{"text_format":"1","workbook":"xlsx","n_sheets":3,"sheets":["ReadMe","応答計算","固有値解析"],"not_rendered":{"charts":5,"images":0,"macros":1,"external_links":0,"defined_names":0,"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":"ReadMe","index":0,"n_rows":25,"n_cols":7,"rows_kept":25,"cut":false,"hidden":false,"merged":[]}
["2自由度系の地震応答解析",null,null,null,"ver.2.5","2020-08-16","伊津野和行"]
[null,null,null,null,null,null,"立命館大学理工学部環境都市工学科"]
["概要",null,null,null,null,null,"izuno@se.ritsumei.ac.jp"]
["【応答計算】","非線形2自由度系の地震応答を計算します．"]
[null,"橋梁をイメージしており，B52セルで1層目（橋脚）は，線形，バイリニア，剛性劣化Clough型を，"]
[null,"2層目（支承）はB53セルで，線形，バイリニア，ハードニングを考慮したバイリニア型を設定することができます．"]
[null,"B2～B14セルの値を入力してください．ゴム支承のハードニングを考慮する場合は，B15とC15セルも入力してください．"]
[null,"減衰は，部材の減衰定数からひずみエネルギー比例減衰を計算しています．"]
[null,"初期剛性を用いた固有周期が，B25とB26セルで計算されます．"]
[null,"F列に地震加速度波形（単位：cm/s/s＝gal）を貼り付け，計算実行ボタンを押せば計算が実行されます．"]
[null,"最大応答はB54～B62セルに出力されます．"]
[null,"数値積分には，安定した陽解法である有理ルンゲ・クッタ法を用いています．"]
[null,"A. Wambecq: Rational Runge-Kutta methods for solving systems of ordinary differential equations, Computing, Vol. 20, Issue 4, pp 333-342, 1978."]
[]
["【固有値解析】","応答計算シートに入力された値を元に，固有値や固有振動モードを計算します．"]
[null,"入力は，応答計算シートにしてください．"]
[]
["【改版履歴】"]
["2018-10-03","ver. 1.0","初版"]
["2019-01-20","ver. 2.0","解法を有理ルンゲ・クッタ法に変更"]
["2019-01-23","ver. 2.1","bug fix"]
["2019-04-02","ver. 2.2","計算進捗状況を表示するのに時間がかかっていたので方法を変更し計算速度向上"]
["2019-07-05","ver. 2.3","地震波の最初が0だとエラーになるのを回避"]
["2019-10-11","ver. 2.4","減衰行列の計算が間違っていたのを修正"]
["2020-08-16","ver. 2.5","加速度の計算方法を修正"]

{"sheet":"応答計算","index":1,"n_rows":3001,"n_cols":15,"rows_kept":3001,"cut":false,"hidden":false,"merged":[]}
["入力データ",null,null,null,"時間 (s)","地震加速度 z(t) (cm/s/s)","Acc. of 1st story (m/s/s)","Acc. of 2nd story (m/s/s)","Vel. of 1st story (m/s)","Vel. of 2nd story (m/s)","Dis. of 1st story (m)","Dis. of 2nd story (m)","Drift of 2nd story (m)","Restoring force of 1st story (kN)","Restoring force of 2nd story (kN)"]
["データ数",3000,null,null,{"$f":"$B$3","v":0.01},0,0,0,0,0,0,0,0,0,0]
["時間刻み",0.01,"s",null,{"$f":"E2+$B$3","v":0.02},0.79300000000000004,0.30017146129986327,1.2377156773075613E-4,2.2891160940836782E-3,-8.3582235944927553E-4,-1.3398878988706193E-3,-1.3552356620866442E-3,-1.2373906762742784E-5,-603.46434460607873,-0.27572617555322432]
["橋脚の質量：m1",2000,"t",null,{"$f":"E3+$B$3","v":0.03},0.79300000000000004,0.28988501919817333,3.0037272025939919E-4,5.1613774175240648E-3,-9.1300782288350403E-4,-1.3025504270659041E-3,-1.3639811865486838E-3,-5.5501584635247233E-5,-587.30884192089593,-1.1678788067381829]
["桁の質量：m2",6000,"t",null,0.04,0.79400000000000004,0.27306144769363522,5.7209987628972173E-4,7.8944405545213515E-3,-9.8795415578826562E-4,-1.2371345515937986E-3,-1.373487935967369E-3,-1.2760789919902325E-4,-558.48653242821979,-2.6382561785912548]
["橋脚の減衰定数：h1",0.02,null,null,0.05,0.79400000000000004,0.25013470018602968,9.3270262856342797E-4,1.0425200480610132E-2,-1.0597325623823474E-3,-1.1453522002043447E-3,-1.3837289388996742E-3,-2.2701740528900931E-4,-517.75375402672364,-4.6527045993557428]
