{"text_format":"1","workbook":"xlsx","n_sheets":3,"sheets":["fortia","polla fortia","Sheet3"],"not_rendered":{"charts":7,"images":0,"macros":1,"external_links":0,"defined_names":24,"comments":0,"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":"fortia","index":0,"n_rows":38,"n_cols":24,"rows_kept":38,"cut":false,"hidden":false,"merged":[[3,8,4,8]]}
["Πρόσθεση φορτίων"]
[null,null,null,null,null,"φορτία",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Γωνία μεταξύ -3Q και άξονα Χ"]
["Q",1,null,"FQq",{"$f":"B3*B4","v":0.5},"3Q",{"$f":"3*B3","v":3},null,"F3Qq",{"$f":"G3*G4","v":1.5},"Συνισταμένη F3Qq και F-3Qq"]
["q",0.5,null,null,null,"q",0.5,null,"γωνία -3Q με άξονα χ",47,{"$f":"2*J3*COS(RADIANS(K6))","v":1.1962472067757388},null,null,null,null,null,null,null,null,null,null,{"$f":"CONCATENATE(\"Γωνία = \",J4)","v":"Γωνία = 47"}]
["s",1,null,null,null,null,null,null,null,{"$f":"180-J4","v":133},"Γωνία με Qq"]
["θ",50,{"$f":"RADIANS(B6)","v":0.87266462599716477},"theta",null,null,null,null,null,"FI",{"$f":"J5/2","v":66.5}]
["γωνία μεταξύ άξονα",null,null,null,null,"F12",{"$f":"2*E3*COS(C6)","v":0.64278760968653936},{"$f":"G7+E3","v":1.1427876096865393}]
["και φορτίων (ίδια για κύκλο και ευθεία)"]
[null,null,"3 φορτία σε κύκλο",null,null,{"$f":"CONCATENATE(\"γωνία =\",B6)","v":"γωνία =50"},null,null,null,null,"3 φορτία σε ευθεία",null,null,null,null,"1 θετικό 3Q και ένα αρνητικό -3Q"]
[]
[null,"Βέλος FQ1",null,"Βέλος -FQ1",null,"Βέλος κεντρικό",null,"Ολική δύναμη",null,"Βέλος FQ1",null,"Βέλος -FQ1",null,"Βέλος κεντρικό",null,"Ολική δύναμη",null,null,"διανυσμα f3Q",null,"διάνυσμα-f3Q",null,"Συνισταμένη των δύο"]
[null,"x","y","x","y","x","y","x","y","x","y","x","y","x","y","x","y",null,"X","Y","Χ","Υ","Χ","Υ"]
[null,{"$f":"0","v":0},0,{"$f":"0","v":0},0,0,0,{"$f":"SUM(F13,D13,B13)","v":0},{"$f":"SUM(G13,E13,C13)","v":0},{"$f":"0","v":0},0,{"$f":"0","v":0},0,0,0,{"$f":"SUM(N13,L13,J13)","v":0},{"$f":"SUM(O13,M13,K13)","v":0},null,0,0,0,0,0,0]
[null,{"$f":"FQq*SIN(theta)","v":0.38302222155948901},{"$f":"FQq*COS(theta)","v":0.32139380484326968},{"$f":"-FQq*SIN(theta)","v":-0.38302222155948901},{"$f":"FQq*COS(theta)","v":0.32139380484326968},0,{"$f":"FQq","v":0.5},{"$f":"SUM(F14,D14,B14)","v":0},{"$f":"SUM(G14,E14,C14)","v":1.1427876096865393},{"$f":"FQq*SIN(theta)*COS(theta)^2","v":0.15825555538987227},{"$f":"FQq*COS(theta)*COS(theta)^2","v":0.13279217815939742},{"$f":"-FQq*SIN(theta)*COS(theta)^2","v":-0.15825555538987227},{"$f":"FQq*COS(theta)*COS(theta)^2","v":0.13279217815939742},0,{"$f":"FQq","v":0.5},{"$f":"SUM(N14,L14,J14)","v":0},{"$f":"SUM(O14,M14,K14)","v":0.76558435631879496},null,0,{"$f":"F3Qq","v":1.5},{"$f":"F3Qq*SIN(RADIANS(J4))","v":1.0970305524287558},{"$f":"-F3Qq*COS(RADIANS(J4))","v":-1.0229975400937477},{"$f":"U14+S14","v":1.0970305524287558},{"$f":"V14+T14","v":0.47700245990625234}]
