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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:id xml:space="preserve">depth</ml:id>
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						<ml:real>500</ml:real>
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						<b>Water density:</b>
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						<ml:real>1026</ml:real>
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								<ml:real>3</ml:real>
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							<ml:real>729.65751165523363</ml:real>
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								<unitReference unit="pounds_per_sq_inch"/>
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						<b>
							<inlineAttr underline="false">B) Material properties:</inlineAttr>
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						<b>
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								<c val="#000">Material: 6061-T6 Aluminum</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>10.0</ml:real>
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								<ml:real>10</ml:real>
								<ml:real>3</ml:real>
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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>0.098</ml:real>
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							<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:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<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>40.0</ml:real>
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						<b>Shear stress:</b>
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						<ml:real>30.0</ml:real>
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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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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
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					<ml:apply>
						<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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			<math optimize="false" disable-calc="false">
				<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>3759398.4962406014</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>
		</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="b">S</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>54000.</ml:real>
						<ml:id xml:space="preserve">psi</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="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>
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		<region region-id="9752" left="210" top="861.6" width="69.6" height="19.8" align-x="245.4" 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>
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			</math>
			<rendering item-idref="17"/>
		</region>
		<region region-id="10498" left="84" top="924" width="436.8" height="15.6" 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="18" display-width="435.6" display-height="14.4"/>
			</picture>
			<rendering item-idref="19"/>
		</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="990.6" width="244.8" height="29.4" align-x="257.4" 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="990.6" width="295.8" height="29.4" 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="1002.6" width="363.6" height="29.4" 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="1009.2" width="359.4" height="29.4" 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>
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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 family="Calibri" charset="0" size="14">
						<b>End cap dimensions</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="10578" left="30" top="1043.4" width="95.4" height="33.6" align-x="44.4" 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="1064.4" width="109.8" height="12" align-x="1163.4" 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>
			</text>
		</region>
		<region region-id="12784" left="1146" top="1080" width="66.6" height="65.4" align-x="1146" align-y="1080" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<metafile mapping-mode="8" x-extent="30.3874" y-extent="30.18898" item-idref="20"/>
			</picture>
			<rendering item-idref="21"/>
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		<region region-id="11423" left="690" top="1071.6" width="151.2" height="19.8" align-x="796.8" 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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				</ml:globalDefine>
			</math>
			<rendering item-idref="22"/>
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			<picture>
				<metafile mapping-mode="8" x-extent="704.2394" y-extent="188.2488" 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>
				</ml:globalDefine>
			</math>
			<rendering item-idref="25"/>
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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>38.0</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
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			<rendering item-idref="26"/>
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			<picture>
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			<picture>
				<metafile mapping-mode="8" x-extent="56.40945" y-extent="30.8126" item-idref="29"/>
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				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ecThickness</ml:id>
					<ml:apply>
						<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>7.981</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>8.625</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</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">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>
			</text>
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			<picture>
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		<region region-id="12673" left="678" top="1221.6" width="148.2" height="19.8" align-x="781.8" align-y="1236" 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">ecGrooveWidth</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.1</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
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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="37"/>
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		<region region-id="11438" left="180" top="1239.6" width="171" height="19.8" align-x="306.6" align-y="1254" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml: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="38"/>
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		<region region-id="12791" left="1200" top="1256.4" width="103.8" 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="39"/>
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		<region region-id="12674" left="786" top="1281.6" width="147" height="19.8" align-x="888.6" align-y="1296" 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">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>
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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>0.322</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">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="42"/>
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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="43"/>
		</region>
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			<picture>
				<png item-idref="44" display-width="435.6" display-height="14.4"/>
			</picture>
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			<picture>
				<png item-idref="46" display-width="435.6" display-height="14.4"/>
			</picture>
			<rendering item-idref="47"/>
		</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="1420.8" width="292.8" height="24.6" 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="1445.4" width="241.2" height="16.8" align-x="712.8" 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="1451.4" width="252.6" height="16.8" 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="1484.4" width="78.6" height="12" align-x="34.8" 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>8.147021455612915</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="48"/>
		</region>
		<region region-id="10465" left="252" top="1484.4" width="78" height="12" align-x="270.6" 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>
		</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="cythin">MS</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>2.691556249579337</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="49"/>
		</region>
		<region region-id="10467" left="492" top="1479.6" width="88.2" height="19.8" align-x="553.8" 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>1</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="50"/>
		</region>
		<region region-id="11301" left="804" top="1479.6" width="109.8" height="23.4" align-x="841.8" 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>58.037564675605893</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="51"/>
		</region>
		<region region-id="11302" left="990" top="1479.6" width="109.2" height="23.4" align-x="1039.8" 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>-0.48179789868809075</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="52"/>
		</region>
		<region region-id="11303" left="1128" top="1479.6" width="106.2" height="23.4" align-x="1180.2" 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="53"/>
		</region>
		<region region-id="12765" left="30" top="1529.4" width="252.6" height="16.8" 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="1535.4" width="229.8" height="16.8" 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>8.7911763429958825</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="54"/>
