="3987" left="6" top="320.25" width="274.5" height="12" align-x="34.5" align-y="330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Reemplazando los vínculos por las reacciones que generan: </text> </region> <region region-id="4477" left="108" top="342" width="254.25" height="92.25" align-x="108" align-y="342" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{720DB9AF-D62C-4ED0-A377-429C22312852}" type="embedded" item-idref="13"/> <rendering item-idref="14"/> </region> <region region-id="3975" left="6" top="452.25" width="476.25" height="24" align-x="19.5" align-y="462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Aunque desconocemos el valor de las reacciones podemos deducir que los diagramas de momento, curvatura y giro deben ser: </text> </region> <region region-id="3993" left="90" top="492" width="279" height="243" align-x="90" align-y="492" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{720DB9AF-D62C-4ED0-A377-429C22312852}" type="embedded" item-idref="15"/> <rendering item-idref="16"/> </region> <region region-id="3999" left="6" top="746.25" width="477.75" height="24" align-x="17.25" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Como todo hiperestático de un grado de libertad se resuelve buscando una ecuación de equilibrio (estática), y una de compatibilidad (cinemática). </text> </region> <region region-id="3802" left="6" top="782.25" width="122.25" height="12" align-x="24" align-y="792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Ecuación de compatibilidad: </text> </region> <region region-id="4010" left="138" top="783" width="53.25" height="16.5" align-x="147.75" align-y="792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095244" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">bb03ef345c59004726ce55466e27d66e</contentHash> <ml:apply> <ml:equal/> <ml:real>0</ml:real> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="A">θ</ml:id> <ml:id xml:space="preserve" subscript="B">θ</ml:id> </ml:apply> </ml:apply> </ml:provenance> </math> <rendering item-idref="17"> <element-image-map> <box left="1.5" top="0.75" width="51.75" height="15" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4484" left="264" top="782.25" width="122.25" height="12" align-x="282" align-y="792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Ecuación de equilibrio: </text> </region> <region region-id="4485" left="378" top="783" width="71.25" height="16.5" align-x="398.25" align-y="792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094884" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">8ce5615e415237e7804bd5164dbce37c</contentHash> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="T">M</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="B">M</ml:id> <ml:id xml:space="preserve" subscript="A">M</ml:id> </ml:apply> </ml:apply> </ml:provenance> </math> <rendering item-idref="18"> <element-image-map> <box left="1.5" top="0.75" width="69.75" height="15" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4036" left="6" top="824.25" width="202.5" height="12" align-x="19.5" align-y="834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Dadas la relación entre curvatura y momento: </text> </region> <region region-id="4480" left="234" top="814.5" width="94.5" height="35.25" align-x="288.75" align-y="834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095244" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352093444" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">de8ad7fe51074853a609f12a97851d32</contentHash> <ml:apply> <ml:equal/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="B">θ</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="B">χ</ml:id> <ml:id xml:space="preserve" subscript="B">L</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="B">M</ml:id> <ml:id xml:space="preserve" subscript="B">L</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:provenance> </math> <rendering item-idref="19"> <element-image-map> <box left="1.5" top="0.75" width="93" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4481" left="372" top="814.5" width="102" height="35.25" align-x="431.25" align-y="834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352093444" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095244" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">6b89b59a6fdcfaf346144fc94643f93f</contentHash> <ml:apply> <ml:equal/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="A">θ</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="A">χ</ml:id> <ml:id xml:space="preserve" subscript="A">L</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="A">M</ml:id> <ml:id xml:space="preserve" subscript="A">L</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:provenance> </math> <rendering item-idref="20"> <element-image-map> <box left="1.5" top="0.75" width="100.5" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="3809" left="12" top="878.25" width="44.25" height="12" align-x="30.75" align-y="888" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Entonces: </text> </region> <region region-id="3810" left="72" top="868.5" width="116.25" height="35.25" align-x="112.5" align-y="888" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">1703caa683980913850b7301ec6895d7</contentHash> <ml:apply> <ml:equal/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="A">M</ml:id> <ml:id xml:space="preserve" subscript="A">L</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="T">M</ml:id> <ml:id xml:space="preserve" subscript="A">M</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="B">L</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:provenance> </math> <rendering item-idref="21"> <element-image-map> <box left="1.5" top="0.75" width="114.75" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4486" left="234" top="868.5" width="105.75" height="35.25" align-x="255.75" align-y="888" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095364" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352093444" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">0f145ca75749c588637916ecf0e8e31a</contentHash> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="A">M</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="T">M</ml:id> <ml:id xml:space="preserve" subscript="B">L</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="B">L</ml:id> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="PB">J</ml:id> <ml:id xml:space="preserve" subscript="A">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:provenance> </math> <rendering item-idref="22"> <element-image-map> <box left="1.5" top="0.75" width="104.25" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4067" left="12" top="938.25" width="33" height="12" align-x="25.5" align-y="948" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Siendo: </text> </region> <region region-id="4085" left="66" top="922.5" width="160.5" height="37.5" align-x="89.25" align-y="948" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352093444" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">bac2e05c12c247baf34136d85daaf776</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="PA">J</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="A">R</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="A">r</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:unitOverride> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>598.3752257384308</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="centimeter" power-numerator="4"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="23"> <element-image-map> <box left="1.5" top="0.75" width="159" height="36" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4487" left="276" top="922.5" width="156" height="37.5" align-x="297.75" align-y="948" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095244" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094604" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">9d971a430b12844fb8108d6e3c38b6ae</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="PB">J</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="B">R</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="B">r</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:unitOverride> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>166.40623586983429</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="centimeter" power-numerator="4"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="24"> <element-image-map> <box left="1.5" top="0.75" width="154.5" height="36" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4069" left="12" top="992.25" width="44.25" height="12" align-x="18.75" align-y="1002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Resulta: </text> </region> <region region-id="3815" left="66" top="982.5" width="146.25" height="35.25" align-x="89.25" align-y="1002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095444" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">3d269b52c74128f665d2a89a5d502f7c</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="A">M</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="PA">J</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="PA">J</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="T">M</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve" subscript="T">M</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.782413350449294</ml:real> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="25"> <element-image-map> <box left="1.5" top="0.75" width="144.75" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4488" left="276" top="982.5" width="144.75" height="35.25" align-x="297.75" align-y="1002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095244" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">242691b041f8c15f4ed84f32f2d486e9</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="B">M</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="PB">J</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="PA">J</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="T">M</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve" subscript="T">M</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.217586649550706</ml:real> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="26"> <element-image-map> <box left="1.5" top="0.75" width="143.25" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4104" left="6" top="1034.25" width="477.75" height="46.5" align-x="28.5" align-y="1044" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Para calcular el máximo momento <region region-id="4191" left="157.5" top="1035" width="15.75" height="16.5" align-x="164.25" align-y="1044" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" subscript="T" xmlns:ml="http://schemas.mathsoft.com/math30">M</ml:id> </math> <rendering item-idref="27"/> </region> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> que se puede aplicar, debemos calcular cuanto tiene que valor </inlineAttr> </f> <region region-id="4192" left="449.25" top="1035" width="15.75" height="16.5" align-x="456" align-y="1044" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" subscript="T" xmlns:ml="http://schemas.mathsoft.com/math30">M</ml:id> </math> <rendering item-idref="28"/> </region> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> para que la sección A alcance la tensión admisible, y el valor de </inlineAttr> </f> <region region-id="4193" left="285.75" top="1052.25" width="15.75" height="16.5" align-x="292.5" align-y="1061.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" subscript="T" xmlns:ml="http://schemas.mathsoft.com/math30">M</ml:id> </math> <rendering item-idref="29"/> </region> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> para que la sección B alcance la tensión admisible.</inlineAttr> </f> </text> </region> <region region-id="4331" left="48" top="1090.5" width="137.25" height="35.25" align-x="133.5" align-y="1110" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="Amax">M</ml:id> <ml:apply> <ml:mult style="thin-space"/> <ml:real>0.782</ml:real> <ml:id xml:space="preserve" subscript="T">M</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="adm">τ</ml:id> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="A">R</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="30"/> </region> <region region-id="4330" left="276" top="1090.5" width="134.25" height="35.25" align-x="360" align-y="1110" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="Bmax">M</ml:id> <ml:apply> <ml:mult style="thin-space"/> <ml:real>0.218</ml:real> <ml:id xml:space="preserve" subscript="T">M</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="adm">τ</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="B">R</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="31"/> </region> <region