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background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="6">ϕ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:mult/> <ml:real>0</ml:real> <ml:id xml:space="preserve">m</ml:id> </ml:apply> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:id xml:space="preserve">b</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">H</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:id xml:space="preserve">G</ml:id> </ml:apply> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">H</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">tanh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">tanh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">tanh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">H</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">G</ml:id> </ml:apply> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">H</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">H</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">tanh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">H</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:otherwise> </ml:program> </ml:define> </math> </region> <region region-id="135" left="6" top="1001.25" width="345.75" height="57.75" align-x="34.5" align-y="1032" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="7">ϕ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">G</ml:id> </ml:apply> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> </region> <region region-id="139" left="24" top="1100.25" width="171.75" height="72.75" align-x="36" align-y="1146" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">S</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:real>6</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> </region> <region region-id="138" left="18" top="1208.25" width="440.25" height="48.75" align-x="46.5" align-y="1230" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="8">ϕ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">t</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">S</ml:id> <ml:apply> <ml:id xml:space="preserve">tanh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">S</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">z</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:real>6</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> </region> <region region-id="144" left="12" top="1298.25" width="647.25" height="59.25" align-x="40.5" 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:function> <ml:id xml:space="preserve" subscript="9">ϕ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> <ml:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:apply> 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xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">tanh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">tanh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">tanh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:otherwise> </ml:program> </ml:apply> </ml:define> </math> </region> 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<ml:real>6</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:id xml:space="preserve">tanh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">z</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:real>6</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> </region> <region region-id="152" left="18" top="1628.25" width="126" height="78.75" align-x="36" align-y="1680" 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">H1</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">tanh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> </region> <region region-id="153" left="24" top="1757.25" width="462.75" height="57.75" align-x="56.25" align-y="1788" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="12">ϕ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">t</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">H1</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">tanh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">tanh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">z</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> </region> <region region-id="155" left="18" top="1932.75" width="75.75" height="221.25" align-x="47.25" align-y="2046" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id 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item-idref="2"/> </region> <region region-id="99" left="576" top="62.25" width="60.75" height="24" align-x="576" align-y="72" 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"> Select from table below </text> </region> <region region-id="74" left="312" top="61.5" width="101.25" height="25.5" align-x="337.5" align-y="78" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ffff" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="w">C</ml:id> <ml:apply> <ml:mult/> <ml:real>1688000</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>6</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="97" left="432" top="66.75" width="45.75" height="15.75" 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show-highlight="true" is-protected="true" z-order="0" background-color="#80ffff" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:mult/> <ml:real>29000</ml:real> <ml:id xml:space="preserve">ksi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="77" left="120" top="72.75" width="75.75" height="15.75" align-x="137.25" align-y="84" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ffff" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">G</ml:id> <ml:apply> <ml:mult/> <ml:real>11200</ml:real> <ml:id xml:space="preserve">ksi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="78" left="222" top="67.5" width="65.25" height="21" align-x="235.5" align-y="84" 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background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> uniformly distributed torque per unit length for cases 4, 7, 10, and 12 or its maximum value for cases 5, 8, and 11 </text> </region> <region region-id="106" left="558" top="110.25" width="180" height="36" align-x="558" align-y="120" 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"> abscissa from left end of point of application of inner torque, or length from left end of applied uniform torque </text> </region> <region region-id="58" left="12" top="114.75" width="73.5" height="15.75" align-x="27.75" align-y="126" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ffff" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T</ml:id> 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show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="6">ϕ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:mult/> <ml:real>0</ml:real> <ml:id xml:space="preserve">m</ml:id> </ml:apply> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:id xml:space="preserve">b</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">H</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:id xml:space="preserve">G</ml:id> </ml:apply> <ml:id 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<ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">H</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">tanh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id 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xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:otherwise> </ml:program> </ml:define> </math> </region> <region region-id="135" left="6" top="1001.25" width="345.75" height="57.75" align-x="34.5" align-y="1032" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="7">ϕ</ml:id> <ml:boundVars> <ml:id 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</ml:parens> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> </region> <region region-id="139" left="24" top="1100.25" width="171.75" height="72.75" align-x="36" align-y="1146" show-border="false" 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