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						<b>Pressure Vessel Calculations</b>
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					<f size="12">Rev<tab/>Author<tab/>
						<tab/>
						<tab/>Date<tab/>
						<tab/>Description</f>
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					<f size="12">9.0 <tab/>Gene Massion<tab/>2013May03<tab/>1) Reformatted PV8.0 to (hopefully) improve usability</f>
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						<tab/>2) Corrected end cap bearing and shear stress to use shell diameter and allow for thickenening at shell end</f>
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						<tab/>
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						<b>A) Environmental Conditions:</b>
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						<b>Misc. stuff</b>
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						<ml:real>1000</ml:real>
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						<ml:real>4000</ml:real>
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						<b>Water density:</b>
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						<ml:real>1026</ml:real>
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								<ml:id xml:space="preserve">m</ml:id>
								<ml:real>3</ml:real>
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					<ml:id xml:space="preserve">a</ml:id>
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							<ml:real>1</ml:real>
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									<ml:real>2</ml:real>
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								<ml:real>999.99999999999989</ml:real>
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									<unitReference unit="pound_force"/>
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						<b>
							<inlineAttr underline="false">B) Material properties:</inlineAttr>
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								<c val="#000">Material: 6AL-4V Ti</c>
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						<b>Modulus of elasticity:</b>
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					<ml:id xml:space="preserve">E</ml:id>
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						<ml:mult/>
						<ml:real>16500</ml:real>
						<ml:id xml:space="preserve">ksi</ml:id>
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						<b>Material density:</b>
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					<ml:id xml:space="preserve" subscript="m">ρ</ml:id>
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						<ml:mult/>
						<ml:real>0.16</ml:real>
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							<ml:div/>
							<ml:id xml:space="preserve">lbf</ml:id>
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								<ml:pow/>
								<ml:id xml:space="preserve">in</ml:id>
								<ml:real>3</ml:real>
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						<b>Poisson's ratio:</b>
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					<ml:id xml:space="preserve">ν</ml:id>
					<ml:real>0.33</ml:real>
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						<b>Yield Stress:</b>
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					<ml:id xml:space="preserve" subscript="y">S</ml:id>
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						<ml:real>120.0</ml:real>
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			<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>Shear stress:</b>
					</f>
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			</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="s">S</ml:id>
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			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">Shear modulus:</p>
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				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
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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:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">G</ml:id>
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						<ml:id xml:space="preserve">psi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>6203007.5187969916</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
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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="base0">r</ml:id>
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			<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>Bearing stress:</b>
					</f>
				</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="b">S</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>125000.</ml:real>
						<ml:id xml:space="preserve">psi</ml:id>
					</ml:apply>
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			</math>
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			<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="16">
						<b>
							<inlineAttr underline="false" line-through="false">C) Factors of safety:</inlineAttr>
						</b>
					</f>
				</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">FofSBuckling</ml:id>
					<ml:real>2</ml:real>
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		<region region-id="9752" left="210" top="861.75" width="68.25" height="19.5" align-x="244.5" align-y="876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">FofS</ml:id>
					<ml:real>1.33</ml:real>
				</ml:globalDefine>
			</math>
			<rendering item-idref="18"/>
		</region>
		<region region-id="10498" left="84" top="924" width="437.25" height="15.75" align-x="84" align-y="924" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="19" display-width="435.75" display-height="14.25"/>
			</picture>
			<rendering item-idref="20"/>
		</region>
		<region region-id="10565" left="0" top="978" width="6000" height="6" align-x="0" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<pageBreak/>
		</region>
		<region region-id="11360" left="246" top="991.5" width="244.5" height="29.25" align-x="257.25" align-y="1014" 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="Calibri" charset="0" size="24">
						<b>1) Shell Calculations</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="10652" left="894" top="991.5" width="295.5" height="29.25" align-x="894" align-y="1014" 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="Calibri" charset="0" size="24">
						<b>2) End Cap (ec) Calculations</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="12445" left="1482" top="1003.5" width="363.75" height="29.25" align-x="1482" align-y="1026" 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="Calibri" charset="0" size="24">
						<b>3) End Cap &amp; O-ring Tab Calculations</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="12447" left="2196" top="1009.5" width="359.25" height="29.25" align-x="2196" align-y="1032" 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="Calibri" charset="0" size="24">
						<b>4) Weights and Dimension changes</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="11313" left="708" top="1031.25" width="112.5" height="16.5" align-x="719.25" align-y="1044" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<f family="Calibri" charset="0" size="14">
						<b>End cap dimensions</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="10578" left="30" top="1043.25" width="95.25" height="16.5" align-x="44.25" align-y="1056" 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="Calibri" charset="0" size="14">
						<b>Shell Dimensions</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="12783" left="1152" top="1064.25" width="109.5" height="12" align-x="1163.25" align-y="1074" 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">End cap tab shear stress</p>
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			<picture>
				<metafile mapping-mode="8" x-extent="30.3874" y-extent="30.18898" item-idref="21"/>
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		<region region-id="11423" left="690" top="1071.75" width="145.5" height="19.5" align-x="791.25" align-y="1086" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ecTabThickness</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.2</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
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			<rendering item-idref="23"/>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ecOD</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>8.0</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
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			</math>
			<rendering item-idref="26"/>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellLength</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>6.0</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="27"/>
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			<picture>
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			<picture>
				<metafile mapping-mode="8" x-extent="56.40945" y-extent="30.8126" item-idref="30"/>
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					<ml:id xml:space="preserve">ecThickness</ml:id>
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						<ml:mult/>
						<ml:real>0.80</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellID</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>1.5</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellOD</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>2.5</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
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			<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">End cap tab</p>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">bearing stress</p>
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			<picture>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ecGrooveWidth</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.1</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ecHoleDiameter</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>1.0</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
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			<rendering item-idref="38"/>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellBaseThickness</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.5</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="39"/>
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		<region region-id="12791" left="1200" top="1256.25" width="103.5" height="12" align-x="1221" align-y="1266" 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">Groove tab shear 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">ecPlugOD</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>7.24</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="40"/>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ecGrooveDepth</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.1</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellWallThickness</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>0.50000000000000011</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
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		</region>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ecGrooveTabThickness</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.2</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="43"/>
		</region>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellWallThickness</ml:id>
					<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>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="44"/>
		</region>
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			<picture>
				<png item-idref="45" display-width="435.75" display-height="14.25"/>
			</picture>
			<rendering item-idref="46"/>
		</region>
		<region region-id="10461" left="84" top="1380" width="437.25" height="15.75" align-x="84" align-y="1380" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="47" display-width="435.75" display-height="14.25"/>
			</picture>
			<rendering item-idref="48"/>
		</region>
		<region region-id="11359" left="0" top="1410" width="6000" height="6" align-x="0" align-y="1410" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<pageBreak/>
		</region>
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			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="GeneText" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<f size="18">
						<b>Shell Results Summary</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="12296" left="876" top="1421.25" width="292.5" height="24" align-x="897" 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="GeneText" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<f size="18">
						<b>Endcap Results Summary</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="11297" left="696" top="1445.25" width="241.5" height="16.5" align-x="712.5" align-y="1458" 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="Calibri" charset="0" size="14">
						<b>2a) Stress in shell base (no holes)</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="10105" left="30" top="1451.25" width="252.75" height="16.5" align-x="30" align-y="1464" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="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>1a) Thin walled cylinder calculation:</b>
					</f>
				</p>
			</text>
		</region>
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			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="GeneText" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<f size="18">
						<b>Weights and Dimension Change Results Summary</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="10463" left="24" top="1484.25" width="78.75" height="24" align-x="34.5" align-y="1494" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="#408080" 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">Von Mises Stress:</p>
			</text>
		</region>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="vmthin">σ</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">ksi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>10.110431058489159</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="49"/>
		</region>
		<region region-id="10465" left="252" top="1484.25" width="78" height="12" align-x="270.75" align-y="1494" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="#408080" 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">Margin of Safety</p>
			</text>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="cythin">MS</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>7.9240076301214781</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="50"/>
		</region>
		<region region-id="10467" left="492" top="1479.75" width="86.25" height="19.5" align-x="552.75" align-y="1494" 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">thinWall</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>0</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="51"/>
		</region>
		<region region-id="11301" left="804" top="1479.75" width="106.5" height="22.5" align-x="841.5" align-y="1494" 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="base">σ</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">ksi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>16.400876718230514</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="52"/>
		</region>
		<region region-id="11302" left="990" top="1479.75" width="99" height="22.5" align-x="1039.5" align-y="1494" 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="base">MS</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>4.501264686020324</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="53"/>
		</region>
