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[]
[]
[]
[]
[]
[]
[]
[]
["Berechnungsprotokoll"]
[]
[]
[]
[null,null,"Bachelorarbeit "]
[]
[]
[null,null,"Fabian Böttinger"]
[]
[]
["Nachgiebiger Verbund - Möglichkeiten der Modellierung"]
[]
[]
["Partial Interaction ­ Ways of Software­supported modelling"]
[]
[]
[]
[]
[]
[null,"Inhaltsverzeichnis"]
[]
[]
[]
[null,"Ausgangssituation und Eingangsgrößen…............................................",null,null,null,"Seite 1"]
[null,"Gammaverfahren für den Anfangszustand (t=0)…......................................................",null,null,null,"Seite 2"]
[null,"Gammaverfahren für den Endzustand (t=ꝏ)…....................................................",null,null,null,"Seite 3"]
[null,"Schubanalogieverfahren nach Kreuzinger…............................................................",null,null,null,"Seite 4"]
[null,"Stabwerksmodelle nach Rautenstrauch..............................................................................",null,null,null,"Seite 5"]
[null,"Zweistabmodell (Federmodell).......................................................................................",null,null,null,"Seite 6"]
[]
[]
[]
[]
[null,"Bearbeiter: ",null,"Fabian","Böttinger"]
[]
[]
[null,"Betreuer: ","Prof. Dr. Ing","Martin","Synold"]
[]
[]
[]
[]
["Ausgangsstiutation und Eingangsgrößen"]
[]
[]
["Ausgangssystem ",null,null,"Belastung"]
[]
[]
[null,null,null,null,"char. Streckenlast",{"$f":"'Gamma-Verfahren_nach_DIN1052'!D9","v":3.75},"KN/m","System",{"$f":"'Gamma-Verfahren_nach_DIN1052'!D12","v":"Einfeldträger"}]
[null,null,null,null,"Feldlänge L",{"$f":"'Gamma-Verfahren_nach_DIN1052'!D13","v":6},"m"]
[null,null,null,null,null,null,null,"Querschnitte",{"$f":"'Gamma-Verfahren_nach_DIN1052'!D26","v":2}]
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[null,null,null,null,"max. Moment Md",{"$f":"'Gamma-Verfahren_nach_DIN1052'!D10","v":24.3},"KNm"]
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[null,null,null,null,"max. Querkraft Vd",{"$f":"'Gamma-Verfahren_nach_DIN1052'!D11","v":16.2},"KN"]
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[]
[]
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["Umgebungsbedingungen "]
["Nutzungsklasse",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!D18","v":1}]
["Kategorie",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!D19","v":"Kategorie A: Wohn- und Aufenthaltsräume "}]
["KLED",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!D20","v":"mittel"}]
["Einbaufeuchte",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!D22","v":"<30%"}]
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[]
["Querschnittswerte",null,null,"Querschnitt 1","Querschnitt 2","Querschnitt 3"]
["Material",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!D30","v":"Beton"},{"$f":"'Gamma-Verfahren_nach_DIN1052'!E30","v":"Vollholz"},{"$f":"'Gamma-Verfahren_nach_DIN1052'!F30","v":"Vollholz"}]
["Festigkeitsklasse",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!D31","v":"C30/37"},{"$f":"'Gamma-Verfahren_nach_DIN1052'!E31","v":"C24"},{"$f":"'Gamma-Verfahren_nach_DIN1052'!F31","v":"C30"}]
["Rohdichte [Kg/m³]",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!D32","v":2500},{"$f":"'Gamma-Verfahren_nach_DIN1052'!E32","v":350},{"$f":"'Gamma-Verfahren_nach_DIN1052'!F32","v":380}]
["E-Modul [N/mm²] ",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!D33","v":33000},{"$f":"'Gamma-Verfahren_nach_DIN1052'!E33","v":11000},{"$f":"'Gamma-Verfahren_nach_DIN1052'!F33","v":12000}]
["Querschnittsfläche Ai [mm²]",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!F42","v":37500},{"$f":"'Gamma-Verfahren_nach_DIN1052'!F43","v":24000},{"$f":"'Gamma-Verfahren_nach_DIN1052'!F44","v":0}]
["Trägheitsmoment Iy [mm4]",null,null,{"$f":"_xlfn.ANCHORARRAY('Gamma-Verfahren_nach_DIN1052'!G42)","v":11250000},{"$f":"'Gamma-Verfahren_nach_DIN1052'!G43","v":80000000},{"$f":"'Gamma-Verfahren_nach_DIN1052'!G44","v":0}]
[]
[]
["Verbindungsmittel",null,null,"Schubfuge 1",null,"Schubfuge 2"]
["Bezeichnung des Verbindungsmittels",null,null,{"$f":"IF('Gamma-Verfahren_nach_DIN1052'!J31=Verbindungsmittel!C17,'Gamma-Verfahren_nach_DIN1052'!J38,'Gamma-Verfahren_nach_DIN1052'!J31)","v":"ASSY PLUS VG - Würth"},null,{"$f":"IF('Gamma-Verfahren_nach_DIN1052'!K31=Verbindungsmittel!C17,'Gamma-Verfahren_nach_DIN1052'!K38,'Gamma-Verfahren_nach_DIN1052'!K31)","v":"Nägel (vorgebohrt) "}]
["Verbindungsmittel Durchmesser [mm]",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!J32","v":6},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!K32","v":5}]
["Verschiebungsmodul Kser [N/mm]",null,null,{"$f":"IF('Gamma-Verfahren_nach_DIN1052'!J31=Verbindungsmittel!C17,'Gamma-Verfahren_nach_DIN1052'!J37,'Gamma-Verfahren_nach_DIN1052'!J33)","v":15000},null,{"$f":"IF('Gamma-Verfahren_nach_DIN1052'!K31=Verbindungsmittel!C17,'Gamma-Verfahren_nach_DIN1052'!K37,'Gamma-Verfahren_nach_DIN1052'!K33)","v":1514.0175139177566}]
["Anzahl der Verbindungsmittelreihen",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!J43","v":1},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!K43","v":1}]
["eff. Verbindungsmittelabstand si [mm]",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!J46","v":100},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!K46","v":0}]
["Art der Verbindung",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!J34","v":"Holz-Holz-Verbindung"},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!K34","v":"Holz-Holz-Verbindung"}]
[]
[]
[]
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[]
[null,null,null,null,null,"Bearbeiter: ","BF"]
[null,null,null,null,null,"Datum: ",{"$f":"TODAY()","v":"2021-08-04"}]
[]
[null,null,null,null,null,null,"Seite 1/6"]
["Gammaverfahren im Anfangszustand (t=0)"]
[]
[]
[]
["Elastizitätsmodul [N/mm²]",null,null,"Querschnitt 1","Querschnitt 2","Querschnitt 3"]
[]
["GZT",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!D54","v":33000},{"$f":"'Gamma-Verfahren_nach_DIN1052'!D55","v":11000},{"$f":"'Gamma-Verfahren_nach_DIN1052'!D56","v":12000}]
["GZG",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!N54","v":33000},{"$f":"'Gamma-Verfahren_nach_DIN1052'!N55","v":11000},{"$f":"'Gamma-Verfahren_nach_DIN1052'!N56","v":12000}]
[]
["Verschiebungsmodul Kser",null,null,"Schubfuge 1",null,"Schubfuge 2"]
[]
["GZT",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!D57","v":10000},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!D58","v":1009.3450092785043}]
["GZG",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!N57","v":15000},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!N58","v":1514.0175139177566}]
[]
["Verbindungsart",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!D59","v":"Holz-Holz-Verbindung"}]
[]
[]
["Nachgiebigkeitskoeffizient",null,null,"GZT",null,"GZG"]
[]
[null,null,"γ1 [-]",{"$f":"'Gamma-Verfahren_nach_DIN1052'!D64","v":0.22783000464203634},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!N64","v":0.30679630514983164}]
[null,null,"γ2 [-]",{"$f":"'Gamma-Verfahren_nach_DIN1052'!D65","v":1},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!N65","v":1}]
[null,null,"γ3 [-]",{"$f":"'Gamma-Verfahren_nach_DIN1052'!D66","v":0},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!N66","v":0}]
[]
["Lage der Spannungsnulllinie (SNL)",null,null,"GZT",null,"GZG"]
[]
[null,null,"a2 [mm]",{"$f":"'Gamma-Verfahren_nach_DIN1052'!D71","v":67.135906486223718},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!N71","v":76.679959607356665}]
[null,null,"a1 [mm]",{"$f":"'Gamma-Verfahren_nach_DIN1052'!D72","v":62.864093513776282},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!N72","v":53.320040392643335}]
[null,null,"a3 [mm]",{"$f":"'Gamma-Verfahren_nach_DIN1052'!D73","v":0},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!N73","v":0}]
[]
[]
[]
[]
[]
[]
["effektive Biegesteifigkeit EIef",null,null,"GZT",null,"GZG"]
[]
[null,null,"EIef [Nmm²]",{"$f":"'Gamma-Verfahren_nach_DIN1052'!D78","v":3555354310607.1982},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!N78","v":3882906213724.4805}]
[null,null,"EIef [KNm²]",{"$f":"D135/10^9","v":3555.3543106071984},null,{"$f":"F135/10^9","v":3882.9062137244805}]
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[]
[null,null,null,null,null,"Bearbeiter: ","BF"]
[null,null,null,null,null,"Datum: ",{"$f":"TODAY()","v":"2021-08-04"}]
[]
[null,null,null,null,null,null,"Seite 2/6"]
["Gammaverfahren im Anfangszustand (t=ꝏ)"]
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[]
[]
["Elastizitätsmodul [N/mm²]",null,null,"Querschnitt 1","Querschnitt 2","Querschnitt 3"]
[]