region-id="4322" left="18" top="1138.5" width="187.5" height="35.25" align-x="47.25" align-y="1158" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="TA">M</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="adm">τ</ml:id> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="A">R</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="PA">J</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> </ml:apply> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">kN</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>6.3731788467355424</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilonewton"/> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="4316" left="258" top="1138.5" width="180" height="35.25" align-x="285.75" align-y="1158" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="TB">M</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="adm">τ</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="B">R</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="PA">J</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> </ml:apply> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">kN</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>9.559768270103314</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilonewton"/> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="4333" left="6" top="1196.25" width="330.75" height="17.25" align-x="9.75" align-y="1206" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> El máximo valor que puede tomar <region region-id="4334" left="153.75" top="1197" width="15.75" height="16.5" align-x="160.5" align-y="1206" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" subscript="T" xmlns:ml="http://schemas.mathsoft.com/math30">M</ml:id> </math> <rendering item-idref="34"/> </region> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> resulta entonces el menor de los dos.</inlineAttr> </f> </text> </region> <region region-id="4336" left="348" top="1197" width="108.75" height="16.5" align-x="369.75" align-y="1206" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="T">M</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:id xml:space="preserve" subscript="TA">M</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">kN</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>6.3731788467355424</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilonewton"/> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> <rendering item-idref="35"/> </region> <region region-id="4417" left="6" top="1238.25" width="114" height="24" align-x="12.75" align-y="1248" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Los momentos de cada barra resultan entonces: </text> </region> <region region-id="4504" left="144" top="1234.5" width="152.25" height="35.25" align-x="167.25" align-y="1254" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095444" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095364" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">b857ab32a793164846fe95f1c43968ef</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="A">M</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="PA">J</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="PA">J</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="T">M</ml:id> </ml:apply> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">kN</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4.9864602144869243</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilonewton"/> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="36"> <element-image-map> <box left="1.5" top="0.75" width="150.75" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4499" left="330" top="1234.5" width="150.75" height="35.25" align-x="351.75" align-y="1254" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095244" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094884" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">fc70293b00242e0a70a38447f6337477</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="B">M</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="PB">J</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="PA">J</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="T">M</ml:id> </ml:apply> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">kN</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1.3867186322486191</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilonewton"/> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="37"> <element-image-map> <box left="1.5" top="0.75" width="149.25" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4458" left="6" top="1292.25" width="129" height="24" align-x="6" align-y="1302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="true" lock-width="true"> Las tensiones tangenciales máximas resultan: </text> </region> <region region-id="4505" left="144" top="1288.5" width="106.5" height="35.25" align-x="163.5" align-y="1308" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095124" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095364" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">677f4cdf07c69a5125c93d29ce1efb70</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="A">τ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="A">M</ml:id> <ml:id xml:space="preserve" subscript="A">R</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">MPa</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>50.000000000000007</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="megapascal"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="38"> <element-image-map> <box left="1.5" top="0.75" width="105" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4500" left="330" top="1288.5" width="117.75" height="35.25" align-x="348" align-y="1308" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094884" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094604" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">3b82c335a2db1e3633fcefa6e90b7a53</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="B">τ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="B">M</ml:id> <ml:id xml:space="preserve" subscript="B">R</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">MPa</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>33.333333333333329</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="megapascal"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="39"> <element-image-map> <box left="1.5" top="0.75" width="116.25" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4459" left="6" top="1346.25" width="116.25" height="24" align-x="6" align-y="1356" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="true" lock-width="true"> Las tensiones tangenciales mínimas: </text> </region> <region region-id="4506" left="144" top="1342.5" width="139.5" height="35.25" align-x="183" align-y="1362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094604" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">02653e3846eff9855b10804c897b5eee</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="min–A">τ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="A">M</ml:id> <ml:id xml:space="preserve" subscript="A">r</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">MPa</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>45.833333333333336</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="megapascal"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="40"> <element-image-map> <box