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								<ml:pow/>
								<ml:real>10</ml:real>
								<ml:real>3</ml:real>
							</ml:apply>
						</ml:apply>
						<ml:id xml:space="preserve">ksi</ml:id>
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				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Material density:</p>
			</text>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="6al4v">ρ</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.16</ml:real>
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							<ml:div/>
							<ml:id xml:space="preserve">lbf</ml:id>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve">in</ml:id>
								<ml:real>3</ml:real>
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				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Poisson's ratio:</p>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ν</ml:id>
					<ml:real>0.31</ml:real>
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				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Yield Stress:</p>
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			<math optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve" subscript="y">S</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>120.0</ml:real>
						<ml:id xml:space="preserve">ksi</ml:id>
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				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Shear stress:</p>
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			<math optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve" subscript="s">S</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>79.8</ml:real>
						<ml:id xml:space="preserve">ksi</ml:id>
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			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Bearing yield stress:</p>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="b">S</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>215</ml:real>
						<ml:id xml:space="preserve">ksi</ml:id>
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			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Shear Modulus:</p>
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			<math optimize="false" disable-calc="false">
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							<ml:div/>
							<ml:id xml:space="preserve">E</ml:id>
							<ml:apply>
								<ml:mult/>
								<ml:real>2</ml:real>
								<ml:parens>
									<ml:apply>
										<ml:plus/>
										<ml:real>1</ml:real>
										<ml:id xml:space="preserve">ν</ml:id>
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								</ml:parens>
							</ml:apply>
						</ml:apply>
						<ml:unitOverride>
							<ml:id xml:space="preserve">ksi</ml:id>
						</ml:unitOverride>
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							<unitedValue>
								<ml:real>6106.8702290076335</ml:real>
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									<unitReference unit="kips_per_sq_inch"/>
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				<p style="Heading 1" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Design Dimensions</p>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellOD</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>2.75</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellID</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real font="0">1.875</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">lidThick</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>.770</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
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			</math>
			<rendering item-idref="20"/>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellWallThickness</ml:id>
					<ml:eval placeholderMultiplicationStyle="default">
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:minus/>
								<ml:id xml:space="preserve">shellOD</ml:id>
								<ml:id xml:space="preserve">shellID</ml:id>
							</ml:apply>
							<ml:real>2</ml:real>
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							<ml:id xml:space="preserve">in</ml:id>
						</ml:unitOverride>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<unitedValue>
								<ml:real>0.43749999999999989</ml:real>
								<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
									<unitReference unit="inch"/>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellLength</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>5.152</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="22"/>
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		<region region-id="625" left="18" top="1098.75" width="169.5" height="15.75" align-x="145.5" 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:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">endCapCompressionDia</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.52</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:define>
			</math>
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		<region region-id="728" left="198" top="1098.75" width="125.25" height="15.75" align-x="288.75" 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:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">oringShearHeight</ml:id>
					<ml:real>1.505</ml:real>
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		<region region-id="624" left="18" top="1118.25" width="190.5" height="20.25" align-x="151.5" align-y="1134" 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">endCapCompressionArea</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>.51499</ml:real>
						<ml:apply>
							<ml:pow/>
