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						<b>Plastic Moment Calculation For Positive Sections</b>
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					<c val="#800000">DOT refers to the Iowa Department of Transportation</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">
					<c val="#800000">OBS refers to the Iowa DOT Office of Bridges and Structures</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"/>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<c val="#800000">Disclaimer: This software is intended for use by Iowa DOT personnel and consultants working for the OBS in their development of projects for the Iowa DOT. Any other use is at the sole discretion of the user. The Iowa DOT makes the software available "AS IS" and assumes no liability nor makes any warranty of any kind, including warranties of noninfringement, fitness or merchantability whether expressed or implied, to the accuracy or functionality of this software. By downloading or using this file, you are agreeing to this disclaimer.</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">
					<c val="#800000">The OBS will only support those persons using this software in connection with Iowa DOT related business.</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">
					<c val="#800000">Please report any errors to the Iowa DOT OBS.</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">This worksheet calculates the plastic moment (M<f family="Arial" charset="0">
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								<sub>p)</sub>
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					</f> and depth to the plastic neutral (Y) axis for positive sections.</p>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Special Unit Definitions:</p>
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							<inlineAttr line-through="false">SPECIFICATION:<tab/>
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					</f>LRFD 5rd Edition, 2010 (U.S. Units).<sp count="2"/>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="85.5">
					<tab/>Appendix D6</p>
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					<tab/>
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							<ml:real>3</ml:real>
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									<c val="#00f">INPUT SECTION</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">Deck Thickness:</p>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Deck Effective Width:</p>
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						<ml:mult/>
						<ml:real>92</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="11"/>
		</region>
		<region region-id="16142" left="546" top="245.25" width="127.5" height="15.75" align-x="559.5" align-y="258" 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" size="14">
						<inlineAttr font-weight="normal" underline="false" line-through="false">
							<c val="#00f">Revision History</c>
						</inlineAttr>
					</f>
				</p>
			</text>
		</region>
		<region region-id="16082" left="30" top="254.25" width="120" height="12" align-x="39" align-y="264" 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">Sacrificial Wearing Surface:</p>
			</text>
		</region>
		<region region-id="16083" left="342" top="255" width="57" height="12.75" align-x="369" align-y="264" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">SWS</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0.5</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="12"/>
		</region>
		<region region-id="16143" left="546" top="266.25" width="276.75" height="78" align-x="551.25" align-y="276" 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">03/02/2011: Case I - Case VII - Absolute value signs added to all distance equations to ensure positive distance values. Case V - CaseVII - Equation d<sub>c</sub> rewritten to solve distance to center of</p>
				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">compression flange. Originally written as d<sub>s </sub>instead of d<sub>c</sub>. Assumption added stating concrete in tension is neglected in equations.</p>
			</text>
		</region>
		<region region-id="16084" left="30" top="278.25" width="140.25" height="12" align-x="39" align-y="288" 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">Concrete Compressive Strength:</p>
			</text>
		</region>
		<region region-id="16085" left="342" top="279" width="48.75" height="16.5" align-x="357" align-y="288" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="c">f</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>3.5</ml:real>
						<ml:id xml:space="preserve">ksi</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="13"/>
		</region>
		<region region-id="16086" left="30" top="302.25" width="147.75" height="12" align-x="30" align-y="312" 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">Width of the Compression Flange:</p>
			</text>
		</region>
		<region region-id="16087" left="342" top="303" width="45" height="16.5" align-x="359.25" align-y="312" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="c">b</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>16</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="14"/>
		</region>
		<region region-id="16088" left="30" top="326.25" width="166.5" height="12" align-x="30" align-y="336" 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">Thickness of the Compression Flange:</p>
			</text>
		</region>
		<region region-id="16089" left="342" top="327" width="44.25" height="16.5" align-x="356.25" align-y="336" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="c">t</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>.75</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="15"/>
		</region>
		<region region-id="16090" left="30" top="350.25" width="123.75" height="12" align-x="30" align-y="360" 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">Width of the Tension Flange:</p>
			</text>
		</region>
		<region region-id="16091" left="342" top="351" width="43.5" height="16.5" align-x="357.75" align-y="360" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="t">b</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>20</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="16"/>
		</region>
		<region region-id="16092" left="30" top="374.25" width="142.5" height="12" align-x="30" align-y="384" 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">Thickness of the Tension Flange:</p>
			</text>
		</region>
		<region region-id="16093" left="342" top="375" width="36" height="16.5" align-x="354.75" align-y="384" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="t">t</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>1</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="17"/>
		</region>
		<region region-id="16120" left="30" top="398.25" width="51.75" height="12" align-x="30" align-y="408" 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">Web Depth:</p>
			</text>
		</region>
		<region region-id="16094" left="342" top="399" width="41.25" height="12.75" align-x="355.5" align-y="408" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">D</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>64</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="18"/>
		</region>
		<region region-id="16096" left="30" top="422.25" width="70.5" height="12" align-x="30" align-y="432" 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">Web Thickness:</p>
			</text>
		</region>
		<region region-id="16097" left="342" top="423" width="55.5" height="16.5" align-x="358.5" align-y="432" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="w">t</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>.4375</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="19"/>
		</region>
		<region region-id="16098" left="30" top="446.25" width="156.75" height="12" align-x="55.5" align-y="456" 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">Compression Flange Yield Strength:</p>
			</text>
		</region>
		<region region-id="16099" left="342" top="447" width="53.25" height="16.5" align-x="363.75" align-y="456" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="yc">F</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>50</ml:real>
						<ml:id xml:space="preserve">ksi</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="20"/>
		</region>
		<region region-id="16100" left="30" top="470.25" width="132.75" height="12" align-x="55.5" align-y="480" 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">Tension Flange Yield Strength:</p>
			</text>
		</region>
		<region region-id="16101" left="342" top="471" width="51.75" height="16.5" align-x="362.25" align-y="480" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="yt">F</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>50</ml:real>
						<ml:id xml:space="preserve">ksi</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="21"/>
		</region>
		<region region-id="16102" left="30" top="494.25" width="87.75" height="12" align-x="55.5" 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="false">
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Web Yield Strength:</p>
			</text>
		</region>
		<region region-id="16103" left="342" top="495" width="55.5" height="16.5" align-x="366" align-y="504" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="yw">F</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>50</ml:real>
						<ml:id xml:space="preserve">ksi</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="22"/>
		</region>
		<region region-id="16104" left="30" top="518.25" width="80.25" height="12" align-x="39" align-y="528" 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">Area of Rebar Top:</p>
			</text>
		</region>
		<region region-id="16105" left="342" top="513" width="48" height="22.5" align-x="362.25" align-y="528" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="rt">A</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0</ml:real>