left="1.5" top="0.75" width="138" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4501" left="330" top="1342.5" width="135" height="35.25" align-x="367.5" align-y="1362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095404" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094884" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">75838050288571843d24ed14c5d59b21</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="min–B">τ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="B">M</ml:id> <ml:id xml:space="preserve" subscript="B">r</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">MPa</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>29.166666666666668</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="megapascal"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="41"> <element-image-map> <box left="1.5" top="0.75" width="133.5" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="3872" left="6" top="1406.25" width="111.75" height="12" align-x="6" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="true" lock-width="true"> Las curvaturas resultan: </text> </region> <region region-id="4507" left="144" top="1396.5" width="140.25" height="35.25" align-x="165.75" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094884" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">c5aee4ad8eb7606a0164642750f2155d</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="A">Χ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="A">M</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.00980392156862745</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="42"> <element-image-map> <box left="1.5" top="0.75" width="138.75" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4502" left="330" top="1396.5" width="137.25" height="35.25" align-x="350.25" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095404" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095364" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">690ed18ebb40e0de619aac4dac2f6acf</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="B">Χ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="B">M</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.00980392156862745</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="43"> <element-image-map> <box left="1.5" top="0.75" width="135.75" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4462" left="6" top="1454.25" width="111.75" height="24" align-x="6" align-y="1464" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="true" lock-width="true"> Y finalmente el giro absoluto máximo: </text> </region> <region region-id="4508" left="144" top="1461" width="93.75" height="16.5" align-x="160.5" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095124" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094604" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">0c1442a8e523f39a6123262cd9798cbc</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="1">θ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="A">Χ</ml:id> 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</f> <f size="11"> <inlineAttr font-weight="normal" underline="false"> Para la siguiente estructura</inlineAttr> </f> </text> </region> <region region-id="3666" left="6" top="26.25" width="480" height="36" align-x="27.75" align-y="36" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="11">a) Determinar el Momento Torsor admisible de la estructura.</f> b)<f size="11"> Trazar diagramas de momentos torsor, curvatura, y giros absolutos a lo largo de la barra.</f> c)<f size="11"> Calcular las tensiones tangenciales para cada sección.</f> </text> </region> <region region-id="4467" left="84" top="72" width="294.75" height="112.5" align-x="84" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{720DB9AF-D62C-4ED0-A377-429C22312852}" type="embedded" item-idref="1"/> <rendering 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is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Aunque desconocemos el valor de las reacciones podemos deducir que los diagramas de momento, curvatura y giro deben ser: </text> </region> <region region-id="3993" left="90" top="492" width="279" height="243" align-x="90" align-y="492" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{720DB9AF-D62C-4ED0-A377-429C22312852}" type="embedded" item-idref="15"/> <rendering item-idref="16"/> </region> <region region-id="3999" left="6" top="746.25" width="477.75" height="24" align-x="17.25" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Como todo hiperestático de un grado de libertad se resuelve buscando una ecuación de equilibrio (estática), y una de compatibilidad (cinemática). </text> </region> <region region-id="3802" left="6" top="782.25" width="122.25" height="12" align-x="24" align-y="792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Ecuación de compatibilidad: </text> </region> <region region-id="4010" left="138" top="783" width="53.25" height="16.5" align-x="147.75" align-y="792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095244" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">bb03ef345c59004726ce55466e27d66e</contentHash> <ml:apply> <ml:equal/> <ml:real>0</ml:real> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="A">θ</ml:id> <ml:id xml:space="preserve" subscript="B">θ</ml:id> </ml:apply> </ml:apply> </ml:provenance> </math> <rendering item-idref="17"> <element-image-map> <box left="1.5" top="0.75" width="51.75" height="15" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4484" left="264" top="782.25" width="122.25" height="12" align-x="282" align-y="792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Ecuación de equilibrio: </text> </region> <region region-id="4485" left="378" top="783" width="71.25" height="16.5" align-x="398.25" align-y="792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094884" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">8ce5615e415237e7804bd5164dbce37c</contentHash> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="T">M</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="B">M</ml:id> <ml:id xml:space="preserve" subscript="A">M</ml:id> </ml:apply> </ml:apply> </ml:provenance> </math> <rendering item-idref="18"> <element-image-map> <box left="1.5" top="0.75" width="69.75" height="15" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4036" left="6" top="824.25" width="202.5" height="12" align-x="19.5" align-y="834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Dadas la relación entre curvatura y momento: </text> </region> <region