[null,{"$f":"-C14/20+18/20*B14","v":0.32865030916137661},{"$f":"B14/10+18/20*C14","v":0.32755664651489164},{"$f":"-E14/20+18/20*D14","v":-0.36078968964570357},{"$f":"D14/10+18/20*E14","v":0.2509522022029938},{"$f":"-G14/20+18/20*F14","v":-2.5000000000000001E-2},{"$f":"F14/10+18/20*G14","v":0.45},{"$f":"-I14/60+18/20*H14","v":-1.9046460161442322E-2},{"$f":"H14/10+18/20*I14","v":1.0285088487178853},{"$f":"J$14-Rx_3*COS(Fi_1)+Ry_3*SIN(Fi_1)","v":0.13545421250149434},{"$f":"K$14-Rx_3*SIN(Fi_1)-Ry_3*COS(Fi_1)","v":7.0146003440336863E-2},{"$f":"L$14-Rx_4*COS(Fi_1)+Ry_4*SIN(Fi_1)","v":-9.2601705189058386E-2},{"$f":"M$14-Rx_4*SIN(Fi_1)-Ry_4*COS(Fi_1)","v":0.12121563298160207},{"$f":"N14-N24","v":4.9999999999999982E-2},{"$f":"IF(C4>0,O14+O24,O14-O24)","v":0.41339745962155611},{"$f":"P14-P24","v":4.9999999999999982E-2},{"$f":"IF(E4>0,Q14+Q23,Q14-Q23)","v":0.67898181594035112},null,{"$f":"S$14-Rx*COS(Fi_1)+Ry*SIN(Fi_1)","v":9.9999999999999978E-2},{"$f":"T$14-Rx*SIN(Fi_1)-Ry*COS(Fi_1)","v":1.3267949192431123},{"$f":"U$14-Rx_1*COS(Fi_1)+Ry_1*SIN(Fi_1)","v":0.90215653947170882},{"$f":"V$14-Rx_1*SIN(Fi_1)-Ry_1*COS(Fi_1)","v":-0.97800732922497469},{"$f":"W$14-Rx_2*COS(Fi_1)+Ry_2*SIN(Fi_1)","v":0.97806599507848746},{"$f":"X$14-Rx_2*SIN(Fi_1)-Ry_2*COS(Fi_1)","v":0.31623108778280884}]
[null,{"$f":"C14/20+18/20*B14","v":0.36078968964570357},{"$f":"-B14/20+18/20*C14","v":0.27010331328096826},{"$f":"E14/20+18/20*D14","v":-0.32865030916137661},{"$f":"-D14/20+18/20*E14","v":0.30840553543691718},{"$f":"G14/20+18/20*F14","v":2.5000000000000001E-2},{"$f":"-F14/20+18/20*G14","v":0.45},{"$f":"I14/60+18/20*H14","v":1.9046460161442322E-2},{"$f":"-H14/20+18/20*I14","v":1.0285088487178853},{"$f":"J$14-Rx_3*COS(Fi_1)+Ry_3*SIN(-Fi_1)","v":9.2601705189058386E-2},{"$f":"K14-Rx_3*SIN(-Fi_1)-Ry_3*COS(-Fi_1)","v":0.12121563298160207},{"$f":"L$14-Rx_4*COS(Fi_1)+Ry_4*SIN(-Fi_1)","v":-0.13545421250149434},{"$f":"M14-Rx_4*SIN(-Fi_1)-Ry_4*COS(-Fi_1)","v":7.0146003440336863E-2},{"$f":"N14-N27","v":-4.9999999999999989E-2},{"$f":"IF(C4>0,O14+O27,O14-O27)","v":0.41339745962155611},{"$f":"P14-P27","v":-4.9999999999999989E-2},{"$f":"IF(E4>0,Q14+Q27,Q14-Q27)","v":0.67898181594035112},null,{"$f":"S$14-Rx*COS(Fi_1)+Ry*SIN(-Fi_1)","v":-0.1},{"$f":"T14-Rx*SIN(-Fi_1)-Ry*COS(-Fi_1)","v":1.3267949192431123},{"$f":"U$14-Rx_1*COS(Fi_1)+Ry_1*SIN(-Fi_1)","v":1.0385562114842084},{"$f":"V14-Rx_1*SIN(-Fi_1)-Ry_1*COS(-Fi_1)","v":-0.83173658890114055},{"$f":"W$14-Rx_2*COS(Fi_1)+Ry_2*SIN(-Fi_1)","v":0.89831618129343827},{"$f":"X14-Rx_2*SIN(-Fi_1)-Ry_2*COS(-Fi_1)","v":0.49964310265983369}]
[null,{"$f":"B14","v":0.38302222155948901},0.32139380484326968,-0.38302222155948901,0.32139380484326968,0,0.5,0,1.1427876096865393,0.15825555538987227,0.13279217815939742,-0.15825555538987227,0.13279217815939742,0,0.5,0,0.76558435631879496,null,{"$f":"S14","v":0},1.5,1.0970305524287558,-1.0229975400937477,{"$f":"W14","v":1.0970305524287558},0.47700245990625234]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Fi_1",{"$f":"RADIANS(30)","v":0.52359877559829882}]
[null,"Βέλος -FQ1",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ΔΙΑΝΥΣΜΑΤΑ",null,"R_",0.2]
[null,"x","y",null,null,null,null,null,"Rx_3",{"$f":"R_*SIN(theta)/3","v":5.1069629541265205E-2},null,null,null,{"$f":"ABS(ATAN2(N14,O14))","v":1.5707963267948966},null,{"$f":"ABS(ATAN2(P14,Q14))","v":1.5707963267948966},"diefth1",{"$f":"PI()/2","v":1.5707963267948966},"dR",0.1]
[null,{"$f":"0","v":0},0,null,null,null,null,null,"Ry_3",{"$f":"R_*COS(theta)/3","v":4.2852507312435957E-2},null,null,null,{"$f":"RADIANS(30)","v":0.52359877559829882},null,{"$f":"RADIANS(30)","v":0.52359877559829882},null,"βέλος σε υ","Rx",{"$f":"R_*COS(R20)","v":1.22514845490862E-17}]