						<ml:apply>
							<ml:pow/>
							<ml:id xml:space="preserve">in</ml:id>
							<ml:real>2</ml:real>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="23"/>
		</region>
		<region region-id="16140" left="552" top="521.25" width="273" height="45" align-x="552" align-y="534" 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">Note: If Rebar is excluded then set A<sub>rt</sub> and A<sub>rb</sub> equal to 0 in<sup>2</sup>. Additionally it is a good idea to set d<sub>tr</sub> and d<sub>br</sub> to 0 in. This way the "Cases" are limited to 1, 2, and 7.</p>
			</text>
		</region>
		<region region-id="16106" left="30" top="542.25" width="96.75" height="12" align-x="39" align-y="552" 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">Area of Rebar Bottom:</p>
			</text>
		</region>
		<region region-id="16107" left="342" top="537" width="50.25" height="22.5" align-x="364.5" align-y="552" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="rb">A</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0</ml:real>
						<ml:apply>
							<ml:pow/>
							<ml:id xml:space="preserve">in</ml:id>
							<ml:real>2</ml:real>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="24"/>
		</region>
		<region region-id="16108" left="30" top="566.25" width="93" height="12" align-x="55.5" align-y="576" 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">Rebar Yield Strength:</p>
			</text>
		</region>
		<region region-id="16109" left="342" top="567" width="52.5" height="16.5" align-x="363" align-y="576" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="yr">F</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>60</ml:real>
						<ml:id xml:space="preserve">ksi</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="25"/>
		</region>
		<region region-id="16110" left="30" top="590.25" width="174" height="12" align-x="55.5" align-y="600" 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">Haunch (Bottomof Deck To Top of Web):</p>
			</text>
		</region>
		<region region-id="16111" left="342" top="591" width="62.25" height="12.75" align-x="381" align-y="600" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">Haunch</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>3</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="26"/>
		</region>
		<region region-id="16112" left="30" top="614.25" width="246" height="12" align-x="30" align-y="624" 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">Distance From Centroid of Top Rebar To Bottom of Deck:</p>
			</text>
		</region>
		<region region-id="16113" left="342" top="615" width="42" height="16.5" align-x="360.75" align-y="624" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="tr">d</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="27"/>
		</region>
		<region region-id="16114" left="30" top="638.25" width="262.5" height="12" align-x="30" align-y="648" 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">Distance From Centroid of Bottom Rebar To Bottom of Deck:</p>
			</text>
		</region>
		<region region-id="16115" left="342" top="639" width="44.25" height="16.5" align-x="363" align-y="648" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="br">d</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:real>0</ml:real>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="28"/>
		</region>
		<region region-id="15597" left="0" top="714" width="6000" height="6" align-x="0" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<pageBreak/>
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									<c val="#00f">CALCULATION SECTION</c>
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								<c val="#00f">Calculate member forces at yield for subsequent calculations</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">Adjust the slab thickness subtracting the sacrificial wearing surface:</p>
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						<ml:id xml:space="preserve">SWS</ml:id>
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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">Top Rebar Force</p>
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						<ml:id xml:space="preserve" subscript="rt">A</ml:id>
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			<math optimize="false" disable-calc="false">
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								<unitReference unit="kip"/>
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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">Slab Force</p>
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								<ml:mult/>
								<ml:real>0.85</ml:real>
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						<ml:id xml:space="preserve">kip</ml:id>
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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">Bot Rebar Force</p>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Compression Flange Force</p>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Web Force</p>
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							<ml:id xml:space="preserve">D</ml:id>
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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">Tension Flange Force</p>
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								<c val="#00f">Calculate M</c>
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								<c val="#00f"> and Y for all conditions (Table D6.1-1)</c>
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								<c val="#00f">Case I - Neutral axis in the web</c>
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							<ml:apply>
								<ml:plus/>
								<ml:apply>
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										<ml:apply>
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											<ml:apply>
												<ml:minus/>
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													<ml:minus/>
													<ml:id xml:space="preserve" subscript="t">P</ml:id>
													<ml:id xml:space="preserve" subscript="c">P</ml:id>
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												<ml:id xml:space="preserve" subscript="s">P</ml:id>
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											<ml:id xml:space="preserve" subscript="rt">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="w">P</ml:id>
								</ml:apply>
								<ml:real>1</ml:real>
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								<c val="#00f">(from top of web)</c>
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							<ml:plus/>
							<ml:apply>
								<ml:plus/>
								<ml:id xml:space="preserve" subscript="1">Y</ml:id>
								<ml:id xml:space="preserve">Haunch</ml:id>
							</ml:apply>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve" subscript="s">t</ml:id>
								<ml:real>2</ml:real>
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						<ml:apply>
							<ml:plus/>
							<ml:apply>
								<ml:plus/>
								<ml:id xml:space="preserve" subscript="1">Y</ml:id>
								<ml:id xml:space="preserve">Haunch</ml:id>
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							<ml:id xml:space="preserve" subscript="tr">d</ml:id>
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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="rb">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:plus/>
							<ml:apply>
								<ml:plus/>
								<ml:id xml:space="preserve" subscript="1">Y</ml:id>
								<ml:id xml:space="preserve">Haunch</ml:id>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="br">d</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="45"/>
		</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" subscript="c">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:plus/>
							<ml:id xml:space="preserve" subscript="1">Y</ml:id>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve" subscript="c">t</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="46"/>
		</region>
		<region region-id="13008" left="84" top="1132.5" width="82.5" height="31.5" align-x="99" align-y="1152" 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="t">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:plus/>
							<ml:apply>
								<ml:minus/>
								<ml:id xml:space="preserve">D</ml:id>
								<ml:id xml:space="preserve" subscript="1">Y</ml:id>
							</ml:apply>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve" subscript="t">t</ml:id>
								<ml:real>2</ml:real>
							</ml:apply>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="47"/>
		</region>
		<region region-id="13717" left="432" top="1155" width="50.25" height="16.5" align-x="447.75" align-y="1164" 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="1">Y</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>-5.7771428571428629</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="48"/>
		</region>
		<region region-id="13013" left="84" top="1168.5" width="317.25" height="31.5" align-x="109.5" align-y="1188" 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="p1">M</ml:id>
					<ml:apply>
						<ml:plus/>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve" subscript="w">P</ml:id>
								<ml:apply>
									<ml:mult/>
									<ml:real>2</ml:real>
									<ml:id xml:space="preserve">D</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve" subscript="1">Y</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:parens>
											<ml:apply>
												<ml:minus/>
												<ml:id xml:space="preserve">D</ml:id>
												<ml:id xml:space="preserve" subscript="1">Y</ml:id>
											</ml:apply>
										</ml:parens>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:apply>
												<ml:mult/>
												<ml:id xml:space="preserve" subscript="s">P</ml:id>
												<ml:id xml:space="preserve" subscript="s">d</ml:id>
