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height="25.5" align-x="50.25" align-y="750" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#00f">Berechnung der Stabkräfte: </c> </inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr font-weight="normal" font-style="normal" line-through="false"> <c val="#00f">(</c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" line-through="false"> <c val="#00f">d</c> </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" line-through="false"> <c val="#00f"> <f family="Arial" charset="0" size="10">abei wurden die Stabkräfte indiziert (als Literalindex), ist nicht</f> </c> </inlineAttr> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" line-through="false"> <c val="#00f"> <tab/> <tab/> <tab/> <tab/> <sp count="6"/>notwendig, man könnte auch mit den obigen Definitionen arbeiten)</c> </inlineAttr> </f> </text> </region> <region region-id="1035" left="24" top="777.75" width="58.5" height="57.75" align-x="42" align-y="810" 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" font="4">F</ml:id> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">F</ml:id> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="1051" left="306" top="800.25" width="154.5" height="12" align-x="327" align-y="810" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Belastung in vektorieller Darstellung</c> </inlineAttr> </f> </text> </region> <region region-id="1169" left="24" top="856.5" width="77.25" height="80.25" align-x="48" align-y="900" 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" font="4" subscript="1">S</ml:id> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:real>2</ml:real> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="s">h</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="1221" left="114" top="847.5" width="71.25" height="98.25" align-x="138.75" align-y="900" 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" font="4" subscript="2">S</ml:id> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">d</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="s">h</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="1223" left="210" top="847.5" width="70.5" height="98.25" align-x="234" align-y="900" 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" font="4" subscript="3">S</ml:id> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:div/> <ml:id xml:space="preserve">d</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="s">h</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="1053" left="306" top="890.25" width="189.75" height="21.75" align-x="336" align-y="900" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Stabvektoren </c> </inlineAttr> </f> <f family="Arial" charset="0" size="8"> <inlineAttr line-through="false"> <c val="#00f">(Vektoren in Stabrichtung, nicht zu</c> </inlineAttr> </f> <f family="Arial" charset="0" size="8"> <inlineAttr line-through="false"> <c val="#00f"> <sp count="27"/>verwechseln mit den Stabkräften) </c> </inlineAttr> </f> </text> </region> <region region-id="1055" left="24" top="972.75" width="473.25" height="57" align-x="47.25" align-y="984" 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"> Die Stabkräfte werden über die Gleichgewichtsbedingung für Kräfte berechnet. Dabei treten die unbekannten Proprtionalitätsfaktoren (k<f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> 1 </c> </inlineAttr> </f>, k<f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> 2 </c> </inlineAttr> </f>, k<f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> 3 </c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">mit</c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> <sp/> </c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">Literalindex)</c> </inlineAttr> </f> auf, die zur Bestimmung der Stabkräfte dienen. Sie geben die Zug- oder Druckkräfte (je nach Vorzeichenkonvetion) in den Stäben bezogen auf die Längeneinheit an.<sp count="3"/> </text> </region> <region region-id="866" left="18" top="1056.75" width="40.5" height="15.75" align-x="37.5" align-y="1068" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">Given</ml:id> </math> <rendering item-idref="21"/> </region> <region region-id="1531" left="360" top="1064.25" width="134.25" height="147" align-x="366.75" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <c val="#00f"> <inlineAttr line-through="false"> <f family="Arial" charset="0" size="10">Die Vektoren </f> </inlineAttr> </c> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">F</c> </inlineAttr> </f> <inlineAttr font-style="normal" underline="false" line-through="false"> <c val="#00f"> <f family="Arial" charset="0" size="10">i</f> </c> </inlineAttr> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f"> und </c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f"> S </c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-style="normal" underline="false" line-through="false"> <c val="#00f"> i </c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <c val="#00f"> <inlineAttr line-through="false"> werden mit Feldindizes (STRG [ ) versehen, damit man auf die einzelnen Komponenten der Vektoren zugreifen kann.</inlineAttr> </c> </f> <inlineAttr line-through="false"> <c val="#00f"> <f family="Arial" charset="0" size="10">Achtung:</f> </c> </inlineAttr> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">ORIGIN wurde auf 1 gestellt (Mathcad 11: Extras - Arbeitsblattoptionen - vordefinierte Variablen, Standardeinstellung ist ORIGIN = 0). </c> </inlineAttr> </f> </text> </region> <region region-id="1062" left="60" top="1086.75" width="169.5" height="24" align-x="205.5" align-y="1098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="1">S</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="2">S</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="3">S</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4">F</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="22"/> </region> <region region-id="1522" left="258" top="1088.25" width="69" height="12" align-x="260.25" align-y="1098" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">x - Komponente</c> </inlineAttr> </f> </text> </region> <region region-id="1064" left="60" top="1122.75" width="169.5" height="24" align-x="205.5" align-y="1134" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="1">S</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="2">S</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="3">S</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4">F</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="23"/> </region> <region region-id="1523" left="258" top="1124.25" width="69" height="12" align-x="258" align-y="1134" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">y - Komponente</c> </inlineAttr> </f> </text> </region> <region region-id="1066" left="60" top="1158.75" width="169.5" height="24" align-x="205.5" align-y="1170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="1">S</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="2">S</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="3">S</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4">F</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="24"/> </region> <region region-id="1524" left="258" top="1160.25" width="69" height="12" align-x="258" align-y="1170" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">z - Komponente</c> </inlineAttr> </f> </text> </region> <region region-id="1722" left="18" top="1248.75" width="233.25" height="17.25" align-x="34.5" align-y="1260" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="System.NullReferenceException: Der Objektverweis wurde nicht auf eine Objektinstanz festgelegt. bei mslisp.StandardBuiltins.contains_hash(Object h, Object k) bei mslisp.StandardBuiltins_contains_hash_Builtin.Invoke(Object[] args) bei mslisp.ApplyExpr.execute(Env e) bei mslisp.IfExpr.execute(Env e) bei mslisp.LambdaExpr.Invoke(Object[] args) bei mslisp.ApplyExpr.execute(Env e) bei mslisp.IfExpr.execute(Env e) bei mslisp.LambdaExpr.Invoke(Object[] args) bei mslisp.ApplyExpr.execute(Env e) bei mslisp.IfExpr.execute(Env e) bei mslisp.LambdaExpr.Invoke(Object[] args) bei mslisp.ApplyExpr.execute(Env e) bei mslisp.LambdaExpr.Invoke(Object[] args) bei mslisp.ApplyFunction.Invoke(Object[] args) bei mslisp.ApplyExpr.execute(Env e) bei mslisp.ApplyExpr.execute(Env e) bei mslisp.LambdaExpr.Invoke(Object[] args) bei mslisp.ApplyExpr.execute(Env e) bei mslisp.HandlerCaseExpr.execute(Env e)" optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k</ml:id> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:sequence> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">float</ml:id> <ml:real>3</ml:real> </ml:sequence> </ml:command> <ml:symResult> <ml:placeholder/> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="1530" left="354" top="1250.25" width="139.5" height="48" align-x="357.75" align-y="1260" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr font-style="normal" line-through="false"> <c val="#00f">Definition von k:= suchen(..) liefert den Lösungsvektor k; man kann nun auf die Feldindizes (STRG [ ) zugreifen</c> </inlineAttr> </f> </text> </region> <region region-id="1532" left="18" top="1366.5" width="46.5" height="33.75" align-x="33" align-y="1386" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> </ml:eval> </math> <rendering item-idref="26"/> </region> <region region-id="1161" left="0" top="1440" width="6000" height="6" align-x="0" align-y="1440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="1184" left="30" top="1482.75" width="73.5" height="19.5" align-x="61.5" align-y="1494" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="1">FS</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve" font="4" subscript="1">S</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="1537" left="150" top="1482.75" width="51.75" height="19.5" align-x="180" align-y="1494" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="1">FS</ml:id> </ml:eval> </math> <rendering item-idref="28"/> </region> <region region-id="1128" left="336" top="1490.25" width="108" height="12" align-x="356.25" align-y="1500" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Stabkraft des Stabes