[null,{"$f":"-FQq*SIN(theta)","v":-0.38302222155948901},{"$f":"FQq*COS(theta)","v":0.32139380484326968},null,null,null,null,null,"Rx_4",{"$f":"-R_*SIN(theta)/3","v":-5.1069629541265205E-2},null,null,null,{"$f":"N20+N21","v":2.0943951023931953},null,{"$f":"P20+P21","v":2.0943951023931953},null,null,"Ry",{"$f":"R_*SIN(diefth1)","v":0.2}]
[null,null,null,null,null,null,null,null,"Ry_4",{"$f":"R_*COS(theta)/3","v":4.2852507312435957E-2},null,null,null,{"$f":"SQRT(N14^2+O14^2)","v":0.5},null,{"$f":"SQRT(P14^2+Q14^2)","v":0.76558435631879496},{"$f":"0.1*SIN(P22)","v":8.6602540378443879E-2},"βέλος της -3Q","Rx_1",{"$f":"R_*COS(diefth2)","v":0.14627074032383411}]
[null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"0.1*SIN(L22)","v":0},{"$f":"0.1*COS(N22)","v":-4.9999999999999982E-2},{"$f":"0.1*SIN(N22)","v":8.6602540378443879E-2},{"$f":"0.1*COS(P22)","v":-4.9999999999999982E-2},"diefth2",{"$f":"ATAN2(U14,V14)","v":-0.75049157835756164},"Ry_1",{"$f":"R_*SIN(diefth2)","v":-0.1363996720124997}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"N20","v":1.5707963267948966},null,{"$f":"P20","v":1.5707963267948966},null,"βέλος συνισταμένης","Rx_2",{"$f":"R_*COS(diefth3)","v":0.18341201487702483}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"N20-N21","v":1.0471975511965979},null,{"$f":"P20-P21","v":1.0471975511965979},"diefth3",{"$f":"ATAN2(W14,X14)","v":0.41015237421866751},"Ry_2",{"$f":"R_*SIN(diefth3)","v":7.9749813785049251E-2}]
[null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"0.1*SIN(L26)","v":0},{"$f":"0.1*COS(N26)","v":4.9999999999999989E-2},{"$f":"0.1*SIN(N26)","v":8.6602540378443879E-2},{"$f":"0.1*COS(P26)","v":4.9999999999999989E-2},{"$f":"0.1*SIN(P26)","v":8.6602540378443879E-2}]
[]
[]
[]
[]
[]
[]
["Σχέδιοφορτίων σε κύκλο",null,null,null,null,null,null,null,"Σχέδιο φορτίων που βρίσκονται σε ευθεία"]
["χ","ψ",null,null,null,null,null,null,"χ","ψ"]
[0,{"$f":"-s","v":-1},null,null,null,null,null,null,0,{"$f":"-s","v":-1}]
[{"$f":"-s*SIN(theta)","v":-0.76604444311897801},{"$f":"-s*COS(theta)","v":-0.64278760968653936},null,null,null,null,null,null,{"$f":"-s/TAN(theta)","v":-0.83909963117728004},{"$f":"-s","v":-1}]
[{"$f":"s*SIN(theta)","v":0.76604444311897801},{"$f":"-s*COS(theta)","v":-0.64278760968653936},null,null,null,null,null,null,{"$f":"s/TAN(theta)","v":0.83909963117728004},{"$f":"-s","v":-1}]

{"sheet":"polla fortia","index":1,"n_rows":97,"n_cols":42,"rows_kept":97,"cut":false,"hidden":false,"merged":[[9,14,11,23],[0,14,1,26]]}
["10 fortia","gonia",40,"rr",0.1,"μήκος πλευρών βέλους",null,null,null,null,null,null,null,null,{"$f":"O10","v":"σύγκριση της δύναμης που ασκεί το αρνητικό φορτίο - 21 Q με τη συνισταμένη 21 φορτίων Q τοποθετημένα σε τόξο κύκλου με γωνία =2 X40° και της συνισταμένης των δυνάμεων των μικρών φορτίων"}]
["Q",1,"qmikro",0.5]
["Fx","Fy",1,null,2,null,3,null,4,null,5,null,6,null,7,null,8,null,9,null,10,null,11,null,12,null,13,null,14,null,15,null,16,null,17,null,18,null,19,null,20]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"O13","v":"σύγκριση της δύναμης που ασκεί το αρνητικό φορτίο - 21 Q με τη συνισταμένη 21 φορτίων Q τοποθετημένα σε τόξο κύκλου με γωνία =2 X40° και της συνισταμένης των δυνάμεων των μικρών φορτίων"}]
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