region-id="4480" left="234" top="814.5" width="94.5" height="35.25" align-x="288.75" align-y="834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095244" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352093444" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">de8ad7fe51074853a609f12a97851d32</contentHash> <ml:apply> <ml:equal/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="B">θ</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="B">χ</ml:id> <ml:id xml:space="preserve" subscript="B">L</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="B">M</ml:id> <ml:id xml:space="preserve" subscript="B">L</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:provenance> </math> <rendering item-idref="19"> <element-image-map> <box left="1.5" top="0.75" width="93" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4481" left="372" top="814.5" width="102" height="35.25" align-x="431.25" align-y="834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352093444" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095244" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">6b89b59a6fdcfaf346144fc94643f93f</contentHash> <ml:apply> <ml:equal/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="A">θ</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="A">χ</ml:id> <ml:id xml:space="preserve" subscript="A">L</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="A">M</ml:id> <ml:id xml:space="preserve" subscript="A">L</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:provenance> </math> <rendering item-idref="20"> <element-image-map> <box left="1.5" top="0.75" width="100.5" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="3809" left="12" top="878.25" width="44.25" height="12" align-x="30.75" align-y="888" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Entonces: </text> </region> <region region-id="3810" left="72" top="868.5" width="116.25" height="35.25" align-x="112.5" align-y="888" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">1703caa683980913850b7301ec6895d7</contentHash> <ml:apply> <ml:equal/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="A">M</ml:id> <ml:id xml:space="preserve" subscript="A">L</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="T">M</ml:id> <ml:id xml:space="preserve" subscript="A">M</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="B">L</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:provenance> </math> <rendering item-idref="21"> <element-image-map> <box left="1.5" top="0.75" width="114.75" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4486" left="234" top="868.5" width="105.75" height="35.25" align-x="255.75" align-y="888" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095364" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352093444" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">0f145ca75749c588637916ecf0e8e31a</contentHash> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="A">M</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="T">M</ml:id> <ml:id xml:space="preserve" subscript="B">L</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="B">L</ml:id> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="PB">J</ml:id> <ml:id xml:space="preserve" subscript="A">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:provenance> </math> <rendering item-idref="22"> <element-image-map> <box left="1.5" top="0.75" width="104.25" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4067" left="12" top="938.25" width="33" height="12" align-x="25.5" align-y="948" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Siendo: </text> </region> <region region-id="4085" left="66" top="922.5" width="160.5" height="37.5" align-x="89.25" align-y="948" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352093444" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">bac2e05c12c247baf34136d85daaf776</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="PA">J</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="A">R</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="A">r</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:unitOverride> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>598.3752257384308</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="centimeter" power-numerator="4"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="23"> <element-image-map> <box left="1.5" top="0.75" width="159" height="36" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4487" left="276" top="922.5" width="156" height="37.5" align-x="297.75" align-y="948" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095244" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094604" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">9d971a430b12844fb8108d6e3c38b6ae</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="PB">J</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="B">R</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="B">r</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:unitOverride> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>166.40623586983429</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="centimeter" power-numerator="4"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="24"> <element-image-map> <box left="1.5" top="0.75" width="154.5" height="36" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4069" left="12" top="992.25" width="44.25" height="12" align-x="18.75" align-y="1002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Resulta: </text> </region> <region region-id="3815" left="66" top="982.5" width="146.25" height="35.25" align-x="89.25" align-y="1002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095444" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">3d269b52c74128f665d2a89a5d502f7c</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="A">M</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="PA">J</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="PA">J</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="T">M</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve" subscript="T">M</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.782413350449294</ml:real> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="25"> <element-image-map> <box left="1.5" top="0.75" width="144.75" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4488" left="276" top="982.5" width="144.75" height="35.25" align-x="297.75" align-y="1002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095244" 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</result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="26"> <element-image-map> <box