["GZT",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!I54","v":18857.142857142859},{"$f":"'Gamma-Verfahren_nach_DIN1052'!I55","v":9322.033898305086},{"$f":"'Gamma-Verfahren_nach_DIN1052'!I56","v":10169.491525423729}]
["GZG",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!S54","v":9428.5714285714294},{"$f":"'Gamma-Verfahren_nach_DIN1052'!S55","v":6875},{"$f":"'Gamma-Verfahren_nach_DIN1052'!S56","v":7500}]
[]
["Verschiebungsmodul Kser",null,null,"Schubfuge 1",null,"Schubfuge 2"]
[]
["GZT",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!I57","v":5764.1973296749256},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!I58","v":742.16544799890028}]
["GZG",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!S57","v":4348.4692283495342},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!S58","v":688.18977905352563}]
[]
["Verbindungsart",null,null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!I59","v":"Holz-Holz-Verbindung"}]
[]
[]
["Nachgiebigkeitskoeffizient",null,null,"GZT",null,"GZG"]
[]
[null,null,"γ1 [-]",{"$f":"'Gamma-Verfahren_nach_DIN1052'!I64","v":0.22936356238614145},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!S64","v":0.30989650061603236}]
[null,null,"γ2 [-]",{"$f":"'Gamma-Verfahren_nach_DIN1052'!I65","v":1},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!S65","v":1}]
[null,null,"γ3 [-]",{"$f":"'Gamma-Verfahren_nach_DIN1052'!I66","v":0},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!S66","v":0}]
[]
["Lage der Spannungsnulllinie (SNL)",null,null,"GZT",null,"GZG"]
[]
[null,null,"a2 [mm]",{"$f":"'Gamma-Verfahren_nach_DIN1052'!I71","v":54.63561413303421},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!S71","v":51.87800140077767}]
[null,null,"a1 [mm]",{"$f":"'Gamma-Verfahren_nach_DIN1052'!I72","v":75.36438586696579},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!S72","v":78.121998599222337}]
[null,null,"a3 [mm]",{"$f":"'Gamma-Verfahren_nach_DIN1052'!I73","v":0},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!S73","v":0}]
[]
[]
[]
[]
[]
[]
["effektive Biegesteifigkeit EIef",null,null,"GZT",null,"GZG"]
[]
[null,null,"EIef [Nmm²]",{"$f":"'Gamma-Verfahren_nach_DIN1052'!I78","v":2546968515656.1909},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!S78","v":1768854558618.1096}]
[null,null,"EIef [KNm²]",{"$f":"D184/10^9","v":2546.9685156561909},null,{"$f":"F184/10^9","v":1768.8545586181096}]
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[]
[]
[]
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[]
[null,null,null,null,null,"Bearbeiter: ","BF"]
[null,null,null,null,null,"Datum: ",{"$f":"TODAY()","v":"2021-08-04"}]
[]
[null,null,null,null,null,null,"Seite 3/6"]
["Schubanalogieverfahren nach Kreuzinger"]
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["Ebene A: ",null,"Anfangszustand",null,"Endzustand"]
[null,null,{"$f":"'Weitere Verfahren'!D8","v":1251250000000},null,{"$f":"'Weitere Verfahren'!F8","v":957905569007.26404},null,"[N/mm²]",null,"Text Weiß"]
["BA",null,{"$f":"'Weitere Verfahren'!D9","v":1251.25},null,{"$f":"'Weitere Verfahren'!F9","v":957.90556900726403},null,"[KN/m²]"]
[]
["SA",null,"∞",null,"∞"]
[]
[]
[]
["Ebene B: ",null,"Anfangszustand",null,"Endzustand"]
[null,null,{"$f":"'Weitere Verfahren'!D26","v":3677142857142.8569},null,{"$f":"'Weitere Verfahren'!F26","v":2872274678111.5884},null,"[N/mm²]",null,"Text Weiß"]
["BB",null,{"$f":"'Weitere Verfahren'!D27","v":3677.1428571428569},null,{"$f":"'Weitere Verfahren'!F27","v":2872.2746781115884},null,"[KN/m²]"]
[]
["SB",null,{"$f":"'Weitere Verfahren'!D34","v":1689.9999999999998},null,{"$f":"'Weitere Verfahren'!F34","v":1126.6666666666667},null,"[KN]"]
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[null,null,null,null,null,"Bearbeiter: ","BF"]
[null,null,null,null,null,"Datum: ",{"$f":"TODAY()","v":"2021-08-04"}]
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[null,null,null,null,null,null,"Seite 4/6"]
["Stabwerksmodelle nach Rautenstrauch"]
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["Ohne Berücksichtigung der Gurtsteifigkeit:"]
[]
["Ersatzsteifigkeit",null,"Anfangszustand",null,"Endzustand"]
[]
["GZT","EI*",{"$f":"'Weitere Verfahren'!D56","v":3.4233333333333333},null,{"$f":"'Weitere Verfahren'!F56","v":1.9732768858587162},null,"[KN/m²]"]
[]
[]
[]
[]
[]
["Mit Berücksichtigung der Gurtsteifigkeit:"]
[]
["Ersatzsteifigkeit",null,"Anfangszustand",null,"Endzustand"]
[]
[null,null,{"$f":"'Weitere Verfahren'!D65","v":3427271233.3615646},null,{"$f":"'Weitere Verfahren'!F65","v":1974951427.6963193},null,"[N/mm²]",null,"Zeile - Text weiß"]
[null,"EI*",{"$f":"C279/10^9","v":3.4272712333615645},null,{"$f":"E279/10^9","v":1.9749514276963194},null,"[KN/m²]"]
[]
[]
["Mit: "]
["el [mm]",{"$f":"'Weitere Verfahren'!D74","v":100}]
["er [mm]",{"$f":"'Weitere Verfahren'!D75","v":100}]
["Ks [N/mm]",{"$f":"'Gamma-Verfahren_nach_DIN1052'!J33","v":15000}]
[]
[]
[]
[null,null,null,null,null,"Bearbeiter: ","BF"]
[null,null,null,null,null,"Datum: ",{"$f":"TODAY()","v":"2021-08-04"}]
[]
[null,null,null,null,null,null,"Seite 5/6"]
["Zweistabmodell / Federmodell"]
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["Schubfuge 1:",null,"Anfangszustand",null,"Endzustand"]
[]
["GZT","KFeder",{"$f":"'Weitere Verfahren'!D92","v":10000},null,{"$f":"'Weitere Verfahren'!F92","v":5764.1973296749256},null,"[N/mm]"]
["GZG","KFeder",{"$f":"'Weitere Verfahren'!D93","v":15000},null,{"$f":"'Weitere Verfahren'!F93","v":4348.4692283495342},null,"[N/mm]"]
[]
[]
[]
["Schubfuge 2:",null,"Anfangszustand",null,"Endzustand"]
[]
["GZT","KFeder",{"$f":"'Weitere Verfahren'!D100","v":1009.3450092785043},null,{"$f":"'Weitere Verfahren'!F100","v":742.16544799890028},null,"[N/mm]"]
["GZG","KFeder",{"$f":"'Weitere Verfahren'!D101","v":1514.0175139177566},null,{"$f":"'Weitere Verfahren'!F101","v":688.18977905352563},null,"[N/mm]"]
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["Modellierungshilfe: "]
[]
["Abstand der Bauteil-Schwerachsen:",null,null,"a",{"$f":"'Weitere Verfahren'!F107","v":130},null,"[mm]"]
["Abstand der Verbindungsmittel:",null,null,"si",{"$f":"'Weitere Verfahren'!F108","v":100},null,"[mm]"]
["Abstand Schwerachse 1 zu Feder:",null,null,"a1",{"$f":"'Weitere Verfahren'!F109","v":30},null,"[mm]"]
["Abstand Schwerachse 2 zu Feder:",null,null,"a2",{"$f":"'Weitere Verfahren'!F110","v":100},null,"[mm]"]
[]
[]
[]
[]
[null,null,null,null,null,"Bearbeiter: ","BF"]
[null,null,null,null,null,"Datum: ",{"$f":"TODAY()","v":"2021-08-04"}]
[]
[null,null,null,null,null,null,"Seite 6/6"]

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["Nachweise des Holzquerschnittes "]
[]
["Für das: ",null,"Gammaverfahren zum Zeitpunkt t=0",null,null,null,null,"<-- Verfahren Wählen (greift auf \"Ergebnisse aus Statik\" zu)"]
["Nachweis auf Biegung und Zug"]
["Aus Normalkraft: "]
[null,null,null,null,null,null,null,"Holz","Normalkraft",{"$f":"VLOOKUP(C3,'Ergebnisse aus Statik '!B5:H17,2,0)*1000","v":121270},"N"]
[null,"σt,0,d ",null,{"$f":"J6/'Gamma-Verfahren_nach_DIN1052'!F43","v":5.0529166666666665},"[N/mm²]",null,null,null,"Moment",{"$f":"VLOOKUP(C3,'Ergebnisse aus Statik '!B5:H17,3,0)*10^6","v":6010000},"Nmm"]
[null,null,null,null,null,null,null,null,"Querkraft",{"$f":"VLOOKUP(C3,'Ergebnisse aus Statik '!B5:H17,4,0)*1000","v":16800},"N"]
[null,"ft,0,d",null,{"$f":"('Gamma-Verfahren_nach_DIN1052'!E38/1.3)*Werkstoffkenngrößen!G7","v":11.692307692307693},"[N/mm²]"]
[]
[]
["Aus Biegemoment: "]
[null,null,null,null,null,null,null,null,"Schnellübersicht: "]
[null,"σm,0,d ",null,{"$f":"(J7/'Gamma-Verfahren_nach_DIN1052'!G43)*'Gamma-Verfahren_nach_DIN1052'!E43/2","v":7.5124999999999993},"[N/mm²]"]
[]
[null,"ft,0,d",null,{"$f":"('Gamma-Verfahren_nach_DIN1052'!E38/1.3)*Werkstoffkenngrößen!I7","v":18.461538461538463},"[N/mm²]",null,null,null,"Holzquerschnitt"]
[]
["Nachweis: ",null,null,null,null,null,null,null,"Biegung und Zug ",null,null,{"$f":"D20","v":0.83908442982456122},"<",1]
[]
[null,null,null,{"$f":"(D7/D9)+(D14/D16)","v":0.83908442982456122},"< ",1,null,null,"Querkrafttragfähigkeit",null,null,{"$f":"D31","v":0.28437499999999999},"<",1]
[]
["Nachweis der Querkrafttragfähigkeit"]
[null,null,null,null,null,null,null,null,"Betonquerschnitt"]
[]
[null,"τd ",null,{"$f":"J8/'Gamma-Verfahren_nach_DIN1052'!F43","v":0.7},"[N/mm²] ",null,null,null,"Betondruckzone ",null,null,{"$f":"D70","v":0.58818823529411768}]
[]
[null,"fv,d",null,{"$f":"('Gamma-Verfahren_nach_DIN1052'!E38/1.3)*Werkstoffkenngrößen!J7","v":2.4615384615384617},"[N/mm²]",null,null,null,"Betonzugzone",null,"VEd ",{"$f":"D84","v":-0.19022745098039215}]
[null,null,null,null,null,null,null,null,null,null,"μEd ",{"$f":"D86","v":6.6326797385620917E-2}]
["Nachweis: "]
[null,null,null,null,null,null,null,null,"!!!!Keine Computergestütze Auswertung des Interaktionsdiagrammes!!!!"]