		<region region-id="11303" left="1128" top="1479.75" width="103.5" height="22.5" align-x="1179" align-y="1494" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:id xml:space="preserve" subscript="base" xmlns:ml="http://schemas.mathsoft.com/math30">smallDefTrue</ml:id>
			</math>
			<rendering item-idref="54"/>
		</region>
		<region region-id="12765" left="30" top="1529.25" width="252.75" height="16.5" align-x="30" align-y="1542" 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>1B) Thick wall cylinder calculation:</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="11307" left="696" top="1535.25" width="229.5" height="16.5" align-x="714" align-y="1548" 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="Calibri" charset="0" size="14">
						<b>2b) Stress in endcap with connector hole</b>
					</f>
				</p>
			</text>
		</region>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="vmthick">σ</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">ksi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>15.797548528889312</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="55"/>
		</region>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="2endCaps">totalWeight</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>12.82016103528677</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="56"/>
		</region>
		<region region-id="12763" left="2322" top="1557.75" width="180" height="22.5" align-x="2440.5" align-y="1572" 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="1endCap">totalWeight</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>8.31074407306521</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="57"/>
		</region>
		<region region-id="12770" left="246" top="1563.75" width="141.75" height="22.5" align-x="338.25" align-y="1578" 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="cythick">MSyield</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>4.7113648832777457</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="58"/>
		</region>
		<region region-id="12771" left="408" top="1563.75" width="144.75" height="22.5" align-x="503.25" align-y="1578" 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="cythick">MSshear</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>3.9461870792008735</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="59"/>
		</region>
		<region region-id="11310" left="774" top="1569.75" width="126" height="22.5" align-x="824.25" 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:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="endcap">σ</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">ksi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>344.09925497534607</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
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		</region>
		<region region-id="11311" left="948" top="1569.75" width="119.25" height="22.5" align-x="1010.25" 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:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="endcap">MS</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>-0.73779203934562743</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="61"/>
		</region>
		<region region-id="11312" left="1074" top="1569.75" width="149.25" height="22.5" align-x="1197.75" 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:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="endcap">smallDefTrue</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>1</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="62"/>
		</region>
		<region region-id="12772" left="24" top="1607.25" width="252.75" height="16.5" align-x="24" align-y="1620" 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>1C) Column Buckling:</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="12757" left="2088" top="1617.75" width="186.75" height="22.5" align-x="2206.5" align-y="1632" 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="2endCaps">wetWeight</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>11.655679402734403</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="63"/>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="1endCap">wetWeight</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>7.1826524915301047</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="64"/>
		</region>
		<region region-id="12773" left="60" top="1638" width="195.75" height="26.25" align-x="159" align-y="1656" 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="critical">pBuckling</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">psi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>687933.98577069049</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="65"/>
		</region>
		<region region-id="12774" left="288" top="1641.75" width="127.5" height="22.5" align-x="359.25" align-y="1656" 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="buckling">MS</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>57.926103581297596</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="66"/>
		</region>
		<region region-id="12820" left="474" top="1641.75" width="139.5" height="22.5" align-x="550.5" align-y="1656" 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="buckling">FOS</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>117.85220716259519</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="67"/>
		</region>
		<region region-id="10458" left="84" top="1698" width="437.25" height="15.75" align-x="84" align-y="1698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="68" display-width="435.75" display-height="14.25"/>
			</picture>
			<rendering item-idref="69"/>
		</region>
		<region region-id="10931" left="744" top="1710" width="437.25" height="15.75" align-x="744" align-y="1710" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="70" display-width="435.75" display-height="14.25"/>
			</picture>
			<rendering item-idref="71"/>
		</region>
		<region region-id="12759" left="2112" top="1722" width="437.25" height="15.75" align-x="2112" align-y="1722" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="72" display-width="435.75" display-height="14.25"/>
			</picture>
			<rendering item-idref="73"/>
		</region>
		<region region-id="12775" left="0" top="1752" width="6000" height="6" align-x="0" align-y="1752" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<pageBreak/>
		</region>
		<region region-id="10808" left="684" top="1764.75" width="261" height="14.25" align-x="684" align-y="1776" 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 size="12">
						<b>PRESS. CASE BASE (No Connector)</b>
					</f>
					<sp count="2"/>
				</p>
			</text>
		</region>
		<region region-id="11442" left="996" top="1763.25" width="280.5" height="51" align-x="996" align-y="1776" 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="0" text-align="inherit" list-style-type="none" tabs="inherit">
					<f size="14">
						<b>Table 24 Case 10a</b>
					</f>
				</p>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">
					<f size="14">
						<b>Solid circular plate simply supported; uniformly distributed pressure from r</b>
					</f>
					<f size="14">
						<b>
							<sub>o </sub>
						</b>
					</f>
					<f size="14">
						<b>to a </b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="9770" left="18" top="1773.75" width="648" height="34.5" align-x="18" align-y="1788" 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" size="14">
						<b>
							<inlineAttr underline="false">Table 28<sp count="2"/>Formulas for membrane stresses and deformations in thin-walled pressure vessels</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 1c: Cylindrical shell; uniform internal or external pressure (ends capped)</inlineAttr>
						</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="10797" left="696" top="1818" width="272.25" height="104.25" align-x="696" align-y="1818" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="74" display-width="270.75" display-height="102.75"/>
			</picture>
			<rendering item-idref="75"/>
		</region>
		<region region-id="10336" left="24" top="1830" width="114" height="101.25" align-x="24" align-y="1830" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="76" display-width="112.5" display-height="99.75"/>
			</picture>
			<rendering item-idref="77"/>
		</region>
		<region region-id="10798" left="1026" top="1836" width="127.5" height="69" align-x="1026" align-y="1836" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="78" display-width="126" display-height="67.5"/>
			</picture>
			<rendering item-idref="79"/>
		</region>
		<region region-id="10337" left="156" top="1847.25" width="99.75" height="16.5" align-x="156" align-y="1860" 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">Mean radius:</f>
				</p>
			</text>
		</region>
		<region region-id="10338" left="246" top="1834.5" width="243.75" height="40.5" align-x="284.25" align-y="1860" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="thin">R</ml:id>
					<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:globalDefine>
			</math>
			<rendering item-idref="80"/>
		</region>
		<region region-id="11294" left="540" top="1845.75" width="72" height="22.5" align-x="578.25" align-y="1860" 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="thin">R</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>1</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="81"/>
		</region>
		<region region-id="10340" left="150" top="1889.25" width="93" height="16.5" align-x="150" 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">Cylinder Height:</f>
				</p>
			</text>
		</region>
		<region region-id="10341" left="246" top="1887.75" width="94.5" height="19.5" align-x="261.75" align-y="1902" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">y</ml:id>
					<ml:id xml:space="preserve">shellLength</ml:id>
				</ml:globalDefine>
			</math>
			<rendering item-idref="82"/>
		</region>
		<region region-id="10342" left="360" top="1887.75" width="49.5" height="19.5" align-x="375.75" align-y="1902" 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">y</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>5.9999999999999991</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="83"/>
		</region>
		<region region-id="10343" left="54" top="1928.25" width="58.5" height="12" align-x="54" align-y="1938" 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>Conditions:</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="10344" left="150" top="1925.25" width="434.25" height="33" align-x="150" align-y="1938" 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">For the expressions in the case to be valid, the following condition must be true (i.e., condition = 1):</f>
				</p>
			</text>
		</region>
		<region region-id="11293" left="702" top="1941.75" width="154.5" height="22.5" align-x="735" align-y="1956" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="base">t</ml:id>
					<ml:id xml:space="preserve">shellBaseThickness</ml:id>
				</ml:globalDefine>
			</math>
			<rendering item-idref="84"/>
		</region>
		<region region-id="10802" left="906" top="1941.75" width="77.25" height="22.5" align-x="939" align-y="1956" 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="base">t</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>0.5</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="85"/>
		</region>
		<region region-id="10803" left="1014" top="1941.75" width="110.25" height="22.5" align-x="1049.25" align-y="1956" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="base">a</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.5</ml:real>
						<ml:id xml:space="preserve">shellID</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="86"/>
		</region>
		<region region-id="10805" left="1182" top="1941.75" width="86.25" height="22.5" align-x="1217.25" align-y="1956" 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="base">a</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>0.74999999999999989</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="87"/>
		</region>
		<region region-id="12721" left="2022" top="1958.25" width="38.25" height="12" align-x="2022" align-y="1968" 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">Shell</p>
			</text>
		</region>
		<region region-id="10345" left="84" top="1969.5" width="234" height="45" align-x="144.75" align-y="1998" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine 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:globalDefine>
			</math>
			<rendering item-idref="88"/>
		</region>
		<region region-id="11295" left="354" top="1969.5" width="151.5" height="45" align-x="480" align-y="1998" 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:div/>
						<ml:id xml:space="preserve" subscript="thin">R</ml:id>
						<ml:id xml:space="preserve">shellWallThickness</ml:id>
					</ml:apply>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>1.9999999999999996</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="89"/>
		</region>
		<region region-id="10347" left="522" top="1983.75" width="86.25" height="19.5" align-x="582.75" align-y="1998" 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">thinWall</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>0</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="90"/>
		</region>
		<region region-id="12722" left="2046" top="1967.25" width="267" height="45.75" align-x="2152.5" align-y="1998" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">crossSectionArea</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">π</ml:id>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">shellOD</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">shellID</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
						<ml:real>4</ml:real>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="91"/>
		</region>
		<region region-id="12723" left="2454" top="1978.5" width="171" height="24.75" align-x="2560.5" align-y="1998" 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">crossSectionArea</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:pow/>
							<ml:id xml:space="preserve">in</ml:id>
							<ml:real>2</ml:real>
						</ml:apply>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>3.1415926535897936</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="2"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="92"/>
		</region>
		<region region-id="10826" left="702" top="1994.25" width="67.5" height="12" align-x="702" align-y="2004" 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">Plate Constant:</p>
			</text>
		</region>
		<region region-id="10934" left="786" top="1976.25" width="120.75" height="55.5" align-x="825.75" align-y="2010" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="base">D</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">E</ml:id>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve" subscript="base">t</ml:id>
								<ml:real>3</ml:real>
							</ml:apply>
						</ml:apply>
						<ml:apply>
							<ml:mult/>
							<ml:real>12</ml:real>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:real>1</ml:real>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">ν</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="93"/>
		</region>
		<region region-id="10935" left="930" top="1998" width="153" height="26.25" align-x="969.75" align-y="2016" 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="base">D</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">lbf</ml:id>
							<ml:id xml:space="preserve">in</ml:id>
						</ml:apply>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>192879.58702726962</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="94"/>
		</region>
		<region region-id="10936" left="1128" top="1990.5" width="75" height="40.5" align-x="1158" align-y="2016" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="17">G</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:plus/>