											</ml:apply>
											<ml:apply>
												<ml:mult/>
												<ml:id xml:space="preserve" subscript="rt">P</ml:id>
												<ml:id xml:space="preserve" subscript="rt">d</ml:id>
											</ml:apply>
										</ml:apply>
										<ml:apply>
											<ml:mult/>
											<ml:id xml:space="preserve" subscript="rb">P</ml:id>
											<ml:id xml:space="preserve" subscript="rb">d</ml:id>
										</ml:apply>
									</ml:apply>
									<ml:apply>
										<ml:mult/>
										<ml:id xml:space="preserve" subscript="c">P</ml:id>
										<ml:id xml:space="preserve" subscript="c">d</ml:id>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve" subscript="t">P</ml:id>
									<ml:id xml:space="preserve" subscript="t">d</ml:id>
								</ml:apply>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="49"/>
		</region>
		<region region-id="13567" left="432" top="1179" width="78.75" height="16.5" align-x="456" align-y="1188" 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="p1">M</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">kip</ml:id>
							<ml:id xml:space="preserve">ft</ml:id>
						</ml:apply>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>10761.128958333331</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="foot"/>
								<unitReference unit="kip"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
				<resultFormat numeric-only="true">
					<decimal precision="0" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/>
					<matrix display-style="auto" expand-nested-arrays="false"/>
					<unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/>
				</resultFormat>
			</math>
			<rendering item-idref="50"/>
		</region>
		<region region-id="13648" left="66" top="1214.25" width="162.75" height="12" align-x="66" align-y="1224" 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">
					<f family="Arial" charset="0">
						<u>
							<inlineAttr font-style="normal" line-through="false">
								<c val="#00f">Case II - Neutral axis in the top flange</c>
							</inlineAttr>
						</u>
					</f>
				</p>
			</text>
		</region>
		<region region-id="13649" left="84" top="1234.5" width="171.75" height="35.25" align-x="101.25" align-y="1254" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="2">Y</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:apply>
							<ml:div/>
							<ml:id xml:space="preserve" subscript="c">t</ml:id>
							<ml:real>2</ml:real>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:div/>
									<ml:apply>
										<ml:minus/>
										<ml:apply>
											<ml:minus/>
											<ml:apply>
												<ml:minus/>
												<ml:apply>
													<ml:plus/>
													<ml:id xml:space="preserve" subscript="w">P</ml:id>
													<ml:id xml:space="preserve" subscript="t">P</ml:id>
												</ml:apply>
												<ml:id xml:space="preserve" subscript="s">P</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="rt">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="c">P</ml:id>
								</ml:apply>
								<ml:real>1</ml:real>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="51"/>
		</region>
		<region region-id="15461" left="336" top="1244.25" width="99" height="12" align-x="336" align-y="1254" 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">
						<i>
							<inlineAttr line-through="false">
								<c val="#00f">(from top of top flange)</c>
							</inlineAttr>
						</i>
					</f>
				</p>
			</text>
		</region>
		<region region-id="13651" left="84" top="1270.5" width="130.5" height="31.5" align-x="100.5" align-y="1290" 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="s">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve" subscript="2">Y</ml:id>
									<ml:id xml:space="preserve">Haunch</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:div/>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="c">t</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="52"/>
		</region>
		<region region-id="13652" left="84" top="1305" width="133.5" height="16.5" align-x="102" align-y="1314" 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="rt">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve" subscript="2">Y</ml:id>
									<ml:id xml:space="preserve">Haunch</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="tr">d</ml:id>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="c">t</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="53"/>
		</region>
		<region region-id="13653" left="84" top="1329" width="138" height="16.5" align-x="104.25" align-y="1338" 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="rb">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve" subscript="2">Y</ml:id>
									<ml:id xml:space="preserve">Haunch</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="br">d</ml:id>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="c">t</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="54"/>
		</region>
		<region region-id="13654" left="84" top="1352.25" width="87.75" height="27.75" align-x="102.75" align-y="1368" 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="w">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:div/>
									<ml:id xml:space="preserve">D</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="c">t</ml:id>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="2">Y</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="55"/>
		</region>
		<region region-id="13726" left="84" top="1384.5" width="102" height="31.5" align-x="99" align-y="1404" 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="t">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:div/>
										<ml:id xml:space="preserve" subscript="t">t</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:id xml:space="preserve">D</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="c">t</ml:id>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="2">Y</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="56"/>
		</region>
		<region region-id="13748" left="432" top="1449" width="45" height="16.5" align-x="447.75" align-y="1458" 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="2">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>0.59203124999999979</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
				<resultFormat numeric-only="true">
					<decimal precision="1" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/>
					<matrix display-style="auto" expand-nested-arrays="false"/>
					<unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/>
				</resultFormat>
			</math>
			<rendering item-idref="57"/>
		</region>
		<region region-id="13749" left="84" top="1462.5" width="323.25" height="35.25" align-x="109.5" align-y="1482" 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="p2">M</ml:id>
					<ml:apply>
						<ml:plus/>
						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:div/>
								<ml:id xml:space="preserve" subscript="c">P</ml:id>
								<ml:apply>
									<ml:mult/>
									<ml:real>2</ml:real>
									<ml:id xml:space="preserve" subscript="c">t</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:parens>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:pow/>
										<ml:id xml:space="preserve" subscript="2">Y</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:apply>
										<ml:pow/>
										<ml:parens>
											<ml:apply>
												<ml:minus/>
												<ml:id xml:space="preserve" subscript="c">t</ml:id>
												<ml:id xml:space="preserve" subscript="2">Y</ml:id>
											</ml:apply>
										</ml:parens>
										<ml:real>2</ml:real>
									</ml:apply>
								</ml:apply>
							</ml:parens>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:apply>
												<ml:mult/>
												<ml:id xml:space="preserve" subscript="s">P</ml:id>
												<ml:id xml:space="preserve" subscript="s">d</ml:id>
											</ml:apply>
											<ml:apply>
												<ml:mult/>
												<ml:id xml:space="preserve" subscript="rt">P</ml:id>
												<ml:id xml:space="preserve" subscript="rt">d</ml:id>
											</ml:apply>
										</ml:apply>
										<ml:apply>
											<ml:mult/>
											<ml:id xml:space="preserve" subscript="rb">P</ml:id>
											<ml:id xml:space="preserve" subscript="rb">d</ml:id>
										</ml:apply>
									</ml:apply>
									<ml:apply>
										<ml:mult/>
										<ml:id xml:space="preserve" subscript="w">P</ml:id>
										<ml:id xml:space="preserve" subscript="w">d</ml:id>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve" subscript="t">P</ml:id>
									<ml:id xml:space="preserve" subscript="t">d</ml:id>
								</ml:apply>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="58"/>
		</region>
		<region region-id="13750" left="432" top="1473" width="78.75" height="16.5" align-x="456" align-y="1482" 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="p2">M</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">kip</ml:id>
							<ml:id xml:space="preserve">ft</ml:id>
						</ml:apply>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>10280.091599934895</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="foot"/>
								<unitReference unit="kip"/>
							</unitMonomial>
						</unitedValue>
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					<decimal precision="0" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/>
					<matrix display-style="auto" expand-nested-arrays="false"/>
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					<f family="Arial" charset="0">
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								<c val="#00f">Case III - Neutral axis in the concrete deck below Prb</c>
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						<ml:id xml:space="preserve" subscript="s">t</ml:id>
						<ml:parens>
							<ml:apply>
								<ml:div/>
								<ml:apply>