[null,null,null,{"$f":"D25/D27","v":0.28437499999999999},"< ",1]
[null,null,null,null,null,null,null,null,"Querkrafttragfähigkeit",null,null,{"$f":"D160","v":9.7582405562164062E-2},"<",1]
[]
[]
[]
[null,null,null,null,null,null,null,null,"Verbindungsmittel "]
[]
[null,null,null,null,null,null,null,null,"Kraft auf Verbindungsmittel ",null,null,{"$f":"VLOOKUP(C3,'Ergebnisse aus Statik '!B5:I16,8,0)","v":8.0760000000000005},"[KN]"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Nachweise der Betonplatte "]
[]
["Nachweis der Betondruckzone "]
[]
["Aus Normalkraft: "]
[]
[null,"σN,0,d",null,{"$f":"J57/'Gamma-Verfahren_nach_DIN1052'!F42","v":-3.2338666666666667},"[N/mm²] "]
[null,null,null,null,null,null,null,"Beton ","Normalkraft",{"$f":"VLOOKUP(C3,'Ergebnisse aus Statik '!B5:H17,5,0)*1000","v":-121270},"N"]
["Aus Biegemoment: ",null,null,null,null,null,null,null,"Moment",{"$f":"VLOOKUP(C3,'Ergebnisse aus Statik '!B5:H17,6,0)*10^6","v":2537000},"Nmm"]
[null,null,null,null,null,null,null,null,"Querkraft",{"$f":"VLOOKUP(C3,'Ergebnisse aus Statik '!B5:H17,7,0)*1000","v":4837.5},"N"]
[null,"σm,0,d",null,{"$f":"(J58/'Gamma-Verfahren_nach_DIN1052'!G42)*'Gamma-Verfahren_nach_DIN1052'!E42/2","v":6.7653333333333334},"[N/mm²] "]
[]
["Superposition: "]
[]
[null,"σc,0,d",null,{"$f":"ABS(D56)+ABS(D60)","v":9.9992000000000001},"[N/mm²] "]
[]
[null,"fc,d ",null,{"$f":"(0.85/1.5)*30","v":17},"[N/mm²] "]
[]
["Nachweis: "]
[]
[null,null,null,{"$f":"D64/D66","v":0.58818823529411768},"< ",1]
[]
[]
[]
["Nachweis der Betonzugzone"]
[]
["Ausmitte: "]
[]
[null,"e",null,{"$f":"ABS(J58/J57)","v":20.920260575575163},"mm"]
[]
[null,"e/hc ",null,{"$f":"D78/'Gamma-Verfahren_nach_DIN1052'!E42","v":0.34867100959291941},"<",0.5]
[]
["---> ",{"$f":"IF(D80<F80,\"DRUCKBELASTUNG MIT GERINGER AUSMITTE\",\"Überprüfen!\")","v":"DRUCKBELASTUNG MIT GERINGER AUSMITTE"}]
[]
[null,"v_Ed ",null,{"$f":"J57/('Gamma-Verfahren_nach_DIN1052'!F42*Nachweise!D66)","v":-0.19022745098039215},null,"bez. Normalkraft"]
[]
[null,"Mü_Ed ",null,{"$f":"J58/(('Gamma-Verfahren_nach_DIN1052'!D42*'Gamma-Verfahren_nach_DIN1052'!E42^2)*Nachweise!D66)","v":6.6326797385620917E-2},null,"bez. Moment"]
[]
[]
[]
[null,"ωtot"]
[]
[null,"As,tot",null,null,"[cm²]"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
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[]
[]
[]
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[]
[]
[]
[]
[]
[]
[]
["Nachweis der Querkrafttragfähigkeit"]
[null,null,null,null,null,null,null,null,"simga_cp",{"$f":"ABS(D56)","v":3.2338666666666667}]
[null,"V_Rd,c",null,{"$f":"((0.1*2*(100*0.005*30)^(1/3)+0.12*J151)*625*60)/1000","v":33.048990557478525},">",{"$f":"((0.542+0.12*J151)*625*48)/1000","v":27.901919999999997}]
[null,"V_Rd,c",null,{"$f":"MAX(D152,F152)","v":33.048990557478525},"[KN]"]
[]
[null,"V_Ed,c ",null,{"$f":"(J59/1.5)/1000","v":3.2250000000000001},"[KN]"]
[]
[]
["Nachweis: "]
[]
[null,"FORMEL ",null,{"$f":"D155/D152","v":9.7582405562164062E-2},"< ",1]
[]
[]
[]
["Nachweis der Verbindungsmittel "]
[]
[]
[null,"F_Rd ",null,{"$f":"10028/1000","v":10.028},"[KN]"]
[]
[null,"F_Vd ",null,{"$f":"VLOOKUP(C3,'Ergebnisse aus Statik '!B5:I14,8,0)","v":8.0760000000000005},"[KN]"]
[]
["Nachweis: "]
[]
[null,"FORMEL ",null,{"$f":"D169/D167","v":0.80534503390506584},"< ",1]

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[]
[null,null,"HOLZQUERSCHNITT",null,null,"BETONQUERSCHNITT",null,null,"VM "]
[null,null,"Normalkraft [KN]","Moment [KNm]","Querkraft [KN]","Normalkraft [KN]","Moment [KNm]","Querkraft [KN]","FVEd [KN]"]
[null,"Gammaverfahren zum Zeitpunkt t=0",121.27,6.01,16.8,-121.27,2.5369999999999999,4.8375000000000004,8.0760000000000005,null,"t=0"]
[null,"Gammaverfahren zum Zeitpunkt t=∞",116.62,7.12,17.015999999999998,-116.62,2.02,4.6500000000000004,7.7750000000000004,null,"t=unendlich"]
[null,"Schubanalogieverfahren zum Zeitpunkt t=0",137.54,4.2759999999999998,12.01,-137.54,1.804,3.9670000000000001,8.08]
[null,"Schubanalogieverfahren zum Zeitpunkt t=∞",138.30799999999999,4.66,12.33,-138.30799999999999,1.327,3.649,7.78]
[null,"Stabwerkmodellverfahren zum Zeitpunkt t=0",122.6,5.61,12.04,-122.6,2.42,4.87,7.46]
[null,"Stabwerkmodellverfahren zum Zeitpunkt t=∞",137.38,4.28,13.04,-137.38,1.84,4.87,8.59]
[null,"Federmodellverfahren zum Zeitpunkt t=0",123.4,5.54,11.53,-123.4,2.39,4.9400000000000004,7.54]
[null,"Federmodellverfahren zum Zeitpunkt t=∞",114.21,6.38,11.46,-114.21,2.75,4.93,6.74]
[null,"Numerische Verfahren gemäß RFEM zum Zeitpunkt t=0",125.09,5.47,9.92,-125.09,2.44,5.82,7.2]
[null,"Numerische Verfahren gemäß RFEM zum Zeitpunkt t=∞",115.99,6.29,10.18,-115.99,2.8,5.39,6]
[null,"Starrer Verbund zum Zeitpunkt t=0",139.47,4.34,2.98,-139.47,1.83,4.6500000000000004,9.3000000000000007]
[null,"Starrer Verbund zum Zeitpunkt t=∞",140.16999999999999,4.7300000000000004,3,-140.16999999999999,1.35,4.6900000000000004,9.3450000000000006]

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[]
[]
[null,null,"Gamma-Verfahren nach DIN 1052"]
[]
[]
[]
[]
[null,null,"Schnittgrößen "]
[null,null,"char. Streckenlast    qk [KN/m]",3.75]
[null,null,"max. Moment        Md [KNm]",24.3,null,null,{"$f":"D10*10^6","v":24300000},"Nmm","Querschnittstypen"]
[null,null,"max. Querkraft      Vd [KN]",16.2,null,null,{"$f":"D11*1000","v":16200},"N"]
[null,null,"Statisches System","Einfeldträger"]
[null,null,"Feldlänge [m]",6]
[null,null,"Abstand der Momenten-Nullpunkte [m]",{"$f":"VLOOKUP('Gamma-Verfahren_nach_DIN1052'!D12,Statisches_System!C5:D7,2,0)","v":6}]
[]
[]
[null,null,"Umgebungsbedingungen "]
[null,null,"Nutzungsklasse",1]
[null,null,"Kategorie","Kategorie A: Wohn- und Aufenthaltsräume "]
[null,null,"KLED","mittel"]
[null,null,"Kombinationsbeiwert Ψ2",{"$f":"VLOOKUP(D19,Kombinationsbeiwerte_Ψ!B3:F15,4,0)","v":0.3}]
[null,null,"Einbaufeuchte","<30%"]
[]
[]
[null,null,"Querschnittstyp","C"]
[null,null,"Anzahl Querschnitte",2]
[]
[]
[null,null,"Querschnittswerte ","Querschnitt 1","Querschnitt 2","Querschnitt 3","Mittelwert","Mittelwert","Verbindungsmittel",null,null,null,null,"Nettoquerschnitte",null,null,"Trägheitsmoment"]
[null,null,"Material","Beton","Vollholz","Vollholz",null,null,null,"VM-Typ QS1/QS2","VM-Typ QS2/QS3"]
[null,null,"Festigkeitsklasse","C30/37","C24","C30","QS 1/2","QS2/3","VM ","Andere ","Nägel (vorgebohrt) ",null,null,"A1",{"$f":"IF(J32>6,(F42-(J32*J36*J43)),F42)","v":37500},null,"I1",{"$f":"IF(AND(J32>6,D25=\"B\"),(D42*((E42-(J43*J32))^3))/12,IF(J32>6,((D42-(J43*J32))*(E42^3))/12,G42))","v":11250000}]
[null,null,"Rohdichte [Kg/m³]",{"$f":"VLOOKUP(D31,Werkstoffkenngrößen!C5:E42,3,0)","v":2500},{"$f":"VLOOKUP(E31,Werkstoffkenngrößen!C5:E42,3,0)","v":350},{"$f":"VLOOKUP(F31,Werkstoffkenngrößen!C5:E42,3,0)","v":380},{"$f":"SQRT(D32*E32)","v":935.4143466934853},{"$f":"SQRT(E32*F32)","v":364.69165057620938},"Durchmesser [mm]",6,5,null,null,"A2",{"$f":"IF(AND(J32>6,K32>6),(F43-(J36*J43*J32+K36*K43*K32)),IF(J32>6,(F43-(J36*J43*J32)),IF(K32>6,(F43-(K32*K36*K43)),F43)))","v":24000},null,"I2",{"$f":"IF(AND(J32>6,K32>6,D25=\"B\"),((D43)*(E43-(J43*J32+K43*K32))^3)/12,IF(AND(J32>6,K32>6),((D43-(J43*J32+K43*K32))*(E43^3))/12,IF(AND(K32>6,D25=\"B\"),((D43)*(E43-(K43*K32))^3)/12,IF(K32>6,((D43-(K43*K32))*(E43^3))/12,IF(AND(J32>6,D25=\"B\"),(D43*((E43-(J43*J32))^3))/12,IF(J32>6,((D43-(J43*J32))*(E43^3))/12,G43))))))","v":80000000}]
[null,null,"E-Modul [N/mm²] ",{"$f":"VLOOKUP(D31,Werkstoffkenngrößen!C2:E42,2,0)","v":33000},{"$f":"VLOOKUP(E31,Werkstoffkenngrößen!C5:E42,2,0)","v":11000},{"$f":"VLOOKUP(F31,Werkstoffkenngrößen!C5:E42,2,0)","v":12000},null,null,"Kser [N/mm]",{"$f":"VLOOKUP($J$31,Verbindungsmittel!C5:D17,2,0)","v":15000},{"$f":"VLOOKUP($K$31,Verbindungsmittel!C5:E17,3,0)","v":1514.0175139177566},null,null,"A3",{"$f":"IF(K32>6,(F44-(K32*K36*K43)),F44)","v":0},null,"I3",{"$f":"IF(AND(K32>6,D25=\"B\"),((D44*((E44-(K43*K32))^3))/12),IF(K32>6,((D44-(K43*K32))*(E44^3))/12,G44))","v":0}]
[null,null,"Verhältnis E-Modul ni",{"$f":"D33/$E$33","v":3},{"$f":"E33/$E$33","v":1},{"$f":"F33/$E$33","v":1.0909090909090908},null,null,"Verbindungsart","Holz-Holz-Verbindung","Holz-Holz-Verbindung"]