							<ml:id xml:space="preserve">in</ml:id>
							<ml:real>2</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">keyCompressionArea</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>.2285</ml:real>
						<ml:apply>
							<ml:pow/>
							<ml:id xml:space="preserve">in</ml:id>
							<ml:real>2</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellIDatORing</ml:id>
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						<ml:mult/>
						<ml:real>2.002</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">keyHeight</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>.625</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">keyWidth</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>.390</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ecPlugOD</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>2.0</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
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				<p style="Heading 1" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Factors of Safety</p>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">minFoSBuckling</ml:id>
					<ml:real>4</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">minFofS</ml:id>
					<ml:real>4</ml:real>
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				<p style="Heading 1" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Thin wall Shell Calcs</p>
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						<b>
							<inlineAttr underline="false">Table 28<sp count="2"/>Formulas for membrane stresses and </inlineAttr>
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							<inlineAttr underline="false">deformations in thin-walled pressure vessels</inlineAttr>
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							<inlineAttr underline="false">Case 1c: Cylindrical shell; uniform internal or external pressure (ends capped)</inlineAttr>
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		<region region-id="173" left="132" top="1356" width="99.75" height="15" align-x="132" align-y="1368" 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">
				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Mean radius:</p>
			</text>
		</region>
		<region region-id="174" left="168" top="1372.5" width="261" height="30.75" align-x="204" align-y="1392" 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="thin">R</ml:id>
					<ml:eval placeholderMultiplicationStyle="default">
						<ml:parens>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:div/>
									<ml:id xml:space="preserve">shellID</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
								<ml:apply>
									<ml:div/>
									<ml:id xml:space="preserve">shellWallThickness</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
						</ml:parens>
						<ml:unitOverride>
							<ml:id xml:space="preserve">in</ml:id>
						</ml:unitOverride>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<unitedValue>
								<ml:real>1.15625</ml:real>
								<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
									<unitReference unit="inch"/>
								</unitMonomial>
							</unitedValue>
						</result>
					</ml:eval>
				</ml:define>
			</math>
			<rendering item-idref="35"/>
		</region>
		<region region-id="167" left="240" top="1422.75" width="134.25" height="15.75" align-x="255.75" align-y="1434" 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">y</ml:id>
					<ml:eval placeholderMultiplicationStyle="default">
						<ml:id xml:space="preserve">shellLength</ml:id>
						<ml:unitOverride>
							<ml:id xml:space="preserve">in</ml:id>
						</ml:unitOverride>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<unitedValue>
								<ml:real>5.152</ml:real>
								<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
									<unitReference unit="inch"/>
								</unitMonomial>
							</unitedValue>
						</result>
					</ml:eval>
				</ml:define>
			</math>
			<rendering item-idref="36"/>
		</region>
		<region region-id="204" left="132" top="1428" width="93" height="15" align-x="132" align-y="1440" 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">
				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Cylinder Height:</p>
			</text>
		</region>
		<region region-id="206" left="42" top="1470" width="380.25" height="30" align-x="42" align-y="1482" 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">
				<p style="Heading 2" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Assumptions: For the expressions in the case to be valid, the following condition must be true (i.e., condition = 1):</p>
			</text>
		</region>
		<region region-id="177" left="36" top="1512" width="197.25" height="38.25" align-x="86.25" align-y="1536" 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">thinWall</ml:id>
					<ml:parens>
						<ml:apply>
							<ml:greaterThan/>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve" subscript="thin">R</ml:id>
								<ml:id xml:space="preserve">shellWallThickness</ml:id>
							</ml:apply>
							<ml:real>10</ml:real>
						</ml:apply>
					</ml:parens>
				</ml:define>
			</math>
			<rendering item-idref="37"/>
		</region>
		<region region-id="178" left="228" top="1512" width="143.25" height="38.25" align-x="331.5" align-y="1536" 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:provenance expr-id="1">
						<originRef doc-id="EB680200-941F-4652-A947-46F72788A88D" version-id="82637E21-2413-4F2D-B489-29878F2336B7" branch-id="00000000-0000-0000-0000-000000000000" revision-num="345131612" is-modified="true" region-id="0" href="C:\Users\magene\AppData\Local\Microsoft\Windows\INetCache\Content.Outlook\1MC61IEY\PV9.0.xmcd" xmlns="http://schemas.mathsoft.com/provenance10">