		</region>
		<region region-id="12761" left="2088" top="1557.6" width="198.6" height="23.4" align-x="2215.2" 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="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>37.2839189077136</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="55"/>
		</region>
		<region region-id="12763" left="2322" top="1557.6" width="194.4" height="23.4" align-x="2445" 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>37.144259583012854</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="56"/>
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		<region region-id="12770" left="246" top="1563.6" width="144" height="23.4" align-x="338.4" 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>2.4210652586768271</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="57"/>
		</region>
		<region region-id="12771" left="408" top="1563.6" width="148.2" height="23.4" align-x="504.6" 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>1.9627294220185134</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="58"/>
		</region>
		<region region-id="11310" left="774" top="1569.6" width="122.4" height="23.4" align-x="824.4" 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>43.012406871918245</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="59"/>
		</region>
		<region region-id="11311" left="948" top="1569.6" width="121.8" height="23.4" align-x="1010.4" 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>-0.30077877158833977</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="60"/>
		</region>
		<region region-id="11312" left="1074" top="1569.6" width="150.6" height="23.4" align-x="1198.2" 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="61"/>
		</region>
		<region region-id="12772" left="24" top="1607.4" width="252.6" height="16.8" 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>
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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">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>-45.877536881013661</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="62"/>
		</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="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>-45.584063623481462</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
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			</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="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>1583.4420653723764</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="64"/>
		</region>
		<region region-id="12774" left="288" top="1641.6" width="121.8" height="23.4" align-x="358.2" 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>0.085058428152357424</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="65"/>
		</region>
		<region region-id="12820" left="474" top="1641.6" width="120" height="23.4" align-x="549.6" 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>2.1701168563047148</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="66"/>
		</region>
		<region region-id="10458" left="84" top="1698" width="436.8" height="15.6" 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="67" display-width="435.6" display-height="14.4"/>
			</picture>
			<rendering item-idref="68"/>
		</region>
		<region region-id="10931" left="744" top="1710" width="436.8" height="15.6" 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="69" display-width="435.6" display-height="14.4"/>
			</picture>
			<rendering item-idref="70"/>
		</region>
		<region region-id="12759" left="2112" top="1722" width="436.8" height="15.6" 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="71" display-width="435.6" display-height="14.4"/>
			</picture>
			<rendering item-idref="72"/>
		</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="1764.6" width="261" height="14.4" 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="1764" width="280.8" height="48.6" 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="1775.4" width="648" height="33" 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="271.8" height="103.8" 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="73" display-width="270.6" display-height="102.6"/>
			</picture>
			<rendering item-idref="74"/>
		</region>
		<region region-id="10336" left="24" top="1830" width="114" height="100.8" 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="75" display-width="112.8" display-height="99.6"/>
			</picture>
			<rendering item-idref="76"/>
		</region>
		<region region-id="10798" left="1026" top="1836" width="127.2" 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="77" display-width="126" display-height="67.8"/>
			</picture>
			<rendering item-idref="78"/>
		</region>
		<region region-id="10337" left="156" top="1847.4" width="99.6" height="16.8" 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="1834.2" width="249" height="41.4" align-x="285" 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="79"/>
		</region>
		<region region-id="11294" left="540" top="1845.6" width="97.2" height="23.4" align-x="577.2" 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>4.1514999999999995</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="80"/>
		</region>
		<region region-id="10340" left="150" top="1889.4" width="93" height="16.8" 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="1887.6" width="97.2" height="19.8" align-x="262.2" 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="81"/>
		</region>
		<region region-id="10342" left="360" top="1887.6" width="58.2" height="19.8" align-x="376.2" 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>38</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="82"/>
		</region>
		<region region-id="10343" left="54" top="1929" width="58.8" height="10.2" 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="1925.4" width="434.4" height="33.6" 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="1941.6" width="162.6" height="23.4" align-x="736.8" 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="83"/>
		</region>
		<region region-id="10802" left="906" top="1941.6" width="79.2" height="23.4" align-x="939.6" 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="84"/>
		</region>
		<region region-id="10803" left="1014" top="1941.6" width="112.8" height="23.4" align-x="1051.2" 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="85"/>
		</region>
		<region region-id="10805" left="1182" top="1941.6" width="88.8" height="23.4" align-x="1218" 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>3.9905</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="86"/>
		</region>
		<region region-id="12721" left="2022" top="1959" width="38.4" height="10.8" 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="1968.6" width="241.8" height="46.8" align-x="145.8" 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="87"/>
		</region>
		<region region-id="11295" left="354" top="1968.6" width="188.4" height="46.8" align-x="483.6" 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>12.892857142857142</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="88"/>
		</region>
		<region region-id="10347" left="522" top="1983.6" width="88.2" height="19.8" align-x="583.8" 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>1</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="89"/>
		</region>
		<region region-id="12722" left="2046" top="1966.8" width="273.6" height="46.8" align-x="2160.6" 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="90"/>
		</region>
		<region region-id="12723" left="2454" top="1978.2" width="182.4" height="25.2" align-x="2569.8" 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>8.3992553044874469</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="2"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="91"/>
		</region>
		<region region-id="10826" left="702" top="1994.4" width="67.8" 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="1975.2" width="120" height="57.6" align-x="826.2" 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="92"/>
		</region>
		<region region-id="10935" left="930" top="1997.4" width="156.6" height="27.6" align-x="969.6" 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>116896.71941046647</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="93"/>
		</region>
		<region region-id="10936" left="1128" top="1990.2" width="73.2" height="41.4" 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="94"/>
		</region>
		<region region-id="10937" left="1236" top="2001.6" width="81.6" height="23.4" 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="95"/>
		</region>
		<region region-id="12724" left="2046" top="2008.8" width="405" height="46.8" align-x="2151.6" 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="96"/>
		</region>
		<region region-id="12725" left="2454" top="2020.2" width="207" height="25.2" align-x="2559" 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>1876.012685418782</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="3"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="97"/>
		</region>
		<region region-id="9798" left="198" top="2028.6" width="189.6" height="46.8" align-x="242.4" 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="98"/>
		</region>
		<region region-id="9800" left="36" top="2051.4" width="162.6" height="16.8" 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="2049.6" width="107.4" height="23.4" align-x="456.6" 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>4.7036850304917737</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="99"/>
		</region>
		<region region-id="10892" left="690" top="2029.2" width="159.6" height="50.4" align-x="742.2" 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="100"/>