[null,null,"Verhältnis Ai/Ai,netto [-] ",{"$f":"F42/O31","v":1},{"$f":"F43/O32","v":1},{"$f":"F44/O33","v":{"$error":"#DIV/0!"}},null,null,"Länge VM [mm]",150,0]
[null,null,"Verhältnis Iyi/Iyi,netto [-]",{"$f":"G42/R31","v":1},{"$f":"G43/R32","v":1},{"$f":"G44/R33","v":{"$error":"#DIV/0!"}},null,null,"Einbindetiefe in QS 2",{"$f":"J35-E42","v":90},{"$f":"K35-E44","v":0}]
[null,null,"Kdef ",{"$f":"IF(D30=\"Beton\",2.5,IF(AND(D30=\"Vollholz\",D22=Werkstoffkenngrößen!F6),VLOOKUP(D18,Kombinationsbeiwerte_Ψ!H3:J5,3,0)+1,IF(AND(D30=\"Sperrholz\",D18=1),0.8,IF(AND(D30=\"Sperrholz\",D18=2),1,IF(AND(D30=\"Sperrholz\",D18=3),2.5,IF(AND(D30=\"Spanplatte P6\",D18=1),2.25,IF(AND(D30=\"Spanplatte P6\",D18=2),3,VLOOKUP(D18,Kombinationsbeiwerte_Ψ!H3:J5,3,0))))))))","v":2.5},{"$f":"IF(E30=\"Beton\",2.5,IF(AND(E30=\"Vollholz\",D22=Werkstoffkenngrößen!F6),VLOOKUP(D18,Kombinationsbeiwerte_Ψ!H3:J5,3,0)+1,IF(AND(E30=\"Sperrholz\",D18=1),0.8,IF(AND(E30=\"Sperrholz\",D18=2),1,IF(AND(E30=\"Sperrholz\",D18=3),2.5,IF(AND(E30=\"Spanplatte P6\",D18=1),2.25,IF(AND(E30=\"Spanplatte P6\",D18=2),3,VLOOKUP(D18,Kombinationsbeiwerte_Ψ!H3:J5,3,0))))))))","v":0.6},{"$f":"IF(F30=\"Beton\",2.5,IF(AND(F30=\"Vollholz\",D22=Werkstoffkenngrößen!F6),VLOOKUP(D18,Kombinationsbeiwerte_Ψ!H3:J5,3,0)+1,IF(AND(F30=\"Sperrholz\",D18=1),0.8,IF(AND(F30=\"Sperrholz\",D18=2),1,IF(AND(F30=\"Sperrholz\",D18=3),2.5,IF(AND(F30=\"Spanplatte P6\",D18=1),2.25,IF(AND(F30=\"Spanplatte P6\",D18=2),3,VLOOKUP(D18,Kombinationsbeiwerte_Ψ!H3:J5,3,0))))))))","v":0.6},null,"Wenn \"Andere VM\":","Kser [N/mm]",15000,0]
[null,null,"Kmod",{"$f":"IF(D30=\"Beton\",1,IF(AND(D30=\"Spanplatte P6\",D18=1),HLOOKUP(D20,'Modifikationsbeiwert Kmod '!D3:H8,5,0),IF(AND(D30=\"Spanplatte P6\",D18=2),HLOOKUP(D20,'Modifikationsbeiwert Kmod '!D3:H8,6,0),IF(D18=1,HLOOKUP(D20,'Modifikationsbeiwert Kmod '!D3:H8,2,0),IF(D18=2,HLOOKUP(D20,'Modifikationsbeiwert Kmod '!D3:H8,3,0),HLOOKUP(D20,'Modifikationsbeiwert Kmod '!D3:H8,4,0))))))","v":1},{"$f":"IF(E30=\"Beton\",1,IF(AND(E30=\"Spanplatte P6\",D18=1),HLOOKUP(D20,'Modifikationsbeiwert Kmod '!D3:H8,5,0),IF(AND(E30=\"Spanplatte P6\",D18=2),HLOOKUP(D20,'Modifikationsbeiwert Kmod '!D3:H8,6,0),IF(D18=1,HLOOKUP(D20,'Modifikationsbeiwert Kmod '!D3:H8,2,0),IF(D18=2,HLOOKUP(D20,'Modifikationsbeiwert Kmod '!D3:H8,3,0),HLOOKUP(D20,'Modifikationsbeiwert Kmod '!D3:H8,4,0))))))","v":0.8},{"$f":"IF(F30=\"Beton\",1,IF(AND(F30=\"Spanplatte P6\",D18=1),HLOOKUP(D20,'Modifikationsbeiwert Kmod '!D3:H8,5,0),IF(AND(F30=\"Spanplatte P6\",D18=2),HLOOKUP(D20,'Modifikationsbeiwert Kmod '!D3:H8,6,0),IF(D18=1,HLOOKUP(D20,'Modifikationsbeiwert Kmod '!D3:H8,2,0),IF(D18=2,HLOOKUP(D20,'Modifikationsbeiwert Kmod '!D3:H8,3,0),HLOOKUP(D20,'Modifikationsbeiwert Kmod '!D3:H8,4,0))))))","v":0.8},null,null,"Bezeichnung der VM","ASSY PLUS VG - Würth"]
[]
[]
[null,null,"Querschnittsabmessungen","Breite [mm]","Höhe [mm]","Ai [mm²]","Iy [mm4]",null,"VM-Abstände","VM-Abstand QS1/QS2","VM-Abstand QS2/QS3"]
[null,null,"Querschnitt 1 ",625,60,{"$f":"D42*E42","v":37500},{"$f":"(D42*E42^3)/12","v":11250000},null,"Kleinster Abstand [mm]",100,null,"Smin"]
[null,null,"Querschnitt 2",120,200,{"$f":"D43*E43","v":24000},{"$f":"(D43*E43^3)/12","v":80000000},null,"Anzahl VM Reihen",1,1]
[null,null,"Querschnitt 3",0,0,{"$f":"D44*E44","v":0},{"$f":"(D44*E44^3)/12","v":0},null,"Größter Abstand [mm]",100,null,"Smax"]
[null,null,"Gesamtquerschnitt",{"$f":"IF(D25=\"B\",(MAX(D42,D44)+D43),MAX(D42:D44))","v":625},{"$f":"IF(D25=\"B\",E43,(E42+E43+E44))","v":260},{"$f":"F42+F43+F44","v":61500}]
[null,null,null,null,null,null,null,null,"wirksamer Abstand [mm]",{"$f":"0.75*(J42/J43)+0.25*(J44/J43)","v":100},{"$f":"0.75*(K42/K43)+0.25*(K44/K43)","v":0}]
[]
[]
[null,null,"Spannungen",null,null,null,null,null,null,null,null,null,"Verformungen"]
[]
[]
[null,null,"Anfangszustand ",null,null,null,null,"Endzustand ",null,null,null,null,"Anfangszustand",null,null,null,null,"Endzustand"]
[]
[null,null,"E0,mean,1 [N/mm²]",{"$f":"D33","v":33000},null,null,null,"E0,mean,1 [N/mm²]",{"$f":"$D$33/(1+$D$21*$D$37)","v":18857.142857142859},null,null,{"$f":"I54/I55","v":2.0228571428571427},"E0,mean,1 [N/mm²]",{"$f":"D33","v":33000},null,null,null,"E0,mean,1 [N/mm²]",{"$f":"D33/(1+D37)","v":9428.5714285714294}]
[null,null,"E0,mean,2 [N/mm²]",{"$f":"$E$33","v":11000},null,null,null,"E0,mean,2 [N/mm²]",{"$f":"$E$33/(1+$D$21*$E$37)","v":9322.033898305086},null,null,{"$f":"I55/I55","v":1},"E0,mean,2 [N/mm²]",{"$f":"$E$33","v":11000},null,null,null,"E0,mean,2 [N/mm²]",{"$f":"$E$33/(1+E37)","v":6875}]
[null,null,"E0,mean,3 [N/mm²]",{"$f":"$F$33","v":12000},null,null,null,"E0,mean,3 [N/mm²]",{"$f":"$F$33/(1+$D$21*$F$37)","v":10169.491525423729},null,null,{"$f":"I56/I55","v":1.0909090909090908},"E0,mean,3 [N/mm²]",{"$f":"$F$33","v":12000},null,null,null,"E0,mean,3 [N/mm²]",{"$f":"$F$33/(1+F37)","v":7500}]
[null,null,"K1 [Nmm]",{"$f":"IF($J$34 = \"Holz-Holz-Verbindung\",'Gamma-Verfahren_nach_DIN1052'!$J$33*2/3,'Gamma-Verfahren_nach_DIN1052'!$J$33*4/3)","v":10000},null,null,null,"K1 [Nmm]",{"$f":"IF($J$34=\"Holz-Holz-Verbindung\",(('Gamma-Verfahren_nach_DIN1052'!$J$33*2/3)/(1+D21*2*SQRT((D37*E37)))),(('Gamma-Verfahren_nach_DIN1052'!$J$33*4/3)/(1+D21*2*SQRT((D37*E37)))))","v":5764.1973296749256},null,null,null,"K1 [Nmm]",{"$f":"IF($J$34 = \"Holz-Holz-Verbindung\",'Gamma-Verfahren_nach_DIN1052'!$J$33,'Gamma-Verfahren_nach_DIN1052'!$J$33*2)","v":15000},null,null,null,"K1 [Nmm]",{"$f":"IF($J$34=\"Holz-Holz-Verbindung\",(('Gamma-Verfahren_nach_DIN1052'!$J$33)/(1+2*SQRT((D37*E37)))),(('Gamma-Verfahren_nach_DIN1052'!$J$33)/(1+2*SQRT((D37*E37)))))","v":4348.4692283495342}]
[null,null,"K3 [Nmm]",{"$f":"IF($K$34 = \"Holz-Holz-Verbindung\",'Gamma-Verfahren_nach_DIN1052'!$K$33*2/3,'Gamma-Verfahren_nach_DIN1052'!$K$33*4/3)","v":1009.3450092785043},null,null,null,"K3 [Nmm]",{"$f":"IF($K$34=\"Holz-Holz-Verbindung\",(('Gamma-Verfahren_nach_DIN1052'!$K$33*2/3)/(1+D21*2*SQRT((F37*E37)))),(('Gamma-Verfahren_nach_DIN1052'!$K$33*4/3)/(1+D21*2*SQRT((F37*E37)))))","v":742.16544799890028},null,null,null,"K3 [Nmm]",{"$f":"IF($K$34 = \"Holz-Holz-Verbindung\",'Gamma-Verfahren_nach_DIN1052'!$K$33,'Gamma-Verfahren_nach_DIN1052'!$K$33*2)","v":1514.0175139177566},null,null,null,"K3 [Nmm]",{"$f":"IF($K$34=\"Holz-Holz-Verbindung\",(('Gamma-Verfahren_nach_DIN1052'!$K$33)/(1+2*SQRT((F37*E37)))),(('Gamma-Verfahren_nach_DIN1052'!$K$33)/(1+2*SQRT((F37*E37)))))","v":688.18977905352563}]
[null,null,"Verbindungsart",{"$f":"J34","v":"Holz-Holz-Verbindung"},null,null,null,"Verbindungsart",{"$f":"J34","v":"Holz-Holz-Verbindung"}]
[]
[null,null,"Abminderungsfaktor Gamma",null,null,null,null,null,null,null,null,null,"Abminderungsfaktor Gamma"]
[]
[]
[null,null,"γ1",{"$f":"1/(1+((3.14^2*$D$54*$F$42*$J$46)/($D$57*($D$14*1000)^2)))","v":0.22783000464203634},null,null,null,"γ1",{"$f":"1/(1+((3.14^2*$I$54*$F$42*$J$46)/($I$57*($D$14*1000)^2)))","v":0.22936356238614145},null,null,null,"γ1",{"$f":"1/(1+((3.14^2*$N$54*$F$42*$J$46)/($N$57*($D$14*1000)^2)))","v":0.30679630514983164},null,null,null,"γ1",{"$f":"1/(1+((3.14^2*$S$54*$F$42*$J$46)/($S$57*($D$14*1000)^2)))","v":0.30989650061603236}]
[null,null,"γ2",1,null,null,null,"γ2",1,null,null,null,"γ2",1,null,null,null,"γ2",1]
[null,null,"γ3",{"$f":"IF(D26=3,(1/(1+((3.14^2*$D$56*$F$44*$K$46)/($D$58*($D$14*1000)^2)))),0)","v":0},null,null,null,"γ3",{"$f":"IF(D26=3,1/(1+((3.14^2*$I$56*$F$44*$K$46)/($I$58*($D$14*1000)^2))),0)","v":0},null,null,null,"γ3",{"$f":"IF(D26=3,(1/(1+((3.14^2*$N$56*$F$44*$K$46)/($N$58*($D$14*1000)^2)))),0)","v":0},null,null,null,"γ3",{"$f":"IF(D26=3,(1/(1+((3.14^2*$S$56*$F$44*$K$46)/($S$58*($D$14*1000)^2)))),0)","v":0}]
[]
[null,null,"Lage der Spannungsnulllinie"]
[]
[]