									<ml:minus/>
									<ml:apply>
										<ml:minus/>
										<ml:apply>
											<ml:plus/>
											<ml:apply>
												<ml:plus/>
												<ml:id xml:space="preserve" subscript="c">P</ml:id>
												<ml:id xml:space="preserve" subscript="w">P</ml:id>
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										</ml:apply>
										<ml:id xml:space="preserve" subscript="rt">P</ml:id>
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									<ml:id xml:space="preserve" subscript="rb">P</ml:id>
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								<ml:id xml:space="preserve" subscript="s">P</ml:id>
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					<f family="Arial" charset="0">
						<i>
							<inlineAttr line-through="false">
								<c val="#00f">(from top of deck)</c>
							</inlineAttr>
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						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:minus/>
								<ml:apply>
									<ml:plus/>
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									<ml:id xml:space="preserve">Haunch</ml:id>
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								<ml:apply>
									<ml:div/>
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									<ml:real>2</ml:real>
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				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="rt">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:id xml:space="preserve" subscript="3">Y</ml:id>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
									<ml:id xml:space="preserve" subscript="tr">d</ml:id>
								</ml:apply>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="rb">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:id xml:space="preserve" subscript="3">Y</ml:id>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
									<ml:id xml:space="preserve" subscript="br">d</ml:id>
								</ml:apply>
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					<ml:id xml:space="preserve" subscript="w">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:div/>
										<ml:id xml:space="preserve">D</ml:id>
										<ml:real>2</ml:real>
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									<ml:id xml:space="preserve" subscript="s">t</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve">Haunch</ml:id>
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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="t">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:div/>
											<ml:id xml:space="preserve" subscript="t">t</ml:id>
											<ml:real>2</ml:real>
										</ml:apply>
										<ml:id xml:space="preserve">D</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve">Haunch</ml:id>
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							<ml:id xml:space="preserve" subscript="3">Y</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:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>10.960906101571061</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="p3">M</ml:id>
					<ml:apply>
						<ml:plus/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:pow/>
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									<ml:real>2</ml:real>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="s">P</ml:id>
							</ml:apply>
							<ml:apply>
								<ml:mult/>
								<ml:real>2</ml:real>
								<ml:id xml:space="preserve" subscript="s">t</ml:id>
							</ml:apply>
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							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
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												<ml:mult/>
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												<ml:id xml:space="preserve" subscript="rt">d</ml:id>
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										<ml:apply>
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									<ml:apply>
										<ml:mult/>
										<ml:id xml:space="preserve" subscript="w">P</ml:id>
										<ml:id xml:space="preserve" subscript="w">d</ml:id>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve" subscript="t">P</ml:id>
									<ml:id xml:space="preserve" subscript="t">d</ml:id>
								</ml:apply>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:define>
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						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">kip</ml:id>
							<ml:id xml:space="preserve">ft</ml:id>
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							<ml:real>10428.060680794055</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="foot"/>
								<unitReference unit="kip"/>
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					<decimal precision="0" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/>
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					<f family="Arial" charset="0">
						<u>
							<inlineAttr font-style="normal" line-through="false">
								<c val="#00f">Case IV - Neutral axis in the concrete deck at Prb</c>
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					</f>
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			</text>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="4">Y</ml:id>
					<ml:apply>
						<ml:minus/>
						<ml:id xml:space="preserve" subscript="s">t</ml:id>
						<ml:id xml:space="preserve" subscript="br">d</ml:id>
					</ml:apply>
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		<region region-id="15530" left="336" top="1796.25" width="78" height="12" align-x="336" align-y="1806" 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">
						<i>
							<inlineAttr line-through="false">
								<c val="#00f">(from top of deck)</c>
							</inlineAttr>
						</i>
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			</text>
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					<ml:id xml:space="preserve" subscript="c">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:minus/>
								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
									<ml:id xml:space="preserve">Haunch</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:div/>
									<ml:id xml:space="preserve" subscript="c">t</ml:id>
									<ml:real>2</ml:real>
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							</ml:apply>
							<ml:id xml:space="preserve" subscript="4">Y</ml:id>
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				</ml:define>
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						<ml:absval/>
						<ml:apply>
							<ml:minus/>
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								<ml:apply>
									<ml:minus/>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
									<ml:id xml:space="preserve" subscript="tr">d</ml:id>
								</ml:apply>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="w">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:div/>
										<ml:id xml:space="preserve">D</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve">Haunch</ml:id>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="4">Y</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="72"/>
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		<region region-id="13886" left="84" top="1900.5" width="146.25" height="31.5" align-x="99" align-y="1920" 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="t">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:div/>
											<ml:id xml:space="preserve" subscript="t">t</ml:id>
											<ml:real>2</ml:real>
										</ml:apply>
										<ml:id xml:space="preserve">D</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve">Haunch</ml:id>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="4">Y</ml:id>
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					</ml:apply>
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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>7.5</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
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					</result>
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			<rendering item-idref="74"/>
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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="p4">M</ml:id>
					<ml:apply>
						<ml:plus/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve" subscript="4">Y</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="s">P</ml:id>
							</ml:apply>
							<ml:apply>
								<ml:mult/>
								<ml:real>2</ml:real>
								<ml:id xml:space="preserve" subscript="s">t</ml:id>
							</ml:apply>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:mult/>
											<ml:id xml:space="preserve" subscript="rt">P</ml:id>
											<ml:id xml:space="preserve" subscript="rt">d</ml:id>
										</ml:apply>
										<ml:apply>
											<ml:mult/>
											<ml:id xml:space="preserve" subscript="c">P</ml:id>
											<ml:id xml:space="preserve" subscript="c">d</ml:id>
										</ml:apply>
									</ml:apply>
									<ml:apply>
										<ml:mult/>
										<ml:id xml:space="preserve" subscript="w">P</ml:id>
										<ml:id xml:space="preserve" subscript="w">d</ml:id>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve" subscript="t">P</ml:id>
									<ml:id xml:space="preserve" subscript="t">d</ml:id>
								</ml:apply>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:define>
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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="p4">M</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">kip</ml:id>
							<ml:id xml:space="preserve">ft</ml:id>
						</ml:apply>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>10481.067708333332</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="foot"/>
								<unitReference unit="kip"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
				<resultFormat numeric-only="true">