							<ml:real>3</ml:real>
							<ml:id xml:space="preserve">ν</ml:id>
						</ml:apply>
						<ml:real>16</ml:real>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="95"/>
		</region>
		<region region-id="10937" left="1236" top="2001.75" width="79.5" height="22.5" align-x="1266" align-y="2016" 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="17">G</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>0.208125</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="96"/>
		</region>
		<region region-id="12724" left="2046" top="2009.25" width="394.5" height="45.75" align-x="2148.75" align-y="2040" 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">internalVolume</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">π</ml:id>
							<ml:apply>
								<ml:div/>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellID</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
								<ml:real>4</ml:real>
							</ml:apply>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:minus/>
								<ml:id xml:space="preserve">shellLength</ml:id>
								<ml:id xml:space="preserve">shellBaseThickness</ml:id>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="97"/>
		</region>
		<region region-id="12725" left="2454" top="2020.5" width="165.75" height="24.75" align-x="2555.25" align-y="2040" 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">internalVolume</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:pow/>
							<ml:id xml:space="preserve">in</ml:id>
							<ml:real>3</ml:real>
						</ml:apply>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>9.71930227204342</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="3"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="98"/>
		</region>
		<region region-id="9798" left="198" top="2029.5" width="182.25" height="45" align-x="240.75" align-y="2058" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="1thin">σ</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">q</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:globalDefine>
			</math>
			<rendering item-idref="99"/>
		</region>
		<region region-id="9800" left="36" top="2051.25" width="162.75" height="16.5" align-x="36" align-y="2064" 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">Meridional (axial) stress:</f>
				</p>
			</text>
		</region>
		<region region-id="9799" left="414" top="2049.75" width="105" height="22.5" align-x="456.75" align-y="2064" 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="1thin">σ</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">ksi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>5.8372600932418681</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="100"/>
		</region>
		<region region-id="10892" left="690" top="2030.25" width="159" height="48.75" align-x="741.75" align-y="2064" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="c_base">M</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:mult/>
								<ml:id xml:space="preserve">q</ml:id>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve" subscript="base">a</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:plus/>
									<ml:real>3</ml:real>
									<ml:id xml:space="preserve">ν</ml:id>
								</ml:apply>
							</ml:parens>
						</ml:apply>
						<ml:real>16</ml:real>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="101"/>
		</region>
		<region region-id="10893" left="858" top="2038.5" width="141.75" height="42" align-x="909.75" align-y="2064" 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="c_base">M</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">lbf</ml:id>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve">in</ml:id>
								<ml:id xml:space="preserve">in</ml:id>
							</ml:apply>
						</ml:apply>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>683.36986325960459</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="0"/>
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="102"/>
		</region>
		<region region-id="11261" left="1050" top="2035.5" width="107.25" height="53.25" align-x="1087.5" align-y="2064" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="base">σ</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>6</ml:real>
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve" subscript="c_base">M</ml:id>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve" subscript="base">t</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="103"/>
		</region>
		<region region-id="11262" left="1170" top="2038.5" width="134.25" height="47.25" align-x="1207.5" align-y="2064" 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="base">σ</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve">lbf</ml:id>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve">in</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
						</ml:apply>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>16400.876718230513</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="-2"/>
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="104"/>
		</region>
		<region region-id="12726" left="2046" top="2061.75" width="282" height="22.5" align-x="2124" 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:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellWeight</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">crossSectionArea</ml:id>
							<ml:id xml:space="preserve">shellLength</ml:id>
						</ml:apply>
						<ml:id xml:space="preserve" subscript="m">ρ</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="105"/>
		</region>
		<region region-id="12727" left="2454" top="2061.75" width="139.5" height="19.5" align-x="2532" 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:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellWeight</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>3.0159289474462017</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="106"/>
		</region>
		<region region-id="9801" left="36" top="2093.25" width="207.75" height="16.5" align-x="36" align-y="2106" 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">Circumferential (hoop) stress:</f>
				</p>
			</text>
		</region>
		<region region-id="9802" left="216" top="2077.5" width="170.25" height="45" align-x="258.75" align-y="2106" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="2thin">σ</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">q</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:globalDefine>
			</math>
			<rendering item-idref="107"/>
		</region>
		<region region-id="9803" left="408" top="2091.75" width="111.75" height="22.5" align-x="450.75" align-y="2106" 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="2thin">σ</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">ksi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>11.674520186483736</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="108"/>
		</region>
		<region region-id="12728" left="2046" top="2086.5" width="327.75" height="40.5" align-x="2150.25" align-y="2112" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellBaseWeight</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:div/>
									<ml:id xml:space="preserve">π</ml:id>
									<ml:real>4</ml:real>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellOD</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve">shellBaseThickness</ml:id>
						</ml:apply>
						<ml:id xml:space="preserve" subscript="m">ρ</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="109"/>
		</region>
		<region region-id="12729" left="2454" top="2092.5" width="214.5" height="24.75" align-x="2558.25" align-y="2112" 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">shellBaseWeight</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>12.634719322640393</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="foot"/>
								<unitReference unit="pound"/>
								<unitReference unit="second" power-numerator="-2"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="110"/>
		</region>
		<region region-id="10896" left="702" top="2101.5" width="162" height="48" align-x="751.5" align-y="2130" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="base">MS</ml:id>
					<ml:parens>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve" subscript="y">S</ml:id>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve" subscript="base">σ</ml:id>
									<ml:id xml:space="preserve">FofS</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:real>1</ml:real>
						</ml:apply>
					</ml:parens>
				</ml:globalDefine>
			</math>
			<rendering item-idref="111"/>
		</region>
		<region region-id="10897" left="942" top="2115.75" width="99" height="22.5" align-x="991.5" align-y="2130" 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="base">MS</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>4.501264686020324</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="112"/>
		</region>
		<region region-id="9373" left="54" top="2156.25" width="130.5" height="12" align-x="54" 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">Von Mises Stress calculation:</p>
			</text>
		</region>
		<region region-id="9374" left="210" top="2142" width="264" height="32.25" align-x="262.5" align-y="2166" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="vmthin">σ</ml:id>
					<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:globalDefine>
			</math>
			<rendering item-idref="113"/>
		</region>
		<region region-id="9806" left="510" top="2151.75" width="114.75" height="22.5" align-x="562.5" align-y="2166" 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="vmthin">σ</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">ksi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>10.110431058489159</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="114"/>
		</region>
		<region region-id="10900" left="690" top="2156.25" width="102.75" height="12" align-x="699" 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="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Q.a is shear stress at a</p>
			</text>
		</region>
		<region region-id="12730" left="2016" top="2156.25" width="40.5" height="12" align-x="2016" 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">End Cap:</p>
			</text>
		</region>
		<region region-id="12731" left="2076" top="2140.5" width="567" height="40.5" align-x="2173.5" align-y="2166" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ecWeightTemp</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:mult style="auto-select"/>
							<ml:id xml:space="preserve" subscript="m">ρ</ml:id>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve">π</ml:id>
								<ml:real>4</ml:real>
							</ml:apply>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:plus/>
								<ml:parens>
									<ml:apply>
										<ml:mult/>
										<ml:apply>
											<ml:pow/>
											<ml:id xml:space="preserve">ecPlugOD</ml:id>
											<ml:real>2</ml:real>
										</ml:apply>
										<ml:id xml:space="preserve">ecThickness</ml:id>
									</ml:apply>
								</ml:parens>
								<ml:parens>
									<ml:apply>
										<ml:mult/>
										<ml:parens>
											<ml:apply>
												<ml:minus/>
												<ml:apply>
													<ml:pow/>
													<ml:id xml:space="preserve">ecOD</ml:id>
													<ml:real>2</ml:real>
												</ml:apply>
												<ml:apply>
													<ml:pow/>
													<ml:id xml:space="preserve">ecPlugOD</ml:id>
													<ml:real>2</ml:real>
												</ml:apply>
											</ml:apply>
										</ml:parens>
										<ml:id xml:space="preserve">ecTabThickness</ml:id>
									</ml:apply>
								</ml:parens>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="115"/>
		</region>
		<region region-id="11266" left="708" top="2167.5" width="111.75" height="43.5" align-x="758.25" align-y="2196" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="a_base">Q</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:neg/>
								<ml:id xml:space="preserve">q</ml:id>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="base">a</ml:id>
						</ml:apply>
						<ml:real>2</ml:real>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="116"/>
		</region>
		<region region-id="10899" left="846" top="2170.5" width="158.25" height="42" align-x="896.25" align-y="2196" 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="a_base">Q</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve">lbf</ml:id>
							<ml:id xml:space="preserve">in</ml:id>
						</ml:apply>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>-2188.9725349657006</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="-1"/>
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="117"/>
		</region>
		<region region-id="12732" left="2076" top="2182.5" width="518.25" height="40.5" align-x="2138.25" align-y="2208" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ecWeight</ml:id>
					<ml:apply>
						<ml:minus/>
						<ml:id xml:space="preserve">ecWeightTemp</ml:id>
						<ml:parens>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:mult/>
										<ml:id xml:space="preserve" subscript="m">ρ</ml:id>
										<ml:apply>
											<ml:div/>
											<ml:id xml:space="preserve">π</ml:id>
											<ml:real>4</ml:real>
										</ml:apply>
									</ml:apply>
									<ml:parens>
										<ml:apply>
											<ml:minus/>
											<ml:apply>
												<ml:pow/>
												<ml:id xml:space="preserve">ecPlugOD</ml:id>
												<ml:real>2</ml:real>
											</ml:apply>
											<ml:apply>
												<ml:pow/>
												<ml:id xml:space="preserve">ecGrooveDepth</ml:id>
												<ml:real>2</ml:real>
											</ml:apply>
										</ml:apply>
									</ml:parens>
								</ml:apply>
								<ml:id xml:space="preserve">ecGrooveWidth</ml:id>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="118"/>
		</region>
		<region region-id="9828" left="54" top="2204.25" width="142.5" height="12" align-x="54" align-y="2214" 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">Margin of safety:</p>
			</text>
		</region>
		<region region-id="9829" left="156" top="2185.5" width="187.5" height="48" align-x="216" 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:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="cythin">MS</ml:id>
					<ml:parens>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve" subscript="y">S</ml:id>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve" subscript="vmthin">σ</ml:id>
									<ml:id xml:space="preserve">FofS</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:real>1</ml:real>
						</ml:apply>
					</ml:parens>
				</ml:globalDefine>
			</math>
			<rendering item-idref="119"/>
		</region>
		<region region-id="9830" left="360" top="2199.75" width="109.5" height="22.5" align-x="420" 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:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="cythin">MS</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>7.9240076301214781</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="120"/>
		</region>
		<region region-id="12733" left="2076" top="2235.75" width="123.75" height="19.5" align-x="2138.25" align-y="2250" 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">ecWeight</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>4.9021160439202847</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="121"/>
		</region>
		<region region-id="10234" left="42" top="2288.25" width="75.75" height="12" align-x="42" align-y="2298" 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">Change in height:</p>
			</text>
		</region>