		</region>
		<region region-id="10893" left="858" top="2038.2" width="172.2" height="43.2" align-x="909.6" 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>2418.2318614835785</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="101"/>
		</region>
		<region region-id="11261" left="1050" top="2034.6" width="108.6" height="55.8" align-x="1089" 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="102"/>
		</region>
		<region region-id="11262" left="1170" top="2038.2" width="143.4" height="48.6" align-x="1207.8" 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>58037.564675605892</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="103"/>
		</region>
		<region region-id="12726" left="2046" top="2061.6" width="296.4" height="23.4" align-x="2127" 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="104"/>
		</region>
		<region region-id="12727" left="2454" top="2061.6" width="152.4" height="19.8" align-x="2535" 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>31.27882675391125</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="105"/>
		</region>
		<region region-id="9801" left="36" top="2093.4" width="207.6" height="16.8" 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="2076.6" width="177" height="46.8" align-x="260.4" 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="106"/>
		</region>
		<region region-id="9803" left="408" top="2091.6" width="107.4" height="23.4" align-x="450.6" 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>9.4073700609835473</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="107"/>
		</region>
		<region region-id="12728" left="2046" top="2086.2" width="339.6" height="41.4" align-x="2155.2" 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="108"/>
		</region>
		<region region-id="12729" left="2454" top="2092.2" width="223.2" height="25.2" align-x="2563.2" 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>92.110657376857958</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="109"/>
		</region>
		<region region-id="10896" left="702" top="2100.6" width="163.8" height="50.4" align-x="751.8" 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="110"/>
		</region>
		<region region-id="10897" left="942" top="2115.6" width="109.2" height="23.4" align-x="991.8" 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>-0.48179789868809075</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="111"/>
		</region>
		<region region-id="9373" left="54" top="2156.4" width="130.8" 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="2141.4" width="270" height="33.6" align-x="265.2" 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="112"/>
		</region>
		<region region-id="9806" left="510" top="2151.6" width="118.2" height="23.4" align-x="563.4" 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>8.147021455612915</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="113"/>
		</region>
		<region region-id="10900" left="690" top="2156.4" width="102.6" 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="2157" width="40.8" height="10.8" 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="2140.2" width="577.8" height="41.4" align-x="2176.2" 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="114"/>
		</region>
		<region region-id="11266" left="708" top="2166.6" width="114" height="45" align-x="759.6" 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="115"/>
		</region>
		<region region-id="10899" left="846" top="2170.2" width="161.4" height="43.2" align-x="896.4" 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>-1455.8491501301048</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="116"/>
		</region>
		<region region-id="12732" left="2076" top="2182.2" width="527.4" height="41.4" align-x="2141.4" 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="117"/>
		</region>
		<region region-id="9828" left="54" top="2204.4" width="142.8" 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="2184.6" width="191.4" height="50.4" align-x="217.2" 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="118"/>
		</region>
		<region region-id="9830" left="360" top="2199.6" width="111" height="23.4" align-x="419.4" 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>2.691556249579337</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="119"/>
		</region>
		<region region-id="12733" left="2076" top="2235.6" width="130.2" height="19.8" align-x="2142" 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>3.0025460769011749</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="120"/>
		</region>
		<region region-id="10234" left="42" top="2288.4" width="75.6" height="24" 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="2268.6" width="250.8" height="46.8" align-x="168.6" 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="121"/>
		</region>
		<region region-id="12734" left="2028" top="2283.6" width="295.8" height="23.4" align-x="2157" 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="122"/>
		</region>
		<region region-id="12735" left="2424" top="2283.6" width="198.6" height="23.4" align-x="2551.2" 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>37.2839189077136</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="123"/>
		</region>
		<region region-id="10236" left="390" top="2285.4" width="151.8" height="27.6" align-x="437.4" 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>0.0060771610593953716</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="124"/>
		</region>
		<region region-id="10901" left="696" top="2281.2" width="183" height="55.8" align-x="771.6" 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="125"/>
		</region>
		<region region-id="10902" left="906" top="2301.6" width="142.8" height="23.4" align-x="981" 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>-0.099110938632145429</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="126"/>
		</region>
		<region region-id="12736" left="2028" top="2313.6" width="394.2" height="23.4" align-x="2152.2" 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="127"/>
		</region>
		<region region-id="12737" left="2430" top="2313.6" width="194.4" height="23.4" align-x="2553" 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>37.144259583012854</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="128"/>
		</region>
		<region region-id="10237" left="42" top="2342.4" width="90.6" 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="2329.2" width="250.8" height="52.2" align-x="206.4" 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="129"/>
		</region>
		<region region-id="10239" left="414" top="2345.4" width="154.8" height="27.6" align-x="464.4" 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>0.0032610671834824609</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="130"/>
		</region>
		<region region-id="10903" left="696" top="2360.4" width="417.6" height="12" align-x="705.6" 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="2350.2" width="580.2" height="41.4" align-x="2150.4" 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="131"/>
		</region>
		<region region-id="10253" left="24" top="2390.4" width="611.4" 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="2386.2" width="558" height="41.4" align-x="2145.6" 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="132"/>
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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="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="133"/>
		</region>
		<region region-id="10277" left="360" top="2403.6" width="108.6" height="23.4" align-x="395.4" 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>72.965751165523358</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
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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="base">smallDefTrue</ml:id>
					<ml:parens>
						<ml:apply>
							<ml:lessThan/>
							<ml:apply>
								<ml:div/>
								<ml:apply>
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									<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="135"/>
		</region>
		<region region-id="11246" left="972" top="2388.6" width="142.2" height="50.4" align-x="1062.6" 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>0.19822187726429086</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="136"/>
		</region>
		<region region-id="11247" left="1146" top="2403.6" width="138" height="23.4" align-x="1257.6" 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="137"/>
		</region>
		<region region-id="12740" left="2034" top="2433.6" width="200.4" height="23.4" align-x="2155.2" 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>-45.877536881013661</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="138"/>
		</region>
		<region region-id="12741" left="2268" top="2433.6" width="196.2" height="23.4" align-x="2385" 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>-45.584063623481462</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="139"/>
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		<region region-id="10278" left="24" top="2434.2" width="322.8" height="46.8" align-x="33" 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>
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								</ml:apply>
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						</ml:define>
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve">q</ml:id>
							<ml:id xml:space="preserve" subscript="pressure">N</ml:id>
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					</ml:define>
				</ml:apply>
			</math>
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				<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>
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			</math>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:apply>
