<description/> <author>Dept. of Architectural Rep.</author> <company/> <keywords/> <revisedBy>Dept. of Architectural Rep.</revisedBy> </userData> <identityInfo> <revision>2</revision> <documentID>62F5DA5A-3423-4A29-BDB4-727CB5A6822A</documentID> <versionID>139BFF98-119B-421B-A8B8-EF70E29327F0</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" 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list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="List"> <blockAttr margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Indent"> <blockAttr margin-left="108" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="24" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Subtitle" base-style="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="18" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="large" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> <mathStyle name="Variables" font-family="Arial CE" font-charset="238" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Constants" font-family="Arial CE" font-charset="238" font-size="10" font-weight="normal" font-style="italic" underline="false"/> <mathStyle name="User 1" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 2" font-family="Courier New" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 3" font-family="System" font-charset="238" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 4" font-family="Script" font-charset="255" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 5" font-family="Roman" font-charset="255" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 6" font-family="Modern" font-charset="255" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="Arial CE" font-charset="238" font-size="10" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="charge" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance" display="false"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results numeric-only="true"> <general precision="3" 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"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="9" orientation="portrait" print-single-page-width="true" page-width="594.75" page-height="842.25"> <margins left="28.34646" right="28.34646" top="28.34646" bottom="28.34646"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="en" UI="en"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="false" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC11" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="cm"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="253" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="161" left="558" top="2.25" width="27" height="13.5" align-x="570.75" align-y="12" 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">A</ml:id> <ml:id xml:space="preserve">A</ml:id> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="170" left="606" top="2.25" width="126" height="60" align-x="606" align-y="12" 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"> Ez azért kell, mert A az Amper mértékegysége, és így töröljük az értékét szimbolikus számítások számára. </text> </region> <region region-id="3" left="12" top="17.25" width="368.25" height="15.75" align-x="12" align-y="30" 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"> Kéttámaszú tartó igénybevételei általános terhek mellett </text> </region> <region region-id="128" left="24" top="56.25" width="506.25" height="72" align-x="24" align-y="66" 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"> A munkalap meghatározza egy kéttámaszú, mindkét végén konzolos tartó igénybevételeit tetszõleges megoszló és koncentrált terhek mellett. A tartót a támaszközzel, valamint a jobb és bal oldali konzol hosszával lehet megadni, ez utóbbiak lehetnek 0 m hosszúak is. A koordináta-rendszer origója a bal oldali támasz. A megoszló terheket, mint x függvényét kell felírni, a koncentrált terheket pedig a helyek és az értékek vektorai adják meg (ld. a példát). </text> </region> <region region-id="233" left="558" top="68.25" width="51" height="13.5" align-x="570.75" align-y="78" 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">N</ml:id> <ml:id xml:space="preserve">newton</ml:id> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="234" left="630" top="68.25" width="57" height="13.5" align-x="648" align-y="78" 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">kN</ml:id> <ml:apply> <ml:mult/> <ml:real>1000</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="130" left="12" top="138.75" width="40.5" height="13.5" align-x="12" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Adatok </text> </region> <region region-id="5" left="30" top="164.25" width="53.25" height="12" align-x="30" align-y="174" 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"> Támaszköz: </text> </region> <region region-id="6" left="96" top="164.25" width="33" height="13.5" align-x="104.25" align-y="174" 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:mult/> <ml:real>8</ml:real> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="8" left="162" top="164.25" width="74.25" height="12" align-x="162" align-y="174" 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"> Bal oldali konzol: </text> </region> <region region-id="9" left="246" top="164.25" width="26.25" height="17.25" align-x="259.5" align-y="174" 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="b">l</ml:id> <ml:real font="0">0</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="174" left="288" top="164.25" width="251.25" height="24" align-x="288" align-y="174" 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"> Ha letiltjuk ezt a két értékadást, akkor a konzolok hatása is belekerül a képletekbe. </text> </region> <region region-id="231" left="96" top="182.25" width="18" height="13.5" align-x="104.25" align-y="192" 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">l</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="10" left="162" top="182.25" width="80.25" height="12" align-x="162" align-y="192" 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"> Jobb oldali konzol: </text> </region> <region region-id="11" left="246" top="182.25" width="23.25" height="17.25" align-x="256.5" align-y="192" 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="j">l</ml:id> <ml:real