		<region region-id="10235" left="120" top="2269.5" width="245.25" height="45" align-x="167.25" align-y="2298" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="thin">Δy</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve">q</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:globalDefine>
			</math>
			<rendering item-idref="122"/>
		</region>
		<region region-id="12734" left="2028" top="2283.75" width="284.25" height="22.5" align-x="2151" align-y="2298" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="2endCaps">totalWeight</ml:id>
					<ml:apply>
						<ml:plus/>
						<ml:id xml:space="preserve">shellWeight</ml:id>
						<ml:apply>
							<ml:mult/>
							<ml:real>2</ml:real>
							<ml:id xml:space="preserve">ecWeight</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="123"/>
		</region>
		<region region-id="12735" left="2424" top="2283.75" width="184.5" height="22.5" align-x="2547" align-y="2298" 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="2endCaps">totalWeight</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>12.82016103528677</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="124"/>
		</region>
		<region region-id="10236" left="390" top="2286" width="148.5" height="26.25" align-x="437.25" align-y="2304" 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="thin">Δy</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>0.00072169761152808543</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="125"/>
		</region>
		<region region-id="10901" left="696" top="2282.25" width="180" height="53.25" align-x="767.25" align-y="2316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="base">ycenter</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:neg/>
									<ml:id xml:space="preserve">q</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve" subscript="base">a</ml:id>
									<ml:real>4</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:apply>
								<ml:mult/>
								<ml:real>64</ml:real>
								<ml:id xml:space="preserve" subscript="base">D</ml:id>
							</ml:apply>
						</ml:apply>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:plus/>
								<ml:real>5</ml:real>
								<ml:id xml:space="preserve">ν</ml:id>
							</ml:apply>
							<ml:apply>
								<ml:plus/>
								<ml:real>1</ml:real>
								<ml:id xml:space="preserve">ν</ml:id>
							</ml:apply>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="126"/>
		</region>
		<region region-id="10902" left="906" top="2298" width="180" height="26.25" align-x="977.25" align-y="2316" 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="base">ycenter</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>-0.00059960248616372828</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="127"/>
		</region>
		<region region-id="12736" left="2028" top="2313.75" width="379.5" height="22.5" align-x="2146.5" align-y="2328" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="1endCap">totalWeight</ml:id>
					<ml:apply>
						<ml:plus/>
						<ml:apply>
							<ml:plus/>
							<ml:id xml:space="preserve">shellWeight</ml:id>
							<ml:id xml:space="preserve">shellBaseWeight</ml:id>
						</ml:apply>
						<ml:id xml:space="preserve">ecWeight</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="128"/>
		</region>
		<region region-id="12737" left="2430" top="2313.75" width="180" height="22.5" align-x="2548.5" align-y="2328" 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="1endCap">totalWeight</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>8.31074407306521</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="129"/>
		</region>
		<region region-id="10237" left="42" top="2342.25" width="90.75" height="24" align-x="42" align-y="2352" 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">Radial displacement </p>
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">of circumference:</p>
			</text>
		</region>
		<region region-id="10238" left="156" top="2330.25" width="245.25" height="50.25" align-x="204.75" align-y="2364" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="max">ΔR</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:id xml:space="preserve">q</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:globalDefine>
			</math>
			<rendering item-idref="130"/>
		</region>
		<region region-id="10239" left="414" top="2346" width="150" height="26.25" align-x="462.75" align-y="2364" 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="max">ΔR</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>0.000590801476103874</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="131"/>
		</region>
		<region region-id="10903" left="696" top="2360.25" width="417.75" height="12" align-x="705.75" 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">check small deflection assumption (deflection &lt; t/2)</p>
			</text>
		</region>
		<region region-id="12738" left="2028" top="2350.5" width="562.5" height="40.5" align-x="2146.5" align-y="2376" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="2endCaps">wetWeight</ml:id>
					<ml:apply>
						<ml:minus/>
						<ml:id xml:space="preserve" subscript="2endCaps">totalWeight</ml:id>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:mult style="auto-select"/>
									<ml:id xml:space="preserve" subscript="sw">ρ</ml:id>
									<ml:apply>
										<ml:div/>
										<ml:id xml:space="preserve">π</ml:id>
										<ml:real>4</ml:real>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellOD</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve">shellLength</ml:id>
									<ml:apply>
										<ml:mult/>
										<ml:real>2</ml:real>
										<ml:id xml:space="preserve">ecTabThickness</ml:id>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="132"/>
		</region>
		<region region-id="10253" left="24" top="2390.25" width="611.25" height="12" align-x="24" align-y="2400" 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">
					<b>Diametral clearance (extrusion gap):</b>
					<sp/>
				</p>
			</text>
		</region>
		<region region-id="12739" left="2028" top="2386.5" width="541.5" height="40.5" align-x="2142" 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:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="1endCap">wetWeight</ml:id>
					<ml:apply>
						<ml:minus/>
						<ml:id xml:space="preserve" subscript="1endCap">totalWeight</ml:id>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:mult style="auto-select"/>
									<ml:id xml:space="preserve" subscript="sw">ρ</ml:id>
									<ml:apply>
										<ml:div/>
										<ml:id xml:space="preserve">π</ml:id>
										<ml:real>4</ml:real>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellOD</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve">shellLength</ml:id>
									<ml:id xml:space="preserve">ecTabThickness</ml:id>
								</ml:apply>
							</ml:parens>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="133"/>
		</region>
		<region region-id="10276" left="222" top="2392.5" width="103.5" height="45" align-x="258.75" align-y="2418" 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="step">P</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:id xml:space="preserve">q</ml:id>
						<ml:id xml:space="preserve" subscript="pressure">N</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="134"/>
		</region>
		<region region-id="10277" left="360" top="2403.75" width="111" height="22.5" align-x="395.25" align-y="2418" 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="step">P</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">psi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>583.72600932418686</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="135"/>
		</region>
		<region region-id="10909" left="708" top="2389.5" width="246.75" height="48" align-x="820.5" align-y="2418" 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="base">smallDefTrue</ml:id>
					<ml:parens>
						<ml:apply>
							<ml:lessThan/>
							<ml:apply>
								<ml:div/>
								<ml:apply>
									<ml:absval/>
									<ml:id xml:space="preserve" subscript="base">ycenter</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="base">t</ml:id>
							</ml:apply>
							<ml:apply>
								<ml:div/>
								<ml:real font="0">1</ml:real>
								<ml:real>2</ml:real>
							</ml:apply>
						</ml:apply>
					</ml:parens>
				</ml:define>
			</math>
			<rendering item-idref="136"/>
		</region>
		<region region-id="11246" left="972" top="2389.5" width="180.75" height="48" align-x="1059.75" align-y="2418" 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:div/>
						<ml:apply>
							<ml:absval/>
							<ml:id xml:space="preserve" subscript="base">ycenter</ml:id>
						</ml:apply>
						<ml:id xml:space="preserve" subscript="base">t</ml:id>
					</ml:apply>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>0.0011992049723274566</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="137"/>
		</region>
		<region region-id="11247" left="1146" top="2403.75" width="136.5" height="22.5" align-x="1257" align-y="2418" 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="base">smallDefTrue</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>1</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="138"/>
		</region>
		<region region-id="12740" left="2034" top="2433.75" width="186.75" height="22.5" align-x="2152.5" align-y="2448" 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="2endCaps">wetWeight</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>11.655679402734403</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="139"/>
		</region>
		<region region-id="12741" left="2268" top="2433.75" width="175.5" height="22.5" align-x="2382" align-y="2448" 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="1endCap">wetWeight</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>7.1826524915301047</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="140"/>
		</region>
		<region region-id="10278" left="24" top="2434.5" width="309.75" height="45" align-x="32.25" align-y="2460" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:apply xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">if</ml:id>
					<ml:define>
						<ml:define>
							<ml:sequence>
								<ml:apply>
									<ml:greaterThan/>
									<ml:id xml:space="preserve">q</ml:id>
									<ml:apply>
										<ml:mult/>
										<ml:real>1500</ml:real>
										<ml:id xml:space="preserve">psi</ml:id>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:indexer/>
									<ml:id xml:space="preserve">P</ml:id>
									<ml:id xml:space="preserve">step</ml:id>
								</ml:apply>
							</ml:sequence>
							<ml:sequence>
								<ml:apply>
									<ml:mult/>
									<ml:real>200</ml:real>
									<ml:id xml:space="preserve">psi</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:indexer/>
									<ml:id xml:space="preserve">P</ml:id>
									<ml:id xml:space="preserve">step</ml:id>
								</ml:apply>
							</ml:sequence>
						</ml:define>
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve">q</ml:id>
							<ml:id xml:space="preserve" subscript="pressure">N</ml:id>
						</ml:apply>
					</ml:define>
				</ml:apply>
			</math>
			<rendering item-idref="141"/>
		</region>
		<region region-id="10279" left="360" top="2445.75" width="58.5" height="19.5" align-x="374.25" align-y="2460" 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">j</ml:id>
					<ml:range>
						<ml:real>0</ml:real>
						<ml:real>10</ml:real>
					</ml:range>
				</ml:define>
			</math>
			<rendering item-idref="142"/>
		</region>
		<region region-id="10281" left="456" top="2445.75" width="69.75" height="22.5" align-x="477.75" align-y="2460" 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:apply>
						<ml:indexer/>
						<ml:id xml:space="preserve">P</ml:id>
						<ml:id xml:space="preserve">j</ml:id>
					</ml:apply>
					<ml:apply>
						<ml:mult/>
						<ml:id xml:space="preserve">j</ml:id>
						<ml:id xml:space="preserve" subscript="step">P</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="143"/>
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		<region region-id="12745" left="2148" top="2478" width="437.25" height="15.75" align-x="2148" align-y="2478" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="144" display-width="435.75" display-height="14.25"/>
			</picture>
			<rendering item-idref="145"/>
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		<region region-id="11031" left="702" top="2508" width="437.25" height="15.75" align-x="702" align-y="2508" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="146" display-width="435.75" display-height="14.25"/>
			</picture>
			<rendering item-idref="147"/>
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		<region region-id="10270" left="12" top="2504.25" width="95.25" height="12" align-x="12" align-y="2514" 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">Extrusion gap (radial):</p>
			</text>
		</region>
		<region region-id="10282" left="138" top="2492.25" width="242.25" height="50.25" align-x="171.75" align-y="2526" 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:apply>
						<ml:indexer/>
						<ml:id xml:space="preserve">ΔR</ml:id>
						<ml:id xml:space="preserve">j</ml:id>
					</ml:apply>
					<ml:parens>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:div/>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:indexer/>
										<ml:id xml:space="preserve">P</ml:id>
										<ml:id xml:space="preserve">j</ml:id>
									</ml:apply>
									<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>
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				</ml:define>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:apply>
						<ml:indexer/>
						<ml:id xml:space="preserve">Gap</ml:id>
						<ml:id xml:space="preserve">j</ml:id>
					</ml:apply>
					<ml:apply>
						<ml:minus/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:minus/>
								<ml:id xml:space="preserve">shellID</ml:id>
								<ml:id xml:space="preserve">ecPlugOD</ml:id>
							</ml:apply>
							<ml:real>2</ml:real>
						</ml:apply>
						<ml:apply>
							<ml:indexer/>
							<ml:id xml:space="preserve">ΔR</ml:id>
							<ml:id xml:space="preserve">j</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="149"/>
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			<plot disable-calc="false" item-idref="150"/>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:apply>
						<ml:indexer/>
						<ml:id xml:space="preserve">P</ml:id>
						<ml:id xml:space="preserve">j</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:matrix rows="11" cols="1">
								<ml:real>0</ml:real>
								<ml:real>583.72600932418686</ml:real>
								<ml:real>1167.4520186483737</ml:real>
								<ml:real>1751.1780279725606</ml:real>
								<ml:real>2334.9040372967474</ml:real>
								<ml:real>2918.6300466209345</ml:real>
								<ml:real>3502.3560559451212</ml:real>
								<ml:real>4086.0820652693083</ml:real>
								<ml:real>4669.8080745934949</ml:real>
								<ml:real>5253.5340839176815</ml:real>
								<ml:real>5837.2600932418691</ml:real>
							</ml:matrix>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
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					</result>
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				<resultFormat>
					<table item-idref="152"/>
				</resultFormat>
			</math>
			<rendering item-idref="153"/>
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		<region region-id="10286" left="528" top="2545.5" width="63.75" height="235.5" align-x="544.5" align-y="2574" 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:div/>
						<ml:apply>
							<ml:indexer/>
							<ml:id xml:space="preserve">Gap</ml:id>
							<ml:id xml:space="preserve">j</ml:id>
						</ml:apply>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:matrix rows="11" cols="1">