[null,null,"a2 [mm]",{"$f":"IF(D25=\"B\",(1/2*(($D$64*$D$54*$F$42*(-1*$E$42+$E$43)-$D$66*$D$56*$F$44*($E$43-$E$44))/($D$64*$F$42*$D$54+$D$65*$F$43*$D$55+$D$66*$F$44*$D$56))),(1/2*(($D$64*$D$54*$F$42*($E$42+$E$43)-$D$66*$F$44*$D$56*($E$43+$E$44))/($D$64*$F$42*$D$54+$D$65*$F$43*$D$55+$D$66*$F$44*$D$66))))","v":67.135906486223718},null,null,null,"a2 [mm]",{"$f":"IF(I37=\"B\",(1/2*(($I$64*$F$42*$I$54*(-1*$E$42+$E$43)-$I$66*$I$56*$F$44*($E$43-$E$44))/($I$64*$I$56*$F$42+$I$65*$I$55*$F$43+$I$66*$I$56*$F$44))),(1/2*(($I$64*$I$54*$F$42*($E$42+$E$43)-$I$66*$I$56*$F$44*($E$43+$E$44))/($I$64*$F$42*$I$54+$I$65*$F$43*$I$55+$I$66*$F$44*$I$56))))","v":54.63561413303421},null,null,null,"a2 [mm]",{"$f":"IF(D25=\"B\",(1/2*(($N$64*$F$42*$N$54*(-1*$E$42+$E$43)-$N$66*$F$44*$N$56*($E$43-$E$44))/($N$64*$F$42*$N$54+$N$65*$F$43*$N$55+$N$66*$F$44*$N$56))),(1/2*(($N$64*$F$42*$N$54*($E$42+$E$43)-$N$66*$F$44*$N$56*($E$43+$E$44))/($N$64*$F$42*$N$54+$N$65*$F$43*$N$55+$N$66*$F$44*$N$56))))","v":76.679959607356665},null,null,null,"a2 [mm]",{"$f":"IF(D25=\"B\",(1/2*(($S$64*$F$42*$S$54*(-1*$E$42+$E$43)-$S$66*$F$44*$S$56*($E$43-$E$44))/($S$64*$F$42*$S$54+$S$65*$F$43*$S$55+$S$66*$F$44*$S$56))),(1/2*(($S$64*$F$42*$S$54*($E$42+$E$43)-$S$66*$F$44*$S$56*($E$43+$E$44))/($S$64*$F$42*$S$54+$S$65*$F$43*$S$55+$S$66*$F$44*$S$56))))","v":51.87800140077767}]
[null,null,"a1 [mm]",{"$f":"IF($D$25=\"B\",(((-1*$E$42)+$E$43)/2)-$D$71,((($E$42)+$E$43)/2)-$D$71)","v":62.864093513776282},null,null,null,"a1 [mm]",{"$f":"IF($D$25=\"B\",(((-1*$E$42)+$E$43)/2)-$I$71,((($E$42)+$E$43)/2)-$I$71)","v":75.36438586696579},null,null,null,"a1 [mm]",{"$f":"IF($D$25=\"B\",(((-1*$E$42)+$E$43)/2)-$N$71,((($E$42)+$E$43)/2)-$N$71)","v":53.320040392643335},null,null,null,"a1 [mm]",{"$f":"IF($D$25=\"B\",(((-1*$E$42)+$E$43)/2)-$S$71,((($E$42)+$E$43)/2)-$S$71)","v":78.121998599222337}]
[null,null,"a3 [mm]",{"$f":"IF(D26=3,IF($D$25=\"B\",((($E$43-$E$44)/2)+$D$71),(($E$43+$E$44)/2)+$D$71),0)","v":0},null,null,null,"a3 [mm]",{"$f":"IF(D26=3,IF($D$25=\"B\",((($E$43-$E$44)/2)+$I$71),(($E$43+$E$44)/2)+$I$71),0)","v":0},null,null,null,"a3 [mm]",{"$f":"IF(D26=3,IF($D$25=\"B\",((($E$43-$E$44)/2)+$N$71),(($E$43+$E$44)/2)+$N$71),0)","v":0},null,null,null,"a3 [mm]",{"$f":"IF(D26=3,IF($D$25=\"B\",((($E$43-$E$44)/2)+$S$71),(($E$43+$E$44)/2)+$S$71),0)","v":0}]
[]
[null,null,"Effektive Biegesteifigkeit",null,null,null,null,null,null,null,null,null,"effektive Biegesteifigket"]
[]
[]
[null,null,"Eief [Nmm²]",{"$f":"((D54*G42)+(D64*D54*F42*(D72^2)))+((D55*G43)+(D65*D55*F43*(D71^2)))+((D56*G44)+(D66*D56*F44*(D73^2)))","v":3555354310607.1982},null,null,null,"Eief [Nmm²]",{"$f":"((I54*G42)+(I64*I54*F42*(I72^2)))+((I55*G43)+(I65*I55*F43*(I71^2)))+((I56*G44)+(I66*I56*F44*(I73^2)))","v":2546968515656.1909},null,null,null,"Eief [Nmm²]",{"$f":"((N54*G42)+(N64*N54*F42*(N72^2)))+((N55*G43)+(N65*N55*F43*(N71^2)))+((N56*G44)+(N66*N56*F44*(N73^2)))","v":3882906213724.4805},null,null,null,"Eief [Nmm²]",{"$f":"((S54*G42)+(S64*S54*F42*(S72^2)))+((S55*G43)+(S65*S55*F43*(S71^2)))+((S56*G44)+(S66*S56*F44*(S73^2)))","v":1768854558618.1096}]
[]
[null,null,"Schwerpunktsspannungen "]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Gebrauchstauglichkeit / Durchbiegung"]
[null,null,"s1,d [N/mm²]",{"$f":"(($G$10/$D$78)*$D$54) * $D$64*$D$72*$D$34","v":9.691079530509402},null,null,null,"s1,d [N/mm²]",{"$f":"(($G$10/$I$78)*$I$54) * $I$64*$I$72*$D$35","v":3.10991971918734}]
[null,null,"s2,d [N/mm²]",{"$f":"(($G$10/$D$78)*$D$55) * $D$65*$D$71*$E$35","v":5.0474372554736471},null,null,null,"s2,d [N/mm²]",{"$f":"(($G$10/$I$78)*$I$55) * $I$65*$I$71*$E$35","v":4.8592495612302207},null,null,null,null,null,"EI [N/mm]","w [mm]","Abweichung"]
[null,null,"s3,d [N/mm²]",{"$f":"(($G$10/$D$78)*$D$56) * $D$66*$D$73*$F$35","v":{"$error":"#DIV/0!"}},null,null,null,"s3,d [N/mm²]",{"$f":"(($G$10/$I$78)*$I$56) * $I$66*$I$73*$F$35","v":{"$error":"#DIV/0!"}},null,null,null,"Loser Verbund ",null,{"$f":"((N54*G42)+(0*N54*F42*(N72^2)))+((N55*G43)+(0*N54*F43*(N71^2)))+((N56*G44)+(0*N56*F44*(N73^2)))","v":1251250000000},{"$f":"IF(D12=\"Einfeldträger\",((D9)*((D13*1000)^4))/(76.8*O85),IF(D12=Kragarm,((D9)*(D13*1000^3))/(6*O85)))","v":50.574425574425575},{"$f":"(100/$P$88)*P85","v":505.23612617141623},{"$f":"P88","v":10.010057269195892}]
[null,null,null,null,null,null,null,null,null,null,null,null,"Anfangszustand ",null,{"$f":"N78","v":3882906213724.4805},{"$f":"IF(D12=\"Einfeldträger\",(D9*((D13*1000)^4))/(76.8*O86),IF(D12=Kragarm,(D9*((D13*1000)^3))/(6*O86)))","v":16.297393374150204},{"$f":"(100/$P$88)*P86","v":162.81019114947955},{"$f":"P88","v":10.010057269195892}]
[null,null,"Randspannungen ",null,null,null,null,null,null,null,null,null,"Endzustand ",null,{"$f":"S78","v":1768854558618.1096},{"$f":"IF(D12=\"Einfeldträger\",(D9*((D13*1000)^4))/(76.8*O87),IF(D12=Kragarm,(D9*((D13*1000)^3))/(6*O87)))","v":35.775270324903083},{"$f":"(100/$P$88)*P87","v":357.39326322332732},{"$f":"P88","v":10.010057269195892}]
[null,null,null,null,null,null,null,null,null,null,null,null,"Starrer Verbund ",null,{"$f":"((N54*G42)+(1*N54*F42*(N72^2)))+((N55*G43)+(1*N55*F43*(N71^2)))+((N56*G44)+(1*N56*F44*(N73^2)))","v":6321767028719.8457},{"$f":"IF(D12=\"Einfeldträger\",(D9*((D13*1000)^4))/(76.8*O88),IF(D12=Kragarm,(D9*((D13*1000)^3))/(6*O88)))","v":10.010057269195892},100,{"$f":"P88","v":10.010057269195892}]
[]
[null,null,"sm,1,d [N/mm²]",{"$f":"(($G$10/$D$78)*$D$54) * ($E$42/2)*$D$36","v":6.7664142300043917},null,null,null,"sm,1,d [N/mm²]",{"$f":"(($G$10/$I$78)*$I$54) * ($E$42/2)*$D$36","v":5.3973408223758348}]
[null,null,"sm,2,d [N/mm²]",{"$f":"(($G$10/$D$78)*$D$55) * ($E$43/2)*$E$36","v":7.5182380333382124},null,null,null,"sm,2,d [N/mm²]",{"$f":"(($G$10/$I$78)*$I$55) * ($E$43/2)*$E$36","v":8.8939232007134752}]
[null,null,"sm,3,d [N/mm²]",{"$f":"(($G$10/$D$78)*$D$56) * ($E$44/2)*$F$36","v":{"$error":"#DIV/0!"}},null,null,null,"sm,3,d [N/mm²]",{"$f":"(($G$10/$I$78)*$I$56) * ($E$44/2)*$F$36","v":{"$error":"#DIV/0!"}}]
[]
[null,null,"Schnittgrößen in den Teilquerschnitten"]
[]
[]
[null,null,"Ief [mm4]",{"$f":"(D34*G42+D64*D34*F42*(D72^2))+(G43+F43*(D71^2))","v":323214028.23701799},null,null,null,"Ief [mm4]",{"$f":"(L54*G42+I64*L54*F42*(I72^2))+(G43+F43*(I71^2))","v":273220258.95220953}]
[]
[null,null,"N1 [KN]",{"$f":"((G10/D97)*D64*D72*D34*F42)/1000","v":121.13849413136752},null,null,null,"N1 [KN]",{"$f":"((G10/I97)*I64*I72*L54*F42)/1000","v":116.62198946952525}]
[null,null,"N2 [KN]",{"$f":"((G10/D97)*D65*D71*E34*F43)/1000","v":121.13849413136755},null,null,null,"N2 [KN]",{"$f":"((G10/I97)*I65*I71*L55*F43)/1000","v":116.6219894695253}]
[]
[null,null,"M1 [KNm]",{"$f":"((G10/D97)*(E42/2)*D34*((D42*(E42^2))/6))/10^6","v":2.5374053362516467},null,null,null,"M1 [KNm]",{"$f":"((G10/I97)*(E42/2)*L54*((D42*(E42^2))/6))/10^6","v":2.024002808390938}]
[null,null,"M2 [KNm]",{"$f":"((G10/D97)*(E43/2)*E34*((D43*(E43^2))/6))/10^6","v":6.014590426670571},null,null,null,"M2 [KNm]",{"$f":"((G10/I97)*(E43/2)*L55*((D43*(E43^2))/6))/10^6","v":7.11513856057078}]
[]
[null,null,"Schubspannungen in neutraler Ebene des Querschnitts 2"]
[]
[]
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[]
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[null,null,"τ1,max,d [N/mm²]",{"$f":"($G$11*D64*D54*F42*D72)/(D78*D42)","v":0.12921439374012536},null,null,null,"τ1,max,d [N/mm²]",{"$f":"($G$11*I64*I54*F42*I72)/(I78*D42)","v":0.1243967887674936}]
[null,null,"τ3,max,d [N/mm²]",{"$f":"($G$11*D66*D56*F44*D73)/(D78*D44)","v":{"$error":"#DIV/0!"}},null,null,null,"τ3,max,d [N/mm²]",{"$f":"($G$11*I66*I56*F44*I73)/(I78*D44)","v":{"$error":"#DIV/0!"}}]
[]
[null,null,"Bemessungswert der Scherkraft in den Anschlussfugen "]
[]
[]
[null,null,"F1,v,Ed [N]",{"$f":"(($G$11 * D64 * D54 * F42 *D72 * J42)/(D78))","v":8075.8996087578353},null,null,null,"F1,v,Ed [N]",{"$f":"(($G$11 * I64 * I54 * F42 *I72 * J42)/I78)","v":7774.7992979683504}]
[null,null,"F3,v,Ed [N]",{"$f":"(($G$11 * D66 * D56 * F44 *D73 * K42)/(D78))","v":0},null,null,null,"F3,v,Ed [N]",{"$f":"(($G$11 * I66 * I56 * F44 *I73 * K42)/(I78))","v":0}]
[]
[]
[]
[null,null,"Bemessungswert der Festigkeit","Breite [mm]","Höhe [mm]","ft,0,d [N/mm²]","fm,d [N/mm²]","fc,0,d [N/mm²]"]