					<decimal precision="0" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/>
					<matrix display-style="auto" expand-nested-arrays="false"/>
					<unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/>
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		<region region-id="13890" left="66" top="1988.25" width="292.5" height="12" align-x="66" align-y="1998" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<text use-page-width="false" push-down="false" lock-width="false">
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					<f family="Arial" charset="0">
						<u>
							<inlineAttr font-style="normal" line-through="false">
								<c val="#00f">Case V - Neutral axis in the concrete deck above Prb and below Prt</c>
							</inlineAttr>
						</u>
					</f>
				</p>
			</text>
		</region>
		<region region-id="13891" left="84" top="2008.5" width="152.25" height="35.25" align-x="101.25" align-y="2028" 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="5">Y</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:id xml:space="preserve" subscript="s">t</ml:id>
						<ml:parens>
							<ml:apply>
								<ml:div/>
								<ml:apply>
									<ml:minus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:apply>
												<ml:plus/>
												<ml:id xml:space="preserve" subscript="rb">P</ml:id>
												<ml:id xml:space="preserve" subscript="c">P</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="w">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="t">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="s">P</ml:id>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:define>
			</math>
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		<region region-id="15531" left="336" top="2018.25" width="78" height="12" align-x="336" align-y="2028" 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">
						<i>
							<inlineAttr line-through="false">
								<c val="#00f">(from top of deck)</c>
							</inlineAttr>
						</i>
					</f>
				</p>
			</text>
		</region>
		<region region-id="13906" left="84" top="2050.5" width="130.5" height="31.5" align-x="100.5" align-y="2070" 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="c">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:minus/>
								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
									<ml:id xml:space="preserve">Haunch</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:div/>
									<ml:id xml:space="preserve" subscript="c">t</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="5">Y</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</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="rt">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:id xml:space="preserve" subscript="5">Y</ml:id>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
									<ml:id xml:space="preserve" subscript="tr">d</ml:id>
								</ml:apply>
							</ml:parens>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="79"/>
		</region>
		<region region-id="13960" left="84" top="2115" width="101.25" height="16.5" align-x="104.25" align-y="2124" 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="rb">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
									<ml:id xml:space="preserve" subscript="br">d</ml:id>
								</ml:apply>
							</ml:parens>
							<ml:id xml:space="preserve" subscript="5">Y</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="80"/>
		</region>
		<region region-id="13981" left="84" top="2162.25" width="132" height="27.75" align-x="102.75" align-y="2178" 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="w">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:div/>
										<ml:id xml:space="preserve">D</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve">Haunch</ml:id>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="5">Y</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="81"/>
		</region>
		<region region-id="13982" left="84" top="2194.5" width="146.25" height="31.5" align-x="99" align-y="2214" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="t">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:div/>
											<ml:id xml:space="preserve" subscript="t">t</ml:id>
											<ml:real>2</ml:real>
										</ml:apply>
										<ml:id xml:space="preserve">D</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve">Haunch</ml:id>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="5">Y</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="82"/>
		</region>
		<region region-id="13983" left="432" top="2217" width="49.5" height="16.5" align-x="447.75" align-y="2226" 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="5">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>10.960906101571061</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="13984" left="84" top="2224.5" width="256.5" height="41.25" align-x="109.5" align-y="2250" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="p5">M</ml:id>
					<ml:apply>
						<ml:plus/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve" subscript="5">Y</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="s">P</ml:id>
							</ml:apply>
							<ml:apply>
								<ml:mult/>
								<ml:real>2</ml:real>
								<ml:id xml:space="preserve" subscript="s">t</ml:id>
							</ml:apply>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:apply>
												<ml:mult/>
												<ml:id xml:space="preserve" subscript="rt">P</ml:id>
												<ml:id xml:space="preserve" subscript="rt">d</ml:id>
											</ml:apply>
											<ml:apply>
												<ml:mult/>
												<ml:id xml:space="preserve" subscript="rb">P</ml:id>
												<ml:id xml:space="preserve" subscript="rb">d</ml:id>
											</ml:apply>
										</ml:apply>
										<ml:apply>
											<ml:mult/>
											<ml:id xml:space="preserve" subscript="c">P</ml:id>
											<ml:id xml:space="preserve" subscript="c">d</ml:id>
										</ml:apply>
									</ml:apply>
									<ml:apply>
										<ml:mult/>
										<ml:id xml:space="preserve" subscript="w">P</ml:id>
										<ml:id xml:space="preserve" subscript="w">d</ml:id>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve" subscript="t">P</ml:id>
									<ml:id xml:space="preserve" subscript="t">d</ml:id>
								</ml:apply>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="84"/>
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		<region region-id="13985" left="432" top="2241" width="78.75" height="16.5" align-x="456" align-y="2250" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="p5">M</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">kip</ml:id>
							<ml:id xml:space="preserve">ft</ml:id>
						</ml:apply>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>10428.060680794055</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="foot"/>
								<unitReference unit="kip"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
				<resultFormat numeric-only="true">
					<decimal precision="0" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/>
					<matrix display-style="auto" expand-nested-arrays="false"/>
					<unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/>
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			<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">
					<f family="Arial" charset="0">
						<u>
							<inlineAttr font-style="normal" line-through="false">
								<c val="#00f">Case VI - Neutral axis in the concrete deck at Prt</c>
							</inlineAttr>
						</u>
					</f>
				</p>
			</text>
		</region>
		<region region-id="14107" left="84" top="2313" width="57" height="16.5" align-x="101.25" align-y="2322" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="6">Y</ml:id>
					<ml:apply>
						<ml:minus/>
						<ml:id xml:space="preserve" subscript="s">t</ml:id>
						<ml:id xml:space="preserve" subscript="tr">d</ml:id>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="86"/>
		</region>
		<region region-id="15593" left="336" top="2312.25" width="78" height="12" align-x="336" align-y="2322" 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">
						<i>
							<inlineAttr line-through="false">
								<c val="#00f">(from top of deck)</c>
							</inlineAttr>
						</i>
					</f>
				</p>
			</text>
		</region>
		<region region-id="14108" left="84" top="2338.5" width="130.5" height="31.5" align-x="100.5" align-y="2358" 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="c">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:minus/>
								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
									<ml:id xml:space="preserve">Haunch</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:div/>
									<ml:id xml:space="preserve" subscript="c">t</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="6">Y</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="87"/>
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		<region region-id="14109" left="84" top="2379" width="101.25" height="16.5" align-x="104.25" align-y="2388" 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="rb">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
									<ml:id xml:space="preserve" subscript="br">d</ml:id>
								</ml:apply>
							</ml:parens>
							<ml:id xml:space="preserve" subscript="6">Y</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="88"/>
		</region>
		<region region-id="14110" left="84" top="2402.25" width="132" height="27.75" align-x="102.75" align-y="2418" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="w">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:div/>
										<ml:id xml:space="preserve">D</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve">Haunch</ml:id>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="6">Y</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="89"/>
		</region>