left="1.5" top="0.75" width="143.25" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4104" left="6" top="1034.25" width="477.75" height="46.5" align-x="28.5" align-y="1044" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Para calcular el máximo momento <region region-id="4191" left="157.5" top="1035" width="15.75" height="16.5" align-x="164.25" align-y="1044" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" subscript="T" xmlns:ml="http://schemas.mathsoft.com/math30">M</ml:id> </math> <rendering item-idref="27"/> </region> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> que se puede aplicar, debemos calcular cuanto tiene que valor </inlineAttr> </f> <region region-id="4192" left="449.25" top="1035" width="15.75" height="16.5" align-x="456" align-y="1044" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" subscript="T" xmlns:ml="http://schemas.mathsoft.com/math30">M</ml:id> </math> <rendering item-idref="28"/> </region> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> para que la sección A alcance la tensión admisible, y el valor de </inlineAttr> </f> <region region-id="4193" left="285.75" top="1052.25" width="15.75" height="16.5" align-x="292.5" align-y="1061.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" subscript="T" xmlns:ml="http://schemas.mathsoft.com/math30">M</ml:id> </math> <rendering item-idref="29"/> </region> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> para que la sección B alcance la tensión admisible.</inlineAttr> </f> </text> </region> <region region-id="4331" left="48" top="1090.5" width="137.25" height="35.25" align-x="133.5" align-y="1110" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="Amax">M</ml:id> <ml:apply> <ml:mult style="thin-space"/> <ml:real>0.782</ml:real> <ml:id xml:space="preserve" subscript="T">M</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="adm">τ</ml:id> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="A">R</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="30"/> </region> <region region-id="4330" left="276" top="1090.5" width="134.25" height="35.25" align-x="360" align-y="1110" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="Bmax">M</ml:id> <ml:apply> <ml:mult style="thin-space"/> <ml:real>0.218</ml:real> <ml:id xml:space="preserve" subscript="T">M</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="adm">τ</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="B">R</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="31"/> </region> <region region-id="4322" left="18" top="1138.5" width="187.5" height="35.25" align-x="47.25" align-y="1158" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="TA">M</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="adm">τ</ml:id> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="A">R</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="PA">J</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> </ml:apply> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">kN</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>6.3731788467355424</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilonewton"/> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="4316" left="258" top="1138.5" width="180" height="35.25" align-x="285.75" align-y="1158" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="TB">M</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="adm">τ</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="B">R</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="PA">J</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> </ml:apply> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">kN</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>9.559768270103314</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilonewton"/> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="4333" left="6" top="1196.25" width="330.75" height="17.25" align-x="9.75" align-y="1206" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> El máximo valor que puede tomar <region region-id="4334" left="153.75" top="1197" width="15.75" height="16.5" align-x="160.5" align-y="1206" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" subscript="T" xmlns:ml="http://schemas.mathsoft.com/math30">M</ml:id> </math> <rendering item-idref="34"/> </region> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> resulta entonces el menor de los dos.</inlineAttr> </f> </text> </region> <region region-id="4336" left="348" top="1197" width="108.75" height="16.5" align-x="369.75" align-y="1206" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="T">M</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:id xml:space="preserve" subscript="TA">M</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">kN</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>6.3731788467355424</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilonewton"/> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> <rendering item-idref="35"/> </region> <region region-id="4417" left="6" top="1238.25" width="114" height="24" align-x="12.75" align-y="1248" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Los momentos de cada barra resultan entonces: </text> </region> <region region-id="4504" left="144" top="1234.5" width="152.25" height="35.25" align-x="167.25" align-y="1254" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095444" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef 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<ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">kN</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4.9864602144869243</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilonewton"/> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="36"> <element-image-map> <box left="1.5" top="0.75" width="150.75" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4499" left="330" top="1234.5" width="150.75" height="35.25" align-x="351.75" align-y="1254" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095244" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094884" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">fc70293b00242e0a70a38447f6337477</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="B">M</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="PB">J</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="PA">J</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="T">M</ml:id> </ml:apply> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">kN</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1.3867186322486191</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilonewton"/> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="37"> <element-image-map> <box