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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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						<b>Misc. stuff</b>
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						<b>A) Environmental Conditions:</b>
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					<ml:id xml:space="preserve">depth</ml:id>
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						<ml:real>350</ml:real>
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						<b>Water density:</b>
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								<ml:real>3</ml:real>
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							<ml:real>510.76025815866353</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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								<c val="#000">Material: 6061-T6 Aluminum</c>
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						<b>Modulus of elasticity:</b>
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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:mult/>
						<ml:real>40.0</ml:real>
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						<b>Shear stress:</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">Shear modulus:</p>
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				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
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					<f family="Calibri" charset="0" size="14">
						<b>Bearing stress:</b>
					</f>
				</p>
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			<math optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve" subscript="b">S</ml:id>
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						<ml:mult/>
						<ml:real>54000.</ml:real>
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			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="Calibri" charset="0" size="16">
						<b>
							<inlineAttr underline="false" line-through="false">C) Factors of safety:</inlineAttr>
						</b>
					</f>
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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="13019" left="372" top="363.75" width="68.25" height="19.5" align-x="406.5" align-y="378" 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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			<rendering item-idref="17"/>
		</region>
		<region region-id="13014" left="48" top="396" width="437.25" height="15.75" align-x="48" align-y="396" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="18" display-width="435.75" display-height="14.25"/>
			</picture>
			<rendering item-idref="19"/>
		</region>
		<region region-id="10565" left="0" top="468" width="6000" height="6" align-x="0" align-y="468" 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="481.5" width="244.5" height="29.25" align-x="257.25" align-y="504" 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="481.5" width="295.5" height="29.25" align-x="894" align-y="504" 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>
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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="24">
						<b>3) End Cap &amp; O-ring Tab Calculations</b>
					</f>
				</p>
			</text>
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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="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="533.25" width="95.25" height="16.5" align-x="44.25" align-y="546" 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>
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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 shear stress</p>
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			<picture>
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		<region region-id="11423" left="690" top="561.75" width="145.5" height="19.5" align-x="791.25" align-y="576" 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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			</math>
			<rendering item-idref="22"/>
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			<picture>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ecOD</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>8.0</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">shellLength</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>3.864</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
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			<picture>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
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						<ml:mult/>
						<ml:real>0.80</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellID</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>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>8.381</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
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			</math>
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			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">End cap tab</p>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">bearing stress</p>
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			<picture>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ecGrooveWidth</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.1</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ecHoleDiameter</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>1.0</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellBaseThickness</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.5</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
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			</math>
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		<region region-id="12791" left="1200" top="746.25" width="103.5" height="12" align-x="1221" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
				<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>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ecGrooveDepth</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.1</ml:real>
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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>0.20000000000000007</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
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						</unitedValue>
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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"/>
		</region>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellWallThickness</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:minus/>
							<ml:id xml:space="preserve">shellOD</ml:id>
							<ml:id xml:space="preserve">shellID</ml:id>
						</ml:apply>
						<ml:real>2</ml:real>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="43"/>
		</region>
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			<picture>
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			</picture>
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			<picture>
				<png item-idref="46" display-width="435.75" display-height="14.25"/>
			</picture>
			<rendering item-idref="47"/>
		</region>
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			<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="911.25" width="292.5" height="24" align-x="897" align-y="930" 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="935.25" width="241.5" height="16.5" align-x="712.5" align-y="948" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
				<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="941.25" width="252.75" height="16.5" align-x="30" align-y="954" 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="974.25" width="78.75" height="24" align-x="34.5" align-y="984" 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>
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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>9.04678211603904</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
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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="cythin">MS</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>2.3244072405153329</ml:real>
					</result>
				</ml:eval>
			</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">thinWall</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>1</ml:real>
					</result>
				</ml:eval>
			</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="cythin">FOS</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>4.4214616298853926</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="51"/>
		</region>
		<region region-id="11301" left="804" top="969.75" width="106.5" height="22.5" align-x="841.5" align-y="984" 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>40.626295272924132</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="52"/>
		</region>
		<region region-id="11302" left="990" top="969.75" width="99.75" height="22.5" align-x="1039.5" align-y="984" 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>-0.25971128384012987</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="53"/>
		</region>
		<region region-id="11303" left="1128" top="969.75" width="103.5" height="22.5" align-x="1179" align-y="984" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:id xml:space="preserve" subscript="base" xmlns:ml="http://schemas.mathsoft.com/math30">smallDefTrue</ml:id>
			</math>
			<rendering item-idref="54"/>
		</region>
		<region region-id="12765" left="30" top="1019.25" width="252.75" height="16.5" align-x="30" 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="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="1025.25" width="229.5" height="16.5" align-x="714" align-y="1038" 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>
		<region region-id="12761" left="2088" top="1047.75" width="184.5" height="22.5" align-x="2211" align-y="1062" 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>7.951569951988783</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="1047.75" width="180" height="22.5" align-x="2440.5" align-y="1062" 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>7.6522205384585282</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
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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="vmthick">σ</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">ksi</ml:id>
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					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>9.49452028769246</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
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					</result>
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			</math>
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		<region region-id="12825" left="186" top="1053.75" width="141.75" height="22.5" align-x="278.25" align-y="1068" 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>2.1676363901092115</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="58"/>
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		<region region-id="12826" left="348" top="1053.75" width="144.75" height="22.5" align-x="443.25" align-y="1068" 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>1.7432535837866112</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="59"/>
		</region>
		<region region-id="11310" left="774" top="1059.75" width="119.25" height="22.5" align-x="824.25" align-y="1074" 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>30.108684810342787</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="60"/>
		</region>
		<region region-id="11311" left="948" top="1056" width="162.75" height="26.25" align-x="1010.25" align-y="1074" 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>-0.0011125308404859036</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="61"/>
		</region>
		<region region-id="13023" left="1128" top="1059.75" width="149.25" height="22.5" align-x="1251.75" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="endcap">smallDefTrue</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>1</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="62"/>
		</region>
		<region region-id="12772" left="24" top="1097.25" width="252.75" height="16.5" align-x="24" align-y="1110" 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>
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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>-0.76772820747869475</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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			<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>-0.65810491184068132</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
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			</math>
			<rendering item-idref="64"/>
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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>4929.9070616911958</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="65"/>
		</region>
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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="buckling">MS</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>3.8260480166017148</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="66"/>
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		<region region-id="12813" left="444" top="1131.75" width="126" height="22.5" align-x="520.5" align-y="1146" 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>9.65209603320343</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="67"/>
		</region>
		<region region-id="10458" left="84" top="1188" width="437.25" height="15.75" align-x="84" align-y="1188" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
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			</picture>
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			<picture>
				<png item-idref="70" display-width="435.75" display-height="14.25"/>
			</picture>
			<rendering item-idref="71"/>
		</region>
		<region region-id="12759" left="2112" top="1212" width="437.25" height="15.75" align-x="2112" align-y="1212" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="72" display-width="435.75" display-height="14.25"/>
			</picture>
			<rendering item-idref="73"/>
		</region>
		<region region-id="12775" left="0" top="1242" width="6000" height="6" align-x="0" align-y="1242" 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="1254.75" width="261" height="14.25" align-x="684" 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">
					<f size="12">
						<b>PRESS. CASE BASE (No Connector)</b>
					</f>
					<sp count="2"/>
				</p>
			</text>