font="0">0</ml:real> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="236" left="36" top="200.25" width="41.25" height="13.5" align-x="48.75" align-y="210" 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">P</ml:id> <ml:apply> <ml:mult/> <ml:real>1</ml:real> <ml:id xml:space="preserve">kN</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="237" left="96" top="200.25" width="27" height="13.5" align-x="108.75" align-y="210" 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">P</ml:id> <ml:id xml:space="preserve">P</ml:id> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="90" left="30" top="218.25" width="75" height="12" align-x="30" align-y="228" 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"> Megoszló terhek: </text> </region> <region region-id="89" left="126" top="218.25" width="39" height="13.5" align-x="150.75" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:id xml:space="preserve">P</ml:id> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="148" left="252" top="218.25" width="223.5" height="12" align-x="252" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Támaszközök közötti egyenletesen megoszló teher </text> </region> <region region-id="176" left="126" top="240.75" width="51" height="29.25" align-x="150.75" align-y="258" 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="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="180" left="252" top="248.25" width="105.75" height="12" align-x="252" align-y="258" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Lineárisan növekvõ teher </text> </region> <region region-id="245" left="126" top="270.75" width="189.75" height="29.25" align-x="150.75" align-y="288" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">Φ</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">l</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="247" left="336" top="278.25" width="100.5" height="12" align-x="336" align-y="288" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Háromszög alakú teher </text> </region> <region region-id="183" left="42" top="308.25" width="255" height="12" align-x="42" align-y="318" 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"> Parabola alakú teherfüggvény (támaszoknál 0, középen P): </text> </region> <region region-id="184" left="60" top="327" width="93" height="18.75" align-x="82.5" align-y="342" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="This variable is undefined." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">c</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="185" left="48" top="356.25" width="24.75" height="13.5" align-x="59.25" align-y="366" 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="15"/> </region> <region region-id="190" left="60" top="380.25" width="33.75" height="13.5" align-x="81.75" align-y="390" 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:id xml:space="preserve">f</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="16"/> </region> <region region-id="188" left="138" top="372.75" width="42.75" height="29.25" align-x="167.25" align-y="390" 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:id xml:space="preserve">f</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">l</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">P</ml:id> </ml:apply> </math> <rendering item-idref="17"/> </region> <region region-id="189" left="216" top="380.25" width="30.75" height="13.5" align-x="234.75" align-y="390" 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:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="18"/> </region> <region region-id="191" left="48" top="416.25" width="73.5" height="13.5" align-x="59.25" align-y="426" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="This variable is undefined." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k</ml:id> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:sequence> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">c</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="222" left="162" top="408.75" width="106.5" height="34.5" align-x="180" align-y="426" 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:transpose/> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:symResult> <ml:matrix rows="1" cols="3"> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">l</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:matrix> </ml:symResult> </ml:symEval> </math> <rendering item-idref="20"/> </region> <region region-id="216" left="48" top="459" width="111" height="21" align-x="72.75" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="220" left="186" top="456.75" width="165.75" height="34.5" align-x="210.75" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:command> <ml:id xml:space="preserve">simplify</ml:id> </ml:command> <ml:symResult> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">l</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">l</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="243" left="396" top="500.25" width="60.75" height="13.5" align-x="407.25" align-y="510" 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:range> <ml:sequence> <ml:real>0</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:real>5</ml:real> <ml:id xml:space="preserve">cm</ml:id> </ml:apply> </ml:sequence> <ml:id xml:space="preserve">l</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="252" left="486" top="500.25" width="24" height="13.5" align-x="497.25" align-y="510" 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:id xml:space="preserve">z</ml:id> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="229" left="18" top="528" width="436.5" height="234" align-x="18" align-y="528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="25"/> <rendering item-idref="26"/> </region> <region region-id="132" left="12" top="786.75" width="51" height="13.5" align-x="12" align-y="798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Számítás </text> </region> <region region-id="64" left="42" top="806.25" width="291.75" height="12" align-x="42" align-y="816" 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"> B támaszerõ számítása az A támaszra felírt nyomatéki egyenletbõl </text> </region> <region region-id="65" left="54" top="824.25" width="24.75" height="13.5" align-x="65.25" align-y="834" 