		<region region-id="14111" left="84" top="2434.5" width="146.25" height="31.5" align-x="99" align-y="2454" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="t">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:div/>
											<ml:id xml:space="preserve" subscript="t">t</ml:id>
											<ml:real>2</ml:real>
										</ml:apply>
										<ml:id xml:space="preserve">D</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve">Haunch</ml:id>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="6">Y</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="90"/>
		</region>
		<region region-id="14112" left="432" top="2457" width="45" height="16.5" align-x="447.75" align-y="2466" 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="6">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>7.5</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="91"/>
		</region>
		<region region-id="14113" left="84" top="2464.5" width="219" height="41.25" align-x="109.5" align-y="2490" 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="p6">M</ml:id>
					<ml:apply>
						<ml:plus/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve" subscript="6">Y</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="s">P</ml:id>
							</ml:apply>
							<ml:apply>
								<ml:mult/>
								<ml:real>2</ml:real>
								<ml:id xml:space="preserve" subscript="s">t</ml:id>
							</ml:apply>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:mult/>
											<ml:id xml:space="preserve" subscript="rb">P</ml:id>
											<ml:id xml:space="preserve" subscript="rb">d</ml:id>
										</ml:apply>
										<ml:apply>
											<ml:mult/>
											<ml:id xml:space="preserve" subscript="c">P</ml:id>
											<ml:id xml:space="preserve" subscript="c">d</ml:id>
										</ml:apply>
									</ml:apply>
									<ml:apply>
										<ml:mult/>
										<ml:id xml:space="preserve" subscript="w">P</ml:id>
										<ml:id xml:space="preserve" subscript="w">d</ml:id>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve" subscript="t">P</ml:id>
									<ml:id xml:space="preserve" subscript="t">d</ml:id>
								</ml:apply>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="92"/>
		</region>
		<region region-id="14114" left="432" top="2481" width="78.75" height="16.5" align-x="456" align-y="2490" 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="p6">M</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">kip</ml:id>
							<ml:id xml:space="preserve">ft</ml:id>
						</ml:apply>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>10481.067708333332</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="foot"/>
								<unitReference unit="kip"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
				<resultFormat numeric-only="true">
					<decimal precision="0" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/>
					<matrix display-style="auto" expand-nested-arrays="false"/>
					<unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/>
				</resultFormat>
			</math>
			<rendering item-idref="93"/>
		</region>
		<region region-id="14124" left="66" top="2516.25" width="233.25" height="12" align-x="66" align-y="2526" 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">
					<f family="Arial" charset="0">
						<u>
							<inlineAttr font-style="normal" line-through="false">
								<c val="#00f">Case VII - Neutral Axis in the concrete deck above Prt</c>
							</inlineAttr>
						</u>
					</f>
				</p>
			</text>
		</region>
		<region region-id="14140" left="84" top="2536.5" width="152.25" height="35.25" align-x="101.25" align-y="2556" 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="7">Y</ml:id>
					<ml:apply>
						<ml:mult/>
						<ml:id xml:space="preserve" subscript="s">t</ml:id>
						<ml:parens>
							<ml:apply>
								<ml:div/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:apply>
												<ml:plus/>
												<ml:id xml:space="preserve" subscript="rb">P</ml:id>
												<ml:id xml:space="preserve" subscript="c">P</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="w">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="t">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="s">P</ml:id>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="94"/>
		</region>
		<region region-id="15594" left="336" top="2546.25" width="78" height="12" align-x="336" align-y="2556" 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">
						<i>
							<inlineAttr line-through="false">
								<c val="#00f">(from top of deck)</c>
							</inlineAttr>
						</i>
					</f>
				</p>
			</text>
		</region>
		<region region-id="14141" left="84" top="2578.5" width="130.5" height="31.5" align-x="100.5" align-y="2598" 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="c">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:minus/>
								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
									<ml:id xml:space="preserve">Haunch</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:div/>
									<ml:id xml:space="preserve" subscript="c">t</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="7">Y</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="95"/>
		</region>
		<region region-id="14142" left="84" top="2619" width="101.25" height="16.5" align-x="104.25" align-y="2628" 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="rb">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:parens>
								<ml:apply>
									<ml:minus/>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
									<ml:id xml:space="preserve" subscript="br">d</ml:id>
								</ml:apply>
							</ml:parens>
							<ml:id xml:space="preserve" subscript="7">Y</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="96"/>
		</region>
		<region region-id="14143" left="84" top="2642.25" width="132" height="27.75" align-x="102.75" align-y="2658" 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="w">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:div/>
										<ml:id xml:space="preserve">D</ml:id>
										<ml:real>2</ml:real>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve">Haunch</ml:id>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="7">Y</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="97"/>
		</region>
		<region region-id="14144" left="84" top="2674.5" width="146.25" height="31.5" align-x="99" 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:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve" subscript="t">d</ml:id>
					<ml:apply>
						<ml:absval/>
						<ml:apply>
							<ml:minus/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:div/>
											<ml:id xml:space="preserve" subscript="t">t</ml:id>
											<ml:real>2</ml:real>
										</ml:apply>
										<ml:id xml:space="preserve">D</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="s">t</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve">Haunch</ml:id>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="7">Y</ml:id>
						</ml:apply>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="98"/>
		</region>
		<region region-id="14145" left="432" top="2697" width="49.5" height="16.5" align-x="447.75" align-y="2706" 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="7">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>10.960906101571061</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
			</math>
			<rendering item-idref="99"/>
		</region>
		<region region-id="14146" left="84" top="2704.5" width="256.5" height="41.25" align-x="109.5" align-y="2730" 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="p7">M</ml:id>
					<ml:apply>
						<ml:plus/>
						<ml:apply>
							<ml:div/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:pow/>
									<ml:id xml:space="preserve" subscript="7">Y</ml:id>
									<ml:real>2</ml:real>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="s">P</ml:id>
							</ml:apply>
							<ml:apply>
								<ml:mult/>
								<ml:real>2</ml:real>
								<ml:id xml:space="preserve" subscript="s">t</ml:id>
							</ml:apply>
						</ml:apply>
						<ml:parens>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:apply>
												<ml:mult/>
												<ml:id xml:space="preserve" subscript="rt">P</ml:id>
												<ml:id xml:space="preserve" subscript="rt">d</ml:id>
											</ml:apply>
											<ml:apply>
												<ml:mult/>
												<ml:id xml:space="preserve" subscript="rb">P</ml:id>
												<ml:id xml:space="preserve" subscript="rb">d</ml:id>
											</ml:apply>
										</ml:apply>
										<ml:apply>
											<ml:mult/>
											<ml:id xml:space="preserve" subscript="c">P</ml:id>
											<ml:id xml:space="preserve" subscript="c">d</ml:id>
										</ml:apply>
									</ml:apply>
									<ml:apply>
										<ml:mult/>
										<ml:id xml:space="preserve" subscript="w">P</ml:id>
										<ml:id xml:space="preserve" subscript="w">d</ml:id>
									</ml:apply>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve" subscript="t">P</ml:id>
									<ml:id xml:space="preserve" subscript="t">d</ml:id>
								</ml:apply>
							</ml:apply>
						</ml:parens>
					</ml:apply>
				</ml:define>
			</math>
			<rendering item-idref="100"/>
		</region>
		<region region-id="14147" left="432" top="2721" width="78.75" height="16.5" align-x="456" align-y="2730" 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="p7">M</ml:id>
					<ml:unitOverride>
						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">kip</ml:id>
							<ml:id xml:space="preserve">ft</ml:id>
						</ml:apply>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>10428.060680794055</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="foot"/>
								<unitReference unit="kip"/>
							</unitMonomial>
						</unitedValue>
					</result>
				</ml:eval>
				<resultFormat numeric-only="true">
					<decimal precision="0" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/>
