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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="yk">f</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>50</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">kN</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="1475" left="12" top="926.25" width="228.75" height="12" align-x="21.75" align-y="936" 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"> Bemessungswert der Zugfestigkeit </text> </region> <region region-id="1476" left="12" top="946.5" width="91.5" height="37.5" align-x="31.5" align-y="966" 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="yd">f</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="yk">f</ml:id> <ml:id xml:space="preserve" subscript="s">γ</ml:id> </ml:apply> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">kN</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>43.478260869565219</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="centimeter" power-numerator="-2"/> <unitReference unit="kilonewton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> <resultFormat numeric-only="true"> <general precision="1" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="20"/> </region> <region region-id="1477" left="12" top="1002.75" width="108" height="13.5" align-x="39" align-y="1014" 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="12"> <inlineAttr font-weight="normal">3. Einwirkungen: </inlineAttr> </f> </text> </region> <region region-id="1593" left="18" top="1018.5" width="69" height="45.75" align-x="42" align-y="1044" 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="Ed">N</ml:id> <ml:matrix rows="3" cols="1"> <ml:real>-100</ml:real> <ml:real>-180</ml:real> <ml:real>-1854</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="1595" left="138" top="1030.5" width="57.75" height="45.75" align-x="160.5" align-y="1056" 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="Ed">V</ml:id> <ml:matrix rows="3" cols="1"> <ml:real>10</ml:real> <ml:real>45</ml:real> <ml:real>117</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="1480" left="12" top="1080.75" width="75" height="13.5" align-x="13.5" align-y="1092" 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="12"> 4. Bemessung </f> </text> </region> <region region-id="1535" left="12" top="1109.25" width="360" height="30" align-x="37.5" 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"> Äquivalenter Querkraftbewehrungsgrad ρf w,cdes Stahlfaserbetons nach Gl. (8.4) des DBV-Merkblatts. </text> </region> <region region-id="1574" left="0" top="1152" width="6008.25" align-x="0" align-y="1152" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="590.25"> <area is-collapsed="true" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="978" bottom-lock-id="981"> <region region-id="950" left="30" top="9" width="176.25" height="129.75" align-x="44.25" align-y="18" 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="d">k</ml:id> <ml:program> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="sl">A</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:id xml:space="preserve">hr</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>60</ml:real> <ml:id xml:space="preserve">cm</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1.6</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">hr</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>100</ml:real> <ml:id xml:space="preserve">cm</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:ifThen> <ml:otherwise> <ml:real>1</ml:real> </ml:otherwise> </ml:program> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve" subscript="sl">A</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:id xml:space="preserve">d</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>60</ml:real> <ml:id xml:space="preserve">cm</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1.6</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">d</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>100</ml:real> <ml:id xml:space="preserve">cm</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:ifThen> <ml:otherwise> <ml:real>1</ml:real> </ml:otherwise> </ml:program> </ml:ifThen> </ml:program> </ml:define> </math> </region> <region region-id="771" left="24" top="180" width="150.75" height="48.75" align-x="39" align-y="198" 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">n</ml:id> <ml:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="f">b</ml:id> <ml:id xml:space="preserve" subscript="w">b</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="f">h</ml:id> </ml:apply> <ml:real>3</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="f">b</ml:id> <ml:id xml:space="preserve" subscript="w">b</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="f">h</ml:id> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:real>3</ml:real> </ml:otherwise> </ml:program> </ml:define> </math> </region> <region region-id="772" left="192" top="180" width="117" height="68.25" align-x="203.25" align-y="198" 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">n</ml:id> <ml:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:id xml:space="preserve" subscript="1">n</ml:id> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve" subscript="f">h</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="1">n</ml:id> </ml:ifThen> <ml:otherwise> <ml:parens> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve" subscript="f">h</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:otherwise> </ml:program> </ml:define> </math> </region> <region