["支承の減衰定数：h2",0.02,null,null,6.0000000000000005E-2,0.79400000000000004,0.2216787442731567,1.3739138903997358E-3,1.269571014591383E-2,-1.1274527698303134E-3,-1.0295220558974448E-3,-1.3946678060716346E-3,-3.5143424387978407E-4,-466.14084121245207,-7.1647126890296517]
["橋脚の初期剛性：k1",450000,"kN/m",null,7.0000000000000007E-2,0.79400000000000004,0.18839361602713664,1.8856559258450664E-3,1.4654428726812304E-2,-1.1903622583226685E-3,-8.925125172900021E-4,-1.4062599182308082E-3,-4.9799821963007838E-4,-404.92690384486548,-10.116546499573817]
["支承の初期剛性：k2",20000,"kN/m",null,0.08,0.79500000000000004,0.15108868386450125,2.4562824283669285E-3,1.6257386645604409E-2,-1.2478725506387502E-3,-7.3767316586004889E-4,-1.4184536342082854E-3,-6.6335353247041269E-4,-335.60917123452322,-13.440636226647019]
["橋脚の降伏後剛性：ky1",100000,"kN/m",null,0.09,0.79500000000000004,0.11066412439562863,3.0728363876887242E-3,1.7469307907140279E-2,-1.2994535592998862E-3,-5.6875902008751559E-4,-1.4311913429298643E-3,-8.4372527306664431E-4,-259.8688552340447,-17.061116464155202]
["支承の降伏後剛性：ky2",1000,"kN/m",null,9.9999999999999992E-2,0.79600000000000004,6.8094335633796424E-2,3.7212869626320816E-3,1.8264371769969416E-2,-1.3447242059795822E-3,-3.8986596269625798E-4,-1.4444078543502084E-3,-1.0349863210112747E-3,-179.54026138186953,-20.89517282567434]
["橋脚の降伏強度：y1",12000,"kN",null,0.10999999999999999,0.79600000000000004,2.4450177258956731E-2,4.3861675913208333E-3,1.8627140483408355E-2,-1.3833827499926754E-3,-2.055864515404068E-4,-1.4580131671158585E-3,-1.2325476896773953E-3,-96.654218967135719,-24.850857257532599]
["支承の降伏強度：y2",200,"kN",null,0.11999999999999998,0.79700000000000004,-1.8987166993020457E-2,5.0488215200097273E-3,1.8552516086798795E-2,-1.4151953486159386E-3,-2.1171191265167313E-5,-1.471873401271616E-3,-1.4308324583094801E-3,-13.655232424072562,-28.816568156835899]
["時間刻みの分割数",10,null,null,0.12999999999999998,0.79700000000000004,-6.1848147451066544E-2,5.7044956542146143E-3,1.8045185703515296E-2,-1.4407006801671011E-3,1.6176149357473424E-4,-1.4861285236342301E-3,-1.628390034020112E-3,68.740796508327662,-32.763335960816775]
["ハードニング開始点(m)とk2に対する倍率",100,1.5,null,0.13999999999999999,0.79800000000000004,-0.10290300128277745,6.3352912071059763E-3,1.7118454486136862E-2,-1.4598862805699818E-3,3.378102405405267E-4,-1.5006292082248975E-3,-1.8198137537062829E-3,148.16603864392943,-36.583151591773792]
["【出力】質量マトリックス",{"$f":"B4","v":2000},0,null,0.15,0.79800000000000004,-0.14113099869813867,6.926457533597297E-3,1.5795966148751252E-2,-1.4730271083849354E-3,5.0264958128041343E-4,-1.5152956858269797E-3,-2.0006058367728194E-3,222.63975957309677,-40.186287946100229]
[null,0,{"$f":"B5","v":6000},null,0.16,0.79900000000000004,-0.17564459333203555,7.4652111485569951E-3,1.4110870635934272E-2,-1.480593536362342E-3,6.5244157281851985E-4,-1.5300667025467682E-3,-2.166827302724661E-3,290.42465260663317,-43.494292519159451]
["剛性マトリックス",{"$f":"B8+B9","v":470000},{"$f":"-B9","v":-20000},null,0.17,0.8,-0.20565594363053621,7.9402125007237857E-3,1.2104663466786857E-2,-1.4832156117460737E-3,7.8374971478467181E-4,-1.5448888248259648E-3,-2.3149451080977526E-3,349.96437600585165,-46.436917674888655]