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="27"/> </region> <region region-id="66" left="72" top="843" width="135" height="47.25" align-x="167.25" align-y="870" 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:integral auto-algorithm="true" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:lambda> <ml:bounds> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="b">l</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">l</ml:id> <ml:id xml:space="preserve" subscript="j">l</ml:id> </ml:apply> </ml:bounds> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>0</ml:real> <ml:id xml:space="preserve">kN</ml:id> </ml:apply> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="28"/> </region> <region region-id="67" left="54" top="894.75" width="90.75" height="29.25" align-x="66.75" align-y="912" 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">B</ml:id> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:Find auto-method="true" method="linear" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">B</ml:id> </ml:apply> <ml:symResult> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="69" left="42" top="938.25" width="291" height="12" align-x="42" align-y="948" 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"> Az A támaszerõt hasonlóan a nyomatéki egyenletbõl számíthatjuk: </text> </region> <region region-id="70" left="54" top="956.25" width="24.75" height="13.5" align-x="65.25" 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:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">Given</ml:id> </math> <rendering item-idref="30"/> </region> <region region-id="151" left="72" top="975" width="156" height="47.25" align-x="188.25" align-y="1002" 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:integral auto-algorithm="true" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">l</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:lambda> <ml:bounds> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="b">l</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">l</ml:id> <ml:id xml:space="preserve" subscript="j">l</ml:id> </ml:apply> </ml:bounds> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>0</ml:real> <ml:id xml:space="preserve">kN</ml:id> </ml:apply> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="31"/> </region> <region region-id="154" left="54" top="1026.75" width="90.75" height="29.25" align-x="66.75" 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 warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:Find auto-method="true" method="linear" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:symResult> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="74" left="42" top="1058.25" width="200.25" height="12" align-x="42" align-y="1068" 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"> A vetületi egyenletet is felírjuk ellenõrzésképp: </text> </region> <region region-id="75" left="54" top="1071" width="156.75" height="47.25" align-x="196.5" align-y="1098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:integral auto-algorithm="false" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:lambda> <ml:bounds> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="b">l</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">l</ml:id> <ml:id xml:space="preserve" subscript="j">l</ml:id> </ml:apply> </ml:bounds> </ml:apply> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> <ml:command> <ml:id xml:space="preserve">simplify</ml:id> </ml:command> <ml:symResult> <ml:real>0</ml:real> </ml:symResult> </ml:symEval> </math> <rendering item-idref="33"/> </region> <region region-id="24" left="30" top="1130.25" width="60.75" height="12" align-x="30" align-y="1140" 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"> Nyíróerõ ábra: </text> </region> <region region-id="114" left="42" top="1146.75" width="189" height="43.5" align-x="66.75" align-y="1170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">T</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:integral auto-algorithm="false" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">τ</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">τ</ml:id> </ml:apply> </ml:lambda> <ml:bounds> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="b">l</ml:id> </ml:apply> <ml:id xml:space="preserve">z</ml:id> </ml:bounds> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">Φ</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:id xml:space="preserve">A</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">Φ</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="34"/> </region> <region region-id="171" left="42" top="1206.75" width="339" height="34.5" align-x="116.25" align-y="1224" 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:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">collect</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:sequence> </ml:command> <ml:symResult> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">l</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">z</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">z</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <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">P</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">Φ</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <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">P</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">Φ</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="35"/> </region> <region region-id="167" left="42" top="1251.75" width="272.25" height="37.5" align-x="170.25" align-y="1272" 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:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">collect</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:sequence> </ml:command> <ml:command> <ml:sequence> <ml:id xml:space="preserve">assume</ml:id> <ml:apply> <ml:and/> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">z</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:lessThan/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:sequence> </ml:command> <ml:symResult> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:apply> <ml:mult/> 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Mathcad Professional 14.0 <description/> <author>Dept. of Architectural Rep.