region-id="773" left="342" top="261" width="27.75" height="12.75" align-x="352.5" align-y="270" 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">n</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0</ml:real> </result> </ml:eval> </math> </region> <region region-id="793" left="24" top="276" width="252.75" height="48.75" align-x="36.75" align-y="294" 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="f">k</ml:id> <ml:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">n</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="f">h</ml:id> <ml:id xml:space="preserve" subscript="w">b</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="f">h</ml:id> <ml:id xml:space="preserve">d</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:real>1.5</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">n</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="f">h</ml:id> <ml:id xml:space="preserve" subscript="w">b</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="f">h</ml:id> <ml:id xml:space="preserve">d</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> </ml:ifThen> <ml:otherwise> <ml:real>1.5</ml:real> </ml:otherwise> </ml:program> </ml:define> </math> </region> <region region-id="1573" left="24" top="340.5" width="270" height="219.75" align-x="51.75" align-y="360" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="w.c">ρf</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <ml:real>4</ml:real> </ml:apply> <ml:program> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id xml:space="preserve" subscript="eq.ctk.II">f</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0.06</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">kN</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:ifThen> <ml:otherwise> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>0.12</ml:real> <ml:id xml:space="preserve" subscript="f">k</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="d">k</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="eq.ctk.II">f</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>0.37</ml:real> <ml:id xml:space="preserve" subscript="yd">f</ml:id> </ml:apply> 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subscript="d">k</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="eq.ctk.II">f</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>0.37</ml:real> <ml:id xml:space="preserve" subscript="yd">f</ml:id> </ml:apply> <ml:real>0.9</ml:real> </ml:apply> </ml:apply> <ml:real>1000</ml:real> </ml:apply> </ml:parens> </ml:otherwise> </ml:program> </ml:ifThen> </ml:program> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.0360360360360359</ml:real> </result> </ml:eval> </ml:define> </math> </region> </area> <rendering item-idref="23"/> </region> <region region-id="1508" left="12" top="1170" width="165" height="111.75" align-x="12" align-y="1170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{0002CE03-0000-0000-C000-000000000046}" type="embedded" item-idref="24"/> <rendering item-idref="25"/> </region> <region region-id="1525" left="396" top="1182" width="13.5" height="11.25" align-x="396" align-y="1182" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{00020906-0000-0000-C000-000000000046}" type="embedded" item-idref="26"/> <rendering item-idref="27"/> </region> <region region-id="1517" left="318" top="1179" width="69" height="16.5" align-x="345" align-y="1188" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="w.c">ρf</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.0360360360360359</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="5" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="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="28"/> </region> <region region-id="1008" left="318" top="1221" width="43.5" height="16.5" align-x="333" align-y="1230" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="d">k</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.25</ml:real> </result> </ml:eval> </math> <rendering item-idref="29"/> </region> <region region-id="1004" left="318" top="1257" width="30.75" height="16.5" align-x="331.5" align-y="1266" 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="f">k</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="30"/> </region> <region region-id="1507" left="12" top="1328.25" width="81.75" height="12" align-x="25.5" align-y="1338" 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"> Innerer Hebelarm z </text> </region> <region region-id="1506" left="12" top="1350" width="254.25" height="33.75" align-x="12" align-y="1350" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{0002CE03-0000-0000-C000-000000000046}" type="embedded" item-idref="31"/> <rendering item-idref="32"/> </region> <region region-id="1597" left="0" top="1389" width="6008.25" align-x="0" align-y="1389" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="1322.25"> <area is-collapsed="true" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="1029" bottom-lock-id="1031"> <region region-id="1526" left="24" top="29.25" width="186.75" height="57" align-x="33.75" align-y="38.25" 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">z</ml:id> <ml:program> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="sl">A</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:mult/> <ml:real>0.8</ml:real> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> </ml:parens> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve" subscript="sl">A</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:mult/> <ml:real>0.9</ml:real> <ml:id