		</region>
		<region region-id="11442" left="996" top="1253.25" width="280.5" height="51" align-x="996" 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="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="1263.75" width="648" height="34.5" align-x="18" align-y="1278" 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>
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			<picture>
				<png item-idref="74" display-width="270.75" display-height="102.75"/>
			</picture>
			<rendering item-idref="75"/>
		</region>
		<region region-id="10336" left="24" top="1320" width="114" height="101.25" align-x="24" align-y="1320" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="76" display-width="112.5" display-height="99.75"/>
			</picture>
			<rendering item-idref="77"/>
		</region>
		<region region-id="10798" left="1026" top="1326" width="127.5" height="69" align-x="1026" align-y="1326" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="78" display-width="126" display-height="67.5"/>
			</picture>
			<rendering item-idref="79"/>
		</region>
		<region region-id="10337" left="156" top="1337.25" width="99.75" height="16.5" align-x="156" align-y="1350" 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="1324.5" width="243.75" height="40.5" align-x="284.25" align-y="1350" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="thin">R</ml:id>
					<ml:parens>
						<ml:apply>
							<ml:plus/>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve">shellID</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve">shellWallThickness</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
						</ml:apply>
					</ml:parens>
				</ml:globalDefine>
			</math>
			<rendering item-idref="80"/>
		</region>
		<region region-id="11294" left="540" top="1335.75" width="96" height="22.5" align-x="578.25" align-y="1350" 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>4.0905000000000005</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="81"/>
		</region>
		<region region-id="10340" left="150" top="1379.25" width="93" height="16.5" align-x="150" align-y="1392" 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="1377.75" width="94.5" height="19.5" align-x="261.75" align-y="1392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">y</ml:id>
					<ml:id xml:space="preserve">shellLength</ml:id>
				</ml:globalDefine>
			</math>
			<rendering item-idref="82"/>
		</region>
		<region region-id="10342" left="360" top="1377.75" width="73.5" height="19.5" align-x="375.75" align-y="1392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml: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>3.8640000000000003</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="83"/>
		</region>
		<region region-id="10343" left="54" top="1418.25" width="58.5" height="12" align-x="54" align-y="1428" 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="1415.25" width="434.25" height="33" align-x="150" align-y="1428" 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="1431.75" width="154.5" height="22.5" align-x="735" align-y="1446" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="base">t</ml:id>
					<ml:id xml:space="preserve">shellBaseThickness</ml:id>
				</ml:globalDefine>
			</math>
			<rendering item-idref="84"/>
		</region>
		<region region-id="10802" left="906" top="1431.75" width="77.25" height="22.5" align-x="939" align-y="1446" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="base">t</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>0.5</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="85"/>
		</region>
		<region region-id="10803" left="1014" top="1431.75" width="110.25" height="22.5" align-x="1049.25" align-y="1446" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="base">a</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.5</ml:real>
						<ml:id xml:space="preserve">shellID</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="86"/>
		</region>
		<region region-id="10805" left="1182" top="1431.75" width="86.25" height="22.5" align-x="1217.25" align-y="1446" 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="87"/>
		</region>
		<region region-id="12721" left="2022" top="1448.25" width="38.25" height="12" align-x="2022" 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="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="1459.5" width="234" height="45" align-x="144.75" align-y="1488" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">thinWall</ml:id>
					<ml:parens>
						<ml:apply>
							<ml:greaterThan/>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve" subscript="thin">R</ml:id>
								<ml:id xml:space="preserve">shellWallThickness</ml:id>
							</ml:apply>
							<ml:real>10</ml:real>
						</ml:apply>
					</ml:parens>
				</ml:globalDefine>
			</math>
			<rendering item-idref="88"/>
		</region>
		<region region-id="11295" left="354" top="1459.5" width="182.25" height="45" align-x="480" align-y="1488" 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>20.452499999999993</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="89"/>
		</region>
		<region region-id="10347" left="522" top="1473.75" width="86.25" height="19.5" align-x="582.75" align-y="1488" 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="90"/>
		</region>
		<region region-id="12722" left="2046" top="1457.25" width="267" height="45.75" align-x="2152.5" align-y="1488" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">crossSectionArea</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">π</ml:id>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">shellOD</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">shellID</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
						<ml:real>4</ml:real>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="91"/>
		</region>
		<region region-id="12723" left="2454" top="1468.5" width="164.25" height="24.75" align-x="2560.5" align-y="1488" 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>5.1402738998036135</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="2"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="92"/>
		</region>
		<region region-id="10826" left="702" top="1484.25" width="67.5" height="12" align-x="702" align-y="1494" 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="1466.25" width="120.75" height="55.5" align-x="825.75" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="base">D</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">E</ml:id>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve" subscript="base">t</ml:id>
								<ml:real>3</ml:real>
							</ml:apply>
						</ml:apply>
						<ml:apply>
							<ml:mult/>
							<ml:real>12</ml:real>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:real>1</ml:real>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">ν</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="93"/>
		</region>
		<region region-id="10935" left="930" top="1488" width="153" height="26.25" align-x="969.75" align-y="1506" 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="94"/>
		</region>
		<region region-id="10936" left="1128" top="1480.5" width="75" height="40.5" align-x="1158" align-y="1506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="17">G</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:plus/>
							<ml:real>3</ml:real>
							<ml:id xml:space="preserve">ν</ml:id>
						</ml:apply>
						<ml:real>16</ml:real>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="95"/>
		</region>
		<region region-id="10937" left="1236" top="1491.75" width="79.5" height="22.5" align-x="1266" align-y="1506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="17">G</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>0.208125</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="96"/>
		</region>
		<region region-id="12724" left="2046" top="1499.25" width="394.5" height="45.75" align-x="2148.75" align-y="1530" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">internalVolume</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">π</ml:id>
							<ml:apply>
								<ml:div/>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellID</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
								<ml:real>4</ml:real>
							</ml:apply>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:minus/>
								<ml:id xml:space="preserve">shellLength</ml:id>
								<ml:id xml:space="preserve">shellBaseThickness</ml:id>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="97"/>
		</region>
		<region region-id="12725" left="2454" top="1510.5" width="179.25" height="24.75" align-x="2555.25" align-y="1530" 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>168.29084463330085</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="3"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="98"/>
		</region>
		<region region-id="9798" left="198" top="1519.5" width="182.25" height="45" align-x="240.75" align-y="1548" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="1thin">σ</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">q</ml:id>
							<ml:id xml:space="preserve" subscript="thin">R</ml:id>
						</ml:apply>
						<ml:apply>
							<ml:mult/>
							<ml:real>2</ml:real>
							<ml:id xml:space="preserve">shellWallThickness</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="99"/>
		</region>
		<region region-id="9800" left="36" top="1541.25" width="162.75" height="16.5" align-x="36" align-y="1554" 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="1539.75" width="105" height="22.5" align-x="456.75" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="1thin">σ</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">ksi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>5.2231620899950322</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="100"/>
		</region>
		<region region-id="10892" left="690" top="1520.25" width="159" height="48.75" align-x="741.75" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="c_base">M</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:mult/>
								<ml:id xml:space="preserve">q</ml:id>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve" subscript="base">a</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:plus/>
									<ml:real>3</ml:real>
									<ml:id xml:space="preserve">ν</ml:id>
								</ml:apply>
							</ml:parens>
						</ml:apply>
						<ml:real>16</ml:real>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="101"/>
		</region>
		<region region-id="10893" left="858" top="1528.5" width="169.5" height="42" align-x="909.75" align-y="1554" 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>1692.7623030385053</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="0"/>
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="102"/>
		</region>
		<region region-id="11261" left="1050" top="1525.5" width="107.25" height="53.25" align-x="1087.5" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="base">σ</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>6</ml:real>
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve" subscript="c_base">M</ml:id>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve" subscript="base">t</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="103"/>
		</region>
		<region region-id="11262" left="1170" top="1528.5" width="141" height="47.25" align-x="1207.5" align-y="1554" 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>40626.29527292413</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="-2"/>
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="104"/>
		</region>
		<region region-id="12726" left="2046" top="1551.75" width="282" height="22.5" align-x="2124" align-y="1566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellWeight</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">crossSectionArea</ml:id>
							<ml:id xml:space="preserve">shellLength</ml:id>
						</ml:apply>
						<ml:id xml:space="preserve" subscript="m">ρ</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="105"/>
		</region>
		<region region-id="12727" left="2454" top="1551.75" width="139.5" height="19.5" align-x="2532" align-y="1566" 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>1.9464777981864341</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="106"/>
		</region>
		<region region-id="9801" left="36" top="1583.25" width="207.75" height="16.5" align-x="36" align-y="1596" 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="1567.5" width="170.25" height="45" align-x="258.75" align-y="1596" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="2thin">σ</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">q</ml:id>
							<ml:id xml:space="preserve" subscript="thin">R</ml:id>
						</ml:apply>
						<ml:id xml:space="preserve">shellWallThickness</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="107"/>
		</region>
		<region region-id="9803" left="408" top="1581.75" width="111.75" height="22.5" align-x="450.75" align-y="1596" 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>10.446324179990064</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="108"/>
		</region>
		<region region-id="12728" left="2046" top="1576.5" width="327.75" height="40.5" align-x="2150.25" align-y="1602" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">shellBaseWeight</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:div/>
									<ml:id xml:space="preserve">π</ml:id>
									<ml:real>4</ml:real>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellOD</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve">shellBaseThickness</ml:id>
						</ml:apply>
						<ml:id xml:space="preserve" subscript="m">ρ</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="109"/>
		</region>
		<region region-id="12729" left="2454" top="1582.5" width="214.5" height="24.75" align-x="2558.25" align-y="1602" 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>86.9727807048767</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="foot"/>
								<unitReference unit="pound"/>
								<unitReference unit="second" power-numerator="-2"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="110"/>
		</region>
		<region region-id="10896" left="702" top="1591.5" width="162" height="48" align-x="751.5" align-y="1620" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="base">MS</ml:id>
					<ml:parens>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve" subscript="y">S</ml:id>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve" subscript="base">σ</ml:id>
									<ml:id xml:space="preserve">FofS</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:real>1</ml:real>