</author> <company/> <keywords/> <revisedBy>Dept. of Architectural Rep.</revisedBy> </userData> <identityInfo> <revision>2</revision> <documentID>62F5DA5A-3423-4A29-BDB4-727CB5A6822A</documentID> <versionID>139BFF98-119B-421B-A8B8-EF70E29327F0</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" 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text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="List"> <blockAttr margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Indent"> <blockAttr margin-left="108" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="24" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Subtitle" base-style="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="18" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="large" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> <mathStyle name="Variables" font-family="Arial CE" font-charset="238" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Constants" font-family="Arial CE" font-charset="238" font-size="10" font-weight="normal" font-style="italic" underline="false"/> <mathStyle name="User 1" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 2" font-family="Courier New" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 3" font-family="System" font-charset="238" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 4" font-family="Script" font-charset="255" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 5" font-family="Roman" font-charset="255" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 6" font-family="Modern" font-charset="255" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="Arial CE" font-charset="238" font-size="10" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="charge" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance" display="false"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results numeric-only="true"> <general precision="3" 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"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="9" orientation="portrait" print-single-page-width="true" page-width="594.75" page-height="842.25"> <margins left="28.34646" right="28.34646" top="28.34646" bottom="28.34646"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="en" UI="en"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="false" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC11" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="cm"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="253" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="161" left="558" top="2.25" width="27" height="13.5" align-x="570.75" align-y="12" 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">A</ml:id> <ml:id xml:space="preserve">A</ml:id> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="170" left="606" top="2.25" width="126" height="60" align-x="606" align-y="12" 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"> Ez azért kell, mert A az Amper mértékegysége, és így töröljük az értékét szimbolikus számítások számára. </text> </region> <region region-id="3" left="12" top="17.25" width="368.25" height="15.75" align-x="12" align-y="30" 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"> Kéttámaszú tartó igénybevételei általános terhek mellett </text> </region> <region region-id="128" left="24" top="56.25" width="506.25" height="72" align-x="24" align-y="66" 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"> A munkalap meghatározza egy kéttámaszú, mindkét végén konzolos tartó igénybevételeit tetszõleges megoszló és koncentrált terhek mellett. A tartót a támaszközzel, valamint a jobb és bal oldali konzol hosszával lehet megadni, ez utóbbiak lehetnek 0 m hosszúak is. A koordináta-rendszer origója a bal oldali támasz. A megoszló terheket, mint x függvényét kell felírni, a koncentrált terheket pedig a helyek és az értékek vektorai adják meg (ld. a példát). </text> </region> <region region-id="233" left="558" top="68.25" width="51" height="13.5" align-x="570.75" align-y="78" 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">N</ml:id> <ml:id xml:space="preserve">newton</ml:id> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="234" left="630" top="68.25" width="57" height="13.5" align-x="648" align-y="78" 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">kN</ml:id> <ml:apply> <ml:mult/> <ml:real>1000</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="130" left="12" top="138.75" width="40.5" height="13.5" align-x="12" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Adatok </text> </region> <region region-id="5" left="30" top="164.25" width="53.25" height="12" align-x="30" align-y="174" 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"> Támaszköz: </text> </region> <region region-id="6" left="96" top="164.25" width="33" height="13.5" align-x="104.25" align-y="174" 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:mult/> <ml:real>8</ml:real> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="8" left="162" top="164.25" width="74.25" height="12" align-x="162" align-y="174" 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"> Bal oldali konzol: </text> </region> <region region-id="9" left="246" top="164.25" width="26.25" height="17.25" align-x="259.5" align-y="174" 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="b">l</ml:id> <ml:real font="0">0</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="174" left="288" top="164.25" width="251.25" height="24" align-x="288" align-y="174" 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"> Ha letiltjuk ezt a két értékadást, akkor a konzolok hatása is belekerül a képletekbe. </text> </region> <region region-id="231" left="96" top="182.25" width="18" height="13.5" align-x="104.25" align-y="192" 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">l</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="10" left="162" top="182.25" width="80.25" height="12" align-x="162" align-y="192" 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"> Jobb oldali konzol: </text> </region> <region region-id="11" left="246" top="182.25" width="23.25" height="17.25" align-x="256.5" align-y="192" 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="j">l</ml:id> <ml:real