DB</c> </inlineAttr> </f> </text> </region> <region region-id="1183" left="30" top="1518.75" width="62.25" height="19.5" align-x="70.5" align-y="1530" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="1">FS</ml:id> </ml:apply> </ml:eval> </math> <rendering item-idref="29"/> </region> <region region-id="1127" left="336" top="1520.25" width="103.5" height="12" align-x="350.25" align-y="1530" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text 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align-x="218.25" align-y="1560" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="v">F</ml:id> </ml:eval> </math> <rendering item-idref="31"/> </region> <region region-id="1126" left="336" top="1550.25" width="88.5" height="12" align-x="387" align-y="1560" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Vertikalkomponente </c> </inlineAttr> </f> </text> </region> <region region-id="1181" left="30" top="1578.75" width="102.75" height="20.25" align-x="51.75" align-y="1590" show-border="false" 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push-down="false" lock-width="true"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Stabkraft des Stabes DA</c> </inlineAttr> </f> </text> </region> <region region-id="1179" left="30" top="1686.75" width="63" height="19.5" align-x="71.25" align-y="1698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="2">FS</ml:id> </ml:apply> </ml:eval> </math> <rendering item-idref="36"/> </region> <region region-id="1123" left="336" top="1688.25" width="103.5" height="12" align-x="350.25" align-y="1698" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Betrag der Stabkraft DA</c> </inlineAttr> </f> </text> </region> <region region-id="1178" left="30" top="1716.75" width="100.5" height="20.25" align-x="51.75" align-y="1728" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="v">F</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="2">FS</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="943" left="204" top="1716.75" width="42" height="20.25" align-x="224.25" 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show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="h">F</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="2">FS</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="945" left="204" top="1752.75" width="42" height="20.25" align-x="224.25" align-y="1764" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id 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<ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve" font="4" subscript="3">S</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="1543" left="150" top="1818.75" width="51.75" height="19.5" align-x="180" align-y="1830" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="3">FS</ml:id> </ml:eval> </math> <rendering item-idref="42"/> </region> <region region-id="1120" left="336" top="1820.25" width="108" height="12" align-x="336" align-y="1830" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Stabkraft des Stabes DC</c> </inlineAttr> </f> </text> </region> <region region-id="1294" left="30" top="1854.75" width="62.25" height="19.5" align-x="70.5" align-y="1866" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="3">FS</ml:id> </ml:apply> </ml:eval> </math> <rendering item-idref="43"/> </region> <region region-id="1119" left="336" top="1856.25" width="103.5" height="12" align-x="350.25" align-y="1866" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Betrag der Stabkraft DC</c> </inlineAttr> </f> </text> </region> <region region-id="1295" left="30" top="1884.75" width="99.75" height="20.25" align-x="51.75" align-y="1896" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="v">F</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="3">FS</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="44"/> </region> <region region-id="1296" left="204" top="1884.75" width="42" height="20.25" align-x="224.25" align-y="1896" 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is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="h">F</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="3">FS</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="46"/> </region> <region region-id="1298" left="204" top="1920.75" width="42" height="20.25" align-x="224.25" align-y="1932" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="h">F</ml:id> </ml:eval> </math> <rendering item-idref="47"/> </region> <region region-id="1300" left="336" top="1922.25" width="96.75" height="12" align-x="387" align-y="1932" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Horizontalkomponente</c> </inlineAttr> </f> </text> </region> <region region-id="1191" left="12" top="1992.75" width="485.25" height="27" align-x="20.25" align-y="2004" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Aus Symmetriegründen müssen die drei Stabkräfte den gleichen Betrag haben; was durch die Rechnung bestätigt wird. </text> </region> <region region-id="1190" left="0" top="2040" width="6000" height="6" align-x="0" align-y="2040" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="954" left="12" top="2046.75" width="211.5" height="13.5" align-x="38.25" align-y="2058" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#00f">Berechnung der Zugkraft in der Kette:</c> </inlineAttr> </f> </text> </region> <region region-id="1199" left="6" top="2076.75" width="489.75" height="25.5" align-x="14.25" align-y="2088" 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"> Aus der Skizze (Draufsicht) erkennt man (x- und y-Richtung wie in Skizze, z-Komponente = 0): <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">(Aus Symmetriegründen müssen alle Zugkräfte gleich groß sein).</c> </inlineAttr> </f> </text> </region> <region region-id="1569" left="318" top="2114.25" width="177.75" height="36" align-x="326.25" align-y="2124" 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"> <f size="10"> <inlineAttr line-through="false"> <c val="#00f">Das Basisdreieck ist gleichseitig </c> </inlineAttr> </f> <f size="10">(Winkel zwischen 2 Ketten ist 60°)</f> <f size="10"> <inlineAttr line-through="false"> <c val="#00f">, daher gilt</c> </inlineAttr> </f> <f family="Symbol" charset="2" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">b = </c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" 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xml:space="preserve" font="4" subscript="h">F</ml:id> <ml:matrix rows="3" cols="1"> <ml:real font="0">0</ml:real> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="h">F</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="1566" left="324" top="2186.25" width="99.75" height="12" align-x="375" align-y="2196" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Horizontalkomponente </c> </inlineAttr> </f> </text> </region> <region region-id="1196" left="18" top="2235.75" width="120" height="57.75" align-x="57.75" align-y="2268" 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" font="4" subscript="KBA">r</ml:id> <ml:apply> <ml:mult/> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:id xml:space="preserve" font="1">sin</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:matrix> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="1197" left="168" top="2235.75" width="120.75" height="57.75" align-x="208.5" align-y="2268" 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" font="4" subscript="KBC">r</ml:id> <ml:apply> <ml:mult/> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:matrix> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="1253" left="324" top="2258.25" width="138.75" height="24" align-x="365.25" align-y="2268" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Richtungsvektoren der Zugkräfte</c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">(ohne Einheiten)</c> </inlineAttr> </f> </text> </region> <region region-id="1554" left="18" top="2316" width="429" height="35.25" align-x="44.25" align-y="2328" 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"> Berechnung der Proportionalitätsfaktoren <f family="Symbol" charset="2" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">l</c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> 1 </c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> und </c> </inlineAttr> </f> <f family="Symbol" charset="2" size="12"> <c val="#00f"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">l</inlineAttr> </c> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> 2 </c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> für die Zugkräfte in den Ketten. </c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <c val="#00f"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(Gleiche Begründung wie für k</inlineAttr> </c> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">1</c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">, k</c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> 2 </c> </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> <f family="Arial" charset="0" size="12">, k</f> </c> </inlineAttr> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> 3 </c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">)</c> </inlineAttr> </f> </text> </region> <region region-id="1551" left="30" top="2362.5" width="66.75" height="33.75" align-x="51.75" align-y="2382" 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="1">λ</ml:id> <ml:apply> <ml:mult/> <ml:real>100</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="52"/> </region> <region region-id="1552" left="180" top="2362.5" width="66.75" height="33.75" align-x="201.75" align-y="2382" 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">λ</ml:id> <ml:apply> <ml:mult/> <ml:real>100</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="53"/> </region> <region region-id="1556" left="318" top="2372.25" width="177.75" height="24" align-x="336.75" align-y="2382" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Starwerte für nummmerische Lösung des Gleichungssystems)</c> </inlineAttr> </f> </text> </region> <region region-id="1369" left="12" top="2406.75" width="40.5" height="15.75" align-x="31.5" align-y="2418" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">Given</ml:id> </math> <rendering item-idref="54"/> </region> <region