xml:space="preserve">d</ml:id> </ml:apply> </ml:parens> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id xml:space="preserve" subscript="sl">A</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:str xml:space="preserve">Längsbewehrung falsch</ml:str> </ml:ifThen> </ml:program> </ml:define> </math> </region> <region region-id="448" left="24" top="135" width="231" height="45.75" align-x="36" align-y="152.25" 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">κ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> 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<math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="l">ρ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="sl">A</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">d</ml:id> </ml:apply> </ml:apply> <ml:real>0.02</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="sl">A</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">d</ml:id> </ml:apply> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:real>0.02</ml:real> </ml:otherwise> </ml:program> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0</ml:real> </result> </ml:eval> </ml:define> </math> </region> <region region-id="1585" left="24" top="280.5" width="124.5" height="16.5" 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<ml:real>-0.0035314285714285712</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meganewton"/> <unitReference unit="meter" power-numerator="-2"/> <unitReference unit="newton" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> </region> <region region-id="1588" left="12" top="534.75" width="339.75" height="72" align-x="45" align-y="577.5" 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" subscript="Rd.ct">V</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0.1</ml:real> <ml:id xml:space="preserve">κ</ml:id> </ml:apply> <ml:apply> <ml:pow/> 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style="auto-select"/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2.4</ml:real> <ml:real>0.1</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="ck">f</ml:id> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>1.2</ml:real> <ml:id xml:space="preserve" subscript="cd">σ</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="cd">f</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:id xml:space="preserve" subscript="w">b</ml:id> </ml:apply> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">MN</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">m</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> 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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="w">ρ</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.31</ml:real> </result> </ml:eval> </math> </region> <region region-id="490" left="30" top="1068.75" width="138" height="31.5" align-x="108" align-y="1088.25" 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">Bauteilverhältniss</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>4.2857142857142856</ml:real> </result> </ml:eval> </ml:define> </math> </region> <region region-id="495" left="24" top="1122.75" width="279.75" height="172.5" align-x="56.25" align-y="1142.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Dieser Wert muss ein Skalar sein." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="w">minρ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:program> <ml:ifThen> <ml:apply> <ml:greaterOrEqual/> <ml:apply> <ml:greaterOrEqual/> <ml:real>5</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> </ml:apply> <ml:real>4</ml:real> </ml:apply> <ml:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:id xml:space="preserve" subscript="Ed">V</ml:id> <ml:id xml:space="preserve" subscript="Rd.ct">V</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:absval/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <ml:real>5</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="w">ρ</ml:id> </ml:apply> </ml:parens> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve" subscript="Ed">V</ml:id> <ml:id xml:space="preserve" subscript="Rd.ct">V</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>0.6</ml:real> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:absval/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <ml:real>5</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:real>0.4</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="w">ρ</ml:id> </ml:apply> </ml:parens> </ml:ifThen> </ml:program> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:greaterThan/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <ml:real>5</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <ml:real>4</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="w">ρ</ml:id> </ml:ifThen> </ml:program> </ml:eval> </ml:define> </math> </region> </area> <rendering item-idref="34"/> </region> <region region-id="1529" left="12" top="1404.75" width="45.75" height="12.75" align-x="21" align-y="1413.75" 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">z</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.28</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="35"/> </region> <region region-id="1502" left="12" top="1428" width="359.25" height="24" align-x="51" align-y="1437.75" 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"> Mindestbewehrungsgrad in Abhängigkeit der Bauteilgeometrie Für Platten nach DIN 1045-1, 13.3.3, und Balken nach DIN 1045-1, 13.2.3 </text> </region> <region region-id="1559" left="84" top="1467.75" width="13.5" height="11.25" align-x="84" align-y="1467.