							<ml:real>-2.87</ml:real>
							<ml:real>-2.8700590801476107</ml:real>
							<ml:real>-2.8701181602952208</ml:real>
							<ml:real>-2.8701772404428314</ml:real>
							<ml:real>-2.870236320590442</ml:real>
							<ml:real>-2.8702954007380526</ml:real>
							<ml:real>-2.8703544808856627</ml:real>
							<ml:real>-2.8704135610332728</ml:real>
							<ml:real>-2.8704726411808834</ml:real>
							<ml:real>-2.8705317213284935</ml:real>
							<ml:real>-2.8705908014761041</ml:real>
						</ml:matrix>
					</result>
				</ml:eval>
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					<table item-idref="154"/>
				</resultFormat>
			</math>
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			<picture>
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			</picture>
			<rendering item-idref="157"/>
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			<pageBreak/>
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					<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>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">
					<b>
						<u>Table 24<sp count="2"/>Formulas for shear, moment and deflection of flat circular plates of constant thickness</u>
					</b>
				</p>
			</text>
		</region>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">
					<b>This file corresponds to Cases 2a - 2d in </b>
					<b>
						<i>Roark's </i>
					</b>
					<b>
						<i>Formulas for Stress and Strain.</i>
					</b>
				</p>
			</text>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">
					<f size="14">
						<b>Annular plate with uniformly distributed pressure q over the portion from r</b>
					</f>
					<f size="14">
						<b>
							<sub>o</sub>
						</b>
					</f>
					<f size="14">
						<b> to a</b>
					</f>
					<f size="14">
						<b>; outer edge simply supported</b>
					</f>
				</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="thick">a</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.5</ml:real>
						<ml:id xml:space="preserve">shellOD</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
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						<ml:id xml:space="preserve">in</ml:id>
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						<unitedValue>
							<ml:real>1.25</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
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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="thick">b</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.5</ml:real>
						<ml:id xml:space="preserve">shellID</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
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						<unitedValue>
							<ml:real>0.74999999999999989</ml:real>
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								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
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			</math>
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					<b>Annular plate with a uniformly distributed pressure q over the portion from r</b>
					<b>
						<sub>o</sub>
					</b>
					<b> to a</b>
				</p>
			</text>
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					<b>Outer edge simply supported, inner edge free</b>
				</p>
			</text>
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					<ml:id xml:space="preserve">L</ml:id>
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			<math optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve">L</ml:id>
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						<ml:id xml:space="preserve">in</ml:id>
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						<unitedValue>
							<ml:real>5.9999999999999991</ml:real>
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								<unitReference unit="inch"/>
							</unitMonomial>
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					<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>
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			<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>
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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="1thick">σ</ml:id>
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						<ml:div/>
						<ml:apply>
							<ml:mult/>
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								<ml:neg/>
								<ml:id xml:space="preserve">q</ml:id>
							</ml:apply>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve" subscript="thick">a</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
						</ml:apply>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve" subscript="thick">a</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve" subscript="thick">b</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
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						<ml:id xml:space="preserve">psi</ml:id>
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						<unitedValue>
							<ml:real>-9120.71889569042</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
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					<ml:id xml:space="preserve" subscript="endcap">t</ml:id>
					<ml:id xml:space="preserve">ecThickness</ml:id>
				</ml:globalDefine>
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				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:id xml:space="preserve">ecOD</ml:id>
						<ml:real>2</ml:real>
					</ml:apply>
				</ml:globalDefine>
			</math>
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					<f family="Arial" charset="0">
						<b>
							<inlineAttr line-through="false">Circumferential stress: </inlineAttr>
						</b>
					</f>
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			</text>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:function>
						<ml:id xml:space="preserve" subscript="2thick">σ</ml:id>
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							<ml:id xml:space="preserve">r</ml:id>
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						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:mult/>
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									<ml:neg/>
									<ml:id xml:space="preserve">q</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve" subscript="thick">a</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" subscript="thick">b</ml:id>
										<ml:real>2</ml:real>
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									<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>
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								<ml:apply>
									<ml:minus/>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve" subscript="thick">a</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve" subscript="thick">b</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
					</ml:apply>
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			</math>
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						<ml:id xml:space="preserve">psi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>-18241.437791380838</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
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			</math>
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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="endcap">b</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:id xml:space="preserve">ecHoleDiameter</ml:id>
						<ml:real>2</ml:real>
					</ml:apply>
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				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">in</ml:id>
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					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>4</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
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						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>0.5</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
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			</math>
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			<math optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve" subscript="rbendcap">M</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.0</ml:real>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="179"/>
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			<math optimize="false" disable-calc="false">
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						<ml:apply>
							<ml:mult/>
							<ml:real>0</ml:real>
							<ml:id xml:space="preserve">in</ml:id>
						</ml:apply>
						<ml:id xml:space="preserve">lbf</ml:id>
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			<math optimize="false" disable-calc="false">
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						<ml:real>0</ml:real>
						<ml:apply>
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							<ml:id xml:space="preserve">in</ml:id>
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				</ml:globalDefine>
			</math>
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			<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="10553" left="144" top="3170.25" width="217.5" height="58.5" align-x="207" align-y="3204" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:function>
						<ml:id xml:space="preserve" subscript="3thick">σ</ml:id>
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							<ml:id xml:space="preserve">r</ml:id>
						</ml:boundVars>
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								<ml:mult/>
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								</ml:apply>
								<ml:apply>
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									<ml:real>2</ml:real>
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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>
										<ml:pow/>
										<ml:id xml:space="preserve" subscript="thick">b</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
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						</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" subscript="thick">a</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve" subscript="thick">b</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
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			<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" subscript="thick">b</ml:id>
					</ml:apply>
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						<ml:id xml:space="preserve">psi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>0</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="183"/>
		</region>
		<region region-id="11086" left="708" top="3219.75" width="87.75" height="22.5" align-x="762" align-y="3234" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="aendcap">y</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="184"/>
		</region>
		<region region-id="11087" left="840" top="3219.75" width="102.75" height="22.5" align-x="891.75" align-y="3234" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="0endcap">r</ml:id>
					<ml:id xml:space="preserve" subscript="endcap">b</ml:id>
				</ml:globalDefine>
			</math>
			<rendering item-idref="185"/>
		</region>
		<region region-id="10548" left="18" top="3260.25" width="187.5" height="12" align-x="27.75" align-y="3270" 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="10552" left="144" top="3236.25" width="152.25" height="58.5" align-x="189.75" align-y="3270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve" subscript="thickb">τ</ml:id>
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						<ml:div/>
						<ml:apply>
							<ml:mult/>
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							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve" subscript="thick">a</ml:id>
								<ml:real>2</ml:real>
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						</ml:apply>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve" subscript="thick">a</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve" subscript="thick">b</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
						</ml:apply>
					</ml:apply>
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			</math>
			<rendering item-idref="186"/>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="thickb">τ</ml:id>
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						<ml:id xml:space="preserve">psi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>9120.71889569042</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
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						</unitedValue>
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				</ml:eval>
			</math>
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			<math optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve" subscript="endcap">D</ml:id>
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						<ml:div/>
						<ml:apply>
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							<ml:apply>
								<ml:pow/>
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								<ml:real>3</ml:real>
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						</ml:apply>
						<ml:apply>
							<ml:mult/>
							<ml:real>12</ml:real>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:real>1</ml:real>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">ν</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
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						<ml:apply>
							<ml:mult/>
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							<ml:id xml:space="preserve">in</ml:id>
						</ml:apply>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>790034.78846369672</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
				<resultFormat numeric-only="true">
					<general precision="5" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/>
					<matrix display-style="auto" expand-nested-arrays="false"/>
					<unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/>
				</resultFormat>
			</math>
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			<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 size="14">Plate Constant</f>
				</p>
			</text>
		</region>
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			<math optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve" subscript="endcap1">C</ml:id>
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								<ml:mult/>
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										<ml:plus/>
										<ml:real>1</ml:real>
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									<ml:real>2</ml:real>
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								<ml:apply>
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									<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
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							<ml:apply>
								<ml:id xml:space="preserve">ln</ml:id>
								<ml:apply>
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									<ml:id xml:space="preserve" subscript="endcap">b</ml:id>
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							</ml:apply>
						</ml:apply>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
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								<ml:apply>
									<ml:minus/>
									<ml:real>1</ml:real>
									<ml:id xml:space="preserve">ν</ml:id>
								</ml:apply>
								<ml:real>4</ml:real>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:apply>
										<ml:div/>
										<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
										<ml:id xml:space="preserve" subscript="endcap">b</ml:id>
									</ml:apply>
									<ml:apply>
										<ml:div/>
										<ml:id xml:space="preserve" subscript="endcap">b</ml:id>
										<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
									</ml:apply>
								</ml:apply>