						<ml:indexer/>
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						<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>
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				</ml:define>
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			<picture>
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			<picture>
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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">Extrusion gap (radial):</p>
			</text>
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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">ΔR</ml:id>
						<ml:id xml:space="preserve">j</ml:id>
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					<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>
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								</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>
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					<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>
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						<ml:apply>
							<ml:indexer/>
							<ml:id xml:space="preserve">ΔR</ml:id>
							<ml:id xml:space="preserve">j</ml:id>
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			<math optimize="false" disable-calc="false">
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						<ml:id xml:space="preserve">P</ml:id>
						<ml:id xml:space="preserve">j</ml:id>
					</ml:apply>
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						<ml:id xml:space="preserve">psi</ml:id>
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						<unitedValue>
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								<ml:real>0</ml:real>
								<ml:real>72.965751165523358</ml:real>
								<ml:real>145.93150233104672</ml:real>
								<ml:real>218.89725349657007</ml:real>
								<ml:real>291.86300466209343</ml:real>
								<ml:real>364.82875582761682</ml:real>
								<ml:real>437.79450699314015</ml:real>
								<ml:real>510.76025815866353</ml:real>
								<ml:real>583.72600932418686</ml:real>
								<ml:real>656.69176048971019</ml:real>
								<ml:real>729.65751165523363</ml:real>
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							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
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				<resultFormat>
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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">Gap</ml:id>
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						<ml:id xml:space="preserve">in</ml:id>
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					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:matrix rows="11" cols="1">
							<ml:real>0.37049999999999977</ml:real>
							<ml:real>0.37017389328165151</ml:real>
							<ml:real>0.36984778656330325</ml:real>
							<ml:real>0.369521679844955</ml:real>
							<ml:real>0.36919557312660684</ml:real>
							<ml:real>0.36886946640825857</ml:real>
							<ml:real>0.36854335968991031</ml:real>
							<ml:real>0.36821725297156205</ml:real>
							<ml:real>0.36789114625321379</ml:real>
							<ml:real>0.36756503953486552</ml:real>
							<ml:real>0.36723893281651732</ml:real>
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				<resultFormat>
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		<region region-id="10354" left="66" top="2760" width="436.8" height="15.6" align-x="66" align-y="2760" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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			<rendering item-idref="156"/>
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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>
		</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">
					<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>
		</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="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>
			<rendering item-idref="159"/>
		</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="thick">a</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>4.3125</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</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="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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			<math optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve" subscript="thick">b</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>3.9905</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
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			</math>
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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>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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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">
					<b>Outer edge simply supported, inner edge free</b>
				</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">L</ml:id>
					<ml:id xml:space="preserve">shellLength</ml:id>
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			</math>
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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>
					</ml:unitOverride>
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						<unitedValue>
							<ml:real>38</ml:real>
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								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
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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 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>
					<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="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" subscript="1thick">σ</ml:id>
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						<ml:id xml:space="preserve">psi</ml:id>
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					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>-5075.5880281221434</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>
			</math>
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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/>
								<ml:apply>
									<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>
				</ml:globalDefine>
			</math>
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					<ml:unitOverride>
						<ml:id xml:space="preserve">psi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>-10151.176056244285</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_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="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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			</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" subscript="endcap">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>4</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="endcap">b</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>0.5</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
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						<ml:real>0.0</ml:real>
						<ml:id xml:space="preserve">lbf</ml:id>
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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 family="Arial" charset="0">
						<b>
							<inlineAttr line-through="false">Radial stress: </inlineAttr>
						</b>
					</f>
				</p>
			</text>
		</region>
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										<ml:real>2</ml:real>
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							<ml:apply>
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								<ml:real>2</ml:real>
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								<ml:apply>
									<ml:minus/>
									<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>
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						<unitedValue>
							<ml:real>0</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
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			</math>
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			<math optimize="false" disable-calc="false">
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						<ml:mult/>
						<ml:real>0</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="183"/>
		</region>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
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				</ml:globalDefine>
			</math>
			<rendering item-idref="184"/>
		</region>
		<region region-id="10548" left="18" top="3260.4" width="187.8" height="12" align-x="27.6" 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="3235.2" width="154.2" height="61.2" align-x="191.4" 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:real>2</ml:real>
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						<ml:apply>
							<ml:minus/>
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								<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>
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						</ml:apply>
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			<math optimize="false" disable-calc="false">
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						<unitedValue>
							<ml:real>5075.5880281221434</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
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			<math optimize="false" disable-calc="false">
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								<ml:real>3</ml:real>
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						<ml:apply>
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								<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>
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							<ml:real>478808.96270527079</ml:real>
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								<unitReference unit="inch"/>