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[null,null,"Querschnitt 2",{"$f":"D43","v":120},200,{"$f":"IF(AND($E$30=\"Vollholz\",$E$32<=700,$E$43<150),VLOOKUP($E$31,Werkstoffkenngrößen!C5:J32,5,0)*($E$38/1.3)*MIN((150/$E$43)^0.2,1.3),VLOOKUP($E$31,Werkstoffkenngrößen!C5:J42,5,0)*($E$38/1.3))","v":8.9230769230769234},{"$f":"IF(AND($E$30=\"Vollholz\",$E$32<=700,$E$43<150),VLOOKUP($E$31,Werkstoffkenngrößen!C5:J32,7,0)*($E$38/1.3)*MIN((150/$E$43)^0.2,1.3),VLOOKUP($E$31,Werkstoffkenngrößen!C5:J42,7,0)*($E$38/1.3))","v":14.76923076923077},{"$f":"VLOOKUP($E$31,Werkstoffkenngrößen!C6:J42,6,0)*($E$38/1.3)","v":12.923076923076923}]
[null,null,"Querschnitt 3",{"$f":"D44","v":0},0,{"$f":"IF(AND($F$30=\"Vollholz\",$F$32<=700,$E$44<150),VLOOKUP($F$31,Werkstoffkenngrößen!C5:J32,5,0)*($F$38/1.3)*MIN((150/$E$44)^0.2,1.3),VLOOKUP($F$31,Werkstoffkenngrößen!C5:J42,5,0)*($F$38/1.3))","v":{"$error":"#DIV/0!"}},{"$f":"IF(AND($F$30=\"Vollholz\",$F$32<=700,$E$44<150),VLOOKUP($F$31,Werkstoffkenngrößen!C5:J32,7,0)*($F$38/1.3)*MIN((150/$E$44)^0.2,1.3),VLOOKUP($F$31,Werkstoffkenngrößen!C5:J42,7,0)*($F$38/1.3))","v":{"$error":"#DIV/0!"}},{"$f":"VLOOKUP($F$31,Werkstoffkenngrößen!C7:J42,6,0)*($F$38/1.3)","v":14.76923076923077},{"$f":"VLOOKUP($F$31,Werkstoffkenngrößen!F7:M28,5,0)*($F$38/1.3)","v":{"$error":"#N/A"}}]
[]
[]
[null,null,"Querschnittsnachweise"]
[]
[]
[null,null,"Tragfähigkeitsnachweise für Querschnitte und Verbindungsmittel"]
[]
[null,null,"Schwerpunktsspannungen "]
[]
[]
[null,null,"s1,d [N/mm²]",{"$f":"(($G$10/$D$78)*$D$54) * $D$64*$D$72*$D$34","v":9.691079530509402},null,null,null,"s1,d [N/mm²]",{"$f":"(($G$10/$I$78)*$I$54) * $I$64*$I$72*$D$35","v":3.10991971918734}]
[null,null,"s2,d [N/mm²]",{"$f":"(($G$10/$D$78)*$D$55) * $D$65*$D$71*$E$35","v":5.0474372554736471},null,null,null,"s2,d [N/mm²]",{"$f":"(($G$10/$I$78)*$I$55) * $I$65*$I$71*$E$35","v":4.8592495612302207}]
[null,null,"s3,d [N/mm²]",{"$f":"(($G$10/$D$78)*$D$56) * $D$66*$D$73*$F$35","v":{"$error":"#DIV/0!"}},null,null,null,"s3,d [N/mm²]",{"$f":"(($G$10/$I$78)*$I$56) * $I$66*$I$73*$F$35","v":{"$error":"#DIV/0!"}}]
[]
[null,null,"Randspannungen "]
[]
[]
[null,null,"sm,1,d [N/mm²]",{"$f":"(($G$10/$D$78)*$D$54) * ($E$42/2)*$D$36","v":6.7664142300043917},null,null,null,"sm,1,d [N/mm²]",{"$f":"(($G$10/$I$78)*$I$54) * ($E$42/2)*$D$36","v":5.3973408223758348}]
[null,null,"sm,2,d [N/mm²]",{"$f":"(($G$10/$D$78)*$D$55) * ($E$43/2)*$E$36","v":7.5182380333382124},null,null,null,"sm,2,d [N/mm²]",{"$f":"(($G$10/$I$78)*$I$55) * ($E$43/2)*$E$36","v":8.8939232007134752}]
[null,null,"sm,3,d [N/mm²]",{"$f":"(($G$10/$D$78)*$D$56) * ($E$44/2)*$F$36","v":{"$error":"#DIV/0!"}},null,null,null,"sm,3,d [N/mm²]",{"$f":"(($G$10/$I$78)*$I$56) * ($E$44/2)*$F$36","v":{"$error":"#DIV/0!"}}]
[]
[null,null,"Verbindungsmittelbeanspruchung"]
[]
[]
[null,null,"F1,v,Ed",{"$f":"((D11*10^3)*D64*D54*F42*D72*J42)/D78","v":8075.8996087578353},null,null,null,"F1,v,Ed",{"$f":"((D11*10^3)*I64*I54*F42*I72*J42)/I78","v":7774.7992979683504}]
[null,null,"F3,v,Ed",{"$f":"((D11*10^3)*D66*D56*F44*D73*K42)/D78","v":0},null,null,null,"F3,v,Ed",{"$f":"((D11*10^3)*I66*I56*F44*I73*K42)/I78","v":0}]
[]
[null,null,"Nachweise der Querschnitte"]
[]
[null,null,"Tragfähigkeitsnachweis der Teilquerschnitte"]
[]
[]
[null,null,"Querschnitt 1 (Druck und Biegung)",{"$f":"(D136/H123)^2 + D143/G123","v":0.407837889822045},null,"≤ 1,00",null,"Querschnitt 1 (Druck und Biegung)",{"$f":"(I136/H123)^2 + I143/G123","v":0.20280698703366837},null,"≤ 1,00"]
[null,null,"Querschnitt 2 (Zug und Biegung)",{"$f":"(D137/F124)^2 + D144/G124","v":0.82901981491599641},null,"≤ 1,00",null,"Querschnitt 2 (Zug und Biegung)",{"$f":"(I137/F124)^2 + I144/G124","v":0.89875036864834423},null,"≤ 1,00"]
[null,null,"Querschnitt 3 (Zug und Biegung)",{"$f":"(D138/F125)^2 + D145/G125","v":{"$error":"#DIV/0!"}},null,"≤ 1,00",null,"Querschnitt 3 (Zug und Biegung)",{"$f":"(I138/F125)^2 + I145/G125","v":{"$error":"#DIV/0!"}},null,"≤ 1,00"]

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[]
[]
[null,null,null,null,null,null,null,null,null,null,"EV"]
[null,"Schubanalogieverfahren nach Kreuzinger",null,null,null,null,null,null,null,null,30000]
[]
[]
["GZT ","Ebene A: ",null,"Anfangszustand",null,"Endzustand"]
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[null,null,null,{"$f":"D8/10^9","v":1251.25},null,{"$f":"F8/10^9","v":957.90556900726403},null,"[KN/m²]"]
[]
[null,null,"aA",{"$f":"(((D8*12)/K4)^(1/4))/10","v":14.957224783092988},null,{"$f":"(((F8*12)/K4)^(1/4))/10","v":13.990900640636477},null,"[cm]"]
[]
[null,null,"SA","∞",null,"∞"]
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[]
["GZG","Ebene A: ",null,"Anfangszustand",null,"Endzustand"]
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[null,null,null,{"$f":"D17/10^9","v":1251.25},null,{"$f":"F17/10^9","v":656.07142857142856},null,"[KN/m²]"]
[]
[null,null,"aA",{"$f":"(((D17*12)/K4)^(1/4))/10","v":14.957224783092988},null,{"$f":"(((F17*12)/K4)^(1/4))/10","v":12.727783492216428},null,"[cm]"]
[]
[null,null,"SA","∞",null,"∞"]
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[null,null,null,{"$f":"D26/10^9","v":3677.1428571428569},null,{"$f":"F26/10^9","v":2872.2746781115884},null,"[KN/m²]"]
[]
[null,null,"aB",{"$f":"(((D26*12)/K4)^(1/4))/10","v":19.583604215712295},null,{"$f":"(((F26*12)/K4)^(1/4))/10","v":18.410750401093289},null,"[cm]"]
[null,null,null,null,null,null,null,null,null,null,null,"AZ","EZ "]
[null,null,"Ct",{"$f":"L32/('Gamma-Verfahren_nach_DIN1052'!J46/10)","v":10},null,{"$f":"M32/('Gamma-Verfahren_nach_DIN1052'!J46/10)","v":6.666666666666667},null,"[KN]",null,null,"Kser",{"$f":"('Gamma-Verfahren_nach_DIN1052'!J33)/100","v":150},{"$f":"L31*2/3","v":100},"[KN/cm]"]
[null,null,"Gt",{"$f":"(D31*(Massenschwerpunkt!C26/10)^2)/('Weitere Verfahren'!D29^2)","v":4.4065779572054886},null,{"$f":"(F31*(Massenschwerpunkt!C26/10)^2)/('Weitere Verfahren'!F29^2)","v":3.3239345609093518},null,"[KN/cm²]",null,null,"Kser,d",{"$f":"L31*2/3","v":100},{"$f":"M31*2/3","v":66.666666666666671},"[KN/cm]","(GZT) "]
[null,null,null,null,null,null,null,null,null,null,"Kser,k",{"$f":"L31","v":150},{"$f":"L31/(1+2*SQRT('Gamma-Verfahren_nach_DIN1052'!D37*'Gamma-Verfahren_nach_DIN1052'!E37))","v":43.484692283495349},"[KN/cm]","(GZG)"]
[null,null,"SB",{"$f":"D32*(D29)^2","v":1689.9999999999998},null,{"$f":"F32*(F29)^2","v":1126.6666666666667},null,"[KN]"]
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["GZG","Ebene B: ",null,"Anfangszustand",null,"Endzustand"]
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[null,null,null,{"$f":"D38/10^9","v":3677.1428571428569},null,{"$f":"F38/10^9","v":1901.25},null,"[KN/m²]"]
[]
[null,null,"aB",{"$f":"(((D38*12)/K4)^(1/4))/10","v":19.583604215712295},null,{"$f":"(((F38*12)/K4)^(1/4))/10","v":16.606373615655933},null,"[cm]"]
[]
[null,null,"Ct",{"$f":"L33/('Gamma-Verfahren_nach_DIN1052'!J46/10)","v":15},null,{"$f":"M33/('Gamma-Verfahren_nach_DIN1052'!J46/10)","v":4.3484692283495345},null,"[KN]"]
[null,null,"Gt",{"$f":"(D43*(Massenschwerpunkt!C26/10)^2)/('Weitere Verfahren'!D41^2)","v":6.6098669358082338},null,{"$f":"(F43*(Massenschwerpunkt!C26/10)^2)/('Weitere Verfahren'!F41^2)","v":2.6648544685940578},null,"[KN/cm²]"]
[]
[null,null,"SB",{"$f":"D44*(D41)^2","v":2535},null,{"$f":"F44*(F41)^2","v":734.89129959107129},null,"[KN]"]
[]
[null,"Stabwerkmodelle nach Rautenstrauch"]
[]
[]
[null,"Ohne Berücksichtigung der Gurtsteifigkeit:"]
[]
[null,null,null,"Anfangszustand",null,"Endzustand"]
[]
[null,"GZT","EI*",{"$f":"('Gamma-Verfahren_nach_DIN1052'!D57/3)*(Massenschwerpunkt!F26^3+Massenschwerpunkt!F27^3)","v":3423333333.3333335},null,{"$f":"('Gamma-Verfahren_nach_DIN1052'!I57/3)*(Massenschwerpunkt!F26^3+Massenschwerpunkt!F27^3)","v":1973276885.8587162},null,"[N/mm²]"]
[null,null,null,{"$f":"D55/10^9","v":3.4233333333333333},null,{"$f":"F55/10^9","v":1.9732768858587162},null,"[KN/m²]"]
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[null,"GZG","EI*",{"$f":"('Gamma-Verfahren_nach_DIN1052'!N57/3)*(Massenschwerpunkt!F26^3+Massenschwerpunkt!F27^3)","v":5135000000},null,{"$f":"('Gamma-Verfahren_nach_DIN1052'!S57/3)*(Massenschwerpunkt!F26^3+Massenschwerpunkt!F27^3)","v":1488625965.8383241},null,"[N/mm²]"]