[null,{"$f":"-B9","v":-20000},{"$f":"B9","v":20000},null,0.18000000000000002,0.80100000000000005,-0.23048911650422627,8.3417297015907395E-3,9.8261775816623747E-3,-1.4815848989638922E-3,8.9359703559455063E-4,-1.5597156545698767E-3,-2.4418862833849564E-3,399.90812919982903,-48.953192398480006]
["a",{"$f":"B4*B5","v":12000000},null,null,0.19000000000000003,0.80200000000000005,-0.24959404693149495,8.6618409815287511E-3,7.3303323544435103E-3,-1.4764810281791964E-3,9.7952877267919116E-4,-1.5745083372391111E-3,-2.545101626743135E-3,439.13884280227182,-50.992684056549194]
["b",{"$f":"B18*B5+C19*B4","v":2860000000},null,null,0.20000000000000004,0.80300000000000005,-0.26255828851029545,8.8946033644039749E-3,4.6768040812077511E-3,-1.4687523293680997E-3,1.0396653053584191E-3,-1.5892362450591923E-3,-2.6226204982901153E-3,466.79722819429691,-52.516580910062771]
["c",{"$f":"B18*C19-C18*C18","v":9000000000},null,null,0.21000000000000005,0.80500000000000005,-0.26911562446681225,9.0361808879352457E-3,1.9285425276732117E-3,-1.4593502077590399E-3,1.0727419410296022E-3,-1.6038777104817347E-3,-2.6730927322186271E-3,482.29999292932416,-53.498515951986924]
["1次モード固有円振動数",{"$f":"SQRT((B21-SQRT(B21*B21-4*B20*B22))/2/B20)","v":1.7859276847860388},"rad/s",null,0.22000000000000006,0.80700000000000005,-0.26915127938520028,9.0849164523694303E-3,-8.4965881765048051E-4,-1.4492424631177279E-3,1.0781340998292318E-3,-1.6184208692445444E-3,-2.695816153870479E-3,485.35148599756769,-53.925102136712049]
["2次モード固有円振動数",{"$f":"SQRT((B21+SQRT(B21*B21-4*B20*B22))/2/B20)","v":15.334399096086162},"rad/s",null,0.23000000000000007,0.80900000000000005,-0.26270378786548265,9.041354462931233E-3,-3.5926565224761835E-3,-1.4393564303416136E-3,1.0558684433386615E-3,-1.6328632668377555E-3,-2.6907488612144372E-3,475.94903914936395,-53.796162522022136]
["1次固有周期：T1",{"$f":"2*PI()/B23","v":3.5181633392576792},"s",null,0.24000000000000007,0.81100000000000005,-0.24996316258732304,8.9082172004053377E-3,-6.2365290270605988E-3,-1.430601970302785E-3,1.0066184091095606E-3,-1.647211648512562E-3,-2.6585060887267253E-3,454.38130735023987,-53.124652039805994]
["2次固有周期：T2",{"$f":"2*PI()/B24","v":0.40974447500738775},"s",null,0.25000000000000006,0.81399999999999995,-0.23126546105886753,8.6903311640044237E-3,-8.7201203553244275E-3,-1.4239049578592777E-3,9.3168435307771464E-4,-1.6614818546126914E-3,-2.6003417537817978E-3,421.21967765645337,-51.936273266697363]
["1次モードのモード形：支承／橋脚",{"$f":"(B18-B4*B23^2)/(-C18)","v":23.181046230471477},null,null,0.26000000000000006,0.81799999999999995,-0.20708391677612739,8.3945009551342053E-3,-1.0986445509599038E-2,-1.4201769237472844E-3,8.3295878307200824E-4,-1.6756989864365017E-3,-2.5181152813816081E-3,377.30293403136716,-50.268798471431353]
["2次モードのモード形：支承／橋脚",{"$f":"(B18-B4*B24^2)/(-C18)","v":-1.4379563804811915E-2},null,null,0.27000000000000007,0.82099999999999995,-0.17801723050120441,8.0293290632208972E-3,-1.2983846698722806E-2,-1.4201413867860509E-3,7.1287905781824707E-4,-1.6898964467922833E-3,-2.4142446515766011E-3,323.71621811389377,-48.171117146155268]