								<unitReference unit="pound_force"/>
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						</unitedValue>
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				<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"/>
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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>
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									<ml:real>2</ml:real>
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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/>
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										<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>
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					<f family="Arial" charset="0">
						<b>
							<inlineAttr line-through="false">Von Mises Stress calculation: </inlineAttr>
						</b>
					</f>
				</p>
			</text>
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										<ml:real>2</ml:real>
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										<ml:real>2</ml:real>
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									<ml:pow/>
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										<ml:apply>
											<ml:minus/>
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												<ml:id xml:space="preserve" subscript="3thick">σ</ml:id>
												<ml:id xml:space="preserve" subscript="thick">a</ml:id>
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											<ml:id xml:space="preserve" subscript="1thick">σ</ml:id>
										</ml:apply>
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									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:real>2</ml:real>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
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			<math optimize="false" disable-calc="false">
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							<ml:real>1</ml:real>
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							<ml:apply>
								<ml:plus/>
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										<ml:apply>
											<ml:plus/>
											<ml:real>1</ml:real>
											<ml:id xml:space="preserve">ν</ml:id>
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										<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
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											<ml:minus/>
											<ml:real>1</ml:real>
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									</ml:apply>
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			<math optimize="false" disable-calc="false">
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								<ml:div/>
								<ml:real>1</ml:real>
								<ml:real>2</ml:real>
							</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: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>
						</ml:parens>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="192"/>
		</region>
		<region region-id="10317" left="18" top="3429.6" width="129" height="23.4" align-x="82.2" align-y="3444" 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="vmthick">σa</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">ksi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>7.527372460684739</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="193"/>
		</region>
		<region region-id="11152" left="696" top="3459.6" width="108" height="23.4" align-x="752.4" align-y="3474" 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="endcap1">C</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>1.4919160781521361</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="194"/>
		</region>
		<region region-id="11153" left="858" top="3459.6" width="108" height="23.4" align-x="914.4" align-y="3474" 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="endcap1">C</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>1.4919160781521361</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="195"/>
		</region>
		<region region-id="11154" left="1014" top="3459.6" width="108" height="23.4" align-x="1070.4" align-y="3474" 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="endcap7">C</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>3.50870625</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="196"/>
		</region>
		<region region-id="10318" left="12" top="3476.4" width="642.6" height="55.2" align-x="78.6" align-y="3516" 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="vmthick">σb</ml:id>
					<ml:apply>
						<ml:sqrt/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:pow/>
										<ml:parens>
											<ml:apply>
												<ml:minus/>
												<ml:id xml:space="preserve" subscript="1thick">σ</ml:id>
												<ml:apply>
													<ml:id xml:space="preserve" subscript="2thick">σ</ml:id>
													<ml:id xml:space="preserve" subscript="thick">b</ml:id>
												</ml:apply>
											</ml:apply>
										</ml:parens>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:parens>
											<ml:apply>
												<ml:minus/>
												<ml:apply>
													<ml:id xml:space="preserve" subscript="2thick">σ</ml:id>
													<ml:id xml:space="preserve" subscript="thick">b</ml:id>
												</ml:apply>
												<ml:apply>
													<ml:id xml:space="preserve" subscript="3thick">σ</ml:id>
													<ml:id xml:space="preserve" subscript="thick">b</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">b</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="197"/>
		</region>
		<region region-id="11160" left="702" top="3517.2" width="438.6" height="55.8" align-x="759" align-y="3552" 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="endcap3">L</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve" subscript="0endcap">r</ml:id>
							<ml:apply>
								<ml:mult/>
								<ml:real>4</ml:real>
								<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
							</ml:apply>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:minus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:mult/>
										<ml:parens>
											<ml:apply>
												<ml:plus/>
												<ml:apply>
													<ml:pow/>
													<ml:parens>
														<ml:apply>
															<ml:div/>
															<ml:id xml:space="preserve" subscript="0endcap">r</ml:id>
															<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
														</ml:apply>
													</ml:parens>
													<ml:real>2</ml:real>
												</ml:apply>
												<ml:real>1</ml:real>
											</ml:apply>
										</ml:parens>
										<ml:apply>
											<ml:id xml:space="preserve">ln</ml:id>
											<ml:apply>
												<ml:div/>
												<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
												<ml:id xml:space="preserve" subscript="0endcap">r</ml:id>
											</ml:apply>
										</ml:apply>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:parens>
											<ml:apply>
												<ml:div/>
												<ml:id xml:space="preserve" subscript="0endcap">r</ml:id>
												<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
											</ml:apply>
										</ml:parens>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
								<ml:real>1</ml:real>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="198"/>
		</region>
		<region region-id="10319" left="18" top="3543.6" width="129.6" height="23.4" align-x="82.8" align-y="3558" 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="vmthick">σb</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">ksi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>8.7911763429958825</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="199"/>
		</region>
		<region region-id="10320" left="12" top="3585.6" width="231" height="23.4" align-x="70.8" align-y="3600" 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="vmthick">σ</ml:id>
					<ml:function>
						<ml:id xml:space="preserve">max</ml:id>
						<ml:boundVars>
							<ml:id xml:space="preserve" subscript="vmthick">σa</ml:id>
							<ml:id xml:space="preserve" subscript="vmthick">σb</ml:id>
						</ml:boundVars>
					</ml:function>
				</ml:globalDefine>
			</math>
			<rendering item-idref="200"/>
		</region>
		<region region-id="10321" left="258" top="3587.4" width="158.4" height="27.6" align-x="315" align-y="3606" 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="vmthick">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>8791.176342995881</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="201"/>
		</region>
		<region region-id="11161" left="702" top="3589.2" width="403.2" height="55.8" align-x="759" align-y="3624" 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="endcap9">L</ml:id>
					<ml:apply>
						<ml:mult style="auto-select"/>
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve" subscript="0endcap">r</ml:id>
							<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:div/>
										<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>
										<ml:id xml:space="preserve">ln</ml:id>
										<ml:apply>
											<ml:div/>
											<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
											<ml:id xml:space="preserve" subscript="0endcap">r</ml:id>
										</ml:apply>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:div/>
										<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:real>1</ml:real>
											<ml:apply>
												<ml:pow/>
												<ml:parens>
													<ml:apply>
														<ml:div/>
														<ml:id xml:space="preserve" subscript="0endcap">r</ml:id>
														<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
													</ml:apply>
												</ml:parens>
												<ml:real>2</ml:real>
											</ml:apply>
										</ml:apply>
									</ml:parens>
								</ml:apply>
