{"text_format":"1","workbook":"xlsx","n_sheets":2,"sheets":["Variante 1","Variante 2"],"not_rendered":{"charts":0,"images":1,"macros":1,"external_links":0,"defined_names":57,"comments":2,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Variante 1","index":0,"n_rows":32,"n_cols":18,"rows_kept":32,"cut":false,"hidden":false,"merged":[[17,9,17,12],[18,9,18,12],[19,9,19,12],[20,9,20,12],[25,9,25,12],[1,9,1,16],[1,0,1,1],[15,9,15,12],[16,9,16,12],[9,0,9,5],[12,0,12,5],[14,0,14,5],[16,0,16,5],[25,0,25,5],[26,0,26,5],[31,0,31,2],[31,3,31,5],[0,0,0,6],[20,0,20,5]]}
["Bauteile ohne rechnerisch erforderliche Querkraftbewehrung\nnach EN 1992-1-1:2004 und DIN EN 1992-1-1/NA:2013-04"]
["Betonfestigkeitsklasse:",null,"C20/25",null,null,null,null,null,null,"Werstoffkennwerte für Beton in [N/mm2]"]
[null,"αct = ",{"$f":"m_alct","v":0.85},"[-]",null,null,null,null,null,"αct = ",0.85]
[null,"γc = ",{"$f":"m_gammac","v":1.5},"[-]",null,null,null,null,null,"γc = ",1.5]
[null,"fck =",{"$f":"VLOOKUP(m_strfck,Werkstoffkennwerte,2,FALSE)","v":20},"[N/mm2]",null,null,null,null,null,null,"fck","fck,cube","fcm","fcd","fctm","fctd","Ecm","ρw,min [‰]"]
[null,"fcd =",{"$f":"VLOOKUP(m_strfck,Werkstoffkennwerte,5,FALSE)","v":11.333333333333334},"[N/mm2]",null,null,null,null,null,"C12/15",12,15,{"$f":"K6+8","v":20},{"$f":"m_alct*K6/m_gammac","v":6.8},{"$f":"POWER(K6,2/3)*0.3","v":1.5724448365253381},{"$f":"0.7*O6*m_alct/m_gammac","v":0.62373645182171733},27000,{"$f":"0.16*O6/500*1000","v":0.50318234768810821}]
[null,"VEd =",75,"[kN]",null,null,null,null,null,"C16/20",16,20,{"$f":"K7+8","v":24},9.0666666666666664,{"$f":"POWER(K7,2/3)*0.3","v":1.9048812623618392},0.75560290073686287,29000,{"$f":"0.16*O7/500*1000","v":0.60956200395578852}]
[null,"h =",20,"[cm]",null,null,null,null,null,"C20/25",20,25,28,11.333333333333334,2.2104188991842313,0.87679949667641166,30000,0.70733404773895403]
[null,"b =",90,"[cm]",null,null,null,null,null,"C25/30",25,30,33,14.166666666666666,2.5649639200150443,1.0174356882726341,31000,0.82078845440481418]
["VRd,c = [CRdc · k · (100 · ρl · fck )1/3 + k1 · σcp] · bw · d",null,null,null,null,null,null,null,null,"C30/37",30,37,38,17,2.896468153816889,1.1489323676806993,33000,0.92686980922140449]
[" ","bw =",90,"[cm]",null,null,null,null,null,"C35/45",35,45,43,19.833333333333332,3.2099624416952368,1.2732851018724438,34000,1.0271879813424758]
[null,"d =",19,"[cm]",null,null," ",null,null,"C40/50",40,50,48,22.666666666666668,3.5088212858554391,1.3918324433893241,35000,1.1228228114737406]
["CRdc = 0.15 / γc",null,null,null,null,null,null,null,null,"C45/55",45,55,53,25.5,3.7954469938578708,1.5055273075636217,36000,1.2145430380345186]
[null,"CRdc =",{"$f":"0.15/m_gammac","v":9.9999999999999992E-2},"[-]",null,null,null,null,null,"C50/60",50,60,{"$f":"K14+8","v":58},{"$f":"m_alct*K14/m_gammac","v":28.333333333333332},{"$f":"POWER(K14,2/3)*0.3","v":4.0716264248923588},{"$f":"0.7*O14*m_alct/m_gammac","v":1.615078481873969},37000,1.3029204559655549]
["k = 1 + (200 / d)1/2 ≤ 2"]
[null,"k =",{"$f":"MIN(1+SQRT(2000/m_d),2)","v":2},"[-]",null,null,null,null,null,"Formeln für Werkstoffkennwerte"]
["ρl = Asl / (bw · d) ≤ 0,02",null,null,null,null,null,null,null,null,"fcm = fck + 8 [N/mm2]"]