region-id="1172" left="66" top="2430.75" width="156.75" height="24" align-x="192.75" align-y="2442" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="KBA">r</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="KBC">r</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="h">F</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="55"/> </region> <region region-id="986" left="66" top="2460.75" width="156.75" height="24" align-x="192.75" align-y="2472" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="KBA">r</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="KBC">r</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="h">F</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="56"/> </region> <region region-id="1368" left="12" top="2496.75" width="103.5" height="20.25" align-x="28.5" align-y="2508" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:Find auto-method="true" method="linear" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:sequence> <ml:id xml:space="preserve" subscript="1">λ</ml:id> <ml:id xml:space="preserve" subscript="2">λ</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="57"/> </region> <region region-id="1570" left="162" top="2504.25" width="124.5" height="12" align-x="184.5" align-y="2514" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="10"> <inlineAttr line-through="false"> <c val="#00f">Man erhält folgende </c> </inlineAttr> </f> <f family="Symbol" charset="2" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">l</c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> Werte</c> </inlineAttr> </f> <f size="10"> <inlineAttr line-through="false"> <c val="#00f"> <sp/> </c> </inlineAttr> </f> </text> </region> <region region-id="1571" left="312" top="2494.5" width="46.5" height="33.75" align-x="327" align-y="2514" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">λ</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> </ml:eval> </math> <rendering item-idref="58"/> </region> <region region-id="1192" left="36" top="2550.75" width="100.5" height="19.5" align-x="78.75" align-y="2562" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="KBA">F</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve" font="4" subscript="KBA">r</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="1574" left="306" top="2558.25" width="189.75" height="12" align-x="324.75" align-y="2568" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Zugkraft zwischen den Fußpunkten B und A</c> </inlineAttr> </f> </text> </region> <region region-id="1269" left="36" top="2604.75" width="63" height="19.5" align-x="77.25" align-y="2616" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="KBA">F</ml:id> </ml:eval> </math> <rendering item-idref="60"/> </region> <region region-id="1270" left="180" top="2604.75" width="73.5" height="19.5" align-x="231.75" align-y="2616" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="KBA">F</ml:id> </ml:apply> </ml:eval> </math> <rendering item-idref="61"/> </region> <region region-id="1274" left="36" top="2664.75" width="102" height="19.5" align-x="79.5" align-y="2676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="KBC">F</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve" font="4" subscript="KBC">r</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="1573" left="306" top="2666.25" width="190.5" height="12" align-x="306" align-y="2676" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Zugkraft zwischen den Fußpunkten B und C</c> </inlineAttr> </f> </text> </region> <region region-id="1275" left="36" top="2718.75" width="63.75" height="19.5" align-x="78" align-y="2730" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="KBC">F</ml:id> </ml:eval> </math> <rendering item-idref="63"/> </region> <region region-id="1276" left="174" top="2718.75" width="74.25" height="19.5" align-x="226.5" align-y="2730" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="KBC">F</ml:id> </ml:apply> </ml:eval> </math> <rendering item-idref="64"/> </region> <region region-id="1653" left="0" top="2766" width="6000" height="6" align-x="0" align-y="2766" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="1577" left="12" top="2784.75" width="243" height="14.25" align-x="39" align-y="2796" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#00f">Bestimmung der Nenndicke für die Ketten:</c> </inlineAttr> </f> </text> </region> <region region-id="1601" left="24" top="2820.75" width="193.5" height="13.5" align-x="66" align-y="2832" 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"> Zulässige Spannung einer Haltekette: </text> </region> <region region-id="1606" left="396" top="2812.5" width="81.75" height="39" align-x="425.25" align-y="2832" 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="zul">σ</ml:id> <ml:apply> <ml:mult/> <ml:real>60</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="65"/> </region> <region region-id="1587" left="30" top="2868" width="59.25" height="38.25" align-x="57.75" align-y="2892" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve" subscript="zul">σ</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="K">F</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> </math> <rendering item-idref="66"/> </region> <region region-id="1613" left="132" top="2882.25" width="361.5" height="27" align-x="141" align-y="2892" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Den Faktor 2 im Nenner tritt auf, da das Kettenglied zwei Querschnitte aufweist</c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">F</c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> K </c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f"> ist Zugkraft in der Kette</c> </inlineAttr> </f> </text> </region> <region region-id="1610" left="30" top="2922.75" width="61.5" height="43.5" align-x="46.5" align-y="2952" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="K">d</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:real>4</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="67"/> </region> <region region-id="1615" left="132" top="2942.25" width="361.5" height="12" align-x="132" align-y="2952" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Querschnittsfläche des Kettengliedes.</c> </inlineAttr> </f> </text> </region> <region region-id="1616" left="30" top="2988.75" width="80.25" height="20.25" align-x="54.75" align-y="3000" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="K">F</ml:id> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="KBC">F</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="68"/> </region> <region region-id="1715" left="132" top="2988.75" width="42" height="13.5" align-x="152.25" align-y="3000" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Stabkraft</c> </inlineAttr> </f> <sp/> </text> </region> <region region-id="1643" left="360" top="2988.75" width="51" height="20.25" align-x="384.75" align-y="3000" 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="K">F</ml:id> <ml:id xml:space="preserve" subscript="K">F</ml:id> </ml:define> </math> <rendering item-idref="69"/> </region> <region region-id="1718" left="426" top="2988.75" width="60" height="20.25" align-x="455.25" align-y="3000" 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="zul">σ</ml:id> <ml:id xml:space="preserve" subscript="zul">σ</ml:id> </ml:define> </math> <rendering item-idref="70"/> </region> <region region-id="1646" left="360" top="3016.5" width="120.75" height="19.5" align-x="391.5" align-y="3024" 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"> <f family="Arial" charset="0" size="8"> <inlineAttr line-through="false"> <c val="#00f">"rückdefinieren", damit symbolisch gerechnet werden kann</c> </inlineAttr> </f> </text> </region> <region region-id="1654" left="30" top="3030.75" width="247.5" height="99.75" align-x="190.5" align-y="3084" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="zul">σ</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="K">F</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="K">d</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">solve</ml:id> <ml:id xml:space="preserve" subscript="K">d</ml:id> </ml:sequence> </ml:command> <ml:symResult> <ml:matrix rows="2" cols="1"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:sqrt/> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve" subscript="K">F</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve" subscript="zul">σ</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:sqrt/> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve" subscript="K">F</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve" subscript="zul">σ</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:matrix> </ml:symResult> </ml:symEval> </math> <rendering item-idref="71"/> </region> <region region-id="1655" left="30" top="3147.75" width="162" height="51" align-x="54" align-y="3180" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="K">d</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="zul">σ</ml:id> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:real>2</ml:real> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="zul">σ</ml:id> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="K">F</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="72"/> </region> <region region-id="1656" left="30" top="3222.75" width="59.25" height="20.25" align-x="52.5" align-y="3234" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="K">d</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> </ml:eval> <resultFormat numeric-only="true"> <general precision="2" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="73"/> </region> <region region-id="1657" left="204" top="3230.25" width="291.75" height="36" align-x="211.5" align-y="3240" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Ein Kettenglied muss mindestens einen Durchmesser von 3,17 mm haben. daher wird auf die nächstgrößere Dimension aufgerundet:</c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">d = 4 mm</c> </inlineAttr> </f> </text> </region> <region region-id="1659" left="0" top="3276" width="6000" height="6" align-x="0" align-y="3276" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="1661" left="12" top="3288.75" width="160.5" height="14.25" align-x="39" align-y="3300" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#00f">Dimensionierung der Stäbe:</c> </inlineAttr> </f> </text> </region> <region region-id="1686" left="12" top="3312.75" width="488.25" height="117.75" align-x="18" align-y="3324" 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"> Die Stäbe sind quadratische Stahlrohre und beidseitig gelenkig geführt (Eulerscher Knickfall 2, das heißt s = L (s... freie Knicklänge, L...Länge des Stahlrohres). <tab/> <tab/> <tab/> Für den Belastungsfall ist I<f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> erf </c> </inlineAttr> </f> zu ermitteln und damit das Stahlrohr so zu dimensionieren, dass Eulersche Knickung gilt. Eine Knicksicherheit <region region-id="1680" left="120" top="3372.75" width="39.75" height="20.25" align-x="143.25" align-y="3384" 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="k">ν</ml:id> <ml:real>5</ml:real> </ml:define> </math> <rendering item-idref="74"/> </region> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> <sp count="2"/>wird angenommen.