							</ml:apply>
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					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="202"/>
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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 family="Arial" charset="0">
						<b>
							<inlineAttr line-through="false">Based on Von Mises stress<sp count="2"/>
							</inlineAttr>
						</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="11186" left="708" top="3661.2" width="604.2" height="55.8" align-x="770.4" align-y="3696" 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="endcap11">L</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:div/>
							<ml:real>1</ml:real>
							<ml:real>64</ml:real>
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						<ml:parens>
							<ml:apply>
								<ml:minus/>
								<ml:apply>
									<ml:minus/>
									<ml:apply>
										<ml:plus/>
										<ml:real>1</ml:real>
										<ml:apply>
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											<ml:real>4</ml:real>
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												<ml:pow/>
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													<ml:apply>
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														<ml:id xml:space="preserve" subscript="0endcap">r</ml:id>
														<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
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												<ml:real>2</ml:real>
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									</ml:apply>
									<ml:apply>
										<ml:mult/>
										<ml:real>5</ml:real>
										<ml:apply>
											<ml:pow/>
											<ml:parens>
												<ml:apply>
													<ml:div/>
													<ml:id xml:space="preserve" subscript="0endcap">r</ml:id>
													<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
												</ml:apply>
											</ml:parens>
											<ml:real>4</ml:real>
										</ml:apply>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:mult/>
										<ml:apply>
											<ml:mult/>
											<ml:real>4</ml:real>
											<ml:apply>
												<ml:pow/>
												<ml:parens>
													<ml:apply>
														<ml:div/>
														<ml:id xml:space="preserve" subscript="0endcap">r</ml:id>
														<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
													</ml:apply>
												</ml:parens>
												<ml:real>2</ml:real>
											</ml:apply>
										</ml:apply>
										<ml:parens>
											<ml:apply>
												<ml:plus/>
												<ml:real>2</ml:real>
												<ml:apply>
													<ml:pow/>
													<ml:parens>
														<ml:apply>
															<ml:div/>
															<ml:id xml:space="preserve" subscript="0endcap">r</ml:id>
															<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
														</ml:apply>
													</ml:parens>
													<ml:real>2</ml:real>
												</ml:apply>
											</ml:apply>
										</ml:parens>
									</ml:apply>
									<ml:apply>
										<ml:id xml:space="preserve">ln</ml:id>
										<ml:apply>
											<ml:div/>
											<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
											<ml:id xml:space="preserve" subscript="0endcap">r</ml:id>
										</ml:apply>
									</ml:apply>
								</ml:apply>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="203"/>
		</region>
		<region region-id="10323" left="18" top="3672.6" width="228.6" height="50.4" align-x="112.8" align-y="3702" 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="cythick">MSyield</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="vmthick">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="204"/>
		</region>
		<region region-id="10324" left="258" top="3693.6" width="144" height="23.4" align-x="350.4" align-y="3708" 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>2.4210652586768271</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="205"/>
		</region>
		<region region-id="10325" left="30" top="3740.4" width="200.4" height="12" align-x="30" align-y="3750" 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">Based on Max. shear stress theory 0.5*Sy</inlineAttr>
						</b>
					</f>
					<sp/>
				</p>
			</text>
		</region>
		<region region-id="11187" left="714" top="3733.2" width="382.8" height="55.8" align-x="776.4" align-y="3768" 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="endcap14">L</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:div/>
							<ml:real>1</ml:real>
							<ml:real>16</ml:real>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:minus/>
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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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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Inner radius:</p>
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									<ml:real>3</ml:real>
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					<ml:id xml:space="preserve" subscript="endcapa">θ</ml:id>
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						<ml:id xml:space="preserve">deg</ml:id>
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							<ml:real>0.54741428475511267</ml:real>
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								<unitReference unit="degree"/>
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			<pageBreak/>
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					<f size="12">
						<b>
							<u>1C Buckling calculation for cylinders:</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>
							<u>Table 35 Formulas for elastic stability of plates and shells</u>
						</b>
					</f>
				</p>
			</text>
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		<region region-id="11219" left="720" top="4148.4" width="200.4" 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>
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			<text use-page-width="false" push-down="false" lock-width="true">
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						<b>Case 20a</b>
					</f>
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		<region region-id="10392" left="120" top="4157.4" width="254.4" height="48.6" 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">
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						<b>Thin tube with closed ends under uniform external pressure, lateral and longitudinal; ends held circular</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="MS Sans Serif" charset="0">
						<b>Thin tube with closed ends under uniform external pressure, lateral and longitudinal</b>
					</f>
				</p>
			</text>
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								<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>
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						</ml:apply>
						<ml:id xml:space="preserve" subscript="endcap">b</ml:id>
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						<ml:id xml:space="preserve">lbf</ml:id>
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					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>4587.9900663379467</ml:real>
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								<unitReference unit="pound_force"/>
							</unitMonomial>
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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="endcap">σ</ml:id>
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						<ml:id xml:space="preserve">psi</ml:id>
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						<unitedValue>
							<ml:real>43012.406871918247</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
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			<math optimize="false" disable-calc="false">
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					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>4.1514999999999995</ml:real>
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						<ml:apply>
							<ml:mult/>
							<ml:real>6</ml:real>
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						</ml:apply>
						<ml:apply>
							<ml:pow/>
							<ml:id xml:space="preserve" subscript="endcap">t</ml:id>
							<ml:real>2</ml:real>
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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:plus/>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve">shellID</ml:id>
								<ml:real>2</ml:real>
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							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve">shellWallThickness</ml:id>
								<ml:real>2</ml:real>
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					<ml:id xml:space="preserve">L</ml:id>
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						<unitedValue>
							<ml:real>38</ml:real>
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								<unitReference unit="inch"/>
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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="endcap">MS</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>-0.30077877158833977</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">For the expressions in the case to be valid, the following condition must be true (i.e., condition = 1):</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">check small deflection assumption (deflection &lt; t/2)</p>
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						<ml:real>10</ml:real>
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						<ml:real>1</ml:real>
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							<ml:id xml:space="preserve" subscript="endcap">t</ml:id>
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						<ml:apply>
							<ml:div/>
							<ml:real font="0">1</ml:real>
							<ml:real>2</ml:real>