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{00020906-0000-0000-C000-000000000046}" type="embedded" item-idref="36"/> <rendering item-idref="37"/> </region> <region region-id="1501" left="12" top="1464.75" width="48.75" height="16.5" align-x="43.5" align-y="1473.75" 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="w">minρ</ml:id> </ml:eval> </math> <rendering item-idref="38"/> </region> <region region-id="1500" left="12" top="1485.75" width="227.25" height="27.75" align-x="12" align-y="1485.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{0002CE03-0000-0000-C000-000000000046}" type="embedded" item-idref="39"/> <rendering item-idref="40"/> </region> <region region-id="1063" left="324" top="1494" width="86.25" height="12" align-x="328.5" align-y="1503.75" 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"> DIN 1045-1<sp count="2"/>Gl. (70) </text> </region> <region region-id="1581" left="492" top="1487.25" width="136.5" height="63.75" align-x="524.25" align-y="1521.75" 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="Rd.ct">V</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kN</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="3" cols="1"> <ml:real>1.1040000000000001E-11</ml:real> <ml:real>1.9871999999999996E-11</ml:real> <ml:real>2.0468159999999998E-10</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilonewton"/> <unitReference unit="newton" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="41"/> </region> <region region-id="1498" left="12" top="1545.75" width="201" height="36" align-x="12" align-y="1545.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{0002CE03-0000-0000-C000-000000000046}" type="embedded" item-idref="42"/> <rendering item-idref="43"/> </region> <region region-id="1066" left="324" top="1554" width="86.25" height="12" align-x="331.5" align-y="1563.75" 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"> DIN 1045-1<sp count="2"/>Gl. (74) </text> </region> <region region-id="1497" left="12" top="1584.75" width="54.75" height="16.5" align-x="41.25" align-y="1593.75" 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="Rd.c">V</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kN</ml:id> </ml:unitOverride> </ml:eval> <resultFormat> <table item-idref="44"/> </resultFormat> </math> <rendering item-idref="45"/> </region> <region region-id="1496" left="12" top="1608" width="16.5" height="12" align-x="17.25" align-y="1617.75" 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"> mit: </text> </region> <region 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xml:space="preserve">cm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.1</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="centimeter" power-numerator="-2"/> <unitReference unit="kilonewton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="1472" left="12" top="846.75" width="74.25" height="13.5" align-x="17.25" align-y="858" 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="12">2.2 Betonstahl</f> </text> </region> <region region-id="1473" left="12" top="866.25" width="142.5" height="12" align-x="55.5" align-y="876" 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"> Teilsicherheitsbeiwert Betonstahl </text> </region> <region region-id="886" left="288" top="867" width="39.75" height="16.5" align-x="304.5" align-y="876" 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">γ</ml:id> <ml:real>1.15</ml:real> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="1474" left="12" top="890.25" width="57.75" height="12" align-x="38.25" 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"> Zugfestigkeit </text> </region> <region region-id="1402" left="102" top="884.25" width="55.5" height="33.75" align-x="120.75" 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" subscript="yk">f</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>50</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">kN</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="1475" left="12" top="926.25" width="228.75" height="12" align-x="21.75" align-y="936" 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"> Bemessungswert der Zugfestigkeit </text> </region> <region region-id="1476" left="12" top="946.5" width="91.5" height="37.5" align-x="31.5" align-y="966" 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="yd">f</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="yk">f</ml:id> <ml:id xml:space="preserve" subscript="s">γ</ml:id> </ml:apply> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">kN</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>43.478260869565219</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="centimeter" power-numerator="-2"/> <unitReference unit="kilonewton"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> <resultFormat numeric-only="true"> <general precision="1" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="20"/> </region> <region region-id="1477" left="12" top="1002.75" width="108" height="13.5" align-x="39" align-y="1014" 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="12"> <inlineAttr font-weight="normal">3. Einwirkungen: </inlineAttr> </f> </text> </region> <region region-id="1593" left="18" top="1018.5" width="69" height="45.75" align-x="42" align-y="1044" 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="Ed">N</ml:id> <ml:matrix