							<hash/>
						</originRef>
						<parentRef doc-id="EB680200-941F-4652-A947-46F72788A88D" version-id="82637E21-2413-4F2D-B489-29878F2336B7" branch-id="00000000-0000-0000-0000-000000000000" revision-num="345131532" is-modified="true" region-id="0" href="C:\Users\magene\AppData\Local\Microsoft\Windows\INetCache\Content.Outlook\1MC61IEY\PV9.0.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">220dce954f46215b402879b583e3cbd6</contentHash>
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve" subscript="thin">R</ml:id>
							<ml:id xml:space="preserve">shellWallThickness</ml:id>
						</ml:apply>
					</ml:provenance>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>2.6428571428571432</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="38">
				<element-image-map>
					<box left="1.5" top="0.75" width="95.25" height="36.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/>
				</element-image-map>
			</rendering>
		</region>
		<region region-id="180" left="360" top="1524.75" width="70.5" height="15.75" align-x="408.75" align-y="1536" 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:provenance expr-id="1">
						<originRef doc-id="EB680200-941F-4652-A947-46F72788A88D" version-id="82637E21-2413-4F2D-B489-29878F2336B7" branch-id="00000000-0000-0000-0000-000000000000" revision-num="345131532" is-modified="true" region-id="0" href="C:\Users\magene\AppData\Local\Microsoft\Windows\INetCache\Content.Outlook\1MC61IEY\PV9.0.xmcd" xmlns="http://schemas.mathsoft.com/provenance10">
							<hash/>
						</originRef>
						<parentRef doc-id="EB680200-941F-4652-A947-46F72788A88D" version-id="82637E21-2413-4F2D-B489-29878F2336B7" branch-id="00000000-0000-0000-0000-000000000000" revision-num="345132412" is-modified="true" region-id="0" href="C:\Users\magene\AppData\Local\Microsoft\Windows\INetCache\Content.Outlook\1MC61IEY\PV9.0.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">d9e3f0c55620159330ad6e00b4e3ed19</contentHash>
						<ml:id xml:space="preserve">thinWall</ml:id>
					</ml:provenance>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>0</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="39">
				<element-image-map>
					<box left="1.5" top="0.75" width="40.5" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/>
				</element-image-map>
			</rendering>
		</region>
		<region region-id="188" left="192" top="1560" width="216" height="38.25" align-x="234" align-y="1584" 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="1thin">σ</ml:id>
					<ml:eval placeholderMultiplicationStyle="default">
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:id xml:space="preserve">designPressure</ml:id>
								<ml:id xml:space="preserve" subscript="thin">R</ml:id>
							</ml:apply>
							<ml:apply>
								<ml:mult/>
								<ml:real>2</ml:real>
								<ml:id xml:space="preserve">shellWallThickness</ml:id>
							</ml:apply>
						</ml:apply>
						<ml:unitOverride>
							<ml:id xml:space="preserve">ksi</ml:id>
						</ml:unitOverride>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<unitedValue>
								<ml:real>8.4848744926765765</ml:real>
								<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
									<unitReference unit="kips_per_sq_inch"/>
								</unitMonomial>
							</unitedValue>
						</result>
					</ml:eval>
				</ml:define>
			</math>
			<rendering item-idref="40"/>
		</region>
		<region region-id="189" left="30" top="1578" width="162.75" height="15" align-x="30" align-y="1590" 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">
				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Meridional (axial) stress:</p>
			</text>
		</region>
		<region region-id="190" left="30" top="1614" width="207.75" height="15" align-x="30" align-y="1626" 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">
				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Circumferential (hoop) stress:</p>
			</text>
		</region>
		<region region-id="191" left="210" top="1602" width="216" height="38.25" align-x="252" align-y="1626" 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="2thin">σ</ml:id>
					<ml:eval placeholderMultiplicationStyle="default">
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:id xml:space="preserve">designPressure</ml:id>
								<ml:id xml:space="preserve" subscript="thin">R</ml:id>
							</ml:apply>
							<ml:id xml:space="preserve">shellWallThickness</ml:id>
						</ml:apply>
						<ml:unitOverride>
							<ml:id xml:space="preserve">ksi</ml:id>
						</ml:unitOverride>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<unitedValue>
								<ml:real>16.969748985353153</ml:real>
								<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
									<unitReference unit="kips_per_sq_inch"/>
								</unitMonomial>
							</unitedValue>
						</result>
					</ml:eval>
				</ml:define>
			</math>
			<rendering item-idref="41"/>
		</region>
		<region region-id="186" left="36" top="1656" width="130.5" height="15" align-x="36" align-y="1668" 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">
				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Von Mises Stress:</p>
			</text>
		</region>
		<region region-id="210" left="168" top="1650" width="306.75" height="27" align-x="219" align-y="1668" 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="vmthin">σ</ml:id>
					<ml:eval placeholderMultiplicationStyle="default">
						<ml:apply>