</c> </inlineAttr> </f> <region region-id="1681" left="12" top="3382.5" width="92.25" height="39" align-x="27.75" align-y="3402" 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">E</ml:id> <ml:apply> <ml:mult/> <ml:real>210000</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="75"/> </region> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> <sp/> </c> </inlineAttr> </f> </text> </region> <region region-id="1719" left="24" top="3444.75" width="66" height="20.25" align-x="46.5" align-y="3456" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="S">F</ml:id> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="3">FS</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="76"/> </region> <region region-id="1671" left="24" top="3489" width="102.75" height="41.25" align-x="39.75" align-y="3516" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">L</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>2</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="s">h</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="77"/> </region> <region region-id="1690" left="180" top="3506.25" width="165" height="12" align-x="201.75" align-y="3516" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Stablänge nach den gegebenen Daten</c> </inlineAttr> </f> </text> </region> <region region-id="1674" left="24" top="3552.75" width="30.75" height="15.75" align-x="37.5" align-y="3564" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">s</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:define> </math> <rendering item-idref="78"/> </region> <region region-id="1675" left="90" top="3552.75" width="45.75" height="15.75" align-x="102" align-y="3564" 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">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>3.7859388972001824</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="79"/> </region> <region region-id="1691" left="180" top="3554.25" width="69" height="12" align-x="189" align-y="3564" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">freie Knicklänge</c> </inlineAttr> </f> </text> </region> <region region-id="1679" left="24" top="3582.75" width="84.75" height="48.75" align-x="50.25" align-y="3612" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="erf">I</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="k">ν</ml:id> <ml:id xml:space="preserve" subscript="S">F</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">s</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="80"/> </region> <region region-id="1692" left="180" top="3602.25" width="303.75" height="41.25" align-x="188.25" align-y="3612" 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"> <f size="10">Das erforderliche Flächenmoment I</f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> erf </c> </inlineAttr> </f> <f size="10"> ergit sich daher zu: </f> <region region-id="1694" left="180" top="3613.5" width="63" height="25.5" align-x="204.75" align-y="3630" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="erf">I</ml:id> <ml:unitOverride> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:unitOverride> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="81"/> </region> </text> </region> <region region-id="1696" left="18" top="3654.75" width="481.5" height="62.25" align-x="26.25" align-y="3666" 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"> Der Vergleich mit dem Datenblatt zeigt, dass man ein <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#00f">Stahlrohr mit dem Nennmaß 50 x 50</c> </inlineAttr> </f> verwenden muss. Für dieses Rohr gilt <region region-id="1697" left="216" top="3661.5" width="67.5" height="21" align-x="228.75" align-y="3678" 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">I</ml:id> <ml:apply> <ml:mult/> <ml:real>19.8</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="82"/> </region> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">. Bei einer Wanddicke des Rohres von </c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">2.9 mm erhält man die Querschnittsfläche </c> </inlineAttr> </f> <region region-id="1698" left="234" top="3685.5" width="76.5" height="25.5" align-x="255.75" align-y="3702" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="r">A</ml:id> <ml:apply> <ml:mult/> <ml:real>5.39</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="83"/> </region> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> (siehe Datenblatt)</c> </inlineAttr> </f> </text> </region> <region region-id="1700" left="18" top="3726" width="453.75" height="33.75" align-x="24.75" align-y="3738" 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"> Als nächstes wird der Schlankheitsgrad <f family="Symbol" charset="2" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">l</c> </inlineAttr> </f> berechnet damit man feststellen kann, ob eine elastische Knickung auftritt<f family="Arial" charset="0">. Füt Stahl S355JO gilt </f> <f family="Symbol" charset="2" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">l</c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> 0 </c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> = 89</c> </inlineAttr> </f> </text> </region> <region region-id="1702" left="30" top="3776.25" width="48" height="40.5" align-x="42.75" align-y="3798" 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">i</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">I</ml:id> <ml:id xml:space="preserve" subscript="r">A</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="84"/> </region> <region region-id="1704" left="102" top="3786.75" width="66" height="15.75" align-x="113.25" align-y="3798" 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">i</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.019166296949998197</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="7"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="85"/> </region> <region region-id="1703" left="180" top="3788.25" width="66" height="12" align-x="180" align-y="3798" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Trägheitsradius</c> </inlineAttr> </f> </text> </region> <region region-id="1706" left="30" top="3850.5" width="34.5" height="33.75" align-x="46.5" align-y="3870" 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">λ</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">s</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="86"/> </region> <region region-id="1707" left="102" top="3858.75" width="49.5" height="15.75" align-x="117" align-y="3870" 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">λ</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>197.53105709867123</ml:real> </result> </ml:eval> </math> <rendering item-idref="87"/> </region> <region region-id="1710" left="180" top="3860.25" width="78" height="12" align-x="217.5" align-y="3870" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Schlankheitsgrad </c> </inlineAttr> </f> </text> </region> <region region-id="1713" left="24" top="3900" width="355.5" height="18.75" align-x="30" align-y="3912" 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"> Da <f family="Symbol" charset="2" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">l</c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> > </c> </inlineAttr> </f> <f family="Symbol" charset="2" size="12"> <c val="#00f"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">l</inlineAttr> </c> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> <f family="Arial" charset="0" size="12">0</f> </c> </inlineAttr> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> <sp count="2"/>ist die Annahme einer elastischen Knickung gerechtfertigt </c> </inlineAttr> </f> </text> </region> <region region-id="1721" left="378" top="3966.75" width="119.25" height="14.25" align-x="392.25" align-y="3978" 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"> <link href=".\..\..\..\..\..\..