						</ml:apply>
					</ml:parens>
				</ml:globalDefine>
			</math>
			<rendering item-idref="111"/>
		</region>
		<region region-id="10897" left="942" top="1605.75" width="99.75" height="22.5" align-x="991.5" align-y="1620" 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>-0.25971128384012987</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="112"/>
		</region>
		<region region-id="9373" left="54" top="1646.25" width="130.5" height="12" align-x="54" align-y="1656" 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="1632" width="264" height="32.25" align-x="262.5" align-y="1656" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="vmthin">σ</ml:id>
					<ml:apply>
						<ml:sqrt/>
						<ml:apply>
							<ml:plus/>
							<ml:apply>
								<ml:minus/>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve" subscript="1thin">σ</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve" subscript="1thin">σ</ml:id>
									<ml:id xml:space="preserve" subscript="2thin">σ</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve" subscript="2thin">σ</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="113"/>
		</region>
		<region region-id="9806" left="510" top="1641.75" width="114.75" height="22.5" align-x="562.5" align-y="1656" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="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>9.04678211603904</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="114"/>
		</region>
		<region region-id="10900" left="690" top="1646.25" width="102.75" height="12" align-x="699" align-y="1656" 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="1646.25" width="40.5" height="12" align-x="2016" align-y="1656" 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="1630.5" width="567" height="40.5" align-x="2173.5" align-y="1656" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ecWeightTemp</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:mult style="auto-select"/>
							<ml:id xml:space="preserve" subscript="m">ρ</ml:id>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve">π</ml:id>
								<ml:real>4</ml:real>
							</ml:apply>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:plus/>
								<ml:parens>
									<ml:apply>
										<ml:mult/>
										<ml:apply>
											<ml:pow/>
											<ml:id xml:space="preserve">ecPlugOD</ml:id>
											<ml:real>2</ml:real>
										</ml:apply>
										<ml:id xml:space="preserve">ecThickness</ml:id>
									</ml:apply>
								</ml:parens>
								<ml:parens>
									<ml:apply>
										<ml:mult/>
										<ml:parens>
											<ml:apply>
												<ml:minus/>
												<ml:apply>
													<ml:pow/>
													<ml:id xml:space="preserve">ecOD</ml:id>
													<ml:real>2</ml:real>
												</ml:apply>
												<ml:apply>
													<ml:pow/>
													<ml:id xml:space="preserve">ecPlugOD</ml:id>
													<ml:real>2</ml:real>
												</ml:apply>
											</ml:apply>
										</ml:parens>
										<ml:id xml:space="preserve">ecTabThickness</ml:id>
									</ml:apply>
								</ml:parens>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="115"/>
		</region>
		<region region-id="11266" left="708" top="1657.5" width="111.75" height="43.5" align-x="758.25" align-y="1686" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="a_base">Q</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:neg/>
								<ml:id xml:space="preserve">q</ml:id>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="base">a</ml:id>
						</ml:apply>
						<ml:real>2</ml:real>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="116"/>
		</region>
		<region region-id="10899" left="846" top="1660.5" width="158.25" height="42" align-x="896.25" align-y="1686" 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>-1019.0944050910733</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="-1"/>
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="117"/>
		</region>
		<region region-id="12732" left="2076" top="1672.5" width="518.25" height="40.5" align-x="2138.25" align-y="1698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">ecWeight</ml:id>
					<ml:apply>
						<ml:minus/>
						<ml:id xml:space="preserve">ecWeightTemp</ml:id>
						<ml:parens>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:mult/>
										<ml:id xml:space="preserve" subscript="m">ρ</ml:id>
										<ml:apply>
											<ml:div/>
											<ml:id xml:space="preserve">π</ml:id>
											<ml:real>4</ml:real>
										</ml:apply>
									</ml:apply>
									<ml:parens>
										<ml:apply>
											<ml:minus/>
											<ml:apply>
												<ml:pow/>
												<ml:id xml:space="preserve">ecPlugOD</ml:id>
												<ml:real>2</ml:real>
											</ml:apply>
											<ml:apply>
												<ml:pow/>
												<ml:id xml:space="preserve">ecGrooveDepth</ml:id>
												<ml:real>2</ml:real>
											</ml:apply>
										</ml:apply>
									</ml:parens>
								</ml:apply>
								<ml:id xml:space="preserve">ecGrooveWidth</ml:id>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="118"/>
		</region>
		<region region-id="9828" left="54" top="1694.25" width="142.5" height="12" align-x="54" align-y="1704" 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="12816" left="138" top="1681.5" width="244.5" height="48" align-x="198" align-y="1710" 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:eval placeholderMultiplicationStyle="default">
						<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>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<ml:real>2.3244072405153329</ml:real>
						</result>
					</ml:eval>
				</ml:globalDefine>
			</math>
			<rendering item-idref="119"/>
		</region>
		<region region-id="12818" left="408" top="1681.5" width="180.75" height="48" align-x="473.25" align-y="1710" 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">FOS</ml:id>
					<ml:eval placeholderMultiplicationStyle="default">
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve" subscript="y">S</ml:id>
							<ml:id xml:space="preserve" subscript="vmthin">σ</ml:id>
						</ml:apply>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<ml:real>4.4214616298853926</ml:real>
						</result>
					</ml:eval>
				</ml:globalDefine>
			</math>
			<rendering item-idref="120"/>
		</region>
		<region region-id="12733" left="2076" top="1725.75" width="123.75" height="19.5" align-x="2138.25" align-y="1740" 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="121"/>
		</region>
		<region region-id="10234" left="42" top="1778.25" width="75.75" height="12" align-x="42" 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">Change in height:</p>
			</text>
		</region>
		<region region-id="10235" left="120" top="1759.5" width="245.25" height="45" align-x="167.25" align-y="1788" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="thin">Δy</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve">q</ml:id>
									<ml:id xml:space="preserve" subscript="thin">R</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve">y</ml:id>
							</ml:apply>
							<ml:apply>
								<ml:mult/>
								<ml:id xml:space="preserve">E</ml:id>
								<ml:id xml:space="preserve">shellWallThickness</ml:id>
							</ml:apply>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:minus/>
								<ml:real>0.5</ml:real>
								<ml:id xml:space="preserve">ν</ml:id>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="122"/>
		</region>
		<region region-id="12734" left="2028" top="1773.75" width="284.25" height="22.5" align-x="2151" align-y="1788" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="2endCaps">totalWeight</ml:id>
					<ml:apply>
						<ml:plus/>
						<ml:id xml:space="preserve">shellWeight</ml:id>
						<ml:apply>
							<ml:mult/>
							<ml:real>2</ml:real>
							<ml:id xml:space="preserve">ecWeight</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="123"/>
		</region>
		<region region-id="12735" left="2424" top="1773.75" width="184.5" height="22.5" align-x="2547" align-y="1788" 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>7.951569951988783</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="124"/>
		</region>
		<region region-id="10236" left="390" top="1776" width="148.5" height="26.25" align-x="437.25" align-y="1794" 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>0.00068619814273518712</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="125"/>
		</region>
		<region region-id="10901" left="696" top="1772.25" width="180" height="53.25" align-x="767.25" align-y="1806" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="base">ycenter</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:neg/>
									<ml:id xml:space="preserve">q</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve" subscript="base">a</ml:id>
									<ml:real>4</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:apply>
								<ml:mult/>
								<ml:real>64</ml:real>
								<ml:id xml:space="preserve" subscript="base">D</ml:id>
							</ml:apply>
						</ml:apply>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:plus/>
								<ml:real>5</ml:real>
								<ml:id xml:space="preserve">ν</ml:id>
							</ml:apply>
							<ml:apply>
								<ml:plus/>
								<ml:real>1</ml:real>
								<ml:id xml:space="preserve">ν</ml:id>
							</ml:apply>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="126"/>
		</region>
		<region region-id="10902" left="906" top="1791.75" width="136.5" height="22.5" align-x="977.25" align-y="1806" 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>-0.0693776570425018</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="127"/>
		</region>
		<region region-id="12736" left="2028" top="1803.75" width="379.5" height="22.5" align-x="2146.5" align-y="1818" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="1endCap">totalWeight</ml:id>
					<ml:apply>
						<ml:plus/>
						<ml:apply>
							<ml:plus/>
							<ml:id xml:space="preserve">shellWeight</ml:id>
							<ml:id xml:space="preserve">shellBaseWeight</ml:id>
						</ml:apply>
						<ml:id xml:space="preserve">ecWeight</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="128"/>
		</region>
		<region region-id="12737" left="2430" top="1803.75" width="180" height="22.5" align-x="2548.5" align-y="1818" 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>7.6522205384585282</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="129"/>
		</region>
		<region region-id="10237" left="42" top="1832.25" width="90.75" height="24" align-x="42" align-y="1842" 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="1820.25" width="245.25" height="50.25" align-x="204.75" align-y="1854" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="max">ΔR</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:id xml:space="preserve">q</ml:id>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve" subscript="thin">R</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:apply>
								<ml:mult/>
								<ml:id xml:space="preserve">E</ml:id>
								<ml:id xml:space="preserve">shellWallThickness</ml:id>
							</ml:apply>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:minus/>
								<ml:real>1</ml:real>
								<ml:apply>
									<ml:div/>
									<ml:id xml:space="preserve">ν</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="130"/>
		</region>
		<region region-id="10239" left="414" top="1836" width="150" height="26.25" align-x="462.75" align-y="1854" 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>0.0035680125363638203</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="131"/>
		</region>
		<region region-id="10903" left="696" top="1850.25" width="417.75" height="12" align-x="705.75" 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">check small deflection assumption (deflection &lt; t/2)</p>
			</text>
		</region>
		<region region-id="12738" left="2028" top="1840.5" width="562.5" height="40.5" align-x="2146.5" align-y="1866" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="2endCaps">wetWeight</ml:id>
					<ml:apply>
						<ml:minus/>
						<ml:id xml:space="preserve" subscript="2endCaps">totalWeight</ml:id>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:mult style="auto-select"/>
									<ml:id xml:space="preserve" subscript="sw">ρ</ml:id>
									<ml:apply>
										<ml:div/>
										<ml:id xml:space="preserve">π</ml:id>
										<ml:real>4</ml:real>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellOD</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve">shellLength</ml:id>
									<ml:apply>
										<ml:mult/>
										<ml:real>2</ml:real>
										<ml:id xml:space="preserve">ecTabThickness</ml:id>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="132"/>
		</region>
		<region region-id="10253" left="24" top="1880.25" width="611.25" height="12" align-x="24" align-y="1890" 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="1876.5" width="541.5" height="40.5" align-x="2142" 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" subscript="1endCap">wetWeight</ml:id>
					<ml:apply>
						<ml:minus/>
						<ml:id xml:space="preserve" subscript="1endCap">totalWeight</ml:id>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:mult style="auto-select"/>
									<ml:id xml:space="preserve" subscript="sw">ρ</ml:id>
									<ml:apply>
										<ml:div/>
										<ml:id xml:space="preserve">π</ml:id>
										<ml:real>4</ml:real>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">shellOD</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve">shellLength</ml:id>
									<ml:id xml:space="preserve">ecTabThickness</ml:id>
								</ml:apply>
							</ml:parens>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="133"/>
		</region>
		<region region-id="10276" left="222" top="1882.5" width="103.5" height="45" align-x="258.75" align-y="1908" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="step">P</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:id xml:space="preserve">q</ml:id>
						<ml:id xml:space="preserve" subscript="pressure">N</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="134"/>
		</region>
		<region region-id="10277" left="360" top="1893.75" width="104.25" height="22.5" align-x="395.25" align-y="1908" 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>51.076025815866352</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="135"/>
		</region>
		<region region-id="10909" left="708" top="1879.5" width="246.75" height="48" align-x="820.5" align-y="1908" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="base">smallDefTrue</ml:id>