[null,"Asl =",4.43,"[cm2]",null,null,null,null,null,"fcd = αct · fck / γc"]
[null,"ρl =",{"$f":"MIN(m_Asl/(m_bw*m_d),0.02)","v":2.5906432748538009E-3},"[-]",null,null,null,null,null,"fctm = 0.3 · fck2/3"]
[null,"k1 =",0.12,"[-]",null,null,null,null,null,"fctd = 0.7 · fctm · αct  / γc"]
["σcp = NEd / Ac < 0,2 · fcd",null,null,null,null,null,null,null,null,"ρw,min = 0.16 · fctm / fyk"]
[null,"NEd =",0,"[kN]"]
[null,"Ac =",1800,"[cm2]",null,null,null,null,null,"Mindestquerkraftbewehrung min asw"]
[null,"σcp =",{"$f":"MIN(m_NEd*10/m_Ac,0.2*m_fcd)","v":0},"[N/mm2]",null,null,null,null,null,"ρw,min =",{"$f":"VLOOKUP(m_strfck,Werkstoffkennwerte,9,FALSE)","v":0.70733404773895403},"[‰]"]
[null,"VRd,c =",{"$f":"(m_CRdc*m_k*POWER(100*m_rhol*m_fck,1/3)+m_k1*m_sigmacp)/10*m_bw*m_d","v":59.179593343894886},"[kN]",null,null,null,null,null,"b / h =",{"$f":" m_b/m_h","v":4.5},"[-]"]
["VRd,c,min = (vmin + k1 · σcp) · bw · d",null,null,null,null,null,null,null,null,"min asw = ρw,min · bw · sin α"]
["vmin = κ1 / γc · (k3  · fck )1/2",null,null,null,null,null,null,null,null,"min asw =",{"$f":"IF(m_bh<4,1,IF(m_bh>5,0,(1-(m_bh-4))))*m_rhowmin*m_bw*SIN(90*PI()/180)/10","v":3.1830032148252934},"[cm2/m]"]
[null,"κ1 =",{"$f":"IF(m_d<=60,0.0525,IF(m_d>=80,0.0375,0.0525-(m_d-60)*(0.0525-0.0375)/(80-60)))","v":5.2499999999999998E-2},"[-]"]
[null,"vmin =",{"$f":"m_kappa1/m_gammac*SQRT(POWER(m_k,3)*m_fck)","v":0.44271887242357311},"[N/mm2]"]
[null,"VRd,c,min =",{"$f":"(m_vmin+m_k1*m_sigmacp)/10*m_bw*m_d","v":75.704927184431},"[kN]"]
[]
["VEd ≤ VRd,c oder VEd ≤ VRd,c,min ",null,null,{"$f":"IF(OR(m_VEd<=m_VRdc,m_VEd<=m_VRdcmin),\" Nachweis wurde erfüllt!\",\" Nachweis wurde nicht erfüllt!\")","v":" Nachweis wurde erfüllt!"}]

{"sheet":"Variante 2","index":1,"n_rows":34,"n_cols":18,"rows_kept":34,"cut":false,"hidden":false,"merged":[[28,0,28,5],[33,0,33,2],[33,3,33,5],[18,0,18,5],[14,0,14,5],[20,9,20,12],[25,9,25,12],[19,9,19,12],[0,0,0,6],[1,9,1,16],[10,0,10,5],[15,9,15,12],[16,9,16,12],[17,9,17,12],[18,9,18,12],[1,0,1,1],[23,0,23,5],[24,0,24,5]]}
["Bauteile ohne rechnerisch erforderliche Querkraftbewehrung\nnach EN 1992-1-1:2004 und DIN EN 1992-1-1/NA:2013-04"]
["Betonfestigkeitsklasse:",null,"C20/25",null,null,null,null,null,null,"Werstoffkennwerte für Beton in [N/mm2]"]
[null,"αct = ",{"$f":"m_alct","v":0.85},"[-]",null,null,null,null,null,"αct = ",0.85]
[null,"γc = ",{"$f":"m_gammac","v":1.5},"[-]",null,null,null,null,null,"γc = ",1.5]
[null,"fck =",{"$f":"VLOOKUP(m_strfck,Werkstoffkennwerte,2,FALSE)","v":20},"[N/mm2]",null,null,null,null,null,null,"fck","fck,cube","fcm","fcd","fctm","fctd","Ecm","ρw,min [‰]"]
[null,"fcd =",{"$f":"VLOOKUP(m_strfck,Werkstoffkennwerte,5,FALSE)","v":11.333333333333334},"[N/mm2]",null,null,null,null,null,"C12/15",12,15,{"$f":"K6+8","v":20},{"$f":"m_alct*K6/m_gammac","v":6.8},{"$f":"POWER(K6,2/3)*0.3","v":1.5724448365253381},{"$f":"0.7*O6*m_alct/m_gammac","v":0.62373645182171733},27000,{"$f":"0.16*O6/500*1000","v":0.50318234768810821}]
[null,"fctd =",{"$f":"VLOOKUP(m_strfck,Werkstoffkennwerte,7,FALSE)","v":0.87679949667641166},"[N/mm2]",null,null,null,null,null,"C16/20",16,20,{"$f":"K7+8","v":24},9.0666666666666664,{"$f":"POWER(K7,2/3)*0.3","v":1.9048812623618392},0.75560290073686287,29000,{"$f":"0.16*O7/500*1000","v":0.60956200395578852}]