\Desktop\Neuer Ordner\Reifeprüfung\pc_Reifeprüfungsaufgaben_MA_2001.mcd" title="doppelklicken" popup="false">zurück zur Startdatei</link> </text> </region> </regions> <binaryContent> <item item-id="1">iVBORw0KGgoAAAANSUhEUgAAAFwAAAAVCAYAAADLuIn8AAAAAXNSR0IArs4c6QAAAARnQU1B 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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" font="4">S2</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" font="4">OS</ml:id> <ml:id xml:space="preserve" font="4">OA</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="1515" left="294" top="690.75" width="84" height="15" align-x="318" align-y="702" 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" font="4">S3</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" font="4">OS</ml:id> <ml:id xml:space="preserve" font="4">OC</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="1262" left="24" top="738.75" width="447" height="25.5" align-x="50.25" align-y="750" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#00f">Berechnung der Stabkräfte: </c> </inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr font-weight="normal" font-style="normal" line-through="false"> <c val="#00f">(</c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" line-through="false"> <c val="#00f">d</c> </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" line-through="false"> <c val="#00f"> <f family="Arial" charset="0" size="10">abei wurden die Stabkräfte indiziert (als Literalindex), ist nicht</f> </c> </inlineAttr> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" line-through="false"> <c val="#00f"> <tab/> <tab/> <tab/> <tab/> <sp count="6"/>notwendig, man könnte auch mit den obigen Definitionen arbeiten)</c> </inlineAttr> </f> </text> </region> <region region-id="1035" left="24" top="777.75" width="58.5" height="57.75" align-x="42" align-y="810" 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" font="4">F</ml:id> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">F</ml:id> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="1051" left="306" top="800.25" width="154.5" height="12" align-x="327" align-y="810" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Belastung in vektorieller Darstellung</c> </inlineAttr> </f> </text> </region> <region region-id="1169" left="24" top="856.5" width="77.25" height="80.25" align-x="48" align-y="900" 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" font="4" subscript="1">S</ml:id> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:real>2</ml:real> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="s">h</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="1221" left="114" top="847.5" width="71.25" height="98.25" align-x="138.75" align-y="900" 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" font="4" subscript="2">S</ml:id> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">d</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="s">h</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="1223" left="210" top="847.5" width="70.5" height="98.25" align-x="234" align-y="900" 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" font="4" subscript="3">S</ml:id> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:div/> <ml:id xml:space="preserve">d</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="s">h</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="1053" left="306" top="890.25" width="189.75" height="21.75" align-x="336" align-y="900" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Stabvektoren </c> </inlineAttr> </f> <f family="Arial" charset="0" size="8"> <inlineAttr line-through="false"> <c val="#00f">(Vektoren in Stabrichtung, nicht zu</c> </inlineAttr> </f> <f family="Arial" charset="0" size="8"> <inlineAttr line-through="false"> <c val="#00f"> <sp count="27"/>verwechseln mit den Stabkräften) </c> </inlineAttr> </f> </text> </region> <region region-id="1055" left="24" top="972.75" width="473.25" height="57" align-x="47.25" align-y="984" 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"> Die Stabkräfte werden über die Gleichgewichtsbedingung für Kräfte berechnet. Dabei treten die unbekannten Proprtionalitätsfaktoren (k<f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> 1 </c> </inlineAttr> </f>, k<f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> 2 </c> </inlineAttr> </f>, k<f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> 3 </c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">mit</c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> <sp/> </c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">Literalindex)</c> </inlineAttr> </f> auf, die zur Bestimmung der Stabkräfte dienen. Sie geben die Zug- oder Druckkräfte (je nach Vorzeichenkonvetion) in den Stäben bezogen auf die Längeneinheit an.<sp count="3"/> </text> </region> <region region-id="866" left="18" top="1056.75" width="40.5" height="15.75" align-x="37.5" align-y="1068" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">Given</ml:id> </math> <rendering item-idref="21"/> </region> <region region-id="1531" left="360" top="1064.25" width="134.25" height="147" align-x="366.75" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <c val="#00f"> <inlineAttr line-through="false"> <f family="Arial" charset="0" size="10">Die Vektoren </f> </inlineAttr> </c> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">F</c> </inlineAttr> </f> <inlineAttr font-style="normal" underline="false" line-through="false"> <c val="#00f"> <f family="Arial" charset="0" size="10">i</f> </c> </inlineAttr> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f"> und </c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f"> S </c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-style="normal" underline="false" line-through="false"> <c val="#00f"> i </c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <c val="#00f"> <inlineAttr line-through="false"> werden mit Feldindizes (STRG [ ) versehen, damit man auf die einzelnen Komponenten der Vektoren zugreifen kann.</inlineAttr> </c> </f> <inlineAttr line-through="false"> <c val="#00f"> <f family="Arial" charset="0" size="10">Achtung:</f> </c> </inlineAttr> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">ORIGIN wurde auf 1 gestellt (Mathcad 11: Extras - Arbeitsblattoptionen - vordefinierte Variablen, Standardeinstellung ist ORIGIN = 0). </c> </inlineAttr> </f> </text> </region> <region region-id="1062" left="60" top="1086.75" width="169.5" height="24" align-x="205.5" align-y="1098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="1">S</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="2">S</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="3">S</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4">F</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="22"/> </region> <region region-id="1522" left="258" top="1088.25" width="69" height="12" align-x="260.25" align-y="1098" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">x - Komponente</c> </inlineAttr> </f> </text> </region> <region region-id="1064" left="60" top="1122.75" width="169.5" height="24" align-x="205.5" align-y="1134" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="1">S</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="2">S</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="3">S</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4">F</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="23"/> </region> <region region-id="1523" left="258" top="1124.25" width="69" height="12" align-x="258" align-y="1134" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">y - Komponente</c> </inlineAttr> </f> </text> </region> <region region-id="1066" left="60" top="1158.75" width="169.5" height="24" align-x="205.5" align-y="1170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="1">S</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="2">S</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">k</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="3">S</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4">F</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="24"/> </region> <region region-id="1524" left="258" top="1160.25" width="69" height="12" align-x="258" align-y="1170" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">z - Komponente</c> </inlineAttr> </f> </text> </region> <region region-id="1722" left="18" top="1248.75" width="233.25" height="17.25" align-x="34.5" align-y="1260" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="System.NullReferenceException: Der Objektverweis wurde nicht auf eine Objektinstanz festgelegt. bei mslisp.StandardBuiltins.contains_hash(Object h, Object k) bei mslisp.StandardBuiltins_contains_hash_Builtin.Invoke(Object[] args) bei mslisp.ApplyExpr.execute(Env e) bei mslisp.IfExpr.execute(Env e) bei mslisp.LambdaExpr.Invoke(Object[] args) bei mslisp.ApplyExpr.execute(Env e) bei mslisp.IfExpr.execute(Env e) bei mslisp.LambdaExpr.Invoke(Object[] args) bei mslisp.ApplyExpr.execute(Env e) bei mslisp.IfExpr.execute(Env e) bei mslisp.LambdaExpr.Invoke(Object[] args) bei mslisp.ApplyExpr.execute(Env e) bei mslisp.LambdaExpr.Invoke(Object[] args) bei mslisp.ApplyFunction.Invoke(Object[] args) bei mslisp.ApplyExpr.execute(Env e) bei mslisp.ApplyExpr.execute(Env e) bei mslisp.LambdaExpr.Invoke(Object[] args) bei mslisp.ApplyExpr.execute(Env e) bei mslisp.HandlerCaseExpr.execute(Env e)" optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k</ml:id> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:sequence> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">float</ml:id> <ml:real>3</ml:real> </ml:sequence> </ml:command> <ml:symResult> <ml:placeholder/> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="1530" left="354" top="1250.25" width="139.5" height="48" align-x="357.75" align-y="1260" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr font-style="normal" line-through="false"> <c val="#00f">Definition von k:= suchen(..) liefert den Lösungsvektor k; man kann nun auf die Feldindizes (STRG [ ) zugreifen</c> </inlineAttr> </f> </text> </region> <region region-id="1532" left="18" top="1366.5" width="46.5" height="33.75" align-x="33" align-y="1386" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> </ml:eval> </math> <rendering item-idref="26"/> </region> <region region-id="1161" left="0" top="1440" width="6000" height="6" align-x="0" align-y="1440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="1184" left="30" top="1482.75" width="73.5" height="19.5" align-x="61.5" align-y="1494" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="1">FS</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve" font="4" subscript="1">S</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="1537" left="150" top="1482.75" width="51.75" height="19.5" align-x="180" align-y="1494" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="1">FS</ml:id> </ml:eval> </math> <rendering item-idref="28"/> </region> <region region-id="1128" left="336" top="1490.25" width="108" height="12" align-x="356.25" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text 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align-x="218.25" align-y="1560" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="v">F</ml:id> </ml:eval> </math> <rendering item-idref="31"/> </region> <region region-id="1126" left="336" top="1550.25" width="88.5" height="12" align-x="387" align-y="1560" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Vertikalkomponente </c> </inlineAttr> </f> </text> </region> <region region-id="1181" left="30" top="1578.75" width="102.75" height="20.25" align-x="51.75" align-y="1590" show-border="false" 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<ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" font="4" subscript="2">S</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="34"/> </region> <region region-id="1540" left="150" top="1650.75" width="52.5" height="19.5" align-x="180.75" align-y="1662" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="2">FS</ml:id> </ml:eval> </math> <rendering item-idref="35"/> </region> <region region-id="1250" left="336" top="1652.25" width="108" height="12" align-x="336" align-y="1662" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Stabkraft des Stabes DA</c> </inlineAttr> </f> </text> </region> <region region-id="1179" left="30" top="1686.75" width="63" height="19.5" align-x="71.25" align-y="1698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="2">FS</ml:id> </ml:apply> </ml:eval> </math> <rendering item-idref="36"/> </region> <region region-id="1123" left="336" top="1688.25" width="103.5" height="12" align-x="350.25" align-y="1698" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Betrag der Stabkraft DA</c> </inlineAttr> </f> </text> </region> <region region-id="1178" left="30" top="1716.75" width="100.5" height="20.25" align-x="51.75" align-y="1728" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="v">F</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="2">FS</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="943" left="204" top="1716.75" width="42" height="20.25" align-x="224.25" align-y="1728" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="v">F</ml:id> </ml:eval> </math> <rendering item-idref="38"/> </region> <region region-id="1122" left="336" top="1718.25" width="88.5" height="12" align-x="387" align-y="1728" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Vertikalkomponente </c> </inlineAttr> </f> </text> </region> <region region-id="1177" left="30" top="1746.75" width="103.5" height="20.25" align-x="51.75" align-y="1758" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="h">F</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="2">FS</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="945" left="204" top="1752.75" width="42" height="20.25" align-x="224.25" align-y="1764" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id 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<ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve" font="4" subscript="3">S</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="1543" left="150" top="1818.75" width="51.75" height="19.5" align-x="180" align-y="1830" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="3">FS</ml:id> </ml:eval> </math> <rendering item-idref="42"/> </region> <region region-id="1120" left="336" top="1820.25" width="108" height="12" align-x="336" align-y="1830" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Stabkraft des Stabes DC</c> </inlineAttr> </f> </text> </region> <region region-id="1294" left="30" top="1854.75" width="62.25" height="19.5" align-x="70.5" align-y="1866" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="3">FS</ml:id> </ml:apply> </ml:eval> </math> <rendering item-idref="43"/> </region> <region region-id="1119" left="336" top="1856.25" width="103.5" height="12" align-x="350.25" align-y="1866" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Betrag der Stabkraft DC</c> </inlineAttr> </f> </text> </region> <region region-id="1295" left="30" top="1884.75" width="99.75" height="20.25" align-x="51.75" align-y="1896" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="v">F</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="3">FS</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="44"/> </region> <region region-id="1296" left="204" top="1884.75" width="42" height="20.25" align-x="224.25" align-y="1896" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="v">F</ml:id> </ml:eval> </math> <rendering item-idref="45"/> </region> <region region-id="1302" left="336" top="1886.25" width="88.5" height="12" align-x="387" align-y="1896" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Vertikalkomponente </c> </inlineAttr> </f> </text> </region> <region region-id="1333" left="30" top="1920.75" width="102.75" height="20.25" align-x="51.75" align-y="1932" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="h">F</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="3">FS</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="46"/> </region> <region region-id="1298" left="204" top="1920.75" width="42" height="20.25" align-x="224.25" align-y="1932" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="h">F</ml:id> </ml:eval> </math> <rendering item-idref="47"/> </region> <region region-id="1300" left="336" top="1922.25" width="96.75" height="12" align-x="387" align-y="1932" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Horizontalkomponente</c> </inlineAttr> </f> </text> </region> <region region-id="1191" left="12" top="1992.75" width="485.25" height="27" align-x="20.25" align-y="2004" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Aus Symmetriegründen müssen die drei Stabkräfte den gleichen Betrag haben; was durch die Rechnung bestätigt wird. </text> </region> <region region-id="1190" left="0" top="2040" width="6000" height="6" align-x="0" align-y="2040" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="954" left="12" top="2046.75" width="211.5" height="13.5" align-x="38.25" align-y="2058" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#00f">Berechnung der Zugkraft in der Kette:</c> </inlineAttr> </f> </text> </region> <region region-id="1199" left="6" top="2076.75" width="489.75" height="25.5" align-x="14.25" align-y="2088" 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"> Aus der Skizze (Draufsicht) erkennt man (x- und y-Richtung wie in Skizze, z-Komponente = 0): <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">(Aus Symmetriegründen müssen alle Zugkräfte gleich groß sein).</c> </inlineAttr> </f> </text> </region> <region region-id="1569" left="318" top="2114.25" width="177.75" height="36" align-x="326.25" align-y="2124" 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"> <f size="10"> <inlineAttr line-through="false"> <c val="#00f">Das Basisdreieck ist gleichseitig </c> </inlineAttr> </f> <f size="10">(Winkel zwischen 2 Ketten ist 60°)</f> <f size="10"> <inlineAttr line-through="false"> <c val="#00f">, daher gilt</c> </inlineAttr> </f> <f family="Symbol" charset="2" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">b = </c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">30° </c> </inlineAttr> </f> </text> </region> <region region-id="1195" left="18" top="2118.75" width="66.75" height="15.75" align-x="34.5" align-y="2130" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">β</ml:id> <ml:apply> <ml:mult/> <ml:real>30</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="48"/> </region> <region region-id="1565" left="18" top="2155.5" width="70.5" height="62.25" align-x="42" align-y="2190" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="h">F</ml:id> <ml:matrix rows="3" cols="1"> <ml:real font="0">0</ml:real> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="h">F</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="1566" left="324" top="2186.25" width="99.75" height="12" align-x="375" align-y="2196" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Horizontalkomponente </c> </inlineAttr> </f> </text> </region> <region region-id="1196" left="18" top="2235.75" width="120" height="57.75" align-x="57.75" align-y="2268" 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" font="4" subscript="KBA">r</ml:id> <ml:apply> <ml:mult/> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:id xml:space="preserve" font="1">sin</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:matrix> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="1197" left="168" top="2235.75" width="120.75" height="57.75" align-x="208.5" align-y="2268" 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" font="4" subscript="KBC">r</ml:id> <ml:apply> <ml:mult/> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:matrix> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="1253" left="324" top="2258.25" width="138.75" height="24" align-x="365.25" align-y="2268" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Richtungsvektoren der Zugkräfte</c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">(ohne Einheiten)</c> </inlineAttr> </f> </text> </region> <region region-id="1554" left="18" top="2316" width="429" height="35.25" align-x="44.25" align-y="2328" 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"> Berechnung der Proportionalitätsfaktoren <f family="Symbol" charset="2" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">l</c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> 1 </c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> und </c> </inlineAttr> </f> <f family="Symbol" charset="2" size="12"> <c val="#00f"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">l</inlineAttr> </c> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> 2 </c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> für die Zugkräfte in den Ketten. </c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <c val="#00f"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(Gleiche Begründung wie für k</inlineAttr> </c> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">1</c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">, k</c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> 2 </c> </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> <f family="Arial" charset="0" size="12">, k</f> </c> </inlineAttr> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> 3 </c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">)</c> </inlineAttr> </f> </text> </region> <region region-id="1551" left="30" top="2362.5" width="66.75" height="33.75" align-x="51.75" align-y="2382" 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="1">λ</ml:id> <ml:apply> <ml:mult/> <ml:real>100</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="52"/> </region> <region