font="0">0</ml:real> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="236" left="36" top="200.25" width="41.25" height="13.5" align-x="48.75" align-y="210" 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">P</ml:id> <ml:apply> <ml:mult/> <ml:real>1</ml:real> <ml:id xml:space="preserve">kN</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="237" left="96" top="200.25" width="27" height="13.5" align-x="108.75" align-y="210" 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">P</ml:id> <ml:id xml:space="preserve">P</ml:id> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="90" left="30" top="218.25" width="75" height="12" align-x="30" align-y="228" 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"> Megoszló terhek: </text> </region> <region region-id="89" left="126" top="218.25" width="39" height="13.5" align-x="150.75" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:id xml:space="preserve">P</ml:id> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="148" left="252" top="218.25" width="223.5" height="12" align-x="252" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Támaszközök közötti egyenletesen megoszló teher </text> </region> <region region-id="176" left="126" top="240.75" width="51" height="29.25" align-x="150.75" align-y="258" 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="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="180" left="252" top="248.25" width="105.75" height="12" align-x="252" align-y="258" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Lineárisan növekvõ teher </text> </region> <region region-id="245" left="126" top="270.75" width="189.75" height="29.25" align-x="150.75" align-y="288" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">Φ</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">l</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="247" left="336" top="278.25" width="100.5" height="12" align-x="336" align-y="288" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Háromszög alakú teher </text> </region> <region region-id="183" left="42" top="308.25" width="255" height="12" align-x="42" align-y="318" 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"> Parabola alakú teherfüggvény (támaszoknál 0, középen P): </text> </region> <region region-id="184" left="60" top="327" width="93" height="18.75" align-x="82.5" align-y="342" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="This variable is undefined." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">c</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="185" left="48" top="356.25" width="24.75" height="13.5" align-x="59.25" align-y="366" 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="15"/> </region> <region region-id="190" left="60" top="380.25" width="33.75" height="13.5" align-x="81.75" align-y="390" 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:id xml:space="preserve">f</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="16"/> </region> <region region-id="188" left="138" top="372.75" width="42.75" height="29.25" align-x="167.25" align-y="390" 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:id xml:space="preserve">f</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">l</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">P</ml:id> </ml:apply> </math> <rendering item-idref="17"/> </region> <region region-id="189" left="216" top="380.25" width="30.75" height="13.5" align-x="234.75" align-y="390" 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:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="18"/> </region> <region region-id="191" left="48" top="416.25" width="73.5" height="13.5" align-x="59.25" align-y="426" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="This variable is undefined." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k</ml:id> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:sequence> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">c</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="222" left="162" top="408.75" width="106.5" height="34.5" align-x="180" align-y="426" 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:transpose/> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:symResult> <ml:matrix rows="1" cols="3"> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">l</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:matrix> </ml:symResult> </ml:symEval> </math> <rendering item-idref="20"/> </region> <region region-id="216" left="48" top="459" width="111" height="21" align-x="72.75" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="220" left="186" top="456.75" width="165.75" height="34.5" align-x="210.75" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:command> <ml:id xml:space="preserve">simplify</ml:id> </ml:command> <ml:symResult> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">l</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">l</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="243" left="396" top="500.25" width="60.75" height="13.5" align-x="407.25" align-y="510" 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:range> <ml:sequence> <ml:real>0</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:real>5</ml:real> <ml:id xml:space="preserve">cm</ml:id> </ml:apply> </ml:sequence> <ml:id xml:space="preserve">l</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="252" left="486" top="500.25" width="24" height="13.5" align-x="497.25" align-y="510" 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:id xml:space="preserve">z</ml:id> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="229" left="18" top="528" width="436.5" height="234" align-x="18" align-y="528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="25"/> <rendering item-idref="26"/> </region> <region region-id="132" left="12" top="786.75" width="51" height="13.5" align-x="12" align-y="798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Számítás </text> </region> <region region-id="64" left="42" top="806.25" width="291.75" height="12" align-x="42" align-y="816" 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"> B támaszerõ számítása az A támaszra felírt nyomatéki egyenletbõl </text> </region> <region region-id="65" left="54" top="824.25" width="24.75" height="13.5" align-x="65.25" align-y="834" 