<description/> <author>jon</author> <company/> <keywords/> <revisedBy>jon</revisedBy> </userData> <identityInfo> <revision>9</revision> <documentID>43D6E26B-C5A8-43B1-855D-FD57AA3D453C</documentID> <versionID>B3EDA77E-857F-4875-840C-F38CC03A210B</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="12" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="small" definition="colon-equal" 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zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="matrix" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="1" orientation="portrait" print-single-page-width="false" page-width="612" page-height="792"> <margins left="72" right="14.04" top="36" bottom="36"/> <header use-full-page-width="true"/> <footer use-full-page-width="true"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="en" UI="en"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC11" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="us" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="301" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="214" left="120" top="6.75" width="272.25" height="42.75" align-x="120" align-y="18" 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"> VON MISES STRESS CALC Test7x7.0 11/27/12 </text> </region> <region region-id="1" left="6" top="66.75" width="75" height="14.25" align-x="6" align-y="78" 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"> REQUIRED:<sp count="5"/> </text> </region> <region region-id="215" left="96" top="66.75" width="414.75" height="28.5" align-x="96" align-y="78" 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"> Find Von Mises Stress given the two normal stress values and the shear stress.<sp count="2"/>From Composite Pro for a given external pressure and end loading. </text> </region> <region region-id="3" left="6" top="114.75" width="44.25" height="14.25" align-x="6" align-y="126" 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"> GIVEN:<sp count="2"/> </text> </region> <region region-id="248" left="96" top="114.75" width="201.75" height="28.5" align-x="109.5" align-y="126" 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"> Lateral External pressure = 4343 psi End Load due to pressure = 198039 lbf. </text> </region> <region region-id="284" left="6" top="156.75" width="61.5" height="14.25" align-x="6" align-y="168" 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"> SOLUTION: </text> </region> <region region-id="266" left="6" top="180.75" width="72.75" height="14.25" align-x="6" align-y="192" 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="false"> Layer 1 (inner): </text> </region> <region region-id="285" left="96" top="186.75" width="49.5" height="14.25" align-x="96" align-y="198" 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"> Sigma -X. </text> </region> <region region-id="286" left="306" top="188.25" width="62.25" height="15.75" align-x="322.5" align-y="198" 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="x">σ</ml:id> <ml:apply> <ml:mult/> <ml:real>26760</ml:real> <ml:id xml:space="preserve">psi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="1"/> </region> <region region-id="287" left="96" top="204.75" width="45" height="14.25" align-x="96" align-y="216" 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"> Sigma-Y: </text> </region> <region region-id="288" left="306" top="206.25" width="62.25" height="15.75" align-x="322.5" align-y="216" 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="y">σ</ml:id> <ml:apply> <ml:mult/> <ml:real>54930</ml:real> <ml:id xml:space="preserve">psi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="289" left="96" top="222.75" width="39.75" height="14.25" align-x="113.25" align-y="234" 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"> Tau-XY </text> </region> <region region-id="290" left="306" top="224.25" width="60.75" height="15.75" align-x="325.5" align-y="234" 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="xy">τ</ml:id> <ml:apply> <ml:mult/> <ml:real>9800</ml:real> <ml:id xml:space="preserve">psi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="291" left="42" top="254.25" width="143.25" height="21.75" align-x="57" align-y="270" 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">σ'</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="x">σ</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="y">σ</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="x">σ</ml:id> <ml:id xml:space="preserve" subscript="y">σ</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="xy">τ</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="292" left="294" top="256.5" width="84.75" height="17.25" align-x="307.5" align-y="270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">σ'</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">psi</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>50513.322005189875</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="pounds_per_sq_inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="4" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="matrix" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="5"/> </region> <region region-id="301" left="6" top="318.75" width="83.25" height="14.25" align-x="6" 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="false"> Layer 10 (outer):<sp count="2"/> </text> </region> <region region-id="293" left="96" top="318.75" width="49.5" height="14.25" align-x="96" 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"> Sigma -X. </text> </region> <region region-id="294" left="306" top="320.25" width="69.75" height="15.75" align-x="330" align-y="330" 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="x10">σ</ml:id> <ml:apply> <ml:mult/> <ml:real>26620</ml:real> <ml:id