{"text_format":"1","workbook":"xlsx","n_sheets":10,"sheets":["Intro & Contents","Comp Force","Comp Moment","Comp Distributed","Comp Special","Tens Force","Tens Moment","Tens Distributed","Calcs1","Calcs2"],"not_rendered":{"charts":0,"images":25,"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":"Intro & Contents","index":0,"n_rows":32,"n_cols":3,"rows_kept":32,"cut":false,"hidden":false,"merged":[[9,1,9,11],[4,1,4,11],[5,1,5,11],[6,1,6,11]]}
[]
[]
[]
[]
[null,"Structural Methods and Ratiocination Techniques"]
[null,"(SMART)"]
[null,"Beam-Columns"]
[]
[]
[null,"TABLE  OF  CONTENTS"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Note:  This Workbook is intended to provide simplified and automated methods of airframe structural analysis."]
[]
[]
[]
[]
[null,null,"Click on Button to go to sheet"]

{"sheet":"Comp Force","index":1,"n_rows":29,"n_cols":12,"rows_kept":29,"cut":false,"hidden":false,"merged":[]}
["Concentrated Intermediate Load"]
[]
["L",20]
["a",8,null,null,null,null,null,null,"sin","cos","1 - cos","kx - sin"]
["P",5000,null,null,null,null,"k",{"$f":"SQRT(B5/(B7*B8))","v":1.17769374287677E-2}]
["W",12000,null,null,null,null,"kL",{"$f":"H5*B3","v":0.23553874857535401},{"$f":"SIN(H6)","v":0.2333668924116348},{"$f":"COS(H6)","v":0.97238875637583166},{"$f":"1-J6","v":2.7611243624168336E-2},{"$f":"H6-I6","v":2.1718561637192046E-3}]
["E",10300000,"psi",null,null,null,"k(L-a)",{"$f":"H5*(B3-B4)","v":0.14132324914521238},{"$f":"SIN(H7)","v":0.14085329456325038},{"$f":"COS(H7)","v":0.99003047903116503},{"$f":"1-J7","v":9.9695209688349662E-3},{"$f":"H7-I7","v":4.6995458196200102E-4}]
["I",3.5,"in4",null,null,null,"ka",{"$f":"H5*B4","v":9.4215499430141597E-2},{"$f":"SIN(H8)","v":9.4076176352507396E-2},{"$f":"COS(H8)","v":0.9955650019174499}]
[]
["Point A at left end",null,null,null,null,null,null,{"$f":"B4","v":8},{"$f":"(E11-E12*B5)*I8/H5","v":57857.052176633435},{"$f":"IF(I10=I13,H10,0)","v":8}]
[null,null,null,"RA",{"$f":"B6*(B3-B4)/B3","v":7200},null,null,{"$f":"PI()/(2*H5)","v":133.37901608935181},{"$f":"IF(AND(H10>B3/2,H10>H11),B6*I7/(H5*I6),0)","v":0},{"$f":"IF(I11=I13,H11,0)","v":0}]
[null,null,null,"qA",{"$f":"-B6/B5*(I7/I6-(B3-B4)/B3)","v":-8.5684042769861961E-3}]
[null,null,null,"Mmax",{"$f":"I13","v":57857.052176633435},"@ x =",{"$f":"J13","v":8},null,{"$f":"MAX(I10:I11)","v":57857.052176633435},{"$f":"J10+J11","v":8}]
[]
[]
[null,null,null,"RA",{"$f":"B6*(I6*(1-J7)-J6*(H7-I7))/(I6*(1-J6)-J6*(H6-I6))","v":5179.2898314444365}]
[null,null,null,"qA",{"$f":"-B6/B5*(L6*K7-K6*L7)/(I6*K6-J6*L6)","v":-4.8072093711328283E-3}]
[null,null,null,"MB",{"$f":"-B6/H5*(H6*SIN(H5*B4)-H5*B4*I6)/(I6-H6*J6)","v":-40414.203371110874}]
[null,null,null,"Ma",{"$f":"(E16-E17*B5)*I8/H5","v":41565.050838327013}]
[]