					<ml:parens>
						<ml:apply>
							<ml:lessThan/>
							<ml:apply>
								<ml:div/>
								<ml:apply>
									<ml:absval/>
									<ml:id xml:space="preserve" subscript="base">ycenter</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="base">t</ml:id>
							</ml:apply>
							<ml:apply>
								<ml:div/>
								<ml:real font="0">1</ml:real>
								<ml:real>2</ml:real>
							</ml:apply>
						</ml:apply>
					</ml:parens>
				</ml:define>
			</math>
			<rendering item-idref="136"/>
		</region>
		<region region-id="11246" left="972" top="1879.5" width="137.25" height="48" align-x="1059.75" align-y="1908" 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>0.13875531408500361</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="137"/>
		</region>
		<region region-id="11247" left="1146" top="1893.75" width="136.5" height="22.5" align-x="1257" align-y="1908" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="base">smallDefTrue</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>1</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="138"/>
		</region>
		<region region-id="12740" left="2034" top="1923.75" width="187.5" height="22.5" align-x="2152.5" align-y="1938" 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>-0.76772820747869475</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="139"/>
		</region>
		<region region-id="12741" left="2268" top="1923.75" width="183" height="22.5" align-x="2382" align-y="1938" 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>-0.65810491184068132</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="140"/>
		</region>
		<region region-id="10278" left="24" top="1924.5" width="309.75" height="45" align-x="32.25" align-y="1950" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:apply xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">if</ml:id>
					<ml:define>
						<ml:define>
							<ml:sequence>
								<ml:apply>
									<ml:greaterThan/>
									<ml:id xml:space="preserve">q</ml:id>
									<ml:apply>
										<ml:mult/>
										<ml:real>1500</ml:real>
										<ml:id xml:space="preserve">psi</ml:id>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:indexer/>
									<ml:id xml:space="preserve">P</ml:id>
									<ml:id xml:space="preserve">step</ml:id>
								</ml:apply>
							</ml:sequence>
							<ml:sequence>
								<ml:apply>
									<ml:mult/>
									<ml:real>200</ml:real>
									<ml:id xml:space="preserve">psi</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:indexer/>
									<ml:id xml:space="preserve">P</ml:id>
									<ml:id xml:space="preserve">step</ml:id>
								</ml:apply>
							</ml:sequence>
						</ml:define>
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve">q</ml:id>
							<ml:id xml:space="preserve" subscript="pressure">N</ml:id>
						</ml:apply>
					</ml:define>
				</ml:apply>
			</math>
			<rendering item-idref="141"/>
		</region>
		<region region-id="10279" left="360" top="1935.75" width="58.5" height="19.5" align-x="374.25" align-y="1950" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">j</ml:id>
					<ml:range>
						<ml:real>0</ml:real>
						<ml:real>10</ml:real>
					</ml:range>
				</ml:define>
			</math>
			<rendering item-idref="142"/>
		</region>
		<region region-id="10281" left="456" top="1935.75" width="69.75" height="22.5" align-x="477.75" align-y="1950" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:apply>
						<ml:indexer/>
						<ml:id xml:space="preserve">P</ml:id>
						<ml:id xml:space="preserve">j</ml:id>
					</ml:apply>
					<ml:apply>
						<ml:mult/>
						<ml:id xml:space="preserve">j</ml:id>
						<ml:id xml:space="preserve" subscript="step">P</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="143"/>
		</region>
		<region region-id="12745" left="2148" top="1968" width="437.25" height="15.75" align-x="2148" align-y="1968" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="144" display-width="435.75" display-height="14.25"/>
			</picture>
			<rendering item-idref="145"/>
		</region>
		<region region-id="11031" left="702" top="1998" width="437.25" height="15.75" align-x="702" align-y="1998" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="146" display-width="435.75" display-height="14.25"/>
			</picture>
			<rendering item-idref="147"/>
		</region>
		<region region-id="10270" left="12" top="1994.25" width="95.25" height="12" align-x="12" 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">Extrusion gap (radial):</p>
			</text>
		</region>
		<region region-id="10282" left="138" top="1982.25" width="242.25" height="50.25" align-x="171.75" align-y="2016" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:apply>
						<ml:indexer/>
						<ml:id xml:space="preserve">ΔR</ml:id>
						<ml:id xml:space="preserve">j</ml:id>
					</ml:apply>
					<ml:parens>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:div/>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:indexer/>
										<ml:id xml:space="preserve">P</ml:id>
										<ml:id xml:space="preserve">j</ml:id>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve" subscript="thin">R</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve">E</ml:id>
									<ml:id xml:space="preserve">shellWallThickness</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:real>1</ml:real>
									<ml:apply>
										<ml:div/>
										<ml:id xml:space="preserve">ν</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
					</ml:parens>
				</ml:define>
			</math>
			<rendering item-idref="148"/>
		</region>
		<region region-id="10283" left="402" top="1990.5" width="213.75" height="40.5" align-x="441" 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:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:apply>
						<ml:indexer/>
						<ml:id xml:space="preserve">Gap</ml:id>
						<ml:id xml:space="preserve">j</ml:id>
					</ml:apply>
					<ml:apply>
						<ml:minus/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:minus/>
								<ml:id xml:space="preserve">shellID</ml:id>
								<ml:id xml:space="preserve">ecPlugOD</ml:id>
							</ml:apply>
							<ml:real>2</ml:real>
						</ml:apply>
						<ml:apply>
							<ml:indexer/>
							<ml:id xml:space="preserve">ΔR</ml:id>
							<ml:id xml:space="preserve">j</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="149"/>
		</region>
		<region region-id="10284" left="18" top="2052" width="322.5" height="171.75" align-x="18" align-y="2052" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<plot disable-calc="false" item-idref="150"/>
			<rendering item-idref="151"/>
		</region>
		<region region-id="10285" left="420" top="2037.75" width="83.25" height="213" align-x="425.25" align-y="2052" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:apply>
						<ml:indexer/>
						<ml:id xml:space="preserve">P</ml:id>
						<ml:id xml:space="preserve">j</ml:id>
					</ml:apply>
					<ml:unitOverride>
						<ml:id xml:space="preserve">psi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:matrix rows="11" cols="1">
								<ml:real>0</ml:real>
								<ml:real>51.076025815866352</ml:real>
								<ml:real>102.1520516317327</ml:real>
								<ml:real>153.22807744759905</ml:real>
								<ml:real>204.30410326346541</ml:real>
								<ml:real>255.38012907933177</ml:real>
								<ml:real>306.4561548951981</ml:real>
								<ml:real>357.53218071106443</ml:real>
								<ml:real>408.60820652693081</ml:real>
								<ml:real>459.68423234279715</ml:real>
								<ml:real>510.76025815866353</ml:real>
							</ml:matrix>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
				<resultFormat>
					<table item-idref="152"/>
				</resultFormat>
			</math>
			<rendering item-idref="153"/>
		</region>
		<region region-id="10286" left="528" top="2035.5" width="60" height="235.5" align-x="544.5" align-y="2064" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:indexer/>
							<ml:id xml:space="preserve">Gap</ml:id>
							<ml:id xml:space="preserve">j</ml:id>
						</ml:apply>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:matrix rows="11" cols="1">
							<ml:real>0.37049999999999977</ml:real>
							<ml:real>0.37014319874636342</ml:real>
							<ml:real>0.369786397492727</ml:real>
							<ml:real>0.36942959623909066</ml:real>
							<ml:real>0.36907279498545426</ml:real>
							<ml:real>0.3687159937318179</ml:real>
							<ml:real>0.36835919247818144</ml:real>
							<ml:real>0.36800239122454509</ml:real>
							<ml:real>0.36764558997090868</ml:real>
							<ml:real>0.36728878871727233</ml:real>
							<ml:real>0.366931987463636</ml:real>
						</ml:matrix>
					</result>
				</ml:eval>
				<resultFormat>
					<table item-idref="154"/>
				</resultFormat>
			</math>
			<rendering item-idref="155"/>
		</region>
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			<picture>
				<png item-idref="156" display-width="435.75" display-height="14.25"/>
			</picture>
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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>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">
					<b>This file corresponds to Cases 2a - 2d in </b>
					<b>
						<i>Roark's </i>
					</b>
					<b>
						<i>Formulas for Stress and Strain.</i>
					</b>
				</p>
			</text>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">
					<f size="14">
						<b>Annular plate with uniformly distributed pressure q over the portion from r</b>
					</f>
					<f size="14">
						<b>
							<sub>o</sub>
						</b>
					</f>
					<f size="14">
						<b> to a</b>
					</f>
					<f size="14">
						<b>; outer edge simply supported</b>
					</f>
				</p>
			</text>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="thick">a</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.5</ml:real>
						<ml:id xml:space="preserve">shellOD</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
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			<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>4.1905</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">
				<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>
			<rendering item-idref="162"/>
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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>
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						<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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					<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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			<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>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>
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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">L</ml:id>
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						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
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						<unitedValue>
							<ml:real>3.8640000000000003</ml:real>
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								<unitReference unit="inch"/>
							</unitMonomial>
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					<f family="MS Sans Serif" charset="0">
						<b>Formulas<sp count="2"/>for normal stresses </b>
					</f>
					<f family="MS Sans Serif" charset="0">
						<b>as a function of radial thickness, r:</b>
					</f>
				</p>
			</text>
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			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="Arial" charset="0">
						<b>
							<inlineAttr line-through="false">Longitudinal stress: </inlineAttr>
						</b>
					</f>
				</p>
			</text>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="1thick">σ</ml:id>
					<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>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>-5481.663843925603</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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			<math optimize="false" disable-calc="false">
				<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:parens>
								<ml:apply>
									<ml:minus/>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve" subscript="thick">a</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve" subscript="thick">b</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
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					<ml:unitOverride>
						<ml:id xml:space="preserve">psi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>-10963.327687851206</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
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					</result>
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			</math>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="endcap">b</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:id xml:space="preserve">ecHoleDiameter</ml:id>
						<ml:real>2</ml:real>
					</ml:apply>
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			<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 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>
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							<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="178"/>
		</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="rbendcap">M</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.0</ml:real>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="179"/>
		</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="raendcap">M</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:mult/>
							<ml:real>0</ml:real>
							<ml:id xml:space="preserve">in</ml:id>
						</ml:apply>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="180"/>
		</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="bendcap">Q</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0</ml:real>
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve">lbf</ml:id>
							<ml:id xml:space="preserve">in</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="181"/>
		</region>
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			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="Arial" charset="0">
						<b>
							<inlineAttr line-through="false">Radial stress: </inlineAttr>
						</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="10553" left="144" top="2660.25" width="217.5" height="58.5" align-x="207" align-y="2694" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:function>
						<ml:id xml:space="preserve" subscript="3thick">σ</ml:id>
						<ml:boundVars>