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			<math optimize="false" disable-calc="false">
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						<ml:id xml:space="preserve" subscript="endcap">t</ml:id>
					</ml:apply>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>0.034016402360228931</ml:real>
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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="endcap">smallDefTrue</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<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>
			</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">number of lobes:</p>
			</text>
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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>
												</ml:apply>
											</ml:apply>
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												<ml:apply>
													<ml:minus/>
													<ml:real>1</ml:real>
													<ml:apply>
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														<ml:real>2</ml:real>
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										</ml:apply>
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													</ml:parens>
													<ml:real>2</ml:real>
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										<ml:real>2</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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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="buckling">FOS</ml:id>
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						<ml:div/>
						<ml:id xml:space="preserve" subscript="critical">pBuckling</ml:id>
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						<ml:real>2.1701168563047148</ml:real>
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							<ml:real>153794.7389694177</ml:real>
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								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
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									<ml:id xml:space="preserve" subscript="bearing">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:define>
			</math>
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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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			<math optimize="false" disable-calc="false">
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						<ml:real>-0.73600199830325685</ml:real>
					</result>
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				<resultFormat numeric-only="true">
					<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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			<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">
					<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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			</picture>
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		<region region-id="12405" left="708" top="5018.4" width="163.8" height="12" align-x="708" align-y="5028" 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">
					<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>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">π</ml:id>
							<ml:parens>
								<ml:id xml:space="preserve">ecPlugOD</ml:id>
							</ml:parens>
						</ml:apply>
						<ml:id xml:space="preserve">ecTabThickness</ml:id>
					</ml:apply>
				</ml:define>
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			<math optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve">shearArea</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:pow/>
							<ml:id xml:space="preserve">in</ml:id>
							<ml:real>2</ml:real>
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						<unitedValue>
							<ml:real>4.5490261623980208</ml:real>
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								<unitReference unit="inch" power-numerator="2"/>
							</unitMonomial>
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					<ml:id xml:space="preserve">shearForce</ml:id>
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						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">q</ml:id>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve">π</ml:id>
								<ml:real>4</ml:real>
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						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve">bearingOD</ml:id>
								<ml:real>2</ml:real>
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						<ml:id xml:space="preserve">lbf</ml:id>
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							<ml:real>36676.586852043052</ml:real>
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								<unitReference unit="pound_force"/>
							</unitMonomial>
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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">shearForce</ml:id>
						<ml:id xml:space="preserve">shearArea</ml:id>
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						<unitedValue>
							<ml:real>8062.513940941808</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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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="shear">MS</ml:id>
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						<ml:real>1.7976870666729941</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>
				</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">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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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">t</ml:id>
					<ml:id xml:space="preserve">shellWallThickness</ml:id>
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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">The critical bending stress is defined by the equation below: </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">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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				<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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						<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>
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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>
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						<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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				<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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						<b>Annular plate with uniform annular line load w at radius r</b>
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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>
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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>
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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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			<math error="This variable is undefined." optimize="false" disable-calc="false">
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								<ml:real>3</ml:real>
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										<ml:pow/>
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			<math error="This variable is undefined." optimize="false" disable-calc="false">
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			<math optimize="false" disable-calc="false">
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									<ml:real>1</ml:real>
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								<ml:apply>
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									<ml:real>2</ml:real>
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									</ml:apply>
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									<ml:apply>
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											<ml:id xml:space="preserve">ν</ml:id>
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										<ml:real>2</ml:real>
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											<ml:minus/>
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											</ml:apply>
										</ml:apply>
									</ml:parens>
								</ml:apply>
							</ml:apply>
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			</math>
			<rendering item-idref="405"/>
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		<region region-id="9187" left="354" top="11580.6" width="303" height="50.4" align-x="410.4" 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">
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						<ml:apply>
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								</ml:apply>
								<ml:id xml:space="preserve" subscript="oring">a</ml:id>
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									</ml:apply>
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								</ml:apply>
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			</math>
			<rendering item-idref="406"/>
		</region>
		<region region-id="9188" left="354" top="11625.6" width="94.8" height="23.4" align-x="410.4" 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>
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						<ml:id xml:space="preserve">lbf</ml:id>
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				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
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						<ml:apply>
							<ml:div/>
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								<ml:apply>
									<ml:pow/>
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								<ml:mult/>
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			<math error="This variable is undefined." optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