[null,null,null,"RA",{"$f":"B6*(K6*K7-I6*L7)/(K6^2-I6*L6)","v":7776.3837411229388},null,null,null,null,"MA",{"$f":"-B6/H5*(L6*K7-K6*L7)/(K6^2-I6*L6)","v":-34595.836819944074}]
[null,null,null,"qA",0,null,null,{"$f":"B4","v":8},{"$f":"K21*COS(H5*H22)+E21*SIN(H$5*H22)/H$5","v":27676.669699576363},"MB",{"$f":"K21+E21*B3-B6*(B3-B4)","v":-23068.161997485309}]
[null,null,null,"Mmax (-)",{"$f":"MIN(K21:K22)","v":-34595.836819944074},null,null,{"$f":"B3/2","v":10},{"$f":"K21*COS(H5*H23)+E21*SIN(H5*H23)/H5-B6*SIN(H5*(H23-B4))/H5","v":19230.223554760425}]
[null,null,null,"Mmax (+)",{"$f":"MAX(I22:I24)","v":27676.669699576363},null,null,{"$f":"B3-B4","v":12},{"$f":"K21*COS(H5*H24)+E21*SIN(H5*H24)/H5-B6*SIN(H5*(H24-B4))/H5","v":10773.109263193925}]
[]
[]
[null,null,null,"RB",{"$f":"B6","v":12000}]
[null,null,null,"qA",{"$f":"B6/B5*K7/J6","v":2.4606259758063378E-2}]
[null,null,null,"Mmax",{"$f":"-B6/H5*(I6*K7+J6*I7)/J6","v":-145959.08121479535}]

{"sheet":"Comp Moment","index":2,"n_rows":31,"n_cols":12,"rows_kept":31,"cut":false,"hidden":false,"merged":[]}
["Concentrated Intermediate Moment"]
[]
["L",1305.654]
["a",0,null,null,null,null,null,null,"sin","cos","1 - cos","kx - sin"]
["P",60607,null,null,null,null,"k",{"$f":"SQRT(B5/(B7*B8))","v":1.9530316644029485E-3}]
["M0",30303.5,null,null,null,null,"kL",{"$f":"H5*B3","v":2.5499836047543671},{"$f":"SIN(H6)","v":0.55769732624806101},{"$f":"COS(H6)","v":-0.83004439176212963},{"$f":"1-J6","v":1.8300443917621296},{"$f":"H6-I6","v":1.992286278506306}]
["E",80000,"psi",null,null,null,"k(L-a)",{"$f":"H5*(B3-B4)","v":2.5499836047543671},{"$f":"SIN(H7)","v":0.55769732624806101},{"$f":"COS(H7)","v":-0.83004439176212963},{"$f":"1-J7","v":1.8300443917621296},{"$f":"H7-I7","v":1.992286278506306}]
["I",198616,"in4",null,null,null,"ka",{"$f":"H5*B4","v":0},{"$f":"SIN(H8)","v":0},{"$f":"COS(H8)","v":1}]
[]
[]
[null,null,null,"RA",{"$f":"-B6/B3","v":-23.20944139871666}]
[null,null,null,"qA",{"$f":"B6/(B5*B3)*(H6*J7/I6-1)","v":-1.836339440307607E-3},null,null,null,{"$f":"B4","v":0},{"$f":"E11*I8/H5-E12*B5*I8/H5","v":0},{"$f":"J12+B6","v":30303.5}]
[null,null,null,"Mmax (-)",{"$f":"MIN(J12:K12)","v":0}]
[null,null,null,"Mmax (+)",{"$f":"MAX(J12:K12)","v":30303.5}]
[]
[]
[null,null,null,"RA",{"$f":"-B6*H5*(COS(H5*B4)-J6)/(I6-H6*J6)","v":-40.499911782114133},null,null,null,{"$f":"B4","v":0},{"$f":"(E17-E18*B5)/H5*I8","v":0},{"$f":"J17+B6","v":30303.5},{"$f":"B6*(I6-H6*J8)/(I6-H6*J6)","v":-22575.371817964442}]
[null,null,null,"qA",{"$f":"-B6*H5/B5*(K6*K7-L6*I7)/(I6*K6-J6*L6)","v":-8.1719156713744052E-4}]
[null,null,null,"Mmax (-)",{"$f":"MIN(J17:L17)","v":-22575.371817964442}]
[null,null,null,"Mmax (+)",{"$f":"MAX(J17:L17)","v":30303.5}]
[]
[]