							<ml:id xml:space="preserve">r</ml:id>
						</ml:boundVars>
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						<ml:apply>
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							<ml:apply>
								<ml:mult/>
								<ml:apply>
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									<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:minus/>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">r</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve" subscript="thick">b</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve">r</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve" subscript="thick">a</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve" subscript="thick">b</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:apply>
						<ml:id xml:space="preserve" subscript="3thick">σ</ml:id>
						<ml:id xml:space="preserve" subscript="thick">b</ml:id>
					</ml:apply>
					<ml:unitOverride>
						<ml:id xml:space="preserve">psi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>0</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="183"/>
		</region>
		<region region-id="11086" left="708" top="2709.75" width="87.75" height="22.5" align-x="762" align-y="2724" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="aendcap">y</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="184"/>
		</region>
		<region region-id="11087" left="840" top="2709.75" width="102.75" height="22.5" align-x="891.75" align-y="2724" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="0endcap">r</ml:id>
					<ml:id xml:space="preserve" subscript="endcap">b</ml:id>
				</ml:globalDefine>
			</math>
			<rendering item-idref="185"/>
		</region>
		<region region-id="10548" left="18" top="2750.25" width="187.5" height="12" align-x="27.75" align-y="2760" 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="2726.25" width="152.25" height="58.5" align-x="189.75" align-y="2760" 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="thickb">τ</ml:id>
					<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="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>
			<rendering item-idref="186"/>
		</region>
		<region region-id="10556" left="390" top="2742" width="142.5" height="26.25" align-x="435.75" align-y="2760" 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="thickb">τ</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">psi</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>5481.663843925603</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="187"/>
		</region>
		<region region-id="11093" left="918" top="2732.25" width="133.5" height="55.5" align-x="970.5" align-y="2766" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="endcap">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="endcap">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="188"/>
		</region>
		<region region-id="11094" left="1104" top="2748" width="179.25" height="26.25" align-x="1156.5" align-y="2766" 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">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>478808.96270527079</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
				<resultFormat numeric-only="true">
					<general precision="5" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/>
					<matrix display-style="auto" expand-nested-arrays="false"/>
					<unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/>
				</resultFormat>
			</math>
			<rendering item-idref="189"/>
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			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<f size="14">Plate Constant</f>
				</p>
			</text>
		</region>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="endcap1">C</ml:id>
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							<ml:apply>
								<ml:mult/>
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										<ml:plus/>
										<ml:real>1</ml:real>
										<ml:id xml:space="preserve">ν</ml:id>
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									<ml:real>2</ml:real>
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								<ml:apply>
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									<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
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							</ml:apply>
							<ml:apply>
								<ml:id xml:space="preserve">ln</ml:id>
								<ml:apply>
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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: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: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:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="190"/>
		</region>
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			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="Arial" charset="0">
						<b>
							<inlineAttr line-through="false">Von Mises Stress calculation: </inlineAttr>
						</b>
					</f>
				</p>
			</text>
		</region>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="vmthick">σa</ml:id>
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											<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">a</ml:id>
												</ml:apply>
											</ml:apply>
										</ml:parens>
										<ml:real>2</ml:real>
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									<ml:apply>
										<ml:pow/>
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											<ml:apply>
												<ml:minus/>
												<ml:apply>
													<ml:id xml:space="preserve" subscript="2thick">σ</ml:id>
													<ml:id xml:space="preserve" subscript="thick">a</ml:id>
												</ml:apply>
												<ml:apply>
													<ml:id xml:space="preserve" subscript="3thick">σ</ml:id>
													<ml:id xml:space="preserve" subscript="thick">a</ml:id>
												</ml:apply>
											</ml:apply>
										</ml:parens>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:parens>
										<ml:apply>
											<ml:minus/>
											<ml:apply>
												<ml:id xml:space="preserve" subscript="3thick">σ</ml:id>
												<ml:id xml:space="preserve" subscript="thick">a</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="1thick">σ</ml:id>
										</ml:apply>
									</ml:parens>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:real>2</ml:real>
						</ml:apply>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="191"/>
		</region>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="endcap4">C</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:div/>
							<ml:real>1</ml:real>
							<ml:real>2</ml:real>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:mult/>
									<ml:parens>
										<ml:apply>
											<ml:plus/>
											<ml:real>1</ml:real>
											<ml:id xml:space="preserve">ν</ml:id>
										</ml:apply>
									</ml:parens>
									<ml:apply>
										<ml:div/>
										<ml:id xml:space="preserve" subscript="endcap">b</ml:id>
										<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:parens>
										<ml:apply>
											<ml:minus/>
											<ml:real>1</ml:real>
											<ml:id xml:space="preserve">ν</ml:id>
										</ml:apply>
									</ml:parens>
									<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:apply>
						</ml:parens>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="192"/>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
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						<ml:mult/>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:div/>
								<ml:real>1</ml:real>
								<ml:real>2</ml:real>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml: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="193"/>
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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">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>8.6098575700746576</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="194"/>
		</region>
		<region region-id="11152" left="696" top="2949.75" width="105.75" height="22.5" align-x="752.25" align-y="2964" 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="11153" left="858" top="2949.75" width="105.75" height="22.5" align-x="914.25" align-y="2964" 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="196"/>
		</region>
		<region region-id="11154" left="1014" top="2949.75" width="105.75" height="22.5" align-x="1070.25" align-y="2964" 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="197"/>
		</region>
		<region region-id="10318" left="12" top="2967.75" width="625.5" height="53.25" align-x="75.75" align-y="3006" 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>
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						<ml:sqrt/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
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										<ml:pow/>
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											<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="198"/>
		</region>
		<region region-id="11160" left="702" top="3008.25" width="429" height="53.25" align-x="757.5" align-y="3042" 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>
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						<ml:parens>
							<ml:apply>
								<ml:minus/>
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										<ml:mult/>
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											<ml:apply>
												<ml:plus/>
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													<ml:pow/>
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														<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/>
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											<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="199"/>
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		<region region-id="10319" left="18" top="3033.75" width="126" height="22.5" align-x="81.75" align-y="3048" 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>9.49452028769246</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="kips_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="200"/>
		</region>
		<region region-id="10320" left="12" top="3075.75" width="222" height="22.5" align-x="68.25" align-y="3090" 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="201"/>
		</region>
		<region region-id="10321" left="258" top="3078" width="153" height="26.25" align-x="314.25" align-y="3096" 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>9494.5202876924577</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="202"/>
		</region>
		<region region-id="11161" left="702" top="3080.25" width="399" height="53.25" align-x="757.5" align-y="3114" 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>
						<ml:mult style="auto-select"/>
						<ml:apply>
							<ml:div/>
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							<ml:id xml:space="preserve" subscript="endcap">a</ml:id>
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							<ml:apply>
								<ml:plus/>
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									<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>
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								</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>
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										<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>
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										</ml:apply>
									</ml:parens>
								</ml:apply>
							</ml:apply>
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			</math>
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			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="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>
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			<math optimize="false" disable-calc="false">
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					<ml:apply>
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						<ml:apply>
							<ml:div/>
							<ml:real>1</ml:real>
							<ml:real>64</ml:real>
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							<ml:apply>
								<ml:minus/>
								<ml:apply>
									<ml:minus/>
									<ml:apply>
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											<ml:real>4</ml:real>
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														<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>
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										<ml:real>5</ml:real>
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											<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>
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											</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="204"/>
		</region>
		<region region-id="10323" left="18" top="3163.5" width="223.5" height="48" align-x="110.25" align-y="3192" 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>
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					</ml:parens>
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			</math>
			<rendering item-idref="205"/>
		</region>
		<region region-id="10324" left="258" top="3183.75" width="141.75" height="22.5" align-x="350.25" align-y="3198" 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>2.1676363901092115</ml:real>
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				</ml:eval>
			</math>
			<rendering item-idref="206"/>
		</region>
		<region region-id="10325" left="30" top="3230.25" width="200.25" height="12" align-x="30" align-y="3240" 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="3224.25" width="375" height="53.25" align-x="774.75" align-y="3258" 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>
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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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								<unitReference unit="inch"/>
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									<ml:real>3</ml:real>
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							<ml:apply>
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				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="endcapa">θ</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">deg</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>0.38318999932857883</ml:real>
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								<unitReference unit="degree"/>
							</unitMonomial>
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			<pageBreak/>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f size="12">
						<b>