					<matrix display-style="auto" expand-nested-arrays="false"/>
					<unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/>
				</resultFormat>
			</math>
			<rendering item-idref="101"/>
		</region>
		<region region-id="15112" left="0" top="2778" width="6000" height="6" align-x="0" align-y="2778" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
			<pageBreak/>
		</region>
		<region region-id="15132" left="48" top="2792.25" width="321.75" height="15" align-x="48" align-y="2802" 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">
								<c val="#00f">Determine plastic neutral axis location and corresponding M</c>
							</inlineAttr>
						</b>
					</f>
					<f family="Arial" charset="0">
						<b>
							<inlineAttr line-through="false">
								<c val="#00f">
									<sub>p</sub>
								</c>
							</inlineAttr>
						</b>
					</f>
					<f family="Arial" charset="0">
						<b>
							<inlineAttr line-through="false">
								<c val="#00f"> and Y</c>
							</inlineAttr>
						</b>
					</f>
				</p>
			</text>
		</region>
		<region region-id="15123" left="84" top="2818.5" width="245.25" height="231.75" align-x="105" align-y="2838" 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="p">M</ml:id>
					<ml:program>
						<ml:ifThen>
							<ml:apply>
								<ml:lessThan/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:apply>
												<ml:plus/>
												<ml:id xml:space="preserve" subscript="t">P</ml:id>
												<ml:id xml:space="preserve" subscript="w">P</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="c">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:div/>
										<ml:apply>
											<ml:minus/>
											<ml:id xml:space="preserve" subscript="s">t</ml:id>
											<ml:id xml:space="preserve" subscript="tr">d</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="s">t</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="s">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="p7">M</ml:id>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:apply>
												<ml:plus/>
												<ml:id xml:space="preserve" subscript="t">P</ml:id>
												<ml:id xml:space="preserve" subscript="w">P</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="c">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:div/>
										<ml:apply>
											<ml:minus/>
											<ml:id xml:space="preserve" subscript="s">t</ml:id>
											<ml:id xml:space="preserve" subscript="tr">d</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="s">t</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="s">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="p6">M</ml:id>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:id xml:space="preserve" subscript="t">P</ml:id>
											<ml:id xml:space="preserve" subscript="w">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="c">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rb">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:mult/>
										<ml:apply>
											<ml:div/>
											<ml:apply>
												<ml:minus/>
												<ml:id xml:space="preserve" subscript="s">t</ml:id>
												<ml:id xml:space="preserve" subscript="tr">d</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="s">t</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="s">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="p5">M</ml:id>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:id xml:space="preserve" subscript="t">P</ml:id>
											<ml:id xml:space="preserve" subscript="w">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="c">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rb">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:mult/>
										<ml:apply>
											<ml:div/>
											<ml:apply>
												<ml:minus/>
												<ml:id xml:space="preserve" subscript="s">t</ml:id>
												<ml:id xml:space="preserve" subscript="br">d</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="s">t</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="s">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="p4">M</ml:id>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:id xml:space="preserve" subscript="t">P</ml:id>
										<ml:id xml:space="preserve" subscript="w">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="c">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:mult/>
											<ml:apply>
												<ml:div/>
												<ml:apply>
													<ml:minus/>
													<ml:id xml:space="preserve" subscript="s">t</ml:id>
													<ml:id xml:space="preserve" subscript="br">d</ml:id>
												</ml:apply>
												<ml:id xml:space="preserve" subscript="s">t</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="s">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="p3">M</ml:id>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:id xml:space="preserve" subscript="t">P</ml:id>
										<ml:id xml:space="preserve" subscript="w">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="c">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:id xml:space="preserve" subscript="s">P</ml:id>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="p2">M</ml:id>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve" subscript="t">P</ml:id>
									<ml:id xml:space="preserve" subscript="w">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:id xml:space="preserve" subscript="c">P</ml:id>
											<ml:id xml:space="preserve" subscript="s">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="p1">M</ml:id>
						</ml:ifThen>
					</ml:program>
				</ml:define>
			</math>
			<rendering item-idref="102"/>
		</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" subscript="p">D</ml:id>
					<ml:program>
						<ml:ifThen>
							<ml:apply>
								<ml:lessThan/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:apply>
												<ml:plus/>
												<ml:id xml:space="preserve" subscript="t">P</ml:id>
												<ml:id xml:space="preserve" subscript="w">P</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="c">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:div/>
										<ml:apply>
											<ml:minus/>
											<ml:id xml:space="preserve" subscript="s">t</ml:id>
											<ml:id xml:space="preserve" subscript="tr">d</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="s">t</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="s">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="7">Y</ml:id>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:apply>
												<ml:plus/>
												<ml:id xml:space="preserve" subscript="t">P</ml:id>
												<ml:id xml:space="preserve" subscript="w">P</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="c">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:div/>
										<ml:apply>
											<ml:minus/>
											<ml:id xml:space="preserve" subscript="s">t</ml:id>
											<ml:id xml:space="preserve" subscript="tr">d</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="s">t</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="s">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="6">Y</ml:id>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:id xml:space="preserve" subscript="t">P</ml:id>
											<ml:id xml:space="preserve" subscript="w">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="c">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rb">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:mult/>
										<ml:apply>
											<ml:div/>
											<ml:apply>
												<ml:minus/>
												<ml:id xml:space="preserve" subscript="s">t</ml:id>
												<ml:id xml:space="preserve" subscript="tr">d</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="s">t</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="s">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="5">Y</ml:id>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:id xml:space="preserve" subscript="t">P</ml:id>
											<ml:id xml:space="preserve" subscript="w">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="c">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rb">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:mult/>
										<ml:apply>
											<ml:div/>
											<ml:apply>
												<ml:minus/>
												<ml:id xml:space="preserve" subscript="s">t</ml:id>
												<ml:id xml:space="preserve" subscript="br">d</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="s">t</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="s">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="4">Y</ml:id>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:id xml:space="preserve" subscript="t">P</ml:id>
										<ml:id xml:space="preserve" subscript="w">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="c">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:mult/>
											<ml:apply>
												<ml:div/>
												<ml:apply>
													<ml:minus/>
													<ml:id xml:space="preserve" subscript="s">t</ml:id>
													<ml:id xml:space="preserve" subscript="br">d</ml:id>
												</ml:apply>
												<ml:id xml:space="preserve" subscript="s">t</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="s">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="3">Y</ml:id>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:id xml:space="preserve" subscript="t">P</ml:id>
										<ml:id xml:space="preserve" subscript="w">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="c">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:id xml:space="preserve" subscript="s">P</ml:id>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:apply>
								<ml:minus/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:id xml:space="preserve" subscript="2">Y</ml:id>