							<ml:sqrt/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:minus/>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve" subscript="1thin">σ</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:mult/>
										<ml:id xml:space="preserve" subscript="1thin">σ</ml:id>
										<ml:id xml:space="preserve" subscript="2thin">σ</ml:id>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve" subscript="2thin">σ</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
						</ml:apply>
						<ml:unitOverride>
							<ml:id xml:space="preserve">ksi</ml:id>
						</ml:unitOverride>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<unitedValue>
								<ml:real>14.696233717161032</ml:real>
								<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
									<unitReference unit="kips_per_sq_inch"/>
								</unitMonomial>
							</unitedValue>
						</result>
					</ml:eval>
				</ml:define>
			</math>
			<rendering item-idref="42"/>
		</region>
		<region region-id="591" left="18" top="1692" width="117" height="15" align-x="18" align-y="1704" show-border="true" show-highlight="true" is-protected="true" z-order="0" background-color="#80ffff" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Factor of safety:</p>
			</text>
		</region>
		<region region-id="595" left="156" top="1686" width="135" height="42.75" align-x="188.25" align-y="1710" show-border="true" show-highlight="true" is-protected="true" z-order="0" background-color="#80ffff" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">FofS</ml:id>
					<ml:eval placeholderMultiplicationStyle="default">
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve" subscript="y">S</ml:id>
							<ml:id xml:space="preserve" subscript="vmthin">σ</ml:id>
						</ml:apply>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<ml:real>8.1653573500177821</ml:real>
						</result>
					</ml:eval>
				</ml:define>
			</math>
			<rendering item-idref="43"/>
		</region>
		<region region-id="592" left="18" top="1752" width="116.25" height="15" align-x="18" align-y="1764" show-border="true" show-highlight="true" is-protected="true" z-order="0" background-color="#80ffff" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Change in height:</p>
			</text>
		</region>
		<region region-id="596" left="156" top="1746" width="305.25" height="38.25" align-x="200.25" align-y="1770" show-border="true" show-highlight="true" is-protected="true" z-order="0" background-color="#80ffff" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="thin">Δy</ml:id>
					<ml:eval placeholderMultiplicationStyle="default">
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:div/>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:mult/>
										<ml:id xml:space="preserve">designPressure</ml:id>
										<ml:id xml:space="preserve" subscript="thin">R</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve">y</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve">E</ml:id>
									<ml:id xml:space="preserve">shellWallThickness</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:real>0.5</ml:real>
									<ml:id xml:space="preserve">ν</ml:id>
								</ml:apply>
							</ml:parens>
						</ml:apply>
						<ml:unitOverride>
							<ml:id xml:space="preserve">in</ml:id>
						</ml:unitOverride>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<unitedValue>
								<ml:real>0.001038209242923906</ml:real>
								<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
									<unitReference unit="inch"/>
								</unitMonomial>
							</unitedValue>
						</result>
					</ml:eval>
				</ml:define>
			</math>
			<rendering item-idref="44"/>
		</region>
		<region region-id="597" left="18" top="1794" width="116.25" height="30" align-x="18" align-y="1806" show-border="true" show-highlight="true" is-protected="true" z-order="0" background-color="#80ffff" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Radial displacement </p>
				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">of circumference:</p>
			</text>
		</region>
		<region region-id="599" left="162" top="1789.5" width="301.5" height="42.75" align-x="207.75" align-y="1818" show-border="true" show-highlight="true" is-protected="true" z-order="0" background-color="#80ffff" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="max">ΔR</ml:id>
					<ml:eval placeholderMultiplicationStyle="default">
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:div/>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve">designPressure</ml:id>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve" subscript="thin">R</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve">E</ml:id>
									<ml:id xml:space="preserve">shellWallThickness</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:real>1</ml:real>
									<ml:apply>
										<ml:div/>
										<ml:id xml:space="preserve">ν</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
						<ml:unitOverride>
							<ml:id xml:space="preserve">in</ml:id>
						</ml:unitOverride>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<unitedValue>
								<ml:real>0.0010362484414591141</ml:real>
								<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
									<unitReference unit="inch"/>
								</unitMonomial>
							</unitedValue>
						</result>
					</ml:eval>
				</ml:define>
			</math>
			<rendering item-idref="45"/>
		</region>
		<region region-id="600" left="24" top="1836" width="402" height="13.5" align-x="24" align-y="1836" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="46" display-width="400.5" display-height="12"/>
			</picture>
			<rendering item-idref="47"/>
		</region>