["モーダルマトリックス：fai",1,1,null,0.28000000000000008,0.82599999999999996,-0.14477503764965097,7.6050171401738894E-3,-1.4667357638400484E-2,-1.4245008444937121E-3,5.7436855434342415E-4,-1.7041142089061049E-3,-2.2916469796477215E-3,261.76482944611143,-45.702035491764057]
[null,{"$f":"(B8+B9-B4*B23*B23)/B9","v":23.181046230471477},{"$f":"(B8+B9-B4*B24*B24)/B9","v":-1.4379563804811915E-2},null,0.29000000000000009,0.83,-0.10816098833784263,7.1331183305330713E-3,-1.5999623268769872E-2,-1.4338181945258604E-3,4.2076695280059714E-4,-1.7183987276154786E-3,-2.1536694446649698E-3,192.94291073426467,-42.928884439906078]
["転置モーダルマトリックス：fai^T",{"$f":"B29","v":1},{"$f":"B30","v":23.181046230471477},null,0.3000000000000001,0.83499999999999996,-6.9055636685681349E-2,6.6262844930481254E-3,-1.6951765150346736E-2,-1.4485056796988232E-3,2.5576082268399407E-4,-1.7327996435324822E-3,-2.0040161617683591E-3,118.90175948694255,-39.92604818144774]
[null,{"$f":"C29","v":1},{"$f":"C30","v":-1.4379563804811915E-2},null,0.31000000000000011,0.83899999999999997,-2.8407659710123542E-2,6.0981241065478919E-3,-1.7504151369904377E-2,-1.4688106161646506E-3,8.3361226468680401E-5,-1.7473632711216083E-3,-1.8467080516653789E-3,41.434020877793245,-36.774153723909556]
["モーダルマトリックスの逆行列：fai^(-1)",{"$f":"MINVERSE(B29:C30)","v":6.1993101279305773E-4},4.3111948401773265E-2,null,0.32000000000000012,0.84399999999999997,1.2641986022411704E-2,5.5647788900184828E-3,-1.7647259433900456E-2,-1.4947227030127732E-3,-9.1450413376435418E-5,-1.7620670654905184E-3,-1.686560332944901E-3,-37.286476599913598,-33.569610849335824]
[null,0.99938006898720699,-4.3111948401773272E-2,null,0.33000000000000013,0.84799999999999998,5.3298016087649981E-2,5.0379253619836752E-3,-1.7380548266824607E-2,-1.5264441445045633E-3,-2.6585303821039685E-4,-1.7770780436931041E-3,-1.5270695444898534E-3,-115.73978369890364,-30.382366308523288]
["転置モーダルマトリックスの逆行列：fai^(-T)",{"$f":"MINVERSE(B31:C32)","v":6.1993101279300689E-4},0.99938006898720699,null,0.34000000000000014,0.85199999999999998,9.2898779352343877E-2,4.5274679227557133E-3,-1.6712576145675583E-2,-1.5638983912415062E-3,-4.3646154829250609E-4,-1.7925106017704924E-3,-1.3712325287025453E-3,-192.65196072226669,-27.272279380310934]
[null,4.3111948401773265E-2,-4.3111948401773265E-2,null,0.35000000000000014,0.85599999999999998,0.13031191860308589,4.0493844564863553E-3,-1.5660385389472221E-2,-1.6067067474999763E-3,-5.985683684087427E-4,-1.8083545627125509E-3,-1.2238988434542261E-3,-265.83420704168088,-24.336176805389208]
["1次モードのひずみエネルギー",{"$f":"B8*B29^2","v":450000},{"$f":"B9*(B30-B29)^2","v":9839976.2375662588},null,0.36000000000000015,0.86,0.16465310940329689,3.6163518264408579E-3,-1.425068725780539E-2,-1.6544628599642109E-3,-7.4837309771584658E-4,-1.8246544286270457E-3,-1.0889558097390028E-3,-333.56258899158689,-21.651542920580553]