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						</ml:apply>
					</ml:apply>
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			</math>
			<rendering item-idref="190"/>
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			<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>
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			<math optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve" subscript="vmthick">σa</ml:id>
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												<ml:id xml:space="preserve" subscript="1thick">σ</ml:id>
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													<ml:id xml:space="preserve" subscript="2thick">σ</ml:id>
													<ml:id xml:space="preserve" subscript="thick">a</ml:id>
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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:id xml:space="preserve" subscript="thick">a</ml:id>
												</ml:apply>
												<ml:apply>
													<ml:id xml:space="preserve" subscript="3thick">σ</ml:id>
													<ml:id xml:space="preserve" subscript="thick">a</ml:id>
												</ml:apply>
											</ml:apply>
										</ml:parens>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:parens>
										<ml:apply>
											<ml:minus/>
											<ml:apply>
												<ml:id xml:space="preserve" subscript="3thick">σ</ml:id>
												<ml:id xml:space="preserve" subscript="thick">a</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="1thick">σ</ml:id>
										</ml:apply>
									</ml:parens>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:real>2</ml:real>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="191"/>
		</region>
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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="endcap4">C</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:div/>
							<ml:real>1</ml:real>
							<ml:real>2</ml:real>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:mult/>
									<ml:parens>
										<ml:apply>
											<ml:plus/>
											<ml:real>1</ml:real>
											<ml:id xml:space="preserve">ν</ml:id>
										</ml:apply>
									</ml:parens>
									<ml:apply>
										<ml:div/>
										<ml:id xml:space="preserve" subscript="endcap">b</ml:id>
										<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:parens>
										<ml:apply>
											<ml:minus/>
											<ml:real>1</ml:real>
											<ml:id xml:space="preserve">ν</ml:id>
										</ml:apply>
									</ml:parens>
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										<ml:div/>
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						<ml:real>1.4919160781521361</ml:real>
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						<ml:real>3.50870625</ml:real>
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							<inlineAttr line-through="false">Based on Von Mises stress<sp count="2"/>
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							<inlineAttr line-through="false">Based on Max. shear stress theory 0.5*Sy</inlineAttr>
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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>
								</ml:apply>
								<ml:parens>
									<ml:apply>
										<ml:minus/>
										<ml:real>2</ml:real>
										<ml:id xml:space="preserve">ν</ml:id>
									</ml:apply>
								</ml:parens>
							</ml:apply>
							<ml:apply>
								<ml:minus/>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve" subscript="thick">a</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve" subscript="thick">b</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
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				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
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						<unitedValue>
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							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
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									<ml:real>3</ml:real>
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							</ml:apply>
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							<ml:apply>
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										<ml:id xml:space="preserve" subscript="endcap17">L</ml:id>
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									<ml:id xml:space="preserve" subscript="endcap7">C</ml:id>
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								<ml:id xml:space="preserve" subscript="endcap14">L</ml:id>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="endcapa">θ</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">deg</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>2.6541298654793342</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="degree"/>
							</unitMonomial>
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			<pageBreak/>
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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">
					<f size="12">
						<b>
							<u>1C Buckling calculation for cylinders:</u>
						</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="10390" left="270" top="4124.25" width="299.25" height="12" align-x="270" align-y="4134" 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>
							<u>Table 35 Formulas for elastic stability of plates and shells</u>
						</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="11219" left="720" top="4148.25" width="200.25" height="12" align-x="720" align-y="4158" 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">Transverse Bending moment / stress</inlineAttr>
						</b>
					</f>
				</p>
			</text>
		</region>
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			<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" size="14">
						<b>Case 20a</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="10392" left="120" top="4155.75" width="254.25" height="54" align-x="120" align-y="4170" 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" size="14">
						<b>Thin tube with closed ends under uniform external pressure, lateral and longitudinal; ends held circular</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="10393" left="372" top="4166.25" width="255" height="24" align-x="372" align-y="4176" 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>Thin tube with closed ends under uniform external pressure, lateral and longitudinal</b>
					</f>
				</p>
			</text>
		</region>
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			<math optimize="false" disable-calc="false">
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						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:mult/>
								<ml:id xml:space="preserve" subscript="endcapb">θ</ml:id>
								<ml:id xml:space="preserve" subscript="endcap">D</ml:id>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:real>1</ml:real>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">ν</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
						<ml:id xml:space="preserve" subscript="endcap">b</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
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		</region>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="endcapt">M</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>36703.920530703581</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="227"/>
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		<region region-id="10423" left="36" top="4224" width="149.25" height="62.25" align-x="36" align-y="4224" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="228" display-width="147.75" display-height="60.75"/>
			</picture>
			<rendering item-idref="229"/>
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		<region region-id="11238" left="888" top="4242" width="147" height="26.25" align-x="938.25" align-y="4260" 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="endcap">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>344099.25497534603</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="230"/>
		</region>
		<region region-id="10425" left="516" top="4251.75" width="89.25" height="22.5" align-x="571.5" align-y="4266" 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="buckling">r</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>1</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="231"/>
		</region>
		<region region-id="11236" left="726" top="4237.5" width="126.75" height="53.25" align-x="776.25" align-y="4266" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="endcap">σ</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:real>6</ml:real>
							<ml:id xml:space="preserve" subscript="endcapt">M</ml:id>
						</ml:apply>
						<ml:apply>
							<ml:pow/>
							<ml:id xml:space="preserve" subscript="endcap">t</ml:id>
							<ml:real>2</ml:real>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="232"/>
		</region>
		<region region-id="11240" left="1086" top="4237.5" width="187.5" height="48" align-x="1148.25" align-y="4266" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="endcap">MS</ml:id>
					<ml:parens>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve" subscript="y">S</ml:id>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve" subscript="endcap">σ</ml:id>
									<ml:id xml:space="preserve">FofS</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:real>1</ml:real>
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					</ml:parens>
				</ml:globalDefine>
			</math>
			<rendering item-idref="233"/>
		</region>
		<region region-id="10424" left="216" top="4246.5" width="261" height="40.5" align-x="271.5" align-y="4272" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="buckling">r</ml:id>
					<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:globalDefine>
			</math>
			<rendering item-idref="234"/>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">L</ml:id>
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						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>5.9999999999999991</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
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			</math>
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		<region region-id="11245" left="1092" top="4305.75" width="119.25" height="22.5" align-x="1154.25" align-y="4320" 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="endcap">MS</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>-0.73779203934562743</ml:real>
					</result>
				</ml:eval>
			</math>
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		</region>
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			<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">For the expressions in the case to be valid, the following condition must be true (i.e., condition = 1):</p>
			</text>
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			<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">check small deflection assumption (deflection &lt; t/2)</p>
			</text>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">condition</ml:id>
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						<ml:greaterThan/>
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							<ml:div/>
							<ml:id xml:space="preserve" subscript="buckling">r</ml:id>
							<ml:id xml:space="preserve">shellWallThickness</ml:id>
						</ml:apply>
						<ml:real>10</ml:real>
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				</ml:define>
			</math>
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			<math optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve">condition</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>0</ml:real>
					</result>
				</ml:eval>
			</math>
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		<region region-id="11251" left="732" top="4381.5" width="225" height="48" align-x="855.75" align-y="4410" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve" subscript="endcap">smallDefTrue</ml:id>
					<ml:apply>
						<ml:lessThan/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:absval/>
								<ml:id xml:space="preserve" subscript="endcapb">y</ml:id>
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							<ml:id xml:space="preserve" subscript="endcap">t</ml:id>
						</ml:apply>
						<ml:apply>
							<ml:div/>
							<ml:real font="0">1</ml:real>
							<ml:real>2</ml:real>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
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		</region>
		<region region-id="11252" left="996" top="4381.5" width="120.75" height="48" align-x="1067.25" align-y="4410" 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:div/>
						<ml:apply>
							<ml:absval/>
							<ml:id xml:space="preserve" subscript="endcapb">y</ml:id>
						</ml:apply>
						<ml:id xml:space="preserve" subscript="endcap">t</ml:id>
					</ml:apply>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>0.16492801144353422</ml:real>
					</result>
				</ml:eval>
			</math>
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						<ml:real>1</ml:real>
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			<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">The critical pressure for the initial buckling of a cylinder<sp count="2"/>is:</p>
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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">number of lobes:</p>
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												<ml:real>2</ml:real>
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										</ml:apply>
										<ml:apply>
											<ml:mult/>
											<ml:apply>
												<ml:mult/>
												<ml:real>12</ml:real>
												<ml:apply>
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													<ml:real>2</ml:real>
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											</ml:apply>
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												<ml:apply>
													<ml:minus/>
													<ml:real>1</ml:real>
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														<ml:real>2</ml:real>
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													<ml:real>2</ml:real>
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										<ml:real>2</ml:real>
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								<ml:real>3165761.6225021402</ml:real>
								<ml:real>4901491.02403408</ml:real>
								<ml:real>7023097.0168862836</ml:real>
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								<ml:real>12423670.969109356</ml:real>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">
					<b>EndCap Flange/Case Bearing Stress: </b>
					<b>
						<sp count="2"/>
					</b>
				</p>
			</text>
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						<ml:real>10</ml:real>
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						<ml:real>10</ml:real>
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						<ml:real>57.926103581297596</ml:real>
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								<ml:real>2</ml:real>
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						<ml:div/>
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								<unitReference unit="pounds_per_sq_inch"/>
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									<ml:id xml:space="preserve">FofS</ml:id>
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							</ml:apply>
							<ml:real>1</ml:real>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">Where experimental values of p<sub>critical</sub> are +/- 20% of p<sub>min</sub> !!!</p>
			</text>
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					<ml:id xml:space="preserve" subscript="bearing">MS</ml:id>
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						<ml:real>14.534823208651424</ml:real>