							<u>1C Buckling calculation for cylinders:</u>
						</b>
					</f>
				</p>
			</text>
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		<region region-id="10390" left="270" top="3614.25" width="299.25" height="12" align-x="270" align-y="3624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="MS Sans Serif" charset="0">
						<b>
							<u>Table 35 Formulas for elastic stability of plates and shells</u>
						</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="11219" left="720" top="3638.25" width="200.25" height="12" align-x="720" align-y="3648" 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>
				</p>
			</text>
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		<region region-id="10392" left="120" top="3645.75" width="254.25" height="54" align-x="120" align-y="3660" 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>
		</region>
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			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="MS Sans Serif" charset="0">
						<b>Thin tube with closed ends under uniform external pressure, lateral and longitudinal</b>
					</f>
				</p>
			</text>
		</region>
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								<ml:mult/>
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							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:real>1</ml:real>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve">ν</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
						<ml:id xml:space="preserve" subscript="endcap">b</ml:id>
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			</math>
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			<math optimize="false" disable-calc="false">
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						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>3211.5930464365642</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
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			<picture>
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			</picture>
			<rendering item-idref="229"/>
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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>
					<ml:unitOverride>
						<ml:id xml:space="preserve">psi</ml:id>
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					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>30108.684810342787</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">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
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					<ml:unitOverride>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>4.0905000000000005</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
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					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:mult/>
							<ml:real>6</ml:real>
							<ml:id xml:space="preserve" subscript="endcapt">M</ml:id>
						</ml:apply>
						<ml:apply>
							<ml:pow/>
							<ml:id xml:space="preserve" subscript="endcap">t</ml:id>
							<ml:real>2</ml:real>
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					</ml:apply>
				</ml:globalDefine>
			</math>
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			<math optimize="false" disable-calc="false">
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							<ml:minus/>
							<ml:apply>
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								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve" subscript="endcap">σ</ml:id>
									<ml:id xml:space="preserve">FofS</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:real>1</ml:real>
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						<ml: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>
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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>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>3.8640000000000003</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="endcap">MS</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>-0.0011125308404859036</ml:real>
					</result>
				</ml:eval>
			</math>
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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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			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">check small deflection assumption (deflection &lt; t/2)</p>
			</text>
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				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
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						</ml:apply>
						<ml:real>10</ml:real>
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			<math optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve">condition</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>1</ml:real>
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			</math>
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			<math optimize="false" disable-calc="false">
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								<ml:absval/>
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							<ml:id xml:space="preserve" subscript="endcap">t</ml:id>
						</ml:apply>
						<ml:apply>
							<ml:div/>
							<ml:real font="0">1</ml:real>
							<ml:real>2</ml:real>
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		<region region-id="11252" left="996" top="3883.5" width="120.75" height="48" align-x="1067.25" align-y="3912" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:apply>
						<ml:div/>
						<ml:apply>
							<ml:absval/>
							<ml:id xml:space="preserve" subscript="endcapb">y</ml:id>
						</ml:apply>
						<ml:id xml:space="preserve" subscript="endcap">t</ml:id>
					</ml:apply>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>0.023811481652160248</ml:real>
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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">smallDefTrue</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>1</ml:real>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="241"/>
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		<region region-id="10430" left="36" top="3914.25" width="254.25" height="12" align-x="36" align-y="3924" 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">The critical pressure for the initial buckling of a cylinder<sp count="2"/>is:</p>
			</text>
		</region>
		<region region-id="10432" left="324" top="3914.25" width="72" height="12" align-x="324" align-y="3924" 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">number of lobes:</p>
			</text>
		</region>
		<region region-id="10433" left="414" top="3909.75" width="59.25" height="19.5" align-x="430.5" align-y="3924" 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">n</ml:id>
					<ml:range>
						<ml:real>2</ml:real>
						<ml:real>10</ml:real>
					</ml:range>
				</ml:globalDefine>
			</math>
			<rendering item-idref="242"/>
		</region>
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			<math optimize="false" disable-calc="false">
				<ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">L</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>35</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="243"/>
		</region>
		<region region-id="13027" left="72" top="3945.75" width="54.75" height="19.5" align-x="89.25" align-y="3960" 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">L</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>35</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="244"/>
		</region>
		<region region-id="12338" left="762" top="3996" width="437.25" height="15.75" align-x="762" align-y="3996" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<picture>
				<png item-idref="245" display-width="435.75" display-height="14.25"/>
			</picture>
			<rendering item-idref="246"/>
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		<region region-id="10434" left="18" top="3975" width="629.25" height="103.5" align-x="40.5" align-y="4026" 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:apply>
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						<ml:mult/>
						<ml:apply>
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							<ml:apply>
								<ml:mult/>
								<ml:id xml:space="preserve">E</ml:id>
								<ml:apply>
									<ml:div/>
									<ml:id xml:space="preserve">shellWallThickness</ml:id>
									<ml:id xml:space="preserve" subscript="buckling">r</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:apply>
								<ml:plus/>
								<ml:real>1</ml:real>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:div/>
										<ml:real>1</ml:real>
										<ml:real>2</ml:real>
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										<ml:pow/>
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											<ml:apply>
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												<ml:apply>
													<ml:mult/>
													<ml:id xml:space="preserve">π</ml:id>
													<ml:id xml:space="preserve" subscript="buckling">r</ml:id>
												</ml:apply>
												<ml:apply>
													<ml:mult/>
													<ml:id xml:space="preserve">n</ml:id>
													<ml:id xml:space="preserve">L</ml:id>
												</ml:apply>
											</ml:apply>
										</ml:parens>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:apply>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:div/>
									<ml:real>1</ml:real>
									<ml:apply>
										<ml:mult/>
										<ml:apply>
											<ml:pow/>
											<ml:id xml:space="preserve">n</ml:id>
											<ml:real>2</ml:real>
										</ml:apply>
										<ml:apply>
											<ml:pow/>
											<ml:parens>
												<ml:apply>
													<ml:plus/>
													<ml:real>1</ml:real>
													<ml:apply>
														<ml:pow/>
														<ml:parens>
															<ml:apply>
																<ml:div/>
																<ml:apply>
																	<ml:mult/>
																	<ml:id xml:space="preserve">n</ml:id>
																	<ml:id xml:space="preserve">L</ml:id>
																</ml:apply>
																<ml:apply>
																	<ml:mult/>
																	<ml:id xml:space="preserve">π</ml:id>
																	<ml:id xml:space="preserve" subscript="buckling">r</ml:id>
																</ml:apply>
															</ml:apply>
														</ml:parens>
														<ml:real>2</ml:real>
													</ml:apply>
												</ml:apply>
											</ml:parens>
											<ml:real>2</ml:real>
										</ml:apply>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:div/>
										<ml:apply>
											<ml:mult/>
											<ml:apply>
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												<ml:id xml:space="preserve">n</ml:id>
												<ml:real>2</ml:real>
											</ml:apply>
											<ml:apply>
												<ml:pow/>
												<ml:id xml:space="preserve">shellWallThickness</ml:id>
												<ml:real>2</ml:real>
											</ml:apply>
										</ml:apply>
										<ml:apply>
											<ml:mult/>
											<ml:apply>
												<ml:mult/>
												<ml:real>12</ml:real>
												<ml:apply>
													<ml:pow/>
													<ml:id xml:space="preserve" subscript="buckling">r</ml:id>
													<ml:real>2</ml:real>
												</ml:apply>
											</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:apply>
									<ml:apply>
										<ml:pow/>
										<ml:parens>
											<ml:apply>
												<ml:plus/>
												<ml:real>1</ml:real>
												<ml:apply>
													<ml:pow/>
													<ml:parens>
														<ml:apply>
															<ml:div/>
															<ml:apply>
																<ml:mult/>
																<ml:id xml:space="preserve">π</ml:id>
																<ml:id xml:space="preserve" subscript="buckling">r</ml:id>
															</ml:apply>
															<ml:apply>
																<ml:mult/>
																<ml:id xml:space="preserve">n</ml:id>
																<ml:id xml:space="preserve">L</ml:id>
															</ml:apply>
														</ml:apply>
													</ml:parens>
													<ml:real>2</ml:real>
												</ml:apply>
											</ml:apply>
										</ml:parens>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="247"/>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">L</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>2.9166666666666665</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="foot"/>
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			</math>
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			<math optimize="false" disable-calc="false">
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					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:matrix rows="9" cols="1">
								<ml:real>30272.22387454925</ml:real>
								<ml:real>13256.731551932231</ml:real>
								<ml:real>7511.626725820468</ml:real>
								<ml:real>6162.3838271139939</ml:real>
								<ml:real>6479.4427572661552</ml:real>
								<ml:real>7535.0185919996056</ml:real>
								<ml:real>9010.02378854822</ml:real>
								<ml:real>10787.691249911914</ml:real>
								<ml:real>12821.982484445567</ml:real>
							</ml:matrix>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
				<resultFormat>
					<table item-idref="249"/>
				</resultFormat>
			</math>
			<rendering item-idref="250"/>
		</region>
		<region region-id="12383" left="684" top="4172.25" width="196.5" height="12" align-x="684" align-y="4182" 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">
					<b>EndCap Flange/Case Bearing Stress: </b>
					<b>
						<sp count="2"/>
					</b>
				</p>
			</text>
		</region>
		<region region-id="10447" left="174" top="4209.75" width="90.75" height="22.5" align-x="210" align-y="4224" 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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		<region region-id="10448" left="294" top="4209.75" width="78" height="22.5" align-x="315.75" align-y="4224" 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>0</ml:real>
					</ml:apply>
					<ml:apply>
						<ml:mult/>
						<ml:id xml:space="preserve" subscript="max">p</ml:id>
						<ml:real>10</ml:real>
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		<region region-id="10449" left="438" top="4209.75" width="78" height="22.5" align-x="459.75" align-y="4224" 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>1</ml:real>
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						<ml:id xml:space="preserve" subscript="max">p</ml:id>
						<ml:real>10</ml:real>
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			</math>
			<rendering item-idref="253"/>