["2次モードのひずみエネルギー",{"$f":"B8*C29^2","v":450000},{"$f":"B9*(C30-C29)^2","v":20579.317989296807},null,0.37000000000000016,0.86399999999999999,0.19513373811214876,3.239695951693052E-3,-1.2518576463826304E-2,-1.7066503618179657E-3,-8.8245035973148137E-4,-1.8414555719781271E-3,-9.6991172061233126E-4,-394.28664402606279,-19.288195516289189]
["1次モードの減衰定数",{"$f":"(B6*B37+B7*C37)/(B37+C37)","v":0.02},null,null,0.38000000000000017,0.86799999999999999,0.22106364542018372,2.929331361182284E-3,-1.0506529034061055E-2,-1.7626488375220865E-3,-9.9777607881094054E-4,-1.8587987236746786E-3,-8.6987473202340053E-4,-446.63568470041446,-17.307873764093493]
["2次モードの減衰定数",{"$f":"(B6*B38+B7*C38)/(B38+C38)","v":0.02},null,null,0.39000000000000018,0.872,0.24186430716696894,2.6935683753514707E-3,-8.2633310077224829E-3,-1.8217478142460988E-3,-1.0917872128320303E-3,-1.8767182594723836E-3,-7.9149167628845825E-4,-489.44526146537919,-15.763025221501877]
["換算質量行列：Ms=fai^T*M*fai",{"$f":"MMULT(MMULT(B31:C32,B16:C17),B29:C30)","v":3226165.4260355351},-1.5575096767861396E-10,null,0.40000000000000019,0.876,0.25708109016024677,2.5389360405625133E-3,-5.842887349640751E-3,-1.8831635181453398E-3,-1.1624366701227526E-3,-1.8952411864628835E-3,-7.3689120081682122E-4,-521.78201018983077,-14.695680565336442]
[null,-1.5620571502950042E-10,2001.2406311313,null,0.4100000000000002,0.88,0.26639293459789554,2.4700426222351328E-3,-3.3029248105799778E-3,-1.9460574008019439E-3,-1.2082373002884966E-3,-1.9143864341697482E-3,-7.0763783349367762E-4,-542.96370263521499,-14.136547959521542]
["換算減衰行列：Cs=2h.omega*M",{"$f":"2*B39*B23*B41","v":230467.92600225634},0,null,0.42000000000000021,0.88400000000000001,0.26961897276486291,2.4894803182653235E-3,-7.0361567510596223E-4,-2.0095558784797118E-3,-1.2282929709213407E-3,-1.934164376175717E-3,-7.0469906152772891E-4,-552.57352763741551,-14.104368525492958]
[null,0,{"$f":"2*B40*B24*C42","v":1227.5129010028284},null,0.43000000000000022,0.88800000000000001,0.26672187191271135,2.5977771347237663E-3,1.8938463144301543E-3,-2.072770786090829E-3,-1.2223157980958653E-3,-1.9545765665521827E-3,-7.2842640594660848E-4,-550.46815975432685,-14.60555224378613]
["Cs.fai^(-1)",{"$f":"MMULT(B43:C44,B33:C34)","v":142.87421478289426},9935.9213340729748,null,0.44000000000000022,0.89100000000000001,0.25780774849335364,2.7933935840867672E-3,4.4287395707271367E-3,-2.1347651015878317E-3,-1.1906289241949846E-3,-1.9756154997307963E-3,-7.7855094968925435E-4,-536.77934257663424,-15.63410311015582]
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["粘性減衰マトリックス：fai^(-T).Cs.fai^(-1)",{"$f":"MMULT(B35:C36,B45:C46)","v":1226.0799982785888},-46.728080032549734,null,0.46000000000000024,0.89800000000000002,0.22304660075262353,3.4304521689417847E-3,9.0783425466053544E-3,-2.2516359815955744E-3,-1.0543906154116245E-3,-2.0194976590110166E-3,-9.5388778020350559E-4,-476.51804885224306,-19.188858506729478]
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["細分化した時間刻み：ddt",{"$f":"B3/B14","v":1E-3},null,null,0.48000000000000026,0.90300000000000002,0.16884685045501338,4.3500567440869454E-3,1.2819840605394511E-2,-2.353877996458786E-3,-8.3361300530545809E-4,-2.0655789113987609E-3,-1.2168766008388873E-3,-378.0094668526699,-24.487623595843857]