left="1.5" top="0.75" width="149.25" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4458" left="6" top="1292.25" width="129" height="24" align-x="6" align-y="1302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="true" lock-width="true"> Las tensiones tangenciales máximas resultan: </text> </region> <region region-id="4505" left="144" top="1288.5" width="106.5" height="35.25" align-x="163.5" align-y="1308" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095124" is-modified="false" region-id="0" 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xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">MPa</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>50.000000000000007</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="megapascal"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="38"> <element-image-map> <box left="1.5" top="0.75" width="105" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4500" left="330" top="1288.5" width="117.75" height="35.25" align-x="348" align-y="1308" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094884" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094604" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">3b82c335a2db1e3633fcefa6e90b7a53</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="B">τ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="B">M</ml:id> <ml:id xml:space="preserve" subscript="B">R</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">MPa</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>33.333333333333329</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="megapascal"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="39"> <element-image-map> <box left="1.5" top="0.75" width="116.25" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4459" left="6" top="1346.25" width="116.25" height="24" align-x="6" align-y="1356" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="true" lock-width="true"> Las tensiones tangenciales mínimas: </text> </region> <region region-id="4506" left="144" top="1342.5" width="139.5" height="35.25" align-x="183" align-y="1362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094604" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">02653e3846eff9855b10804c897b5eee</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="min–A">τ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="A">M</ml:id> <ml:id xml:space="preserve" subscript="A">r</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">MPa</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>45.833333333333336</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="megapascal"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="40"> <element-image-map> <box left="1.5" top="0.75" width="138" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4501" left="330" top="1342.5" width="135" height="35.25" align-x="367.5" align-y="1362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095404" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094884" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">75838050288571843d24ed14c5d59b21</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="min–B">τ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="B">M</ml:id> <ml:id xml:space="preserve" subscript="B">r</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">MPa</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>29.166666666666668</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="megapascal"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="41"> <element-image-map> <box left="1.5" top="0.75" width="133.5" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="3872" left="6" top="1406.25" width="111.75" height="12" align-x="6" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="true" lock-width="true"> Las curvaturas resultan: </text> </region> <region region-id="4507" left="144" top="1396.5" width="140.25" height="35.25" align-x="165.75" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094884" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095324" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">c5aee4ad8eb7606a0164642750f2155d</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="A">Χ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="A">M</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve" subscript="PA">J</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.00980392156862745</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="42"> <element-image-map> <box left="1.5" top="0.75" width="138.75" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4502" left="330" top="1396.5" width="137.25" height="35.25" align-x="350.25" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095404" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095364" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">690ed18ebb40e0de619aac4dac2f6acf</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="B">Χ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="B">M</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve" subscript="PB">J</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.00980392156862745</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="43"> <element-image-map> <box left="1.5" top="0.75" width="135.75" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4462" left="6" top="1454.25" width="111.75" height="24" align-x="6" align-y="1464" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="true" lock-width="true"> Y finalmente el giro absoluto máximo: </text> </region> <region region-id="4508" left="144" top="1461" width="93.75" height="16.5" align-x="160.5" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095124" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352094604" is-modified="false" region-id="0" href="C:\Users\Felipe\Dropbox\Ejercicio - Torsion.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">0c1442a8e523f39a6123262cd9798cbc</contentHash> <ml:define> <ml:id xml:space="preserve" subscript="1">θ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="A">Χ</ml:id> <ml:id xml:space="preserve" subscript="A">L</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.0392156862745098</ml:real> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="44"> <element-image-map> <box left="1.5" top="0.75" width="92.25" height="15" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4503" left="330" top="1461" width="90.75" height="16.5" align-x="346.5" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="784BFC85-5597-40FF-96BE-9ADE4FD06D26" version-id="E588A210-5A48-4999-9DB3-263E0638A2A8" branch-id="00000000-0000-0000-0000-000000000000" revision-num="352095244" is-modified="false" region-id="0" 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