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<ml:id xml:space="preserve" subscript="ar">f</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>12000</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="1798" left="150" top="60.75" width="54.75" height="13.5" align-x="176.25" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Belastung </p> </text> </region> <region region-id="1799" left="12" top="78.75" width="58.5" height="15.75" align-x="29.25" align-y="90" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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</ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="1786" left="384" top="432.75" width="110.25" height="13.5" align-x="384" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="10">Ortsvektor</f> OA </p> </text> </region> <region region-id="1787" left="264" top="492.75" width="82.5" height="75.75" align-x="290.25" align-y="534" 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">OB</ml:id> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:apply> 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xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4">OC</ml:id> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">d</ml:id> </ml:apply> <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">hl</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="1790" left="384" top="636.75" width="110.25" height="13.5" align-x="384" align-y="648" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="10">Ortsvektor</f> OC</p> </text> </region> <region region-id="1859" left="24" top="702.75" width="82.5" height="15" align-x="48" align-y="714" 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">S1</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" font="4">OS</ml:id> <ml:id xml:space="preserve" font="4">OB</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="1865" left="150" top="702.75" width="84" height="15" align-x="174.75" align-y="714" 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">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="16"/> </region> <region region-id="1869" left="282" top="702.75" width="84" height="15" align-x="306" align-y="714" 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="17"/> </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"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial" charset="0"> <b> <i> <inlineAttr line-through="false"> <c val="#00f">Berechnung der Stabkräfte: </c> </inlineAttr> </i> </b> </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> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial" charset="0" 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> </p> </text> </region> <region region-id="1842" left="30" top="775.5" width="86.25" height="61.5" align-x="64.5" 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" subscript="m">far</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" subscript="ar">f</ml:id> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="18"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Belastung in vektorieller Darstellung</c> </inlineAttr> </f> </p> </text> </region> <region region-id="1768" left="30" top="856.5" width="87" height="79.5" align-x="54" 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:div/> <ml:real>-2</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">hl</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="1908" left="132" top="848.25" width="81" height="96.75" align-x="156.75" 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">hl</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="1775" left="222" top="848.25" width="80.25" height="96.75" align-x="246" 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">hl</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="s">h</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="21"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="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> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial" charset="0" size="8"> <inlineAttr line-through="false"> <c val="#00f"> <sp count="27"/>verwechseln mit den Stabkräften) </c> </inlineAttr> </f> </p> </text> </region> <region region-id="1817" left="24" top="960.75" width="473.25" height="57" align-x="47.25" align-y="972" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Die Stabkräfte werden über die Gleichgewichtsbedingung für Kräfte berechnet.</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">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"> <sub>1</sub> </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"> <sub>2</sub> </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"> <sub>3 </sub> </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"> <sub> <sp/> </sub> </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"/> </p> </text> </region> <region region-id="1978" left="24" top="1049.25" width="55.5" height="32.25" align-x="46.5" 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:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">k</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1</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="22"/> </region> <region region-id="1979" left="132" top="1049.25" width="56.25" height="32.25" align-x="155.25" align-y="1068" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">k</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1</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="23"/> </region> <region region-id="1980" left="234" top="1049.25" width="55.5" height="32.25" align-x="256.5" 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:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">k</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1</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="24"/> </region> <region region-id="1936" left="24" top="1104.75" width="33.75" height="15" align-x="39.75" align-y="1116" 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="25"/> </region> <region region-id="1937" left="366" top="1112.25" width="134.25" height="147" align-x="372.75" align-y="1122" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <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"> <b> <i> <inlineAttr line-through="false"> <c val="#00f">F</c> </inlineAttr> </i> </b> </f> <b> <inlineAttr font-style="normal" underline="false" line-through="false"> <c val="#00f"> <sub> <f family="Arial" charset="0" size="10">i</f> </sub> </c> </inlineAttr> </b> <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"> <b> <c val="#00f"> <i>S</i> </c> </b> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <b> <inlineAttr font-style="normal" underline="false" line-through="false"> <c val="#00f"> <sub>i</sub> </c> </inlineAttr> </b> </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> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <inlineAttr line-through="false"> <c val="#00f"> <f