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[null,null,null,null,0.50000000000000022,0.90800000000000003,0.10048386426231069,5.4762078098125255E-3,1.5317518373629636E-2,-2.4364073064413764E-3,-5.5002392768335815E-4,-2.1135075216935344E-3,-1.545784472426676E-3,-250.95435807225618,-31.092278010855445]
["橋脚の履歴復元力モデル","クラフ",{"$f":"IF(B52=\"線形\",1,IF(B52=\"クラフ\",2,3))","v":2},null,0.51000000000000023,0.91,6.3006701116334218E-2,6.0876950439512746E-3,1.6027198200940226E-2,-2.4692065935276752E-3,-3.9309957734049133E-4,-2.1380240530465182E-3,-1.7264760338897526E-3,-180.49332546494659,-34.71391480633951]
["支承の履歴復元力モデル","バイリニア＋ハードニング",{"$f":"IF(B53=\"線形\",1,IF(B53=\"バイリニア\",2,3))","v":3},null,0.52000000000000024,0.91200000000000003,2.4558919750395456E-2,6.7136875640589743E-3,1.6356002304041526E-2,-2.4959573374903178E-3,-2.3131902487127188E-4,-2.162785481441908E-3,-1.9127322772658239E-3,-107.73122371588953,-38.442985644090712]
["橋脚の絶対最大加速度",{"$f":"MAX(MAX(G2:INDIRECT(\"g\"&INDIRECT(\"b2\"))),-MIN(G2:INDIRECT(\"g\"&INDIRECT(\"b2\"))))","v":8.2343404704891405},"m/s/s",null,0.53000000000000025,0.91400000000000003,-1.3723033832117426E-2,7.3373823544384594E-3,1.6299263589691228E-2,-2.5164785001405344E-3,-6.9355926036832613E-5,-2.1876026018371854E-3,-2.0995299570500184E-3,-34.834692094745243,-42.178968476234452]
["桁の絶対最大加速度",{"$f":"MAX(MAX(H2:INDIRECT(\"h\"&INDIRECT(\"b2\"))),-MIN(H2:INDIRECT(\"h\"&INDIRECT(\"b2\"))))","v":0.13603867390866214},"m/s/s",null,0.54000000000000026,0.91600000000000004,-5.1512549607589074E-2,7.9551697972259326E-3,1.5860911385024195E-2,-2.5311434861912626E-3,9.1380917766071279E-5,-2.2127890197878213E-3,-2.2857672586376302E-3,37.560216352879401,-45.899861183254814]
["橋脚の最大速度",{"$f":"MAX(MAX(I2:INDIRECT(\"i\"&INDIRECT(\"b2\"))),-MIN(I2:INDIRECT(\"i\"&INDIRECT(\"b2\"))))","v":0.49049797355725139},"m/s",null,0.55000000000000027,0.91700000000000004,-8.7733811933969758E-2,8.5511805883055712E-3,1.5052553961169361E-2,-2.5399232489916736E-3,2.4614989177373692E-4,-2.2381352620540222E-3,-2.4666514877293329E-3,107.38338477944649,-49.509918016838711]
["支承の最大速度",{"$f":"MAX(MAX(J2:INDIRECT(\"j\"&INDIRECT(\"b2\"))),-MIN(J2:INDIRECT(\"j\"&INDIRECT(\"b2\"))))","v":1.2386439768539912},"m/s",null,0.56000000000000028,0.91800000000000004,-0.12148215006642338,9.1122543537575096E-3,1.3894858454466971E-2,-2.5430334109205212E-3,3.911224725774033E-4,-2.2635489355758826E-3,-2.6381716330296698E-3,172.88014289157894,-52.929118142582766]
["橋脚の最大変位",{"$f":"MAX(MAX(K2:INDIRECT(\"k\"&INDIRECT(\"b2\"))),-MIN(K2:INDIRECT(\"k\"&INDIRECT(\"b2\"))))","v":6.9690357470771971E-2},"m",null,0.57000000000000028,0.91900000000000004,-0.15197339250596847,9.6270754051543082E-3,1.2416874949674906E-2,-2.5408809093933234E-3,5.2290876190706586E-4,-2.2889698910553021E-3,-2.7968420265472227E-3,232.51593777618075,-56.088034732346046]