region-id="1552" left="180" top="2362.5" width="66.75" height="33.75" align-x="201.75" align-y="2382" 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">λ</ml:id> <ml:apply> <ml:mult/> <ml:real>100</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="53"/> </region> <region region-id="1556" left="318" top="2372.25" width="177.75" height="24" align-x="336.75" align-y="2382" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Starwerte für nummmerische Lösung des Gleichungssystems)</c> </inlineAttr> </f> </text> </region> <region region-id="1369" left="12" top="2406.75" width="40.5" height="15.75" align-x="31.5" align-y="2418" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">Given</ml:id> </math> <rendering item-idref="54"/> </region> <region region-id="1172" left="66" top="2430.75" width="156.75" height="24" align-x="192.75" align-y="2442" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="KBA">r</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="KBC">r</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="h">F</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="55"/> </region> <region region-id="986" left="66" top="2460.75" width="156.75" height="24" align-x="192.75" align-y="2472" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="KBA">r</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="KBC">r</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="4" subscript="h">F</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="56"/> </region> <region region-id="1368" left="12" top="2496.75" width="103.5" height="20.25" align-x="28.5" align-y="2508" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:Find auto-method="true" method="linear" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:sequence> <ml:id xml:space="preserve" subscript="1">λ</ml:id> <ml:id xml:space="preserve" subscript="2">λ</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="57"/> </region> <region region-id="1570" left="162" top="2504.25" width="124.5" height="12" align-x="184.5" align-y="2514" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="10"> <inlineAttr line-through="false"> <c val="#00f">Man erhält folgende </c> </inlineAttr> </f> <f family="Symbol" charset="2" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">l</c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> Werte</c> </inlineAttr> </f> <f size="10"> <inlineAttr line-through="false"> <c val="#00f"> <sp/> </c> </inlineAttr> </f> </text> </region> <region region-id="1571" left="312" top="2494.5" width="46.5" height="33.75" align-x="327" align-y="2514" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">λ</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:unitOverride> </ml:eval> </math> <rendering item-idref="58"/> </region> <region region-id="1192" left="36" top="2550.75" width="100.5" height="19.5" align-x="78.75" align-y="2562" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="KBA">F</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve" font="4" subscript="KBA">r</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="1574" left="306" top="2558.25" width="189.75" height="12" align-x="324.75" align-y="2568" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Zugkraft zwischen den Fußpunkten B und A</c> </inlineAttr> </f> </text> </region> <region region-id="1269" left="36" top="2604.75" width="63" height="19.5" align-x="77.25" align-y="2616" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="KBA">F</ml:id> </ml:eval> </math> <rendering item-idref="60"/> </region> <region region-id="1270" left="180" top="2604.75" width="73.5" height="19.5" align-x="231.75" align-y="2616" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="KBA">F</ml:id> </ml:apply> </ml:eval> </math> <rendering item-idref="61"/> </region> <region region-id="1274" left="36" top="2664.75" width="102" height="19.5" align-x="79.5" align-y="2676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="KBC">F</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve" font="4" subscript="KBC">r</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="1573" left="306" top="2666.25" width="190.5" height="12" align-x="306" align-y="2676" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Zugkraft zwischen den Fußpunkten B und C</c> </inlineAttr> </f> </text> </region> <region region-id="1275" left="36" top="2718.75" width="63.75" height="19.5" align-x="78" align-y="2730" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="KBC">F</ml:id> </ml:eval> </math> <rendering item-idref="63"/> </region> <region region-id="1276" left="174" top="2718.75" width="74.25" height="19.5" align-x="226.5" align-y="2730" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="KBC">F</ml:id> </ml:apply> </ml:eval> </math> <rendering item-idref="64"/> </region> <region region-id="1653" left="0" top="2766" width="6000" height="6" align-x="0" align-y="2766" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="1577" left="12" top="2784.75" width="243" height="14.25" align-x="39" align-y="2796" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#00f">Bestimmung der Nenndicke für die Ketten:</c> </inlineAttr> </f> </text> </region> <region region-id="1601" left="24" top="2820.75" width="193.5" height="13.5" align-x="66" align-y="2832" 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"> Zulässige Spannung einer Haltekette: </text> </region> <region region-id="1606" left="396" top="2812.5" width="81.75" height="39" align-x="425.25" align-y="2832" 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="zul">σ</ml:id> <ml:apply> <ml:mult/> <ml:real>60</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="65"/> </region> <region region-id="1587" left="30" top="2868" width="59.25" height="38.25" align-x="57.75" align-y="2892" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve" subscript="zul">σ</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="K">F</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> </math> <rendering item-idref="66"/> </region> <region region-id="1613" left="132" top="2882.25" width="361.5" height="27" align-x="141" align-y="2892" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Den Faktor 2 im Nenner tritt auf, da das Kettenglied zwei Querschnitte aufweist</c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">F</c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> K </c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f"> ist Zugkraft in der Kette</c> </inlineAttr> </f> </text> </region> <region region-id="1610" left="30" top="2922.75" width="61.5" height="43.5" align-x="46.5" align-y="2952" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="K">d</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:real>4</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="67"/> </region> <region region-id="1615" left="132" top="2942.25" width="361.5" height="12" align-x="132" align-y="2952" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Querschnittsfläche des Kettengliedes.</c> </inlineAttr> </f> </text> </region> <region region-id="1616" left="30" top="2988.75" width="80.25" height="20.25" align-x="54.75" align-y="3000" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="K">F</ml:id> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="KBC">F</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="68"/> </region> <region region-id="1715" left="132" top="2988.75" width="42" height="13.5" align-x="152.25" align-y="3000" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Stabkraft</c> </inlineAttr> </f> <sp/> </text> </region> <region region-id="1643" left="360" top="2988.75" width="51" height="20.25" align-x="384.75" align-y="3000" 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="K">F</ml:id> <ml:id xml:space="preserve" subscript="K">F</ml:id> </ml:define> </math> <rendering item-idref="69"/> </region> <region region-id="1718" left="426" top="2988.75" width="60" height="20.25" align-x="455.25" align-y="3000" 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="zul">σ</ml:id> <ml:id xml:space="preserve" subscript="zul">σ</ml:id> </ml:define> </math> <rendering item-idref="70"/> </region> <region region-id="1646" left="360" top="3016.5" width="120.75" height="19.5" align-x="391.5" align-y="3024" 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"> <f family="Arial" charset="0" size="8"> <inlineAttr line-through="false"> <c val="#00f">"rückdefinieren", damit symbolisch gerechnet werden kann</c> </inlineAttr> </f> </text> </region> <region region-id="1654" left="30" top="3030.75" width="247.5" height="99.75" align-x="190.5" align-y="3084" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="zul">σ</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="K">F</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="K">d</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">solve</ml:id> <ml:id xml:space="preserve" subscript="K">d</ml:id> </ml:sequence> </ml:command> <ml:symResult> <ml:matrix rows="2" cols="1"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:sqrt/> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve" subscript="K">F</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve" subscript="zul">σ</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:sqrt/> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve" subscript="K">F</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve" subscript="zul">σ</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:matrix> </ml:symResult> </ml:symEval> </math> <rendering item-idref="71"/> </region> <region region-id="1655" left="30" top="3147.75" width="162" height="51" align-x="54" align-y="3180" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="K">d</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="zul">σ</ml:id> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:real>2</ml:real> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="zul">σ</ml:id> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="K">F</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="72"/> </region> <region