family="Arial" charset="0" size="10">Achtung:</f> </c> </inlineAttr> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="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> </p> </text> </region> <region region-id="1938" left="66" top="1134.75" width="193.5" height="24" align-x="219" align-y="1146" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml: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" subscript="m">far</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="26"/> </region> <region region-id="1939" left="288" top="1136.25" width="69" height="12" align-x="290.25" align-y="1146" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">x - Komponente</c> </inlineAttr> </f> </p> </text> </region> <region region-id="1940" left="66" top="1170.75" width="193.5" height="24" align-x="219" align-y="1182" 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" subscript="m">far</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="27"/> </region> <region region-id="1941" left="288" top="1172.25" width="69" height="12" align-x="288" align-y="1182" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">y - Komponente</c> </inlineAttr> </f> </p> </text> </region> <region region-id="1942" left="66" top="1206.75" width="193.5" height="24" align-x="219" align-y="1218" 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> 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text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Vertikalkomponente </c> </inlineAttr> </f> </p> </text> </region> <region region-id="1177" left="30" top="1746.75" width="112.5" height="19.5" align-x="54" align-y="1758" 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="WarnRedefinedUDScalar" 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="46"/> </region> <region region-id="945" left="204" top="1752.75" width="96.75" height="19.5" align-x="226.5" align-y="1764" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="h">F</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1649.5721976846444</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="47"/> </region> <region region-id="1121" left="336" top="1754.25" width="96.75" height="12" align-x="387" align-y="1764" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Horizontalkomponente</c> </inlineAttr> </f> </p> </text> </region> <region region-id="1292" left="30" top="1818.75" width="75.75" height="19.5" align-x="61.5" align-y="1830" 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">FS</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">k</ml:id> <ml:id xml:space="preserve" font="4" subscript="3">S</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="48"/> </region> <region region-id="1543" left="150" top="1797.75" width="129" height="57.75" align-x="180" align-y="1830" show-border="false" show-highlight="true" 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" font="4" subscript="3">FS</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="3" cols="1"> <ml:real>-1428.5714285714287</ml:real> <ml:real>-824.78609884232242</ml:real> <ml:real>-4000</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="49"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Stabkraft des Stabes DC</c> </inlineAttr> </f> </p> </text> </region> <region region-id="1294" left="30" top="1854.75" width="114.75" 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 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> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4326.7873110859227</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="50"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Betrag der Stabkraft DC</c> </inlineAttr> </f> </p> </text> </region> <region region-id="1295" left="30" top="1884.75" width="108.75" height="19.5" align-x="54" align-y="1896" 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="WarnRedefinedUDScalar" 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="51"/> </region> <region region-id="1296" left="204" top="1884.75" width="96.75" height="19.5" align-x="226.5" align-y="1896" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="v">F</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4000.0000000000005</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="52"/> </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="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Vertikalkomponente </c> </inlineAttr> </f> </p> </text> </region> <region region-id="1333" left="30" top="1920.75" width="111.75" height="19.5" align-x="54" align-y="1932" 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="WarnRedefinedUDScalar" 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="53"/> </region> <region region-id="1298" left="204" top="1920.75" width="96.75" height="19.5" align-x="226.5" align-y="1932" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="h">F</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1649.5721976846444</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="54"/> </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="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Horizontalkomponente</c> </inlineAttr> </f> </p> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Aus Symmetriegründen müssen die drei Stabkräfte den gleichen Betrag haben; was durch die</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Rechnung bestätigt wird. </p> </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="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0"> <b> <i> <inlineAttr line-through="false"> <c val="#00f">Berechnung der Zugkraft in der Kette:</c> </inlineAttr> </i> </b> </f> </p> </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"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Aus der Skizze (Draufsicht) erkennt man (x- und y-Richtung wie in Skizze, z-Komponente = 0): </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">(Aus Symmetriegründen müssen alle Zugkräfte gleich groß sein).