		<region region-id="345" left="12" top="1859.25" width="231" height="15.75" align-x="12" align-y="1872" 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">
				<p style="Heading 1" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Thick wall Shell Calcs</p>
			</text>
		</region>
		<region region-id="602" left="36" top="1889.25" width="386.25" height="69" align-x="36" align-y="1902" 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">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="Calibri" charset="0" size="14">
						<b>
							<inlineAttr underline="false">Table 32<sp count="2"/>Formulas for thick-walled vessels under internal and external loading</inlineAttr>
						</b>
					</f>
				</p>
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="Calibri" charset="0" size="14">
						<b>
							<inlineAttr underline="false">Case 1d Cylindrical disk or shell; uniform external pressure in all directions, ends capped</inlineAttr>
						</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="651" left="18" top="1962" width="126" height="134.25" align-x="18" align-y="1962" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="48" display-width="124.5" display-height="132.75"/>
			</picture>
			<rendering item-idref="49"/>
		</region>
		<region region-id="677" left="168" top="1988.25" width="51.75" height="25.5" align-x="169.5" align-y="1998" 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">
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">a = shellOR</p>
			</text>
		</region>
		<region region-id="673" left="264" top="1988.25" width="46.5" height="25.5" align-x="264" align-y="1998" 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">
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">a = shellIR</p>
			</text>
		</region>
		<region region-id="676" left="168" top="2002.5" width="149.25" height="30.75" align-x="210.75" align-y="2022" 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">shellIR</ml:id>
					<ml:eval placeholderMultiplicationStyle="default">
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve">shellOD</ml:id>
							<ml:real>2</ml:real>
						</ml:apply>
						<ml:unitOverride>
							<ml:id xml:space="preserve">in</ml:id>
						</ml:unitOverride>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<unitedValue>
								<ml:real>1.375</ml:real>
								<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
									<unitReference unit="inch"/>
								</unitMonomial>
							</unitedValue>
						</result>
					</ml:eval>
				</ml:define>
			</math>
			<rendering item-idref="50"/>
		</region>
		<region region-id="675" left="168" top="2040.75" width="268.5" height="15.75" align-x="216" align-y="2052" 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">shellOR</ml:id>
					<ml:eval placeholderMultiplicationStyle="default">
						<ml:apply>
							<ml:plus/>
							<ml:id xml:space="preserve">shellIR</ml:id>
							<ml:apply>
								<ml:mult/>
								<ml:real>0.5</ml:real>
								<ml:id xml:space="preserve">shellWallThickness</ml:id>
							</ml:apply>
						</ml:apply>
						<ml:unitOverride>
							<ml:id xml:space="preserve">in</ml:id>
						</ml:unitOverride>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<unitedValue>
								<ml:real>1.59375</ml:real>
								<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
									<unitReference unit="inch"/>
								</unitMonomial>
							</unitedValue>
						</result>
					</ml:eval>
				</ml:define>
			</math>
			<rendering item-idref="51"/>
		</region>
		<region region-id="674" left="168" top="2064.75" width="134.25" height="15.75" align-x="183.75" align-y="2076" 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">L</ml:id>
					<ml:eval placeholderMultiplicationStyle="default">
						<ml:id xml:space="preserve">shellLength</ml:id>
						<ml:unitOverride>
							<ml:id xml:space="preserve">in</ml:id>
						</ml:unitOverride>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<unitedValue>
								<ml:real>5.152</ml:real>
								<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
									<unitReference unit="inch"/>
								</unitMonomial>
							</unitedValue>
						</result>
					</ml:eval>
				</ml:define>
			</math>
			<rendering item-idref="52"/>
		</region>
		<region region-id="637" left="12" top="2154.75" width="579.75" height="12.75" align-x="12" align-y="2166" 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">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="MS Sans Serif" charset="0">
						<b>Formulas<sp count="2"/>for normal stresses </b>
					</f>
					<f family="MS Sans Serif" charset="0">
						<b>as a function of radial thickness, r:</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="682" left="24" top="2198.25" width="143.25" height="12" align-x="24" align-y="2208" 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">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="Arial" charset="0">
						<b>
							<inlineAttr line-through="false">Longitudinal stress: </inlineAttr>
						</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="320" left="150" top="2190" width="257.25" height="42.75" align-x="198" align-y="2214" 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="1thick">σ</ml:id>
					<ml:eval placeholderMultiplicationStyle="default">
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:neg/>
									<ml:id xml:space="preserve">designPressure</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellOR</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:apply>