[null,null,null,"RA",{"$f":"-B6*H5*(K6*I7-I6*K7)/(K6^2-I6*L6)","v":0},null,null,null,null,"MA",{"$f":"-B6*(K6*K7-L6*I7)/(K6^2-I6*L6)","v":-30303.5}]
[null,null,null,"qA",0,null,null,{"$f":"B4","v":0},{"$f":"K23*J8+E23*I8/H5","v":-30303.5},"MB",{"$f":"E23*B3+K23+B6","v":0}]
[null,null,null,"Mmax (-)",{"$f":"MIN(I24:I25)","v":-30303.5},null,null,14,{"$f":"I24+B6","v":0}]
[null,null,null,"Mmax (+)",{"$f":"MAX(I24:I25)","v":0}]
[]
[]
[null,null,null,"RB",0]
[null,null,null,"qA",{"$f":"-B6*H5/B5*I7/J6","v":6.5610981058677098E-4}]
[null,null,null,"Mmax",{"$f":"B6*COS(H5*B4)/J6","v":-36508.288352708056}]

{"sheet":"Comp Distributed","index":3,"n_rows":86,"n_cols":40,"rows_kept":86,"cut":false,"hidden":false,"merged":[]}
["Distributed Load"]
[]
["L",40,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x","kx","k*sin","cos","x-a","k(x-a)","cos","sin","V","V'"]
["a",10,"Case 1",null,null,null,null,null,null,"W",{"$f":"B12*(B6+B7)/2","v":50},null,"Q",{"$f":"B13/B12","v":0.15},"(wb-wa)/(b - a)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"B4+B12/2","v":20},{"$f":"N$5*AE4","v":0.22360679774997896},{"$f":"N$5*SIN(AF4)","v":2.4792186880390706E-3},{"$f":"COS(AF4)","v":0.97510399321047936},{"$f":"AE4-B$4","v":10},{"$f":"N$5*AI4","v":0.11180339887498948},{"$f":"COS(AJ4)","v":0.99375650770459845},{"$f":"SIN(AJ4)","v":0.11157062066135646},{"$f":"AC$9*AH4-B$6*AL4/N$5-N$4*(1-AK4)/N$5^2","v":5.0212319926791888},{"$f":"-AC$9*AG4-B$6*AK4-N$4*AL4/N$5","v":-2.5478212891131449}]
["b",30,null,null,null,null,null,null,null,"RA",{"$f":"K4*(B3-B14)/B3","v":22.5},null,"k",{"$f":"SQRT(B8/(B9*B10))","v":1.1180339887498949E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AE4-AM4/AN4","v":21.970794425077983},0.2456409492707389,2.7188136293362524E-3,0.9699816594098486,11.970794425077983,0.13383755039574943,0.99105711612607861,0.13343834747125838,{"$f":"AC$9*AH5-B$6*AL5/N$5-N$4*(1-AK5)/N$5^2","v":-0.2921030841108827},{"$f":"-AC$9*AG5-B$6*AK5-N$4*AL5/N$5","v":-2.8440349461828456}]
["wa",1,null,null,null,null,null,null,null,"RB",{"$f":"K4-K5","v":27.5},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.868087148395983,0.24449264700851475,2.7063588177282973E-3,0.9702602617842464,11.868087148395983,0.13268924813352526,0.99120969024573691,0.13230022661715371,-7.9103037548655664E-4,-2.828630733135185]
["wb",4,null,null,null,null,null,null,null,"qA",{"$f":"Calcs1!F44","v":-5.6687552035424493E-4},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.867807497055772,0.2444895204114812,2.7063249008922488E-3,0.97026101861637437,11.867807497055772,0.1326861215364917,0.99121010389038822,0.13229712750322992,-5.8652851464557898E-9,-2.8285887854479794]