[null,null,null,{"$f":"D58/10^9","v":5.1349999999999998},null,{"$f":"F58/10^9","v":1.4886259658383241},null,"[KN/m²]"]
[]
[null,"Mit Berücksichtigung der Gurtsteifigkeit:"]
[]
[null,null,null,"Anfangszustand",null,"Endzustand"]
[]
[null,"GZT","EI*",{"$f":"(Massenschwerpunkt!F26^3+Massenschwerpunkt!F27^3)/((3/'Gamma-Verfahren_nach_DIN1052'!D57)-(('Weitere Verfahren'!D74^3+'Weitere Verfahren'!D75^3)/(2*('Weitere Verfahren'!D74+'Weitere Verfahren'!D75)^2)*((Massenschwerpunkt!F26^2/('Gamma-Verfahren_nach_DIN1052'!D54*'Gamma-Verfahren_nach_DIN1052'!G42))+(Massenschwerpunkt!F27^2/('Gamma-Verfahren_nach_DIN1052'!D55*'Gamma-Verfahren_nach_DIN1052'!G43)))))","v":3427271233.3615646},null,{"$f":"(Massenschwerpunkt!F26^3+Massenschwerpunkt!F27^3)/((3/'Gamma-Verfahren_nach_DIN1052'!I57)-(('Weitere Verfahren'!D74^3+'Weitere Verfahren'!D75^3)/(2*('Weitere Verfahren'!D74+'Weitere Verfahren'!D75)^2)*((Massenschwerpunkt!F26^2/('Gamma-Verfahren_nach_DIN1052'!I54*'Gamma-Verfahren_nach_DIN1052'!G42))+(Massenschwerpunkt!F27^2/('Gamma-Verfahren_nach_DIN1052'!I55*'Gamma-Verfahren_nach_DIN1052'!G43)))))","v":1974951427.6963193},null,"[N/mm²]"]
[null,null,null,{"$f":"D65/10^9","v":3.4272712333615645},null,{"$f":"F65/10^9","v":1.9749514276963194},null,"[KN/m²]"]
[]
[]
[null,"GZG","EI*",{"$f":"(Massenschwerpunkt!F26^3+Massenschwerpunkt!F27^3)/((3/'Gamma-Verfahren_nach_DIN1052'!N57)-(('Weitere Verfahren'!D74^3+'Weitere Verfahren'!D75^3)/(2*('Weitere Verfahren'!D74+'Weitere Verfahren'!D75)^2)*((Massenschwerpunkt!F26^2/('Gamma-Verfahren_nach_DIN1052'!N54*'Gamma-Verfahren_nach_DIN1052'!G42))+(Massenschwerpunkt!F27^2/('Gamma-Verfahren_nach_DIN1052'!N55*'Gamma-Verfahren_nach_DIN1052'!G43)))))","v":5143865374.0347939},null,{"$f":"(Massenschwerpunkt!F26^3+Massenschwerpunkt!F27^3)/((3/'Gamma-Verfahren_nach_DIN1052'!S57)-(('Weitere Verfahren'!D74^3+'Weitere Verfahren'!D75^3)/(2*('Weitere Verfahren'!D74+'Weitere Verfahren'!D75)^2)*((Massenschwerpunkt!F26^2/('Gamma-Verfahren_nach_DIN1052'!S54*'Gamma-Verfahren_nach_DIN1052'!G42))+(Massenschwerpunkt!F27^2/('Gamma-Verfahren_nach_DIN1052'!S55*'Gamma-Verfahren_nach_DIN1052'!G43)))))","v":1490065855.954509},null,"[N/mm²]"]
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[]
[]
[]
["*","eff.Abstand zum linkem VM: ",null,100,"mm",null,"Hinweis: "]
["*","eff. Abstand zum rechten VM: ",null,100,"mm",null,"Wenn VM-Abstand gleich",null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!J42/'Gamma-Verfahren_nach_DIN1052'!J43","v":100},"einsetzen"]
[]
[]
[null,"*eff. = effektiver VM Abstand = Abstand durch Anzahl der Reihen "]
[]
[]
[]
[null,"Federmodelle"]
[]
[]
[null,"!!!BEI WECHSELNDEM VM ABSTAND SIND DIE FEDERSTEIFIGKEITEN GETRENNT ZU ERMITTELN UND ZU MODELLIEREN!!! "]
[]
[null,"Schubfuge 1"]
[]
[]
[null,null,null,"Anfangszustand",null,"Endzustand"]
[]
[null,"GZT","KFeder",{"$f":"'Gamma-Verfahren_nach_DIN1052'!J43*'Gamma-Verfahren_nach_DIN1052'!D57","v":10000},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!J43*'Gamma-Verfahren_nach_DIN1052'!I57","v":5764.1973296749256},null,"[N/mm]"]
[null,"GZG","KFeder",{"$f":"'Gamma-Verfahren_nach_DIN1052'!J43*'Gamma-Verfahren_nach_DIN1052'!N57","v":15000},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!J43*'Gamma-Verfahren_nach_DIN1052'!S57","v":4348.4692283495342},null,"[N/mm]"]
[]
[null,"Schubfuge 2"]
[]
[]
[null,null,null,"Anfangszustand",null,"Endzustand"]
[]
[null,"GZT","KFeder",{"$f":"'Gamma-Verfahren_nach_DIN1052'!K43*'Gamma-Verfahren_nach_DIN1052'!D58","v":1009.3450092785043},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!K43*'Gamma-Verfahren_nach_DIN1052'!I58","v":742.16544799890028},null,"[N/mm]"]
[null,"GZG","KFeder",{"$f":"'Gamma-Verfahren_nach_DIN1052'!K43*'Gamma-Verfahren_nach_DIN1052'!N58","v":1514.0175139177566},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!K43*'Gamma-Verfahren_nach_DIN1052'!S58","v":688.18977905352563},null,"[N/mm]"]
[]
[]
[]
[null,"Modellierungshilfe: "]
[]
[null,"Abstand der Bauteil-Schwerachsen:",null,null,"a",{"$f":"Massenschwerpunkt!C26","v":130},null,"[mm]"]
[null,"Abstand der Verbindungsmittel:",null,null,"si",{"$f":"'Gamma-Verfahren_nach_DIN1052'!J42","v":100},null,"[mm]"]
[null,"Abstand Schwerachse 1 zu Feder:",null,null,"a1",{"$f":"Massenschwerpunkt!F26","v":30},null,"[mm]"]
[null,"Abstand Schwerachse 2 zu Feder:",null,null,"a2",{"$f":"Massenschwerpunkt!F27","v":100},null,"[mm]"]

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[]
[null,"Massenschwerpunkt des Gesamtquerschnittes "]
[]
[]
[null,"Schwerpunktkoordinaten","Querschnitt 1","m1","Querschnitt 2 ","m2","Querschnitt 3","m3","Verbundquerschnitt"]
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[null,"Y",{"$f":"'Gamma-Verfahren_nach_DIN1052'!D45/2","v":312.5},{"$f":"C11*'Gamma-Verfahren_nach_DIN1052'!F42/10^6","v":93.75},{"$f":"'Gamma-Verfahren_nach_DIN1052'!D45/2","v":312.5},{"$f":"E11*'Gamma-Verfahren_nach_DIN1052'!F43/10^6","v":8.4},{"$f":"'Gamma-Verfahren_nach_DIN1052'!D45/2","v":312.5},{"$f":"G11*'Gamma-Verfahren_nach_DIN1052'!F44/10^6","v":0},{"$f":"(C8*$D$8+E8*$F$8+G8*$H$8)/($D$8+$F$8+$H$8)","v":312.5}]
[null,"Z",{"$f":"'Gamma-Verfahren_nach_DIN1052'!E42/2","v":30},null,{"$f":"IF('Gamma-Verfahren_nach_DIN1052'!D25=\"B\",'Gamma-Verfahren_nach_DIN1052'!E43/2,'Gamma-Verfahren_nach_DIN1052'!E42+'Gamma-Verfahren_nach_DIN1052'!E43/2)","v":160},null,{"$f":"IF('Gamma-Verfahren_nach_DIN1052'!D25=\"B\",'Gamma-Verfahren_nach_DIN1052'!E43-'Gamma-Verfahren_nach_DIN1052'!E44/2,'Gamma-Verfahren_nach_DIN1052'!E42+'Gamma-Verfahren_nach_DIN1052'!E43+'Gamma-Verfahren_nach_DIN1052'!E44/2)","v":260},null,{"$f":"(C9*$D$8+E9*$F$8+G9*$H$8)/($D$8+$F$8+$H$8)","v":40.690161527165927}]
[]
[null,"Masse [Kg/m³]",{"$f":"'Gamma-Verfahren_nach_DIN1052'!D32","v":2500},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!E32","v":350},null,{"$f":"'Gamma-Verfahren_nach_DIN1052'!F32","v":380}]
[]
[null,"Schwerpunktabstände","Querschnitt 1","m1","Querschnitt 2 ","m2","Querschnitt 3","m3","Verbundquerschnitt","Kontrolle"]
[null,"X",{"$f":"I7-C7","v":0},null,{"$f":"I7-E7","v":0},null,{"$f":"I7-G7","v":0},null,{"$f":"C14*D15+E14*F15+G14*H15","v":0},{"$f":"I14","v":0}]
[null,"Y",{"$f":"I8-C8","v":0},{"$f":"D8","v":93.75},{"$f":"I8-E8","v":0},{"$f":"F8","v":8.4},{"$f":"I8-G8","v":0},{"$f":"G18*'Gamma-Verfahren_nach_DIN1052'!F51/10^6","v":0},{"$f":"C15*D15+E15*F15+G15*H15","v":0},{"$f":"I15","v":0}]
[null,"Z",{"$f":"I9-C9","v":10.690161527165927},null,{"$f":"I9-E9","v":-119.30983847283407},null,{"$f":"I9-G9","v":-219.30983847283409},null,{"$f":"C16*D15+E16*F15+G16*H15","v":-5.6843418860808015E-13},{"$f":"I16","v":-5.6843418860808015E-13}]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Abstand Schwerpunkte ",null,null,"Abstand QS zur Fuge"]
[null,"a1-2",{"$f":"Massenschwerpunkt!E9-Massenschwerpunkt!C9","v":130},null,"ZB",{"$f":"'Gamma-Verfahren_nach_DIN1052'!E42-Massenschwerpunkt!C9","v":30}]
[null,"a2-3",{"$f":"G9-E9","v":100},null,"ZH",{"$f":"C26-F26","v":100}]

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[]
[]
[null,null,"Verbindungsmittel ","Kser (QS1/2) [Nmm]","Kser (QS2/3) [Nmm]","K1/3 (Holz-Holz)","K1/3 (Holz-Stahl)"]
[null,null,"Stabdübel",{"$f":"(('Gamma-Verfahren_nach_DIN1052'!G32)^1.5)*(('Gamma-Verfahren_nach_DIN1052'!J32))/23","v":7463.2751671687993},{"$f":"(('Gamma-Verfahren_nach_DIN1052'!H32)^1.5)*(('Gamma-Verfahren_nach_DIN1052'!K32))/23","v":1514.0175139177566},{"$f":"2/3*D5","v":4975.5167781125328},{"$f":"2*F5","v":9951.0335562250657}]
[null,null,"Passbolzen",{"$f":"(('Gamma-Verfahren_nach_DIN1052'!G32)^1.5)*(('Gamma-Verfahren_nach_DIN1052'!J32))/23","v":7463.2751671687993},{"$f":"(('Gamma-Verfahren_nach_DIN1052'!H32)^1.5)*(('Gamma-Verfahren_nach_DIN1052'!K32))/23","v":1514.0175139177566},{"$f":"2/3*D5","v":4975.5167781125328},{"$f":"2*F5","v":9951.0335562250657}]
[null,null,"Bolzen",{"$f":"(('Gamma-Verfahren_nach_DIN1052'!G32)^1.5)*(('Gamma-Verfahren_nach_DIN1052'!J32))/23","v":7463.2751671687993},{"$f":"(('Gamma-Verfahren_nach_DIN1052'!H32)^1.5)*(('Gamma-Verfahren_nach_DIN1052'!K32))/23","v":1514.0175139177566},{"$f":"2/3*D5","v":4975.5167781125328},{"$f":"2*F5","v":9951.0335562250657}]