								<ml:minus/>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellOR</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellIR</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
						</ml:apply>
						<ml:unitOverride>
							<ml:id xml:space="preserve">ksi</ml:id>
						</ml:unitOverride>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<unitedValue>
								<ml:real>-25.11426293650273</ml:real>
								<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
									<unitReference unit="kips_per_sq_inch"/>
								</unitMonomial>
							</unitedValue>
						</result>
					</ml:eval>
				</ml:define>
			</math>
			<rendering item-idref="53"/>
		</region>
		<region region-id="681" left="24" top="2258.25" width="167.25" height="12" align-x="24" align-y="2268" 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">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="Arial" charset="0">
						<b>
							<inlineAttr line-through="false">Circumferential stress: </inlineAttr>
						</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="291" left="150" top="2244" width="279" height="42.75" align-x="213" align-y="2268" 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:function>
						<ml:id xml:space="preserve" subscript="2thick">σ</ml:id>
						<ml:boundVars>
							<ml:id xml:space="preserve">r</ml:id>
						</ml:boundVars>
					</ml:function>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:neg/>
									<ml:id xml:space="preserve">designPressure</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellOR</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">shellIR</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">r</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve">r</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">shellOR</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">shellIR</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="54"/>
		</region>
		<region region-id="641" left="156" top="2308.5" width="176.25" height="22.5" align-x="246" align-y="2322" 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:apply>
						<ml:id xml:space="preserve" subscript="2thick">σ</ml:id>
						<ml:id xml:space="preserve">shellIR</ml:id>
					</ml:apply>
					<ml:unitOverride>
						<ml:id xml:space="preserve">psi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>-50228.525873005456</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="55"/>
		</region>
		<region region-id="680" left="24" top="2360.25" width="114.75" height="12" align-x="24" align-y="2370" 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">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="Arial" charset="0">
						<b>
							<inlineAttr line-through="false">Radial stress: </inlineAttr>
						</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="294" left="150" top="2346" width="279" height="42.75" align-x="213" align-y="2370" 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:function>
						<ml:id xml:space="preserve" subscript="3thick">σ</ml:id>
						<ml:boundVars>
							<ml:id xml:space="preserve">r</ml:id>
						</ml:boundVars>
					</ml:function>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:neg/>
									<ml:id xml:space="preserve">designPressure</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellOR</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">r</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">shellIR</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve">r</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">shellOR</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">shellIR</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="56"/>
		</region>
		<region region-id="642" left="156" top="2398.5" width="181.5" height="22.5" align-x="251.25" align-y="2412" 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:apply>
						<ml:id xml:space="preserve" subscript="3thick">σ</ml:id>
						<ml:id xml:space="preserve">shellOR</ml:id>
					</ml:apply>
					<ml:unitOverride>
						<ml:id xml:space="preserve">psi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>-6420.9861025660566</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="57"/>
		</region>
		<region region-id="679" left="24" top="2438.25" width="95.25" height="12" align-x="33.75" align-y="2448" 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">
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<f family="Arial" charset="0">
						<b>
							<inlineAttr line-through="false">Shear stress @ b: </inlineAttr>
						</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="297" left="150" top="2430" width="241.5" height="42.75" align-x="195.75" align-y="2454" 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="thickb">τ</ml:id>
					<ml:eval placeholderMultiplicationStyle="default">
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:id xml:space="preserve">designPressure</ml:id>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellOR</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:apply>
								<ml:minus/>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellOR</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellIR</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
						</ml:apply>
						<ml:unitOverride>
							<ml:id xml:space="preserve">ksi</ml:id>
						</ml:unitOverride>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<unitedValue>
								<ml:real>25.11426293650273</ml:real>
								<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
									<unitReference unit="kips_per_sq_inch"/>
								</unitMonomial>
							</unitedValue>
						</result>
					</ml:eval>
				</ml:define>
			</math>