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						<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>
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		</region>
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				</ml:globalDefine>
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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>
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									<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>
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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="415"/>
		</region>
		<region region-id="5685" left="36" top="11814" width="4797.6" 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/>
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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 size="12">
						<b>
							<u>E) WEIGHT &amp; DISPLACEMENT CHANGE CALCULATION:</u>
						</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="7109" left="6" top="11847" width="101.4" height="11.4" 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="11889" width="38.4" height="10.8" 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="11889" width="90.6" height="10.8" 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="11866.8" width="189.6" height="46.8" align-x="195.6" 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">
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					<ml:apply>
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						<ml:apply>
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							<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="416"/>
		</region>
		<region region-id="10962" left="492" top="11878.2" width="94.2" height="28.8" align-x="519.6" 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>8.3992553044874469</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="2"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="417"/>
		</region>
		<region region-id="10963" left="54" top="11931" width="67.8" height="10.8" 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="11908.8" width="326.4" height="46.8" align-x="193.8" 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="418"/>
		</region>
		<region region-id="10965" left="492" top="11920.2" width="127.8" height="28.8" align-x="517.8" 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>1876.012685418782</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="3"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="419"/>
		</region>
		<region region-id="10966" left="54" top="11973" width="70.8" height="10.8" 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="11950.8" width="190.8" height="46.8" align-x="196.2" 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">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="o">vc</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">shellOD</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:real>4</ml:real>
						</ml:apply>
						<ml:id xml:space="preserve">shellLength</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="420"/>
		</region>
		<region region-id="10968" left="492" top="11962.2" width="123" height="28.8" align-x="520.2" 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">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="o">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>2220.1978894615554</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="3"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="421"/>
		</region>
		<region region-id="10969" left="54" top="12009" width="30.6" height="10.8" 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="12003.6" width="165.6" height="23.4" align-x="203.4" 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="422"/>
		</region>
		<region region-id="10971" left="492" top="12003.6" width="106.8" height="23.4" align-x="527.4" 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>31.27882675391125</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="423"/>
		</region>
		<region region-id="7090" left="6" top="12051" width="40.8" height="10.8" 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="12051" width="33" height="10.8" 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="12069" width="18.6" height="10.8" 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="12046.8" width="204.6" height="46.8" align-x="217.2" 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>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="424"/>
		</region>
		<region region-id="7094" left="402" top="12058.2" width="105" height="28.8" align-x="433.2" 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">
					<ml:id xml:space="preserve" subscript="tab">v</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>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="425"/>
		</region>
		<region region-id="10940" left="102" top="12117" width="22.8" height="10.8" 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>
		</region>
		<region region-id="10770" left="192" top="12100.8" width="339" height="46.8" align-x="229.2" align-y="12132" 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="plug">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">ecPlugOD</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:real>4</ml:real>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:minus/>
								<ml:id xml:space="preserve">ecThickness</ml:id>
								<ml:id xml:space="preserve">ecTabThickness</ml:id>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="426"/>
		</region>
		<region region-id="10771" left="534" top="12118.2" width="111" height="28.8" align-x="571.2" align-y="12138" 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="plug">v</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>24.701212061821256</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="3"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="427"/>
		</region>
		<region region-id="10939" left="102" top="12159" width="20.4" height="10.8" 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>
			</text>
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		<region region-id="7099" left="192" top="12153.6" width="111.6" height="23.4" align-x="226.2" 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">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="cap">V</ml:id>
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						<ml:plus/>
						<ml:id xml:space="preserve" subscript="plug">v</ml:id>
						<ml:id xml:space="preserve" subscript="tab">v</ml:id>
					</ml:apply>
				</ml:globalDefine>
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		</region>
		<region region-id="7100" left="306" top="12148.2" width="108" height="28.8" align-x="340.2" 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">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="cap">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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					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>34.7543085533086</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="3"/>
							</unitMonomial>
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			</math>
			<rendering item-idref="429"/>
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		<region region-id="10938" left="102" top="12189" width="33.6" height="10.8" align-x="102" align-y="12198" 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>
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			<math optimize="false" disable-calc="false">
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						<ml:id xml:space="preserve" subscript="m">ρ</ml:id>
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		<region region-id="7103" left="306" top="12189.6" width="102" height="23.4" align-x="343.8" align-y="12204" 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="cap">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>3.405922238224242</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
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			</math>
			<rendering item-idref="431"/>
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		<region region-id="7104" left="6" top="12231" width="57.6" height="10.8" 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>
			</text>
		</region>
		<region region-id="7291" left="192" top="12225.6" width="136.2" height="23.4" align-x="238.8" 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:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<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>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="432"/>
		</region>
		<region region-id="7293" left="498" top="12225.6" width="118.2" height="23.4" align-x="544.8" 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">
					<ml:id xml:space="preserve" subscript="dry">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>38.090671230359739</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="433"/>
		</region>
		<region region-id="7292" left="192" top="12249.6" width="220.2" height="23.4" align-x="240" 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>
					<ml:apply>
						<ml:minus/>
						<ml:id xml:space="preserve" subscript="dry">Wp</ml:id>
						<ml:apply>
							<ml:mult/>
							<ml:parens>
								<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>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="434"/>
		</region>
		<region region-id="7294" left="498" top="12249.6" width="120" height="23.4" align-x="546" 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: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>-44.949787638735138</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
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			</math>
			<rendering item-idref="435"/>
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