</c> </inlineAttr> </f> </p> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <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> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <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> </p> </text> </region> <region region-id="1195" left="18" top="2118.75" width="66.75" height="15.75" align-x="36" 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="55"/> </region> <region region-id="1565" left="18" top="2156.25" width="74.25" height="60.75" align-x="42" align-y="2190" 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="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="56"/> </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="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Horizontalkomponente </c> </inlineAttr> </f> </p> </text> </region> <region region-id="1196" left="18" top="2235.75" width="129.75" height="57" 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="57"/> </region> <region region-id="1197" left="168" top="2236.5" width="130.5" height="56.25" 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="58"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Richtungsvektoren der Zugkräfte</c> </inlineAttr> </f> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">(ohne Einheiten)</c> </inlineAttr> </f> </p> </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="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">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"> <sub>1</sub> </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"> <sub>2</sub> </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> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="12"> <c val="#00f"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(Gleiche Begründung wie für k</inlineAttr> </c> </f> <sub> <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> </sub> <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"> <sub>2</sub> </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"> <sub>3</sub> </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> </p> </text> </region> <region region-id="1551" left="30" top="2363.25" width="72" height="32.25" align-x="53.25" 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="59"/> </region> <region region-id="1552" left="180" top="2363.25" width="72.75" height="32.25" align-x="204" 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="60"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Starwerte für nummmerische Lösung des Gleichungssystems)</c> </inlineAttr> </f> </p> </text> </region> <region region-id="1369" left="12" top="2406.75" width="33.75" height="15" align-x="27.75" align-y="2418" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">Given</ml:id> </math> <rendering item-idref="61"/> </region> <region region-id="1172" left="66" top="2430.75" width="163.5" height="24" align-x="199.5" 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="62"/> </region> <region region-id="986" left="66" top="2460.75" width="163.5" height="24" align-x="199.5" 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="63"/> </region> <region region-id="1368" left="12" top="2496.75" width="102" height="19.5" align-x="28.5" align-y="2508" 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: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="64"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <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> </p> </text> </region> <region region-id="1571" left="312" top="2492.25" width="102" height="36.75" align-x="327" align-y="2514" 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> <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> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="2" cols="1"> <ml:real>952.3809523808477</ml:real> <ml:real>952.3809523808477</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter" power-numerator="-1"/> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="65"/> </region> <region region-id="1192" left="36" top="2550.75" width="102" 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 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="66"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Zugkraft zwischen den Fußpunkten B und A</c> </inlineAttr> </f> </p> </text> </region> <region region-id="1269" left="36" top="2583.75" width="134.25" height="57.75" align-x="77.25" align-y="2616" 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" font="4" subscript="KBA">F</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="3" cols="1"> <ml:real>476.19047619042379</ml:real> <ml:real>-824.78609884223192</ml:real> <ml:real>0</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="67"/> </region> <region region-id="1270" left="180" top="2604.75" width="120" 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 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> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>952.3809523808477</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="68"/> </region> <region region-id="1274" left="36" top="2664.75" width="103.5" 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 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="69"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Zugkraft zwischen den Fußpunkten B und C</c> </inlineAttr> </f> </p> </text> </region> <region region-id="1275" left="36" top="2697.75" width="135" height="57.75" align-x="78" align-y="2730" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="4" subscript="KBC">F</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="3" cols="1"> <ml:real>-476.19047619042379</ml:real> <ml:real>-824.78609884223192</ml:real> <ml:real>0</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="70"/> </region> <region region-id="1276" left="174" top="2718.75" width="120.75" 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 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> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>952.3809523808477</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="newton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="71"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0"> <b> <inlineAttr line-through="false"> <c val="#00f">Bestimmung der Nenndicke für die Ketten:</c> </inlineAttr> </b> </f> </p> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Zulässige Spannung einer Haltekette:</p> </text> </region> <region region-id="1606" left="396" top="2813.25" width="93.75" height="37.5" align-x="430.5" 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="72"/> </region> <region region-id="1587" left="30" top="2868.75" width="82.5" height="37.5" align-x="63" 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">amp</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="73"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Den Faktor 2 im Nenner tritt auf, da das Kettenglied zwei Querschnitte aufweist</c> </inlineAttr> </f> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="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"> <sub>K</sub> </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> </p> </text> </region> <region region-id="1610" left="30" top="2923.5" width="84" height="42.75" align-x="61.5" 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">amp</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="74"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Querschnittsfläche des Kettengliedes.