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					<general precision="2" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/>
					<matrix display-style="auto" expand-nested-arrays="false"/>
					<unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/>
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			<pageBreak/>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">
					<b>
						<u>Table 35 Formulas for elastic stability of plates and shells</u>
					</b>
				</p>
			</text>
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			</picture>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<b>EndCap Flange Shear Thru Stress </b>
				</p>
			</text>
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					<f size="14">
						<b>Case 15a</b>
					</f>
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					<f size="14">
						<b>Thin walled circular tube under uniform longitudinal compression; ends not constrained</b>
					</f>
				</p>
			</text>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shearArea</ml:id>
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						<ml:mult/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">π</ml:id>
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								<ml:id xml:space="preserve">ecPlugOD</ml:id>
							</ml:parens>
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						<ml:id xml:space="preserve">ecTabThickness</ml:id>
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			<math optimize="false" disable-calc="false">
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						<ml:apply>
							<ml:pow/>
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							<ml:real>2</ml:real>
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							<ml:real>4.5490261623980208</ml:real>
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								<unitReference unit="inch" power-numerator="2"/>
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							<ml:mult/>
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								<ml:real>4</ml:real>
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						<ml:parens>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve">bearingOD</ml:id>
								<ml:real>2</ml:real>
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							<ml:real>293412.69481634442</ml:real>
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								<unitReference unit="pound_force"/>
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					<b>Thin walled circular tube under uniform longitudinal compression</b>
				</p>
			</text>
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						<ml:id xml:space="preserve">shearArea</ml:id>
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						<unitedValue>
							<ml:real>64500.111527534464</ml:real>
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								<unitReference unit="pounds_per_sq_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" subscript="shear">MS</ml:id>
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									<ml:id xml:space="preserve">FofS</ml:id>
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							</ml:apply>
							<ml:real>1</ml:real>
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					<ml:id xml:space="preserve" subscript="shear">MS</ml:id>
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						<ml:real>0.398843533336497</ml:real>
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			<pageBreak/>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">
					<b>
						<u>Notation file</u>
					</b>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">Provides a description of Table 35 and the notation used.</p>
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					<b>Enter dimensions and properties:</b>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">Radius of curvature of tube:</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">r</ml:id>
					<ml:id xml:space="preserve" subscript="buckling">r</ml:id>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">Tube thickness:</p>
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					<b>Note</b>: The ratio r/t must be greater than 10 for this document to be valid.</p>
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					<b>Calculation procedure:</b>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">Most accurate for very long tubes, but applicable if length is several times as great as</p>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">which is the length of a half-wave of buckling. Tests indicate an actual buckling strength of from 40 to 60% of this theoretical value, or approximately</p>
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					<b>References:</b>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">Ref. 6.<sp count="2"/>Heck, O. S., and H. Ebner: Methods and Formulas for Calculating the Strength of Plate and Shell Construction as Used in Airplane Design, <i>Natl. Adv. Comm. Aeron., Tech. Memo.</i>785, 1936.</p>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"/>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">Ref. 12.<sp count="2"/>Lundquist, E. E.: Strength Tests of Thin-walled Duralumin Cylinders in Compression, <i>Natl. Adv. Comm. Aeron., Rept.</i> 473, 1933.</p>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"/>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">Ref. 13.<sp count="2"/>Wilson, W. M., and N. M. Newmark: The Strength of Thin Cylindrical Shells as Columns, <i>Eng. Exp. Sta. Univ. Ill., Bull.</i> 255, 1933.</p>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"/>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">Ref. 24.<sp count="2"/>Batdorf, S. B., M. Schildcrout, and M. Stein: Critical Stress of Thin-walled Cylinders in Axial Compression, <i>Natl. Adv. Comm. Aeron., Tech. Note</i> 1343, 1947.</p>
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					<b>End of Section</b>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">NASA<sp count="2"/>Space Vehicle Design Criteria NASA SP-8007 Sept 1965, revised Aug 1968</p>
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								<ml:real>2</ml:real>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Honbun Eq. 2.2</p>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Timoshenko strength of materials part 2 page 189</p>
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								<ml:real>3</ml:real>
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										<ml:real>1</ml:real>
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						<b>
							<inlineAttr line-through="false">END CAP DEFLECTION AND STRESSES:</inlineAttr>
						</b>
					</f>
					<sp count="2"/>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Superposition of pressure loading of the annulus and line loading of the connector/penetrator hole in the center.</p>
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							<inlineAttr line-through="false">in*lbf / in<sp count="2"/>
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					<b>CONNECTOR LINE LOAD: </b>
					<sp/>
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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>
					</b>
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						<b>Annular plate with uniform annular line load w at radius r</b>
					</f>
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						<b>
							<sub>o</sub>
						</b>
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						<b>; outer edge simply supported</b>
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					<b>This file corresponds to Cases 1a - 1d in </b>
					<b>
						<i>Roark's Formulas for Stress and Strain.</i>
					</b>
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					<b>Annular plate with a uniform annular line load w at a radius r</b>
					<b>
						<sub>o</sub>
					</b>
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					<b>Outer edge simply supported, inner edge free</b>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Area of Connector:<sp count="2"/>
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							<u>Stresses in tabs:</u>
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							<inlineAttr line-through="false">A) Top tab: </inlineAttr>
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							<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 uniform annular line load w at radius r</b>
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							<sub>o</sub>
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						<b>; outer edge free</b>
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					<b>Case 1l:</b>
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						<b>Outer edge free, inner edge fixed</b>
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							<ml:real>3.62</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">Margin:</p>
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			<pageBreak/>
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					<f size="12">
						<b>
							<u>B) O-ring groove tab:</u>
						</b>
					</f>
				</p>
			</text>
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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>
						</b>
					</f>
				</p>
			</text>
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			<text use-page-width="false" push-down="false" lock-width="true">
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					<f family="MS Sans Serif" charset="0">
						<b>Annular plate with uniform annular line load w at radius r</b>
					</f>
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						<b>
							<sub>o</sub>
						</b>
					</f>
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						<b>; outer edge free</b>
					</f>
				</p>
			</text>
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			<picture>
				<png item-idref="383" display-width="243" display-height="89.25"/>
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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">
					<b>Case 1l:</b>
				</p>
			</text>
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			<text use-page-width="false" push-down="false" lock-width="true">
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						<b>Outer edge free, inner edge fixed</b>
					</f>
				</p>
			</text>
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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">For o-ring tab:</p>
			</text>
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						<ml:apply>
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								<ml:mult/>
								<ml:real>4</ml:real>
								<ml:id xml:space="preserve" subscript="oring">a</ml:id>
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							<ml:apply>
								<ml:plus/>
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												<ml:id xml:space="preserve" subscript="oring">a</ml:id>
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										<ml:real>2</ml:real>
									</ml:apply>
									<ml:real>1</ml:real>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:real>2</ml:real>
									<ml:apply>
										<ml:id xml:space="preserve">ln</ml:id>
										<ml:apply>
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											<ml:id xml:space="preserve" subscript="oring">a</ml:id>
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									</ml:apply>
								</ml:apply>
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				</ml:globalDefine>
			</math>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
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					<ml:apply>
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						<ml:apply>
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							<ml:id xml:space="preserve" subscript="oring">a</ml:id>
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							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
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										<ml:apply>
											<ml:plus/>
											<ml:real>1</ml:real>
											<ml:id xml:space="preserve">ν</ml:id>
										</ml:apply>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
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										<ml:apply>
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										<ml:apply>
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											<ml:real>1</ml:real>
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										<ml:real>4</ml:real>
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										<ml:apply>
											<ml:minus/>
											<ml:real>1</ml:real>
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														<ml:id xml:space="preserve" subscript="oring">a</ml:id>
													</ml:apply>
												</ml:parens>
												<ml:real>2</ml:real>
											</ml:apply>
										</ml:apply>
									</ml:parens>
								</ml:apply>
							</ml:apply>
						</ml:parens>
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				</ml:globalDefine>
			</math>
			<rendering item-idref="406"/>
		</region>
		<region region-id="9187" left="354" top="11581.5" width="315" height="48" align-x="412.5" align-y="11610" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math error="This variable is undefined." optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="oringrb">M</ml:id>
					<ml:apply>
						<ml:mult style="auto-select"/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:neg/>
									<ml:id xml:space="preserve" subscript="oring">w</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="oring">a</ml:id>
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							<ml:id xml:space="preserve" subscript="oring8">C</ml:id>
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						<ml:parens>
							<ml:apply>
								<ml:minus/>
								<ml:apply>
									<ml:div/>
									<ml:apply>
										<ml:mult/>
										<ml:id xml:space="preserve" subscript="oring0">r</ml:id>
										<ml:id xml:space="preserve" subscript="oring9">C</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="oring">b</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="oring9">L</ml:id>
							</ml:apply>
						</ml:parens>
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				</ml:globalDefine>
			</math>
			<rendering item-idref="407"/>
		</region>
		<region region-id="9188" left="354" top="11625.75" width="96" height="22.5" align-x="412.5" align-y="11640" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math error="This variable is undefined." optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="oringrb">M</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">lbf</ml:id>
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				</ml:eval>
			</math>
			<rendering item-idref="408"/>
		</region>
		<region region-id="9189" left="6" top="11648.25" width="336" height="53.25" align-x="68.25" align-y="11682" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math error="This variable is undefined." optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="oringmax">y</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:neg/>
									<ml:id xml:space="preserve" subscript="oring">w</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve" subscript="oring">a</ml:id>
									<ml:real>4</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:apply>
								<ml:mult/>
								<ml:id xml:space="preserve" subscript="oring">b</ml:id>
								<ml:id xml:space="preserve" subscript="oring">D</ml:id>
							</ml:apply>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:minus/>
								<ml:apply>
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									<ml:apply>