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		<region region-id="12419" left="798" top="4215.75" width="138" height="19.5" align-x="875.25" align-y="4230" 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">bearingOD</ml:id>
					<ml:id xml:space="preserve">shellOD</ml:id>
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			<rendering item-idref="254"/>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">bearingID</ml:id>
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			<math optimize="false" disable-calc="false">
				<ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">bearingOD</ml:id>
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						<ml:mult/>
						<ml:real>8.0</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" subscript="critical">pBuckling</ml:id>
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						<ml:mult/>
						<ml:real font="0">0.8</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="critical">pBuckling</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>4929.9070616911958</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
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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:id xml:space="preserve">bearingArea</ml:id>
					<ml:apply>
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						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve">π</ml:id>
							<ml:real>4</ml:real>
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						<ml:parens>
							<ml:apply>
								<ml:minus/>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">bearingOD</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve">bearingID</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
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			</math>
			<rendering item-idref="259"/>
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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">bearingArea</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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					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>0.23847751293583744</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="2"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="260"/>
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		<region region-id="10453" left="180" top="4291.5" width="213.75" height="45" align-x="251.25" align-y="4320" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="buckling">MS</ml:id>
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						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve" subscript="critical">pBuckling</ml:id>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve">q</ml:id>
									<ml:id xml:space="preserve">FofSBuckling</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:real>1</ml:real>
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					</ml:parens>
				</ml:globalDefine>
			</math>
			<rendering item-idref="261"/>
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		<region region-id="10455" left="432" top="4305.75" width="120.75" height="22.5" align-x="503.25" align-y="4320" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="buckling">MS</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>3.8260480166017148</ml:real>
					</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="buckling">FOS</ml:id>
					<ml:eval placeholderMultiplicationStyle="default">
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve" subscript="critical">pBuckling</ml:id>
							<ml:id xml:space="preserve">q</ml:id>
						</ml:apply>
						<result xmlns="http://schemas.mathsoft.com/math30">
							<ml:real>9.65209603320343</ml:real>
						</result>
					</ml:eval>
				</ml:globalDefine>
			</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">bearingForce</ml:id>
					<ml:apply>
						<ml:mult/>
						<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>
							</ml:apply>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve">bearingOD</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:define>
			</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">bearingForce</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">lbf</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>25673.610796430134</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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			<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">Where experimental values of p<sub>critical</sub> are +/- 20% of p<sub>min</sub> !!!</p>
			</text>
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		<region region-id="12400" left="702" top="4438.5" width="146.25" height="42" align-x="756.75" align-y="4464" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="bearing">σ</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:id xml:space="preserve">bearingForce</ml:id>
						<ml:id xml:space="preserve">bearingArea</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="268"/>
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		<region region-id="12401" left="870" top="4446" width="150" height="26.25" align-x="923.25" align-y="4464" 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="bearing">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>107656.31727859238</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pounds_per_sq_inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
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			</math>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="bearing">MS</ml:id>
					<ml:parens>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve" subscript="b">S</ml:id>
								<ml:apply>
									<ml:mult/>
									<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>
						</ml:apply>
					</ml:parens>
				</ml:define>
			</math>
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		<region region-id="12403" left="1068" top="4503.75" width="115.5" height="22.5" align-x="1133.25" align-y="4518" 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="bearing">MS</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>-0.62285999757608135</ml:real>
					</result>
				</ml:eval>
				<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"/>
				</resultFormat>
			</math>
			<rendering item-idref="271"/>
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		<region region-id="12434" left="0" top="4530" width="6000" height="6" align-x="0" align-y="4530" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<pageBreak/>
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			<picture>
				<png item-idref="272" display-width="435.75" display-height="14.25"/>
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		<region region-id="12405" left="708" top="4592.25" width="163.5" height="12" align-x="708" align-y="4602" 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>
		</region>
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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>
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		<region region-id="12436" left="1140" top="4612.5" width="132.75" height="24.75" align-x="1208.25" align-y="4632" 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">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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					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>4.5490261623980208</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="2"/>
							</unitMonomial>
						</unitedValue>
					</result>
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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:id xml:space="preserve">shearForce</ml:id>
					<ml:apply>
						<ml:mult/>
						<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>
							</ml:apply>
						</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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			</math>
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			<math optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve">shearForce</ml:id>
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						<ml:id xml:space="preserve">lbf</ml:id>
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							<ml:real>25673.610796430134</ml:real>
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								<unitReference unit="pound_force"/>
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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">σ</ml:id>
					<ml:apply>
						<ml:div/>
						<ml:id xml:space="preserve">shearForce</ml:id>
						<ml:id xml:space="preserve">shearArea</ml:id>
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		<region region-id="12414" left="1014" top="4710" width="139.5" height="26.25" align-x="1056.75" align-y="4728" 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="shear">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>5643.7597586592656</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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		<region region-id="12416" left="828" top="4747.5" width="175.5" height="48" align-x="884.25" align-y="4776" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="shear">MS</ml:id>
					<ml:parens>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve" subscript="s">S</ml:id>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve" subscript="shear">σ</ml:id>
									<ml:id xml:space="preserve">FofS</ml:id>
								</ml:apply>
							</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>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>2.9966958095328482</ml:real>
					</result>
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			</math>
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			</picture>
			<rendering item-idref="283"/>
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			<pageBreak/>
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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">
					<f family="Arial" charset="0">
						<b>
							<inlineAttr line-through="false">END CAP DEFLECTION AND STRESSES:</inlineAttr>
						</b>
					</f>
					<sp count="2"/>
				</p>
			</text>
		</region>
		<region region-id="8757" left="324" top="7538.25" width="305.25" height="24" align-x="324" align-y="7548" 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">Superposition of pressure loading of the annulus and line loading of the connector/penetrator hole in the center.</p>
			</text>
		</region>
		<region region-id="8743" left="24" top="7982.25" width="48.75" height="12" align-x="24" align-y="7992" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="Arial" charset="0">
						<b>
							<inlineAttr line-through="false">in*lbf / in<sp count="2"/>
							</inlineAttr>
						</b>
					</f>
				</p>
			</text>
		</region>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<b>CONNECTOR LINE LOAD: </b>
					<sp/>
				</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="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>
		<region region-id="8889" left="30" top="8891.25" width="303.75" height="35.25" align-x="30" align-y="8904" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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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 uniform annular line load w at radius r</b>
					</f>
					<f size="14">
						<b>
							<sub>o</sub>
						</b>
					</f>
					<f size="14">
						<b>; outer edge simply supported</b>
					</f>
				</p>
			</text>
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		<region region-id="8890" left="378" top="8900.25" width="271.5" height="24" align-x="378" align-y="8910" 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">
					<b>This file corresponds to Cases 1a - 1d in </b>
					<b>
						<i>Roark's Formulas for Stress and Strain.</i>
					</b>
				</p>
			</text>
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					<b>Annular plate with a uniform annular line load w at a radius r</b>
					<b>
						<sub>o</sub>
					</b>
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					<b>Outer edge simply supported, inner edge free</b>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Area of Connector:<sp count="2"/>
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							<u>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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								<unitReference unit="inch"/>
								<unitReference unit="pound_force"/>
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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">Loading on tab:</p>
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				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
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							<ml:apply>
								<ml:pow/>
								<ml:id xml:space="preserve" subscript="cyl_oring">ID</ml:id>
								<ml:real>2</ml:real>
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			<math error="This variable is undefined." optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
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			<math optimize="false" disable-calc="false">
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
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			<math optimize="false" disable-calc="false">
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			</math>
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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">
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						<inlineAttr font-weight="normal" line-through="false">
							<c val="#0ff">Applied</c>
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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">
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							<c val="#0ff">Unit </c>
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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">
					<f family="Arial" charset="0">
						<inlineAttr font-weight="normal" line-through="false">
							<c val="#0ff">Load @</c>
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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">
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							<c val="#0ff">OD of</c>
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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">
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						<f family="Arial" charset="0">
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							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