										<ml:id xml:space="preserve" subscript="s">t</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve">Haunch</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="c">t</ml:id>
							</ml:apply>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve" subscript="t">P</ml:id>
									<ml:id xml:space="preserve" subscript="w">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:id xml:space="preserve" subscript="c">P</ml:id>
											<ml:id xml:space="preserve" subscript="s">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve" subscript="1">Y</ml:id>
									<ml:id xml:space="preserve">Haunch</ml:id>
								</ml:apply>
								<ml:id xml:space="preserve" subscript="s">t</ml:id>
							</ml:apply>
						</ml:ifThen>
					</ml:program>
				</ml:define>
			</math>
			<rendering item-idref="103"/>
		</region>
		<region region-id="15408" left="84" top="3321" width="199.5" height="33" align-x="107.25" align-y="3330" 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="cp">D</ml:id>
					<ml:program>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve" subscript="t">P</ml:id>
									<ml:id xml:space="preserve" subscript="w">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:id xml:space="preserve" subscript="c">P</ml:id>
											<ml:id xml:space="preserve" subscript="s">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:id xml:space="preserve" subscript="1">Y</ml:id>
						</ml:ifThen>
						<ml:otherwise>
							<ml:apply>
								<ml:mult/>
								<ml:real>0</ml:real>
								<ml:id xml:space="preserve">in</ml:id>
							</ml:apply>
						</ml:otherwise>
					</ml:program>
				</ml:define>
			</math>
			<rendering item-idref="104"/>
		</region>
		<region region-id="16118" left="72" top="3508.5" width="236.25" height="231.75" align-x="98.25" align-y="3528" 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">Case</ml:id>
					<ml:program>
						<ml:ifThen>
							<ml:apply>
								<ml:lessThan/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:apply>
												<ml:plus/>
												<ml:id xml:space="preserve" subscript="t">P</ml:id>
												<ml:id xml:space="preserve" subscript="w">P</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="c">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:div/>
										<ml:apply>
											<ml:minus/>
											<ml:id xml:space="preserve" subscript="s">t</ml:id>
											<ml:id xml:space="preserve" subscript="tr">d</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="s">t</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="s">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:real>7</ml:real>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:apply>
												<ml:plus/>
												<ml:id xml:space="preserve" subscript="t">P</ml:id>
												<ml:id xml:space="preserve" subscript="w">P</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="c">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:div/>
										<ml:apply>
											<ml:minus/>
											<ml:id xml:space="preserve" subscript="s">t</ml:id>
											<ml:id xml:space="preserve" subscript="tr">d</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="s">t</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="s">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:real>6</ml:real>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:id xml:space="preserve" subscript="t">P</ml:id>
											<ml:id xml:space="preserve" subscript="w">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="c">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rb">P</ml:id>
								</ml:apply>
								<ml:apply>
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									<ml:apply>
										<ml:mult/>
										<ml:apply>
											<ml:div/>
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												<ml:id xml:space="preserve" subscript="s">t</ml:id>
												<ml:id xml:space="preserve" subscript="tr">d</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="s">t</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="s">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:real>5</ml:real>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:id xml:space="preserve" subscript="t">P</ml:id>
											<ml:id xml:space="preserve" subscript="w">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="c">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rb">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:mult/>
										<ml:apply>
											<ml:div/>
											<ml:apply>
												<ml:minus/>
												<ml:id xml:space="preserve" subscript="s">t</ml:id>
												<ml:id xml:space="preserve" subscript="br">d</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="s">t</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="s">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:real>4</ml:real>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:id xml:space="preserve" subscript="t">P</ml:id>
										<ml:id xml:space="preserve" subscript="w">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="c">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:mult/>
											<ml:apply>
												<ml:div/>
												<ml:apply>
													<ml:minus/>
													<ml:id xml:space="preserve" subscript="s">t</ml:id>
													<ml:id xml:space="preserve" subscript="br">d</ml:id>
												</ml:apply>
												<ml:id xml:space="preserve" subscript="s">t</ml:id>
											</ml:apply>
											<ml:id xml:space="preserve" subscript="s">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:real>3</ml:real>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:id xml:space="preserve" subscript="t">P</ml:id>
										<ml:id xml:space="preserve" subscript="w">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="c">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:id xml:space="preserve" subscript="s">P</ml:id>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:real>2</ml:real>
						</ml:ifThen>
						<ml:ifThen>
							<ml:apply>
								<ml:greaterOrEqual/>
								<ml:apply>
									<ml:plus/>
									<ml:id xml:space="preserve" subscript="t">P</ml:id>
									<ml:id xml:space="preserve" subscript="w">P</ml:id>
								</ml:apply>
								<ml:apply>
									<ml:plus/>
									<ml:apply>
										<ml:plus/>
										<ml:apply>
											<ml:plus/>
											<ml:id xml:space="preserve" subscript="c">P</ml:id>
											<ml:id xml:space="preserve" subscript="s">P</ml:id>
										</ml:apply>
										<ml:id xml:space="preserve" subscript="rb">P</ml:id>
									</ml:apply>
									<ml:id xml:space="preserve" subscript="rt">P</ml:id>
								</ml:apply>
							</ml:apply>
							<ml:real>1</ml:real>
						</ml:ifThen>
					</ml:program>
				</ml:define>
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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">
								<c val="#00f">Positive flexure plastic moment summary</c>
							</inlineAttr>
						</b>
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			</text>
		</region>
		<region region-id="15319" left="84" top="3824.25" width="3" height="12" align-x="84" align-y="3834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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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">Case</ml:id>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>2</ml:real>
					</result>
				</ml:eval>
				<resultFormat numeric-only="true">
					<decimal precision="0" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/>
					<matrix display-style="auto" expand-nested-arrays="false"/>
					<unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/>
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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="p">M</ml:id>
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						<ml:apply>
							<ml:mult/>
							<ml:id xml:space="preserve">kip</ml:id>
							<ml:id xml:space="preserve">ft</ml:id>
						</ml:apply>
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					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>10280.091599934895</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="foot"/>
								<unitReference unit="kip"/>
							</unitMonomial>
						</unitedValue>
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				<resultFormat numeric-only="true">
					<decimal precision="0" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/>
					<matrix display-style="auto" expand-nested-arrays="false"/>
					<unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/>
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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">(Plastic Moment)</p>
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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="cp">D</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</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
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			<rendering item-idref="108"/>
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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">(Depth of Web in Compression)</p>
			</text>
		</region>
		<region region-id="15645" left="84" top="3897" width="51" height="16.5" align-x="101.25" align-y="3906" 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="p">D</ml:id>
					<ml:unitOverride>
						<ml:id xml:space="preserve">in</ml:id>
					</ml:unitOverride>
					<result xmlns="http://schemas.mathsoft.com/math30">
						<unitedValue>
							<ml:real>10.342031249999998</ml:real>
							<unitMonomial xmlns="http://schemas.mathsoft.com/units10">
								<unitReference unit="inch"/>
							</unitMonomial>
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			<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">(Distance From Top Of Deck To Plastic N.A.)</p>
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