</c> </inlineAttr> </f> </p> </text> </region> <region region-id="1616" left="30" top="2988.75" width="82.5" height="19.5" align-x="57" 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:apply> <ml:absval/> <ml:id xml:space="preserve" font="4" subscript="KBC">F</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="75"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Stabkraft</c> </inlineAttr> </f> <sp/> </p> </text> </region> <region region-id="1643" left="360" top="2988.75" width="55.5" height="19.5" align-x="387" 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="76"/> </region> <region region-id="1718" left="426" top="2988.75" width="70.5" height="19.5" align-x="460.5" 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="77"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="8"> <inlineAttr line-through="false"> <c val="#00f">"rückdefinieren", damit symbolisch gerechnet werden kann</c> </inlineAttr> </f> </p> </text> </region> <region region-id="1654" left="30" top="3033.75" width="278.25" height="93.75" align-x="207" 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="78"/> </region> <region region-id="1655" left="30" top="3147.75" width="190.5" height="50.25" align-x="56.25" align-y="3180" 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">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="79"/> </region> <region region-id="1656" left="30" top="3222.75" width="81.75" height="19.5" align-x="54.75" align-y="3234" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="K">d</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>3.1788481800591333</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="2" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="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="80"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="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> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">d = 4 mm</c> </inlineAttr> </f> </p> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0"> <b> <inlineAttr line-through="false"> <c val="#00f">Dimensionierung der Stäbe:</c> </inlineAttr> </b> </f> </p> </text> </region> <region region-id="1686" left="12" top="3312.75" width="488.25" height="115.5" 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"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">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/> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">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"> <sub>erf</sub> </c> </inlineAttr> </f> zu ermitteln und damit das Stahlrohr so zu dimensionieren, dass Eulersche Knickung gilt. </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Eine Knicksicherheit <region region-id="1680" left="121.5" top="3370.5" width="39.75" height="19.5" align-x="144.75" align-y="3381.75" 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="81"/> </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> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <region region-id="1681" left="12" top="3390.75" width="101.25" height="37.5" align-x="30" align-y="3409.5" 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="82"/> </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> </p> </text> </region> <region region-id="1719" left="24" top="3444.75" width="68.25" height="19.5" align-x="48.75" align-y="3456" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="S">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="83"/> </region> <region region-id="1671" left="24" top="3489.75" width="118.5" height="40.5" align-x="40.5" 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">hl</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="84"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Stablänge nach den gegebenen Daten</c> </inlineAttr> </f> </p> </text> </region> <region region-id="1674" left="24" top="3552.75" width="47.25" height="15" align-x="53.25" 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">sec</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:define> </math> <rendering item-idref="85"/> </region> <region region-id="1675" left="90" top="3552.75" width="84.75" height="15.75" align-x="117.75" 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">sec</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="86"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">freie Knicklänge</c> </inlineAttr> </f> </p> </text> </region> <region region-id="1679" left="24" top="3583.5" width="111.75" height="47.25" align-x="54" align-y="3612" 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="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">sec</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="87"/> </region> <region region-id="1692" left="180" top="3602.25" width="303.75" height="40.5" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <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"> <sub>erf</sub> </c> </inlineAttr> </f> <f size="10"> ergit sich daher zu: </f> <region region-id="1694" left="180" top="3618" width="78" height="24.75" align-x="208.5" align-y="3634.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="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> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>14.961106431982989</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="centimeter" power-numerator="4"/> </unitMonomial> </unitedValue> </result> </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="88"/> </region> </p> </text> </region> <region region-id="1696" left="18" top="3654.75" width="481.5" height="61.5" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Der Vergleich mit dem Datenblatt zeigt, dass man ein <f family="Arial" charset="0"> <b> <inlineAttr line-through="false"> <c val="#00f">Stahlrohr mit dem Nennmaß 50 x 50</c> </inlineAttr> </b> </f> verwenden muss. Für dieses Rohr gilt <region region-id="1697" left="215.25" top="3669.75" width="72.75" height="21" align-x="228.75" align-y="3686.25" 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="89"/> </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> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="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="234.75" top="3691.5" width="83.25" height="24.75" align-x="258.75" align-y="3708" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml: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="90"/> </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> </p> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">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"> <sub>0</sub> </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> </p> </text> </region> <region region-id="1702" left="30" top="3777.75" width="54" height="38.25" align-x="43.5" 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="91"/> </region> <region region-id="1704" left="102" top="3786.75" width="69" height="15.75" align-x="114" 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="92"/> </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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr line-through="false"> <c val="#00f">Trägheitsradius</c> </inlineAttr> </f> </p> </text> </region> <region region-id="1706" left="30" top="3851.25" width="51.75" height="32.25" align-x="46.5" align-y="3870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> 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