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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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					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>3.62</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
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			<math error="This variable is undefined." optimize="false" disable-calc="false">
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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="endcap_tab">w</ml:id>
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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:unitOverride>
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						<unitedValue>
							<ml:real>4</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
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			<math optimize="false" disable-calc="false">
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								<ml:apply>
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										<ml:apply>
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											<ml:real>1</ml:real>
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										<ml:pow/>
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											<ml:apply>
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												<ml:id xml:space="preserve" subscript="endcap_tab">a</ml:id>
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										</ml:parens>
										<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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							<ml:apply>
								<ml:minus/>
								<ml:real>1</ml:real>
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											</ml:apply>
										</ml:parens>
										<ml:real>2</ml:real>
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										<ml:apply>
											<ml:plus/>
											<ml:real>1</ml:real>
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												<ml:real>2</ml:real>
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													<ml:apply>
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								<ml:real>4</ml:real>
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													<ml:real>2</ml:real>
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								<ml:real>1</ml:real>
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								<ml:apply>
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									<ml:apply>
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										<ml:apply>
											<ml:plus/>
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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:apply>
										<ml:id xml:space="preserve">ln</ml:id>
										<ml:apply>
											<ml:div/>
											<ml:id xml:space="preserve" subscript="endcap_tab">a</ml:id>
											<ml:id xml:space="preserve" subscript="endcap_tab">b</ml:id>
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									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
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										<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>
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									<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="endcap_tab">b</ml:id>
														<ml:id xml:space="preserve" subscript="endcap_tab">a</ml:id>
													</ml:apply>
												</ml:parens>
												<ml:real>2</ml:real>
											</ml:apply>
										</ml:apply>
									</ml:parens>
								</ml:apply>
							</ml:apply>
						</ml:parens>
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								<ml:real>4</ml:real>
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											<ml:id xml:space="preserve">ln</ml:id>
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												<ml:div/>
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									<ml:apply>
										<ml:pow/>
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											<ml:apply>
												<ml:div/>
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												<ml:id xml:space="preserve" subscript="endcap_tab">a</ml:id>
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								</ml:apply>
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			<math optimize="false" disable-calc="false">
				<ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30">
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								<ml:real>4</ml:real>
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										<ml:real>4</ml:real>
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												<ml:real>2</ml:real>
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			<math error="This variable is undefined." optimize="false" disable-calc="false">
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			<math error="This variable is undefined." optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
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			<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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			<math error="This variable is undefined." optimize="false" disable-calc="false">
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					<ml:id xml:space="preserve" subscript="endcap_tab">MS</ml:id>
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		<region region-id="7422" left="0" top="10674" width="6000" height="6" align-x="0" align-y="10674" 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>B) O-ring groove tab:</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>
							<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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						<b>
							<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">For o-ring tab:</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">Loading on tab:</p>
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							<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>
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									<ml:apply>
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										<ml:apply>
											<ml:div/>
											<ml:id xml:space="preserve" subscript="oring">a</ml:id>
											<ml:id xml:space="preserve" subscript="oring">b</ml:id>
										</ml:apply>
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								</ml:apply>
								<ml:apply>
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										<ml:apply>
											<ml:div/>
											<ml:apply>
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												<ml:id xml:space="preserve">ν</ml:id>
											</ml:apply>
											<ml:real>4</ml:real>
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										<ml:apply>
											<ml:minus/>
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											<ml:apply>
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												<ml:parens>
													<ml:apply>
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														<ml:id xml:space="preserve" subscript="oring">a</ml:id>
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												<ml:real>2</ml:real>
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										</ml:apply>
									</ml:parens>
								</ml:apply>
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								<ml:real>4</ml:real>
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															<ml:id xml:space="preserve" subscript="oring">a</ml:id>
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													<ml:real>2</ml:real>
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												<ml:real>1</ml:real>
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											<ml:id xml:space="preserve">ln</ml:id>
											<ml:apply>
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												<ml:id xml:space="preserve" subscript="oring">a</ml:id>
												<ml:id xml:space="preserve" subscript="oring0">r</ml:id>
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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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				<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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				<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="11456.25" width="107.25" height="12" align-x="6" align-y="11466" 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>
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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">Cylinder:</p>
			</text>
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		<region region-id="10960" left="54" top="11498.25" width="90.75" height="12" align-x="54" align-y="11508" 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>
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			<math optimize="false" disable-calc="false">
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					<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="390"/>
		</region>
		<region region-id="10962" left="492" top="11488.5" width="84" height="27.75" align-x="518.25" align-y="11508" 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>5.1402738998036135</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="2"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="391"/>
		</region>
		<region region-id="10963" left="54" top="11540.25" width="67.5" height="12" align-x="54" align-y="11550" 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="11519.25" width="314.25" height="45.75" align-x="192" align-y="11550" 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="392"/>
		</region>
		<region region-id="10965" left="492" top="11530.5" width="102" height="27.75" align-x="516" align-y="11550" 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>168.29084463330085</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="3"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="393"/>
		</region>
		<region region-id="10966" left="54" top="11582.25" width="70.5" height="12" align-x="54" align-y="11592" 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="11561.25" width="186" height="45.75" align-x="195" align-y="11592" 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="394"/>
		</region>
		<region region-id="10968" left="492" top="11572.5" width="105" height="27.75" align-x="519" align-y="11592" 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>213.16636545439246</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch" power-numerator="3"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="395"/>
		</region>
		<region region-id="10969" left="54" top="11618.25" width="30.75" height="12" align-x="54" align-y="11628" 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="11613.75" width="159" height="22.5" align-x="203.25" align-y="11628" 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="396"/>
		</region>
		<region region-id="10971" left="492" top="11613.75" width="96.75" height="22.5" align-x="527.25" align-y="11628" 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>1.9464777981864341</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="397"/>
		</region>
		<region region-id="7090" left="6" top="11660.25" width="40.5" height="12" align-x="6" align-y="11670" 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="11660.25" width="33" height="12" align-x="102" align-y="11670" 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="11678.25" width="18.75" height="12" align-x="102" align-y="11688" 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="11657.25" width="198" height="45.75" align-x="216.75" align-y="11688" 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="398"/>
		</region>
		<region region-id="7094" left="402" top="11668.5" width="102" height="27.75" align-x="432.75" align-y="11688" 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="399"/>
		</region>
		<region region-id="10940" left="102" top="11726.25" width="22.5" height="12" align-x="102" align-y="11736" 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="11711.25" width="327.75" height="45.75" align-x="229.5" align-y="11742" 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="400"/>
		</region>
		<region region-id="10771" left="534" top="11728.5" width="108.75" height="27.75" align-x="571.5" align-y="11748" 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="401"/>
		</region>
		<region region-id="10939" left="102" top="11768.25" width="20.25" height="12" align-x="102" align-y="11778" 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>
		</region>
		<region region-id="7099" left="192" top="11763.75" width="111" height="22.5" align-x="225.75" align-y="11778" 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>
					<ml:apply>
						<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>
			</math>
			<rendering item-idref="402"/>
		</region>
		<region region-id="7100" left="306" top="11758.5" width="105" height="27.75" align-x="339.75" align-y="11778" 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>
						</ml:apply>
					</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>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="403"/>
		</region>
		<region region-id="10938" left="102" top="11798.25" width="33.75" height="12" align-x="102" align-y="11808" 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="7102" left="192" top="11793.75" width="94.5" height="22.5" align-x="229.5" align-y="11808" 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">W</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:id xml:space="preserve" subscript="cap">V</ml:id>
						<ml:id xml:space="preserve" subscript="m">ρ</ml:id>
					</ml:apply>
				</ml:globalDefine>
			</math>
			<rendering item-idref="404"/>
		</region>
		<region region-id="7103" left="306" top="11799.75" width="99" height="22.5" align-x="343.5" align-y="11814" 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>
				</ml:eval>
			</math>
			<rendering item-idref="405"/>
		</region>
		<region region-id="7104" left="6" top="11840.25" width="57.75" height="12" align-x="6" align-y="11850" 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="11835.75" width="134.25" height="22.5" align-x="237.75" align-y="11850" 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="406"/>
		</region>
		<region region-id="7293" left="498" top="11835.75" width="107.25" height="22.5" align-x="543.75" align-y="11850" 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>8.758322274634919</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="pound_force"/>
							</unitMonomial>
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