[null,"VEd =",32.4,"[kN]",null,null,null,null,null,"C20/25",20,25,28,11.333333333333334,2.2104188991842313,0.87679949667641166,30000,0.70733404773895403]
[null,"h =",18,"[cm]",null,null,null,null,null,"C25/30",25,30,33,14.166666666666666,2.5649639200150443,1.0174356882726341,31000,0.82078845440481418]
[null,"b =",100,"[cm]",null,null,null,null,null,"C30/37",30,37,38,17,2.896468153816889,1.1489323676806993,33000,0.92686980922140449]
["VRd,c = I · bw / S · (fctd · fctd + αl · σcp · fctd)1/2 ",null,null,null,null,null,null,null,null,"C35/45",35,45,43,19.833333333333332,3.2099624416952368,1.2732851018724438,34000,1.0271879813424758]
[" ","I =",48600,"[cm4]",null,null," ",null,null,"C40/50",40,50,48,22.666666666666668,3.5088212858554391,1.3918324433893241,35000,1.1228228114737406]
[null,"bw =",100,"[cm]",null,null,null,null,null,"C45/55",45,55,53,25.5,3.7954469938578708,1.5055273075636217,36000,1.2145430380345186]
[null,"S =",4050,"[cm3]",null,null,null,null,null,"C50/60",50,60,{"$f":"K14+8","v":58},{"$f":"m_alct*K14/m_gammac","v":28.333333333333332},{"$f":"POWER(K14,2/3)*0.3","v":4.0716264248923588},{"$f":"0.7*O14*m_alct/m_gammac","v":1.615078481873969},37000,1.3029204559655549]
["αl = lx / lpt2 ≤ 1,0"]
[null,"lx =",1,"[m]",null,null,null,null,null,"Formeln für Werkstoffkennwerte"]
[null,"lpt2 =",1,"[m]",null,null,null,null,null,"fcm = fck + 8 [N/mm2]"]
[null,"αl =",{"$f":"MIN(m_lx/m_lpt2,1)","v":1},"[-]",null,null,null,null,null,"fcd = αct · fck / γc"]
["σcp = NEd / Ac < 0,2 · fcd",null,null,null,null,null,null,null,null,"fctm = 0.3 · fck2/3"]
[null,"NEd =",0,"[kN]",null,null,null,null,null,"fctd = 0.7 · fctm · αct  / γc"]
[null,"Ac =",1800,"[cm2]",null,null,null,null,null,"ρw,min = 0.16 · fctm / fyk"]
[null,"σcp =",{"$f":"MIN(m_NEd*10/m_Ac,0.2*m_fcd)","v":0},"[N/mm2]"]
[null,"VRd,c =",{"$f":"(m_I/m_S*m_bw*SQRT(m_fctd*m_fctd+m_all*m_sigmacp*m_fctd)/10)","v":105.21593960116941},"[kN]",null,null,null,null,null,"Mindestquerkraftbewehrung min asw"]
["VRd,c,min = (vmin + k1 · σcp) · bw · d",null,null,null,null,null,null,null,null,"ρw,min =",{"$f":"VLOOKUP(m_strfck,Werkstoffkennwerte,9,FALSE)","v":0.70733404773895403},"[‰]"]
["vmin = κ1 / γc · (k3  · fck )1/2",null,null,null,null,null,null,null,null,"b / h =",{"$f":" m_b/m_h","v":5.5555555555555554},"[-]"]
[null,"κ1 =",{"$f":"IF(m_d<=60,0.0525,IF(m_d>=80,0.0375,0.0525-(m_d-60)*(0.0525-0.0375)/(80-60)))","v":5.2499999999999998E-2},"[-]",null,null,null,null,null,"min asw = ρw,min · bw · sin α"]
[null,"k1 =",0.12,"[-]",null,null,null,null,null,"min asw =",{"$f":"IF(m_bh<4,1,IF(m_bh>5,0,(1-(m_bh-4))))*m_rhowmin*m_bw*SIN(90*PI()/180)/10","v":0},"[cm2/m]"]
[null,"d =",18,"[cm]"]
["k = 1 + (200 / d)1/2 ≤ 2"]
[null,"k =",{"$f":"MIN(1+SQRT(2000/m_d),2)","v":2},"[-]"]
[null,"vmin =",{"$f":"m_kappa1/m_gammac*SQRT(POWER(m_k,3)*m_fck)","v":0.44271887242357311},"[N/mm2]"]
[null,"VRd,c,min =",{"$f":"(m_vmin+m_k1*m_sigmacp)/10*m_bw*m_d","v":79.689397036243165},"[kN]"]
[]
["VEd ≤ VRd,c oder VEd ≤ VRd,c,min ",null,null,{"$f":"IF(OR(m_VEd<=m_VRdc,m_VEd<=m_VRdcmin),\" Nachweis wurde erfüllt!\",\" Nachweis wurde nicht erfüllt!\")","v":" Nachweis wurde erfüllt!"}]