rows="3" cols="1"> <ml:real>-100</ml:real> <ml:real>-180</ml:real> <ml:real>-1854</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="1595" left="138" top="1030.5" width="57.75" height="45.75" align-x="160.5" align-y="1056" 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="Ed">V</ml:id> <ml:matrix rows="3" cols="1"> <ml:real>10</ml:real> <ml:real>45</ml:real> <ml:real>117</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="1480" left="12" top="1080.75" width="75" height="13.5" align-x="13.5" align-y="1092" 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="12"> 4. Bemessung </f> </text> </region> <region region-id="1535" left="12" top="1109.25" width="360" height="30" align-x="37.5" 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"> Äquivalenter Querkraftbewehrungsgrad ρf w,cdes Stahlfaserbetons nach Gl. (8.4) des DBV-Merkblatts. </text> </region> <region region-id="1574" left="0" top="1152" width="6008.25" align-x="0" align-y="1152" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="590.25"> <area is-collapsed="true" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="978" bottom-lock-id="981"> <region region-id="950" left="30" top="9" width="176.25" height="129.75" align-x="44.25" align-y="18" 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="d">k</ml:id> <ml:program> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="sl">A</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:program> <ml:ifThen> <ml:apply> 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align-x="0" align-y="1389" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="1322.25"> <area is-collapsed="true" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="1029" bottom-lock-id="1031"> <region region-id="1526" left="24" top="29.25" width="186.75" height="57" align-x="33.75" align-y="38.25" 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">z</ml:id> <ml:program> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="sl">A</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:mult/> <ml:real>0.8</ml:real> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> </ml:parens> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve" subscript="sl">A</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:mult/> <ml:real>0.9</ml:real> <ml:id xml:space="preserve">d</ml:id> </ml:apply> </ml:parens> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id xml:space="preserve" subscript="sl">A</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:str xml:space="preserve">Längsbewehrung falsch</ml:str> </ml:ifThen> </ml:program> </ml:define> </math> </region> <region region-id="448" left="24" top="135" width="231" height="45.75" align-x="36" align-y="152.25" 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">κ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> 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<math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="l">ρ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="sl">A</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">d</ml:id> </ml:apply> </ml:apply> <ml:real>0.02</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="sl">A</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">d</ml:id> </ml:apply> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:real>0.02</ml:real> </ml:otherwise> </ml:program> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0</ml:real> </result> </ml:eval> </ml:define> </math> </region> <region region-id="1585" left="24" top="280.5" width="124.5" height="16.5" align-x="42" align-y="289.5" 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" subscript="c">A</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="f">b</ml:id> <ml:id xml:space="preserve" subscript="f">h</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">hr</ml:id> <ml:id xml:space="preserve" subscript="f">h</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.525</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> </region> <region region-id="1586" left="30" top="357" width="167.25" height="63.75" align-x="51.75" align-y="391.5" 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" subscript="cd">σ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="Ed">N</ml:id> <ml:id xml:space="preserve" subscript="c">A</ml:id> </ml:apply> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">MN</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">m</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="3" cols="1"> <ml:real>-0.00019047619047619048</ml:real> <ml:real>-0.00034285714285714285</ml:real> <ml:real>-0.0035314285714285712</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meganewton"/> <unitReference unit="meter" power-numerator="-2"/> <unitReference unit="newton" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> </region> <region region-id="1588" left="12" top="534.75" width="339.75" height="72" align-x="45" align-y="577.5" 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" subscript="Rd.ct">V</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0.1</ml:real> <ml:id xml:space="preserve">κ</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>100</ml:real> <ml:id xml:space="preserve" subscript="l">ρ</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="ck">f</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">MN</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">m</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>0.12</ml:real> <ml:id xml:space="preserve" subscript="cd">σ</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="w">b</ml:id> </ml:apply> <ml:id xml:space="preserve">d</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kN</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="3" cols="1"> <ml:real>1.1040000000000002E-08</ml:real> <ml:real>1.9871999999999998E-08</ml:real> <ml:real>2.0468159999999998E-07</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilonewton"/> <unitReference unit="newton" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> </region> <region region-id="1589" left="18" top="757.5" width="229.5" height="48" align-x="48" align-y="787.