[null,null,"Gewindestangen",{"$f":"(('Gamma-Verfahren_nach_DIN1052'!G32)^1.5)*(('Gamma-Verfahren_nach_DIN1052'!J32))/23","v":7463.2751671687993},{"$f":"(('Gamma-Verfahren_nach_DIN1052'!H32)^1.5)*(('Gamma-Verfahren_nach_DIN1052'!K32))/23","v":1514.0175139177566},{"$f":"2/3*D5","v":4975.5167781125328},{"$f":"2*F5","v":9951.0335562250657}]
[null,null,"Schrauben (vorgebohrt) ",{"$f":"(('Gamma-Verfahren_nach_DIN1052'!G32)^1.5)*(('Gamma-Verfahren_nach_DIN1052'!J32))/23","v":7463.2751671687993},{"$f":"(('Gamma-Verfahren_nach_DIN1052'!H32)^1.5)*(('Gamma-Verfahren_nach_DIN1052'!K32))/23","v":1514.0175139177566},{"$f":"2/3*D5","v":4975.5167781125328},{"$f":"2*F5","v":9951.0335562250657}]
[null,null,"Nägel (vorgebohrt) ",{"$f":"(('Gamma-Verfahren_nach_DIN1052'!G32)^1.5)*(('Gamma-Verfahren_nach_DIN1052'!J32))/23","v":7463.2751671687993},{"$f":"(('Gamma-Verfahren_nach_DIN1052'!H32)^1.5)*(('Gamma-Verfahren_nach_DIN1052'!K32))/23","v":1514.0175139177566},{"$f":"2/3*D5","v":4975.5167781125328},{"$f":"2*F5","v":9951.0335562250657}]
[null,null,"Nägel (nicht vorgebohrt) ",{"$f":"(('Gamma-Verfahren_nach_DIN1052'!G32)^1.5)*(('Gamma-Verfahren_nach_DIN1052'!J32)^0.8)/30","v":3998.5799626152375},{"$f":"(('Gamma-Verfahren_nach_DIN1052'!H32)^1.5)*(('Gamma-Verfahren_nach_DIN1052'!K32)^0.8)/30","v":841.28564681358012},{"$f":"2/3*D11","v":2665.719975076825},{"$f":"2*F11","v":5331.43995015365}]
[null,null,"Klammern ",{"$f":"(('Gamma-Verfahren_nach_DIN1052'!G32)^1.5)*(('Gamma-Verfahren_nach_DIN1052'!J32)^0.8)/80","v":1499.4674859807142},{"$f":"(('Gamma-Verfahren_nach_DIN1052'!H32)^1.5)*(('Gamma-Verfahren_nach_DIN1052'!K32)^0.8)/80","v":315.48211755509254},999.64499065380937,1999.2899813076187]
[null,null,"Ringdübel Typ A",{"$f":"(('Gamma-Verfahren_nach_DIN1052'!G32))*(('Gamma-Verfahren_nach_DIN1052'!J32))/2","v":2806.243040080456},{"$f":"(('Gamma-Verfahren_nach_DIN1052'!H32))*(('Gamma-Verfahren_nach_DIN1052'!K32))/2","v":911.72912644052349},1870.8286933869706,3741.6573867739412]
[null,null,"Scheibendübel Typ B ",{"$f":"(('Gamma-Verfahren_nach_DIN1052'!G32))*(('Gamma-Verfahren_nach_DIN1052'!J32))/2","v":2806.243040080456},{"$f":"(('Gamma-Verfahren_nach_DIN1052'!H32))*(('Gamma-Verfahren_nach_DIN1052'!K32))/2","v":911.72912644052349},1870.8286933869706,3741.6573867739412]
[null,null,"Scheibendübel Typ C1 bis C9",{"$f":"(1.5*('Gamma-Verfahren_nach_DIN1052'!G32))*(('Gamma-Verfahren_nach_DIN1052'!J32))/4","v":2104.6822800603422},{"$f":"(1.5*('Gamma-Verfahren_nach_DIN1052'!H32))*(('Gamma-Verfahren_nach_DIN1052'!K32))/4","v":683.7968448303925},1403.121520040228,2806.243040080456]
[null,null,"Scheibendübel Typ C10, C11",{"$f":"(('Gamma-Verfahren_nach_DIN1052'!G32))*(('Gamma-Verfahren_nach_DIN1052'!J32))/2","v":2806.243040080456},{"$f":"(('Gamma-Verfahren_nach_DIN1052'!H32))*(('Gamma-Verfahren_nach_DIN1052'!K32))/2","v":911.72912644052349},1870.8286933869706,3741.6573867739412]
[null,null,"Andere ",{"$f":"'Gamma-Verfahren_nach_DIN1052'!J37","v":15000},{"$f":"'Gamma-Verfahren_nach_DIN1052'!K37","v":0},{"$f":"2/3*D17","v":10000},{"$f":"2*F17","v":20000}]
[]
[]
[]
[null,null,"Verbindungsart ","Anzahl VM Reihen"]
[null,null,"Holz-Holz-Verbindung",1]
[null,null,"Holz-Stahl-Verbindung",2]
[null,null,null,3]
[null,null,null,4]
[null,null,null,5]
[null,null,null,6]
[null,null,null,7]
[null,null,null,8]
[null,null,null,9]
[null,null,null,10]

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[null,"veränderliche Einwirkung","Ψ0","Ψ1","Ψ2","KLED ",null,"Nutzungsklasse ","KLED","Kdef","kdef (Spanplatte)"]
[null,"Nutzlasten Qk,N",null,null,null,null,null,1,"ständig",0.6,2.25]
[null,"Kategorie A: Wohn- und Aufenthaltsräume ",0.7,0.5,0.3,"mittel",null,2,"lang",0.8,3]
[null,"Kategorie B: Büros ",0.7,0.5,0.3,"mittel",null,3,"mittel",2]
[null,"Kategorie C: Versammlungsräume ",0.7,0.7,0.6,"kurz",null,null,"kurz"]
[null,"Kategorie D: Verkaufssräume ",0.7,0.7,0.6,"mittel",null,null,"sehr kurz"]
[null,"Kategorie E: Lagerräume",1,0.9,0.8,"lang"]
[null,"Verkehrslasten Qk,V "]
[null,"Kategorie F: Verkehrsflächen, Fahrzeuglast < 25 kN  ",0.7,0.7,0.6,"mittel"]
[null,"Kategorie G: Flächen für den Betrieb miit Gegengewichtsstaplern ",0.7,0.5,0.3,"mittel"]
[null,"Kategorie H: Dächer (nicht begehbar) ",0,0,0,"kurz"]
[null,"Schnee und Eislasten Qk,S "]
[null,"Orte bis NN +1000m ",0.5,0.2,0,"kurz"]
[null,"Orte über NN +1000m ",0.7,0.5,0.2,"mittel"]
[null,"Windlasten Qk,W "]
[]
[]
[]
[]
[null,"Holzarten"]
[null,"Vollholz"]
[null,"Brettschichtholz"]
[null,"Sperrholz"]
[null,"Spanplatte P6"]
["(","Beton",")"]
[null,"Furnierschichtholz"]
[null,"Balkenschichtholz"]
[null,"Brettsperrholz"]
[null,"Massivholzplatten"]
[null,"Spanplatte"]

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[null,"Kmod","NKL ","ständig","lang","mittel","kurz","sehr kurz"]
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[null,null,2,0.6,0.7,0.8,0.9,1.1000000000000001]
[null,null,3,0.5,0.55000000000000004,0.65,0.7,0.9]
[null,"Spannplatten",1,0.3,0.45,0.65,0.85,1.1000000000000001]
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[null,null,null,null,null,null,"Festigkeitskennwerte"]
[null,null,null,null,null,null,"Zug","Druck","Biegung","Schub/Torsion"]
[null,"Holzeigenschaften","Holzart","E0,mean [N/mm²]","rk [Kg/m³]","Einbaufeuchte","ft,0,k [N/mm²]","fc,0,k [N/mm²]","fm,y,k [N/mm²]","fv,k [N/mm²]"]
[null,"Nadelholz","C16",8000,310,"<30%"]
[null,null,"C24",11000,350,"≥30%",14.5,21,24,4]
[null,null,"C30",12000,380,null,19,24,30,4]
[null,null,"C35",13000,400,null,22.5,25,35,4]
[null,null,"C40",14000,420,null,26,27,40,4]
[null,"Laubholz","D30",11000,530,null,18,24,30,3.9]
[null,null,"D35",12000,540,null,21,25,35,4.0999999999999996]
[null,null,"D40",13000,550,null,24,27,40,4.2]
[null,null,"D60",17000,700,null,26,33,60,4.8]
[null,"BSH ","GL24c",11000,365,null,17,21.5,24,3.5]
[null,null,"GL24h",11500,385,null,19.2,24,24,3.5]
[null,null,"GL28c",12500,390,null,19.5,24,28,3.5]
[null,null,"GL28h",12600,425,null,22.3,28,28,3.5]
[null,null,"GL30c",13000,390,null,19.5,24.5,30,3.5]
[null,null,"GL30h",13600,430,null,24,30,30,3.5]
[null,null,"GL32c",13500,400,null,19.5,24.5,32,3.5]
[null,null,"GL32h ",14200,440,null,25.6,32,32,3.5]
[null,"Sperrholz","F20/10 E40/20",4000,350]
[null,null,"F20/15 E30/25",4000,350]
[null,null,"F40/30 E60/40",4400,600]
[null,null,"F50/25 E70/25",5500,600]
[null,null,"F60/10 E90/10",5500,600]
[null,"Spanplatte P6","t >6 bis 13",2500,650,null,10.5,14.1,16.5,7.8]
[null,null,"t >13 bis 20",2400,600,null,9.5,13.3,15,7.3]
[null,null,"t >20 bis 25",2100,550,null,8.5,12.8,13.3,6.8]
[null,null,"t >25 bis 32",1900,550,null,8.3000000000000007,12.2,12.5,6.5]
[null,null,"t >32 bis 40 ",1800,500,null,7.8,11.9,11.7,6]
[null,null,"t >40 ",1700,500,null,7.5,10.4,10,5.5]
[]
[null,"Beton","C12/15",27000,2500,null,1.6,12,20]
[null,null,"C16/20",29000,2500,null,1.9,16,24]
[null,null,"C20/25",30000,2500,null,2.2000000000000002,20,28]
[null,null,"C25/30",31000,2500,null,2.6,25,33]
[null,null,"C30/37",33000,2500,null,2.9,30,38]
[null,null,"C35/45",34000,2500,null,3.2,35,43]
[null,null,"C40/50",35000,2500,null,3.5,40,48]
[null,null,"C45/55",36000,2500,null,3.8,45,53]
[null,null,"C50/60",37000,2500,null,4.0999999999999996,50,58]

{"sheet":"Statisches_System","index":10,"n_rows":13,"n_cols":6,"rows_kept":13,"cut":false,"hidden":true,"merged":[]}
[]
[]
[]
[null,null,"Tragsystem","Abstand M=0-Punkte","Durchbiegung w"]
[null,null,"Einfeldträger",{"$f":"'Gamma-Verfahren_nach_DIN1052'!$D$13","v":6},{"$f":"('Gamma-Verfahren_nach_DIN1052'!G10*('Gamma-Verfahren_nach_DIN1052'!D13:E13)^4)/(76.8*'Gamma-Verfahren_nach_DIN1052'!E167)","v":{"$error":"#DIV/0!"}},{"$error":"#DIV/0!"}]
[null,null,"Durchlaufträger",{"$f":"0.8*'Gamma-Verfahren_nach_DIN1052'!$D$13","v":4.8000000000000007}]
[null,null,"Kragarm",{"$f":"2*'Gamma-Verfahren_nach_DIN1052'!$D$13","v":12}]
[]
[]
[null,null,"Anzahl Querschnitte","Querschnittstypen"]
[null,null,1,"A"]
[null,null,2,"B"]
[null,null,3,"C"]