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										<ml:id xml:space="preserve" subscript="oring9">C</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="oring8">C</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="oring3">C</ml:id>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="409"/>
		</region>
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			<math error="This variable is undefined." optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="oring">σ</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:real>6</ml:real>
							<ml:id xml:space="preserve" subscript="oringrb">M</ml:id>
						</ml:apply>
						<ml:apply>
							<ml:pow/>
							<ml:id xml:space="preserve" subscript="oring">t</ml:id>
							<ml:real>2</ml:real>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="410"/>
		</region>
		<region region-id="9208" left="516" top="11667.75" width="81.75" height="22.5" align-x="559.5" align-y="11682" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math error="This variable is undefined." optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
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						<ml:id xml:space="preserve">psi</ml:id>
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			<math error="This variable is undefined." optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
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						<ml:id xml:space="preserve">in</ml:id>
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				</ml:eval>
			</math>
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		</region>
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			<math error="This variable is undefined." optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="oringb">Q</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve" subscript="oring">w</ml:id>
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						</ml:apply>
						<ml:id xml:space="preserve" subscript="oring">b</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="413"/>
		</region>
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			<math error="This variable is undefined." optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="oringb">Q</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve">lbf</ml:id>
							<ml:id xml:space="preserve">in</ml:id>
						</ml:apply>
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				</ml:eval>
			</math>
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			<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">Margin:</p>
			</text>
		</region>
		<region region-id="9199" left="366" top="11755.5" width="186" height="48" align-x="421.5" align-y="11784" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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									<ml:mult/>
									<ml:apply>
										<ml:absval/>
										<ml:id xml:space="preserve" subscript="oring">σ</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve">FofS</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:real>1</ml:real>
						</ml:apply>
					</ml:parens>
				</ml:globalDefine>
			</math>
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		</region>
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			<math error="This variable is undefined." optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="oring">MS</ml:id>
				</ml:eval>
			</math>
			<rendering item-idref="416"/>
		</region>
		<region region-id="5685" left="36" top="11814" width="4797.75" height="6" align-x="36" align-y="11814" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<pageBreak/>
		</region>
		<region region-id="7017" left="24" top="11820.75" width="324" height="14.25" align-x="24" align-y="11832" 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 size="12">
						<b>
							<u>E) WEIGHT &amp; DISPLACEMENT CHANGE CALCULATION:</u>
						</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="7109" left="6" top="11846.25" width="107.25" height="12" align-x="6" align-y="11856" 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">
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<b>
						<u>1. Case Weight Calc.:</u>
					</b>
					<sp count="2"/>
				</p>
			</text>
		</region>
		<region region-id="7077" left="6" top="11888.25" width="38.25" height="12" align-x="6" align-y="11898" 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">Cylinder:</p>
			</text>
		</region>
		<region region-id="10960" left="54" top="11888.25" width="90.75" height="12" align-x="54" align-y="11898" 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">cross sectional area:</p>
			</text>
		</region>
		<region region-id="10961" left="168" top="11867.25" width="186.75" height="45.75" align-x="194.25" align-y="11898" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="x">ac</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">π</ml:id>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">shellOD</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">shellID</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
						<ml:real>4</ml:real>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="417"/>
		</region>
		<region region-id="10962" left="492" top="11878.5" width="90.75" height="27.75" align-x="518.25" align-y="11898" 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="x">ac</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:pow/>
							<ml:id xml:space="preserve">in</ml:id>
							<ml:real>2</ml:real>
						</ml:apply>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>3.1415926535897936</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="2"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="418"/>
		</region>
		<region region-id="10963" left="54" top="11930.25" width="67.5" height="12" align-x="54" align-y="11940" 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">internal volume:</p>
			</text>
		</region>
		<region region-id="10964" left="168" top="11909.25" width="314.25" height="45.75" align-x="192" align-y="11940" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="i">vc</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">π</ml:id>
							<ml:apply>
								<ml:div/>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellID</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
								<ml:real>4</ml:real>
							</ml:apply>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:minus/>
								<ml:id xml:space="preserve">shellLength</ml:id>
								<ml:id xml:space="preserve">shellBaseThickness</ml:id>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="419"/>
		</region>
		<region region-id="10965" left="492" top="11920.5" width="88.5" height="27.75" align-x="516" align-y="11940" 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="i">vc</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:pow/>
							<ml:id xml:space="preserve">in</ml:id>
							<ml:real>3</ml:real>
						</ml:apply>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>9.71930227204342</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="3"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="420"/>
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		<region region-id="10966" left="54" top="11972.25" width="70.5" height="12" align-x="54" align-y="11982" 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">external volume:</p>
			</text>
		</region>
		<region region-id="10967" left="168" top="11951.25" width="186" height="45.75" align-x="195" align-y="11982" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
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								<ml:id xml:space="preserve">π</ml:id>
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									<ml:real>2</ml:real>
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							<ml:real>4</ml:real>
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			</math>
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			<math optimize="false" disable-calc="false">
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					<ml:unitOverride>
						<ml:apply>
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							<ml:id xml:space="preserve">in</ml:id>
							<ml:real>3</ml:real>
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					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>29.45243112740431</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="3"/>
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		<region region-id="10969" left="54" top="12008.25" width="30.75" height="12" align-x="54" align-y="12018" 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">weight:</p>
			</text>
		</region>
		<region region-id="10970" left="168" top="12003.75" width="159" height="22.5" align-x="203.25" align-y="12018" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="cyl">W</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve" subscript="x">ac</ml:id>
							<ml:id xml:space="preserve">shellLength</ml:id>
						</ml:apply>
						<ml:id xml:space="preserve" subscript="m">ρ</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="423"/>
		</region>
		<region region-id="10971" left="492" top="12003.75" width="96.75" height="22.5" align-x="527.25" align-y="12018" 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="cyl">W</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>3.0159289474462017</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="424"/>
		</region>
		<region region-id="7090" left="6" top="12050.25" width="40.5" height="12" align-x="6" align-y="12060" 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">End Cap:</p>
			</text>
		</region>
		<region region-id="10942" left="102" top="12050.25" width="33" height="12" align-x="102" align-y="12060" 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">volume:</p>
			</text>
		</region>
		<region region-id="10941" left="102" top="12068.25" width="18.75" height="12" align-x="102" align-y="12078" 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">Tab:</p>
			</text>
		</region>
		<region region-id="7093" left="186" top="12047.25" width="198" height="45.75" align-x="216.75" align-y="12078" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="tab">v</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:id xml:space="preserve">π</ml:id>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">ecOD</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:real>4</ml:real>
						</ml:apply>
						<ml:id xml:space="preserve">ecTabThickness</ml:id>
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		<region region-id="7094" left="402" top="12058.5" width="102" height="27.75" align-x="432.75" align-y="12078" 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">
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					<ml:unitOverride>
						<ml:apply>
							<ml:pow/>
							<ml:id xml:space="preserve">in</ml:id>
							<ml:real>3</ml:real>
						</ml:apply>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>10.053096491487338</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="3"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="426"/>
		</region>
		<region region-id="10940" left="102" top="12116.25" width="22.5" height="12" align-x="102" align-y="12126" 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">Plug:</p>
			</text>
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			<math optimize="false" disable-calc="false">
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								<ml:id xml:space="preserve">π</ml:id>
								<ml:apply>
									<ml:pow/>
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									<ml:real>2</ml:real>
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							</ml:apply>
							<ml:real>4</ml:real>
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							<ml:apply>
								<ml:minus/>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="plug">v</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:pow/>
							<ml:id xml:space="preserve">in</ml:id>
							<ml:real>3</ml:real>
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					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>24.701212061821256</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="3"/>
							</unitMonomial>
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		<region region-id="10939" left="102" top="12158.25" width="20.25" height="12" align-x="102" align-y="12168" 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">Cap:</p>
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			<math optimize="false" disable-calc="false">
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		<region region-id="7100" left="306" top="12148.5" width="105" height="27.75" align-x="339.75" align-y="12168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
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							<ml:real>34.7543085533086</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="3"/>
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			<text use-page-width="false" push-down="false" lock-width="true">
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			<math optimize="false" disable-calc="false">
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			<math optimize="false" disable-calc="false">
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					<ml:unitOverride>
						<ml:id xml:space="preserve">lbf</ml:id>
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					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>5.560689368529375</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
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		<region region-id="7104" left="6" top="12230.25" width="57.75" height="12" align-x="6" align-y="12240" 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">Total Weight:</p>
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		<region region-id="7291" left="192" top="12225.75" width="134.25" height="22.5" align-x="237.75" align-y="12240" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve" subscript="dry">Wp</ml:id>
					<ml:apply>
						<ml:plus/>
						<ml:id xml:space="preserve" subscript="cyl">W</ml:id>
						<ml:apply>
							<ml:mult style="auto-select"/>
							<ml:real font="0">2</ml:real>
							<ml:id xml:space="preserve" subscript="cap">W</ml:id>
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			<rendering item-idref="433"/>
		</region>
		<region region-id="7293" left="498" top="12225.75" width="114" height="22.5" align-x="543.75" align-y="12240" 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">
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						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>14.137307684504952</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
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			<rendering item-idref="434"/>
		</region>
		<region region-id="7292" left="192" top="12249.75" width="215.25" height="22.5" align-x="238.5" align-y="12264" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="wet">Wp</ml:id>
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						<ml:id xml:space="preserve" subscript="dry">Wp</ml:id>
						<ml:apply>
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								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve" subscript="o">vc</ml:id>
									<ml:apply>
										<ml:mult/>
										<ml:real>2</ml:real>
										<ml:id xml:space="preserve" subscript="tab">v</ml:id>
									</ml:apply>
								</ml:apply>
							</ml:parens>
							<ml:id xml:space="preserve" subscript="sw">ρ</ml:id>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="wet">Wp</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>12.300337909153592</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
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