["支承の最大変位",{"$f":"MAX(MAX(L2:INDIRECT(\"l\"&INDIRECT(\"b2\"))),-MIN(L2:INDIRECT(\"l\"&INDIRECT(\"b2\"))))","v":0.31367739819527962},"m",null,0.58000000000000029,0.92,-0.17851122761247951,1.0085604472992912E-2,1.0655058959770774E-2,-2.5339828692488194E-3,6.3847218430049474E-4,-2.3143464354203973E-3,-2.9395364461421141E-3,284.91558642043742,-58.924505979152201]
["層間最大変位",{"$f":"MAX(MAX(M2:INDIRECT(\"m\"&INDIRECT(\"b2\"))),-MIN(M2:INDIRECT(\"m\"&INDIRECT(\"b2\"))))","v":0.35520664481940856},"m",null,0.5900000000000003,0.92100000000000004,-0.20049770473693865,1.0479219634843953E-2,8.6523146632511774E-3,-2.5229502400210824E-3,7.3518002562881395E-4,-2.3396334753421825E-3,-3.0635334649746822E-3,328.88455448552992,-61.384532420188741]
["橋脚の最大復元力",{"$f":"MAX(MAX(N2:INDIRECT(\"n\"&INDIRECT(\"b2\"))),-MIN(N2:INDIRECT(\"n\"&INDIRECT(\"b2\"))))","v":16302.377854789131},"kN",null,0.60000000000000031,0.92100000000000004,-0.21744561363471704,1.0800887740048212E-2,6.4569891354615211E-3,-2.5084169085326014E-3,8.1085882824221377E-4,-2.364792566371763E-3,-3.1665722876838853E-3,363.43384552581904,-63.423383009466626]
["支承の最大復元力",{"$f":"MAX(MAX(O2:INDIRECT(\"o\"&INDIRECT(\"b2\"))),-MIN(O2:INDIRECT(\"o\"&INDIRECT(\"b2\"))))","v":545.08323177103102},"kN",null,0.61000000000000032,0.92200000000000004,-0.22898888839795112,1.1045320961576312E-2,4.1215814649862041E-3,-2.4911430328954541E-3,8.6384150800810949E-4,-2.389792116438744E-3,-3.2469010956321211E-3,387.80143161949456,-65.00655024989868]
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[null,null,null,null,null,null,"換算質量行列Ms"]
["固有振動数","f1",{"$f":"C15/2/PI()","v":0.28423921903836241},null,null,null,{"$f":"MMULT(G15:H16,G2:H3)","v":3226165.4260355351},2.4920154828578234E-10]
["Hz","f2",{"$f":"C16/2/PI()","v":2.4405454154860045},null,null,null,2.4874680093489587E-10,2001.2406311312996]
[null,null,null,null,null,null,"換算減衰行列Cs"]
["固有周期","T1",{"$f":"1/C18","v":3.5181633392576792},null,null,null,{"$f":"2*F10*C15*G18","v":230467.92600225634},0]
["s","T2",{"$f":"1/C19","v":0.40974447500738781},null,null,null,0,{"$f":"2*F11*C16*H19","v":1227.5129010028281}]
[null,null,null,null,null,null,"F-t*Cs"]
["減衰","この秒以上","この振動数以上",null,null,null,{"$f":"MMULT(G9:H10,G21:H22)","v":142.87421478285694},1226.7519276868932]
[0.1,{"$f":"$F$31/(A25-SQRT(A25*A25-$F$30*$F$31))","v":19.565862380649051},{"$f":"(A25+SQRT(A25*A25-$F$30*$F$31))/$F$31","v":13.572813746390308},null,"減衰行列","F-t*Cs*F-1",9935.9213340729766,-52.920472850544947]
[0.2,{"$f":"$F$31/(A26-SQRT(A26*A26-$F$30*$F$31))","v":39.242343639646272},{"$f":"(A26+SQRT(A26*A26-$F$30*$F$31))/$F$31","v":27.222363667420382},null,{"$f":"MMULT(G24:H25,G27:H28)","v":1226.0799982785888},-46.728080032550835,"モーダルマトリックスの逆行列F-1"]
[0.3,58.894140279875792,40.854789899940059,null,-46.728080032550459,430.63843257356257,{"$f":"MINVERSE(G2:H3)","v":6.1993101279293229E-4},4.3111948401773272E-2]
[0.4,78.539801922874702,54.48296029270282,null,null,null,0.99938006898720699,-4.3111948401773272E-2]
[0.5,98.183013102089333,68.109430801881118,null,"レイリー減衰の係数"]
[0.6,117.82499977489748,81.735051872549079,null,"α",{"$f":"2*C18*C19*(C18*F11-C19*F10)/(C18*C18-C19*C19)","v":1.0183538385175725E-2}]