			<rendering item-idref="58"/>
		</region>
		<region region-id="678" left="24" top="2492.25" width="141" height="24" align-x="24" align-y="2502" 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">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="Arial" charset="0">
						<b>
							<inlineAttr line-through="false">Von Mises Stress calculation: </inlineAttr>
						</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="693" left="24" top="2512.5" width="624.75" height="42.75" align-x="86.25" align-y="2544" 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="vmthick">σa</ml:id>
					<ml:apply>
						<ml:sqrt/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:pow/>
										<ml:parens>
											<ml:apply>
												<ml:minus/>
												<ml:id xml:space="preserve" subscript="1thick">σ</ml:id>
												<ml:apply>
													<ml:id xml:space="preserve" subscript="2thick">σ</ml:id>
													<ml:id xml:space="preserve">shellOR</ml:id>
												</ml:apply>
											</ml:apply>
										</ml:parens>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:parens>
											<ml:apply>
												<ml:minus/>
												<ml:apply>
													<ml:id xml:space="preserve" subscript="2thick">σ</ml:id>
													<ml:id xml:space="preserve">shellOR</ml:id>
												</ml:apply>
												<ml:apply>
													<ml:id xml:space="preserve" subscript="3thick">σ</ml:id>
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				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Factor of Safety (Von Mises stress)<sp count="2"/>
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				<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Factor of Safety (Max. shear stress theory 0.5*Sy) </p>
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								<ml:real font="0">0.5</ml:real>
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						<b>Formulas for change in outer and inner radii, and change in length:</b>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Outer radius:</p>
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													<ml:real>2</ml:real>
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											<ml:real>2</ml:real>
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												<ml:plus/>
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								<ml:apply>
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										<ml:real>2</ml:real>
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									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">shellIR</ml:id>
										<ml:real>2</ml:real>
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								</ml:apply>
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						</ml:apply>
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							<ml:id xml:space="preserve">in</ml:id>
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								<ml:real>-0.0033898676581733036</ml:real>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Inner radius:</p>
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								<ml:id xml:space="preserve">E</ml:id>
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							<ml:apply>
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								<ml:apply>
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										<ml:real>2</ml:real>
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										<ml:apply>
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											<ml:real>2</ml:real>
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								<ml:apply>
									<ml:minus/>
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										<ml:pow/>
										<ml:id xml:space="preserve">shellOR</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">shellIR</ml:id>
										<ml:real>2</ml:real>
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								</ml:apply>
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						</ml:apply>
						<ml:unitOverride>
							<ml:id xml:space="preserve">in</ml:id>
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						<result xmlns="http://schemas.mathsoft.com/math30">
							<unitedValue>
								<ml:real>0.0036474542811686375</ml:real>
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				<p style="Heading 1" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Bottom endcap</p>
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					<b>
						<u>Table 24<sp count="2"/>Formulas for shear, moment and deflection of flat circular plates of constant thickness</u>
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						<b>Annular plate with uniformly distributed pressure q over the portion from r</b>
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							<sub>o</sub>
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						<b> to a</b>
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						<b>; outer edge simply supported</b>
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					<b>Annular plate with a uniformly distributed pressure q over the portion from r</b>
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						<sub>o</sub>
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					<b> to a</b>
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					<b>This file corresponds to Cases 2a - 2d in </b>
					<b>
						<i>Roark's </i>
					</b>
					<b>
						<i>Formulas for Stress and Strain.</i>
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					<b>Outer edge simply supported, inner edge free</b>
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