region-id="1656" left="30" top="3222.75" width="59.25" height="20.25" align-x="52.5" align-y="3234" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="K">d</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> </ml:eval> <resultFormat numeric-only="true"> <general precision="2" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="73"/> </region> <region region-id="1657" left="204" top="3230.25" width="291.75" height="36" align-x="211.5" align-y="3240" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Ein Kettenglied muss mindestens einen Durchmesser von 3,17 mm haben. daher wird auf die nächstgrößere Dimension aufgerundet:</c> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">d = 4 mm</c> </inlineAttr> </f> </text> </region> <region region-id="1659" left="0" top="3276" width="6000" height="6" align-x="0" align-y="3276" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="1661" left="12" top="3288.75" width="160.5" height="14.25" align-x="39" align-y="3300" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#00f">Dimensionierung der Stäbe:</c> </inlineAttr> </f> </text> </region> <region region-id="1686" left="12" top="3312.75" width="488.25" height="117.75" align-x="18" align-y="3324" 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"> Die Stäbe sind quadratische Stahlrohre und beidseitig gelenkig geführt (Eulerscher Knickfall 2, das heißt s = L (s... freie Knicklänge, L...Länge des Stahlrohres). <tab/> <tab/> <tab/> Für den Belastungsfall ist I<f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> erf </c> </inlineAttr> </f> zu ermitteln und damit das Stahlrohr so zu dimensionieren, dass Eulersche Knickung gilt. Eine Knicksicherheit <region region-id="1680" left="120" top="3372.75" width="39.75" height="20.25" align-x="143.25" align-y="3384" 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="k">ν</ml:id> <ml:real>5</ml:real> </ml:define> </math> <rendering item-idref="74"/> </region> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> <sp count="2"/>wird angenommen.</c> </inlineAttr> </f> <region region-id="1681" left="12" top="3382.5" width="92.25" height="39" align-x="27.75" align-y="3402" 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">E</ml:id> <ml:apply> <ml:mult/> <ml:real>210000</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="75"/> </region> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> <sp/> </c> </inlineAttr> </f> </text> </region> <region region-id="1719" left="24" top="3444.75" width="66" height="20.25" align-x="46.5" align-y="3456" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="S">F</ml:id> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="3">FS</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="76"/> </region> <region region-id="1671" left="24" top="3489" width="102.75" height="41.25" align-x="39.75" align-y="3516" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">L</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>2</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="s">h</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="77"/> </region> <region region-id="1690" left="180" top="3506.25" width="165" height="12" align-x="201.75" align-y="3516" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Stablänge nach den gegebenen Daten</c> </inlineAttr> </f> </text> </region> <region region-id="1674" left="24" top="3552.75" width="30.75" height="15.75" align-x="37.5" align-y="3564" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">s</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:define> </math> <rendering item-idref="78"/> </region> <region region-id="1675" left="90" top="3552.75" width="45.75" height="15.75" align-x="102" align-y="3564" 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">s</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>3.7859388972001824</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="79"/> </region> <region region-id="1691" left="180" top="3554.25" width="69" height="12" align-x="189" align-y="3564" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">freie Knicklänge</c> </inlineAttr> </f> </text> </region> <region region-id="1679" left="24" top="3582.75" width="84.75" height="48.75" align-x="50.25" align-y="3612" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="erf">I</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="k">ν</ml:id> <ml:id xml:space="preserve" subscript="S">F</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">s</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="80"/> </region> <region region-id="1692" left="180" top="3602.25" width="303.75" height="41.25" align-x="188.25" align-y="3612" 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"> <f size="10">Das erforderliche Flächenmoment I</f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> erf </c> </inlineAttr> </f> <f size="10"> ergit sich daher zu: </f> <region region-id="1694" left="180" top="3613.5" width="63" height="25.5" align-x="204.75" align-y="3630" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Diese Variable ist nicht definiert." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="erf">I</ml:id> <ml:unitOverride> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:unitOverride> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="81"/> </region> </text> </region> <region region-id="1696" left="18" top="3654.75" width="481.5" height="62.25" align-x="26.25" align-y="3666" 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"> Der Vergleich mit dem Datenblatt zeigt, dass man ein <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#00f">Stahlrohr mit dem Nennmaß 50 x 50</c> </inlineAttr> </f> verwenden muss. Für dieses Rohr gilt <region region-id="1697" left="216" top="3661.5" width="67.5" height="21" align-x="228.75" align-y="3678" 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">I</ml:id> <ml:apply> <ml:mult/> <ml:real>19.8</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="82"/> </region> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">. Bei einer Wanddicke des Rohres von </c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">2.9 mm erhält man die Querschnittsfläche </c> </inlineAttr> </f> <region region-id="1698" left="234" top="3685.5" width="76.5" height="25.5" align-x="255.75" align-y="3702" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="r">A</ml:id> <ml:apply> <ml:mult/> <ml:real>5.39</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="83"/> </region> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> (siehe Datenblatt)</c> </inlineAttr> </f> </text> </region> <region region-id="1700" left="18" top="3726" width="453.75" height="33.75" align-x="24.75" align-y="3738" 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"> Als nächstes wird der Schlankheitsgrad <f family="Symbol" charset="2" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">l</c> </inlineAttr> </f> berechnet damit man feststellen kann, ob eine elastische Knickung auftritt<f family="Arial" charset="0">. Füt Stahl S355JO gilt </f> <f family="Symbol" charset="2" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">l</c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> 0 </c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> = 89</c> </inlineAttr> </f> </text> </region> <region region-id="1702" left="30" top="3776.25" width="48" height="40.5" align-x="42.75" align-y="3798" 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">i</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">I</ml:id> <ml:id xml:space="preserve" subscript="r">A</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="84"/> </region> <region region-id="1704" left="102" top="3786.75" width="66" height="15.75" align-x="113.25" align-y="3798" 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">i</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.019166296949998197</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="7"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="85"/> </region> <region region-id="1703" left="180" top="3788.25" width="66" height="12" align-x="180" align-y="3798" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Trägheitsradius</c> </inlineAttr> </f> </text> </region> <region region-id="1706" left="30" top="3850.5" width="34.5" height="33.75" align-x="46.5" align-y="3870" 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">λ</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">s</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="86"/> </region> <region region-id="1707" left="102" top="3858.75" width="49.5" height="15.75" align-x="117" align-y="3870" 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">λ</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>197.53105709867123</ml:real> </result> </ml:eval> </math> <rendering item-idref="87"/> </region> <region region-id="1710" left="180" top="3860.25" width="78" height="12" align-x="217.5" align-y="3870" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Schlankheitsgrad </c> </inlineAttr> </f> </text> </region> <region region-id="1713" left="24" top="3900" width="355.5" height="18.75" align-x="30" align-y="3912" 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"> Da <f family="Symbol" charset="2" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f">l</c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> > </c> </inlineAttr> </f> <f family="Symbol" charset="2" size="12"> <c val="#00f"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">l</inlineAttr> </c> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> <f family="Arial" charset="0" size="12">0</f> </c> </inlineAttr> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#00f"> <sp count="2"/>ist die Annahme einer elastischen Knickung gerechtfertigt </c> </inlineAttr> </f> </text> </region> <region region-id="1721" left="378" top="3966.75" width="119.25" height="14.25" align-x="392.25" align-y="3978" 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"> <link href=".\..\..\..\..\..\..\Desktop\Neuer Ordner\Reifeprüfung\pc_Reifeprüfungsaufgaben_MA_2001.mcd" title="doppelklicken" popup="false">zurück zur Startdatei</link> </text> </region> </regions> <binaryContent> <item item-id="1">iVBORw0KGgoAAAANSUhEUgAAAFwAAAAVCAYAAADLuIn8AAAAAXNSR0IArs4c6QAAAARnQU1B 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