xml:space="preserve">psi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="295" left="96" top="336.75" width="45" height="14.25" align-x="96" align-y="348" 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"> Sigma-Y: </text> </region> <region region-id="296" left="306" top="338.25" width="69.75" height="15.75" align-x="330" align-y="348" 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="y10">σ</ml:id> <ml:apply> <ml:mult/> <ml:real>51820</ml:real> <ml:id xml:space="preserve">psi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="297" left="96" top="354.75" width="39.75" height="14.25" align-x="113.25" align-y="366" 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"> Tau-XY </text> </region> <region region-id="298" left="306" top="356.25" width="68.25" height="15.75" align-x="333" align-y="366" 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="xy10">τ</ml:id> <ml:apply> <ml:mult/> <ml:real>9309</ml:real> <ml:id xml:space="preserve">psi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="299" left="42" top="392.25" width="187.5" height="21.75" align-x="63.75" align-y="408" 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="10'">σ</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="x10">σ</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="y10">σ</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="x10">σ</ml:id> <ml:id xml:space="preserve" subscript="y10">σ</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="xy10">τ</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="300" left="294" top="394.5" width="91.5" height="19.5" align-x="314.25" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="10'">σ</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">psi</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>47691.307834866522</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="pounds_per_sq_inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="4" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="matrix" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="10"/> </region> <region region-id="130" left="42" top="714" width="437.25" height="15.75" align-x="42" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="11" display-width="435.75" display-height="14.25"/> </picture> <rendering item-idref="12"/> </region> <region region-id="52" left="12" top="738" width="6000" height="6" align-x="12" align-y="738" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="77" left="6" top="744" width="477.75" height="99.75" align-x="6" 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"> Materials<sp count="20"/>E<sp count="2"/>(psi)<sp count="15"/> <f family="Symbol" charset="2">n</f> <sp count="24"/> <f family="Symbol" charset="2">r</f> <sp count="2"/>(lb/in^3)<sp count="26"/>S<f size="8"> y </f> <sp count="19"/>G<f size="5"> (psi)<sp count="8"/> </f> 6061-T6<sp count="20"/>10.0E6<sp count="14"/>.300<sp count="25"/>.0980<sp count="27"/>35 kpsi 7075-76<sp count="20"/>10.5E6<sp count="14"/>.3300<sp count="23"/>.1010<sp count="27"/>67 kpsi Titanium (pure)<sp count="9"/>15.5E6<sp count="14"/>.3400<sp count="23"/>.1630<sp count="27"/>55 kpsi Titanium 6AL-4V<sp count="5"/>17.0E6<sp count="14"/>.3250<sp count="23"/>.1610<sp count="27"/>120kpsi S.S. 17-4 ph<sp count="14"/>28.5E6<sp count="13"/>.3000<sp count="24"/>.2800<sp count="26"/>178kpsi S.S. 316<sp count="20"/>27.6E6<sp count="14"/>.305<sp count="25"/>.280<sp count="28"/>30 kpsi<sp count="12"/>10.6E6<sp count="21"/> </text> </region> <region region-id="213" left="48" top="876" width="12.75" height="13.5" align-x="48" align-y="876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="13" display-width="11.25" display-height="12"/> </picture> <rendering item-idref="14"/> </region> <region region-id="111" left="126" top="876.75" width="176.25" height="14.25" align-x="126" 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"> Convert deg Rankine to deg Fahienheit </text> </region> <region region-id="110" left="306" top="878.25" width="60.75" height="13.5" align-x="318" 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:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:mult/> <ml:real>-459.69</ml:real> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="112" left="126" top="894.75" width="162" height="14.25" align-x="126" align-y="906" 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"> Convert deg Kelvin<sp count="2"/>to deg Celcius </text> </region> <region region-id="113" left="312" top="896.25" width="62.25" height="13.5" align-x="325.5" align-y="906" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:mult/> <ml:real>-273.16</ml:real> <ml:id xml:space="preserve">K</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="200" left="126" top="912.75" width="130.5" height="14.25" align-x="126" align-y="924" 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"> Convert depth Meters to bar </text> </region> <region region-id="201" left="312" top="914.25" width="72" height="13.5" align-x="324.75" align-y="924" 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">Z</ml:id> <ml:apply> <ml:mult/> <ml:real>.1006649</ml:real> <ml:id xml:space="preserve">bar</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="202" left="126" top="930.75" width="133.5" height="14.25" align-x="126" align-y="942" 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"> Convert depth Meters to psig </text> </region> <region region-id="203" left="312" top="932.25" width="69.75" height="13.5" align-x="324.75" align-y="942" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:mult/> <ml:real>1.460016</ml:real> <ml:id xml:space="preserve">psi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="114" left="6" top="960" width="436.5" height="6" align-x="6" align-y="960" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="19" display-width="435" 