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="27"/> </region> <region region-id="66" left="72" top="843" width="135" height="47.25" align-x="167.25" align-y="870" 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:integral auto-algorithm="true" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:lambda> <ml:bounds> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="b">l</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">l</ml:id> <ml:id xml:space="preserve" subscript="j">l</ml:id> </ml:apply> </ml:bounds> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>0</ml:real> <ml:id xml:space="preserve">kN</ml:id> </ml:apply> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="28"/> </region> <region region-id="67" left="54" top="894.75" width="90.75" height="29.25" align-x="66.75" align-y="912" 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">B</ml:id> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:Find auto-method="true" method="linear" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">B</ml:id> </ml:apply> <ml:symResult> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="69" left="42" top="938.25" width="291" height="12" align-x="42" align-y="948" 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"> Az A támaszerõt hasonlóan a nyomatéki egyenletbõl számíthatjuk: </text> </region> <region region-id="70" left="54" top="956.25" width="24.75" height="13.5" align-x="65.25" 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:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">Given</ml:id> </math> <rendering item-idref="30"/> </region> <region region-id="151" left="72" top="975" width="156" height="47.25" align-x="188.25" align-y="1002" 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:integral auto-algorithm="true" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">l</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:lambda> <ml:bounds> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="b">l</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">l</ml:id> <ml:id xml:space="preserve" subscript="j">l</ml:id> </ml:apply> </ml:bounds> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>0</ml:real> <ml:id xml:space="preserve">kN</ml:id> </ml:apply> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="31"/> </region> <region region-id="154" left="54" top="1026.75" width="90.75" height="29.25" align-x="66.75" 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 warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:Find auto-method="true" method="linear" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:symResult> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="74" left="42" top="1058.25" width="200.25" height="12" align-x="42" align-y="1068" 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"> A vetületi egyenletet is felírjuk ellenõrzésképp: </text> </region> <region region-id="75" left="54" top="1071" width="156.75" height="47.25" align-x="196.5" align-y="1098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:integral auto-algorithm="false" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:lambda> <ml:bounds> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="b">l</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">l</ml:id> <ml:id xml:space="preserve" subscript="j">l</ml:id> </ml:apply> </ml:bounds> </ml:apply> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> <ml:command> <ml:id xml:space="preserve">simplify</ml:id> </ml:command> <ml:symResult> <ml:real>0</ml:real> </ml:symResult> </ml:symEval> </math> <rendering item-idref="33"/> </region> <region region-id="24" left="30" top="1130.25" width="60.75" height="12" align-x="30" align-y="1140" 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"> Nyíróerõ ábra: </text> </region> <region region-id="114" left="42" top="1146.75" width="189" height="43.5" align-x="66.75" align-y="1170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">T</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:integral auto-algorithm="false" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">τ</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">τ</ml:id> </ml:apply> </ml:lambda> <ml:bounds> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="b">l</ml:id> </ml:apply> <ml:id xml:space="preserve">z</ml:id> </ml:bounds> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">Φ</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:id xml:space="preserve">A</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">Φ</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="34"/> </region> <region region-id="171" left="42" top="1206.75" width="339" height="34.5" align-x="116.25" align-y="1224" 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:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">collect</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:sequence> </ml:command> <ml:symResult> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">l</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">z</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">z</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <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">P</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">Φ</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <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">P</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">Φ</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="35"/> </region> <region region-id="167" left="42" top="1251.75" width="272.25" height="37.5" align-x="170.25" align-y="1272" 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:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">collect</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:sequence> </ml:command> <ml:command> <ml:sequence> <ml:id xml:space="preserve">assume</ml:id> <ml:apply> <ml:and/> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">z</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:lessThan/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:sequence> </ml:command> <ml:symResult> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">P</ml:id> </ml:apply> <ml:apply> <ml:mult/> 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