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Dieser Wert hat die Einheiten Kraft^-1, muss jedoch die Einheiten Unitless." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="Rd.c">V</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2.4</ml:real> <ml:real>0.1</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="ck">f</ml:id> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>1.2</ml:real> <ml:id xml:space="preserve" subscript="cd">σ</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="cd">f</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:id xml:space="preserve" subscript="w">b</ml:id> </ml:apply> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">MN</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">m</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kN</ml:id> </ml:unitOverride> </ml:eval> </ml:define> <resultFormat> <table item-idref="33"/> </resultFormat> </math> </region> <region region-id="440" left="24" top="899.25" width="106.5" height="158.25" align-x="42" align-y="908.25" 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" subscript="w">ρ</ml:id> <ml:program> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="ck">f</ml:id> <ml:real>16</ml:real> </ml:apply> <ml:real>0.61</ml:real> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="ck">f</ml:id> <ml:real>20</ml:real> </ml:apply> <ml:real>0.70</ml:real> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="ck">f</ml:id> <ml:real>25</ml:real> </ml:apply> 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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="w">ρ</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.31</ml:real> </result> </ml:eval> </math> </region> <region region-id="490" left="30" top="1068.75" width="138" height="31.5" align-x="108" align-y="1088.25" 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">Bauteilverhältniss</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>4.2857142857142856</ml:real> </result> </ml:eval> </ml:define> </math> </region> <region region-id="495" left="24" top="1122.75" width="279.75" height="172.5" align-x="56.25" align-y="1142.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="Dieser Wert muss ein Skalar sein." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="w">minρ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:program> <ml:ifThen> <ml:apply> <ml:greaterOrEqual/> <ml:apply> <ml:greaterOrEqual/> <ml:real>5</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> </ml:apply> <ml:real>4</ml:real> </ml:apply> <ml:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:id xml:space="preserve" subscript="Ed">V</ml:id> <ml:id xml:space="preserve" subscript="Rd.ct">V</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:absval/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <ml:real>5</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="w">ρ</ml:id> </ml:apply> </ml:parens> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve" subscript="Ed">V</ml:id> <ml:id xml:space="preserve" subscript="Rd.ct">V</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>0.6</ml:real> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:absval/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <ml:real>5</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:real>0.4</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="w">ρ</ml:id> </ml:apply> </ml:parens> </ml:ifThen> </ml:program> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:greaterThan/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <ml:real>5</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:id xml:space="preserve">hr</ml:id> </ml:apply> <ml:real>4</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="w">ρ</ml:id> </ml:ifThen> </ml:program> </ml:eval> </ml:define> </math> </region> </area> <rendering item-idref="34"/> </region> <region region-id="1529" left="12" top="1404.75" width="45.75" height="12.75" align-x="21" align-y="1413.75" 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">z</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.28</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="35"/> </region> <region region-id="1502" left="12" top="1428" width="359.25" height="24" align-x="51" align-y="1437.75" 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"> Mindestbewehrungsgrad in Abhängigkeit der Bauteilgeometrie Für Platten nach DIN 1045-1, 13.3.3, und Balken nach DIN 1045-1, 13.2.3 </text> </region> <region region-id="1559" left="84" top="1467.75" width="13.5" height="11.25" align-x="84" align-y="1467.75" show-border="false" show-highlight="false" 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item-idref="39"/> <rendering item-idref="40"/> </region> <region region-id="1063" left="324" top="1494" width="86.25" height="12" align-x="328.5" align-y="1503.75" 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"> DIN 1045-1<sp count="2"/>Gl. 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