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Mathcad Professional 14.0 <description/> <author>jon</author> <company/> <keywords/> <revisedBy>jon</revisedBy> </userData> <identityInfo> <revision>9</revision> <documentID>43D6E26B-C5A8-43B1-855D-FD57AA3D453C</documentID> <versionID>B3EDA77E-857F-4875-840C-F38CC03A210B</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="12" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="small" 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matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC11" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="us" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="301" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="214" left="120" top="6.75" width="272.25" height="42.75" align-x="120" align-y="18" 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"> VON MISES STRESS CALC Test7x7.0 11/27/12 </text> </region> <region region-id="1" left="6" top="66.75" width="75" height="14.25" align-x="6" align-y="78" 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"> REQUIRED:<sp count="5"/> </text> </region> <region region-id="215" left="96" top="66.75" width="414.75" height="28.5" align-x="96" align-y="78" 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"> Find Von Mises Stress given the two normal stress values and the shear stress.<sp count="2"/>From Composite Pro for a given external pressure and end loading. </text> </region> <region region-id="3" left="6" top="114.75" width="44.25" height="14.25" align-x="6" align-y="126" 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"> GIVEN:<sp count="2"/> </text> </region> <region region-id="248" left="96" top="114.75" width="201.75" height="28.5" align-x="109.5" align-y="126" 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"> Lateral External pressure = 4343 psi End Load due to pressure = 198039 lbf. </text> </region> <region region-id="284" left="6" top="156.75" width="61.5" height="14.25" align-x="6" align-y="168" 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"> SOLUTION: </text> </region> <region region-id="266" left="6" top="180.75" width="72.75" height="14.25" align-x="6" align-y="192" 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="false"> Layer 1 (inner): </text> </region> <region region-id="285" left="96" top="186.75" width="49.5" height="14.25" align-x="96" align-y="198" 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"> Sigma -X. </text> </region> <region region-id="286" left="306" top="188.25" width="62.25" height="15.75" align-x="322.5" align-y="198" 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="x">σ</ml:id> <ml:apply> <ml:mult/> <ml:real>26760</ml:real> <ml:id xml:space="preserve">psi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="1"/> </region> <region region-id="287" left="96" top="204.75" width="45" height="14.25" align-x="96" align-y="216" 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"> Sigma-Y: </text> </region> <region region-id="288" left="306" top="206.25" width="62.25" height="15.75" align-x="322.5" align-y="216" 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="y">σ</ml:id> <ml:apply> <ml:mult/> <ml:real>54930</ml:real> <ml:id xml:space="preserve">psi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="289" left="96" top="222.75" width="39.75" height="14.25" align-x="113.25" align-y="234" 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"> Tau-XY </text> </region> <region region-id="290" left="306" top="224.25" width="60.75" height="15.75" align-x="325.5" align-y="234" 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="xy">τ</ml:id> <ml:apply> <ml:mult/> <ml:real>9800</ml:real> <ml:id xml:space="preserve">psi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="291" left="42" top="254.25" width="143.25" height="21.75" align-x="57" align-y="270" 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">σ'</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="x">σ</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="y">σ</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="x">σ</ml:id> <ml:id xml:space="preserve" subscript="y">σ</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="xy">τ</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="292" left="294" top="256.5" width="84.75" height="17.25" align-x="307.5" align-y="270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">σ'</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">psi</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>50513.322005189875</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="pounds_per_sq_inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="4" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="matrix" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="5"/> </region> <region region-id="301" left="6" top="318.75" width="83.25" height="14.25" align-x="6" 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="false"> Layer 10 (outer):<sp count="2"/> </text> </region> <region region-id="293" left="96" top="318.75" width="49.5" height="14.25" align-x="96" 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"> Sigma -X. </text> </region> <region region-id="294" left="306" top="320.25" width="69.75" height="15.75" align-x="330" align-y="330" 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="x10">σ</ml:id> <ml:apply> <ml:mult/> <ml:real>26620</ml:real> <ml:id xml:space="preserve">psi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="295" left="96" top="336.75" width="45" height="14.25" align-x="96" align-y="348" 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"> Sigma-Y: </text> </region> <region region-id="296" left="306" top="338.25" width="69.75" height="15.75" align-x="330" align-y="348" 