[0.7,137.46628694267179,95.360187697472824,null,"β",{"$f":"2*(C18*F10-C19*F11)/(C18*C18-C19*C19)","v":1.46800592946614E-2}]
[0.8,157.10713699766217,108.9850202977639]
[0.9,176.74769567700258,122.60965077120694]
[1,{"$f":"$F$31/(A34-SQRT(A34*A34-$F$30*$F$31))","v":196.38805040922941},136.2341397667131]
[]
["f","h"]
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[{"$f":"A37+0.1","v":0.2},{"$f":"$F$30/2/A38+$F$31*A38/2","v":2.6926851892405453E-2}]
[{"$f":"A38+0.1","v":0.30000000000000004},1.9174572869492083E-2]
[0.4,1.5665434840401934E-2]
[0.5,1.3853553208841076E-2]
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[0.7,1.2411976742542723E-2]
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[1.2,1.3051176570620059E-2]
[1.3,1.3458784074289805E-2]
[1.4000000000000001,1.3913019500968597E-2]
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[4.5,3.4161637678007672E-2]
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[5.5999999999999961,4.2013410523728291E-2]
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[5.899999999999995,4.4169186646808363E-2]
[5.9999999999999947,4.4888806082748811E-2]
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[6.3999999999999932,4.7771778679258282E-2]
[6.4999999999999929,4.8493541814201478E-2]
[6.5999999999999925,{"$f":"$F$30/2/A102+$F$31*A102/2","v":4.9215675853077692E-2}]
[{"$f":"A102+0.1","v":6.6999999999999922},4.9938164188248146E-2]
[{"$f":"A103+0.1","v":6.7999999999999918},5.0660991188993976E-2]
[{"$f":"A104+0.1","v":6.8999999999999915},5.1384142130724939E-2]
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[11.299999999999976,8.3392934058428583E-2]
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[11.499999999999975,8.485310348278878E-2]
[11.599999999999975,8.5583289529086615E-2]
[11.699999999999974,8.6313540821853427E-2]
[11.799999999999974,8.7043855702280695E-2]
[11.899999999999974,8.7774232567318144E-2]
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[12.199999999999973,8.9965719827974328E-2]
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[12.599999999999971,9.2888482222445015E-2]
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[12.799999999999971,9.4350173954003663E-2]
[12.89999999999997,9.5081093240688891E-2]
[12.99999999999997,{"$f":"$F$30/2/A166+$F$31*A166/2","v":9.5812059968574864E-2}]
[13.099999999999969,9.6543073051221853E-2]
[13.199999999999969,9.7274131435112585E-2]
[{"$f":"A168+0.1","v":13.299999999999969},9.8005234098414468E-2]
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[13.499999999999968,9.9467568327304065E-2]
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[18.899999999999999,0.13899596611193582]
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[19.400000000000006,{"$f":"$F$30/2/A230+$F$31*A230/2","v":0.14265903748773048}]
[19.500000000000007,0.14339169449179937]
[19.600000000000009,0.14412436523016076]
[{"$f":"A232+0.1","v":19.70000000000001},0.14485704949366296]
[{"$f":"A233+0.1","v":19.800000000000011},0.14558974707737965]
[{"$f":"A234+0.1","v":19.900000000000013},0.14632245778050351]
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