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="y10">σ</ml:id> <ml:apply> <ml:mult/> <ml:real>51820</ml:real> <ml:id xml:space="preserve">psi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="297" left="96" top="354.75" width="39.75" height="14.25" align-x="113.25" align-y="366" 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"> Tau-XY </text> </region> <region region-id="298" left="306" top="356.25" width="68.25" height="15.75" align-x="333" align-y="366" 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="xy10">τ</ml:id> <ml:apply> <ml:mult/> <ml:real>9309</ml:real> <ml:id xml:space="preserve">psi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="299" left="42" top="392.25" width="187.5" height="21.75" align-x="63.75" align-y="408" 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="10'">σ</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="x10">σ</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="y10">σ</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="x10">σ</ml:id> <ml:id xml:space="preserve" subscript="y10">σ</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="xy10">τ</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="300" left="294" top="394.5" width="91.5" height="19.5" align-x="314.25" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="10'">σ</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">psi</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>47691.307834866522</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="pounds_per_sq_inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="4" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="matrix" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="10"/> </region> <region region-id="130" left="42" top="714" width="437.25" height="15.75" align-x="42" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="11" display-width="435.75" display-height="14.25"/> </picture> <rendering item-idref="12"/> </region> <region region-id="52" left="12" top="738" width="6000" height="6" align-x="12" align-y="738" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="77" left="6" top="744" width="477.75" height="99.75" align-x="6" 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"> Materials<sp count="20"/>E<sp count="2"/>(psi)<sp count="15"/> <f family="Symbol" charset="2">n</f> <sp count="24"/> <f family="Symbol" charset="2">r</f> <sp count="2"/>(lb/in^3)<sp count="26"/>S<f size="8"> y </f> <sp count="19"/>G<f size="5"> (psi)<sp count="8"/> </f> 6061-T6<sp count="20"/>10.0E6<sp count="14"/>.300<sp count="25"/>.0980<sp count="27"/>35 kpsi 7075-76<sp count="20"/>10.5E6<sp count="14"/>.3300<sp count="23"/>.1010<sp count="27"/>67 kpsi Titanium (pure)<sp count="9"/>15.5E6<sp count="14"/>.3400<sp count="23"/>.1630<sp count="27"/>55 kpsi Titanium 6AL-4V<sp count="5"/>17.0E6<sp count="14"/>.3250<sp count="23"/>.1610<sp count="27"/>120kpsi S.S. 17-4 ph<sp count="14"/>28.5E6<sp count="13"/>.3000<sp count="24"/>.2800<sp count="26"/>178kpsi S.S. 316<sp count="20"/>27.6E6<sp count="14"/>.305<sp count="25"/>.280<sp count="28"/>30 kpsi<sp count="12"/>10.6E6<sp count="21"/> </text> </region> <region region-id="213" left="48" top="876" width="12.75" height="13.5" align-x="48" align-y="876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="13" display-width="11.25" display-height="12"/> </picture> <rendering item-idref="14"/> </region> <region region-id="111" left="126" top="876.75" width="176.25" height="14.25" align-x="126" 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"> Convert deg Rankine to deg Fahienheit </text> </region> <region region-id="110" left="306" top="878.25" width="60.75" height="13.5" align-x="318" 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:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:mult/> 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item-idref="16"/> </region> <region region-id="200" left="126" top="912.75" width="130.5" height="14.25" align-x="126" align-y="924" 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"> Convert depth Meters to bar </text> </region> <region region-id="201" left="312" top="914.25" width="72" height="13.5" align-x="324.75" align-y="924" 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">Z</ml:id> <ml:apply> <ml:mult/> <ml:real>.1006649</ml:real> <ml:id xml:space="preserve">bar</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="202" left="126" top="930.75" width="133.5" height="14.25" align-x="126" align-y="942" 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"> Convert depth Meters to psig </text> </region> <region region-id="203" left="312" top="932.25" width="69.75" height="13.5" align-x="324.75" align-y="942" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:mult/> <ml:real>1.460016</ml:real> <ml:id xml:space="preserve">psi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="114" left="6" top="960" width="436.5" height="6" align-x="6" align-y="960" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="19" display-width="435" display-height="4.5"/> </picture> <rendering item-idref="20"/> </region> <region region-id="206" left="24" top="978" width="344.25" height="7.5" align-x="24" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="21" display-width="342.75" display-height="6"/> </picture> <rendering item-idref="22"/> </region> <region region-id="209" left="18" top="1002" width="438" height="15" align-x="18" align-y="1002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="23" display-width="436.5" display-height="13.5"/> </picture> <rendering item-idref="24"/> </region> <region region-id="210" left="12" top="1038" width="437.25" height="15.75" align-x="12" align-y="1038" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png 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