["P",1000,null,null,null,null,null,null,null,"Mmax",{"$f":"AC11","v":387.34128711691034},"@ x =",{"$f":"AC12","v":21.867807494982188},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.867807494982198,0.24448952038829794,2.7063249006407603E-3,0.97026101862198622,11.867807494982198,0.13268612151330844,0.99121010389345521,0.13229712748025044,-9.9475983006414026E-14,-2.8285887851369429]
["E",80000,"psi",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(RA - qA*P)",null,{"$f":"K5-K7*B8","v":23.066875520354245},null,21.867807494982163,0.24448952038829755,2.7063249006407564E-3,0.97026101862198633,11.867807494982163,0.13268612151330805,0.99121010389345532,0.13229712748025005,6.9277916736609768E-14,-2.8285887851369385]
["I",100,"in4",null,null,null,null,null,null,null,null,null,null,"wa/k",{"$f":"B6/N5","v":89.442719099991592},null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AC9*SIN(AF10)/N5-B6*(1-AK10)/N5^2-N4*(AJ10-AL10)/N5^3","v":387.34128711691034},null,21.867807494982188,0.24448952038829783,2.706324900640759E-3,0.97026101862198622,11.867807494982188,0.13268612151330833,0.99121010389345532,0.13229712748025033,4.4408920985006262E-14,-2.828588785136942]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Q/k2",{"$f":"N4/N5^2","v":1200},null,null,null,null,null,null,null,null,null,null,null,null,"Mmax",{"$f":"IF(AC9<0,\"NA\",AC10)","v":387.34128711691034}]
["b - a",{"$f":"B5-B4","v":20},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x",{"$f":"IF(AC2<0,\"NA\",AE10)","v":21.867807494982188}]
["wb-wa",{"$f":"B7-B6","v":3},"Case 2"]
["Xcg",{"$f":"(B6*(B5+2*B4)+B7*(2*B5+B4))*B12/(6*K4)","v":22},null,null,null,null,null,null,null,"RA",{"$f":"Calcs1!F102","v":13.599077205753263},null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"T14-V14-X14","v":0}]
[null,null,null,null,null,null,null,null,null,"RB",{"$f":"K4-K14","v":36.400922794246739}]
[null,null,null,null,null,null,null,null,null,"qA",{"$f":"Calcs1!J101","v":-2.6321874884825929E-4}]
[null,null,null,null,null,null,null,null,null,"MB",{"$f":"Calcs1!T103","v":-358.21901390419345},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x","kx","k*sin","cos","x-a","k(x-a)","cos","sin","V","V'"]
[null,null,null,null,null,null,null,null,null,"Mmax (+)",{"$f":"AC28","v":203.20828753560895},"@ x =",{"$f":"AC29","v":18.353650447276511},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"B4+B12/2","v":20},{"$f":"N$5*AE18","v":0.22360679774997896},{"$f":"N$5*SIN(AF18)","v":2.4792186880390706E-3},{"$f":"COS(AF18)","v":0.97510399321047936},{"$f":"AE18-B$4","v":10},{"$f":"N$5*AI18","v":0.11180339887498948},{"$f":"COS(AJ18)","v":0.99375650770459845},{"$f":"SIN(AJ18)","v":0.11157062066135646},{"$f":"AC$19*AH18-B$6*AL18/N$5-N$4*(1-AK18)/N$5^2","v":-3.9541902977098697},{"$f":"-AC$19*AG18-B$6*AK18-N$4*AL18/N$5","v":-2.5250011234381882}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(RA - qA*P)",null,{"$f":"K14-K16*B8","v":13.862295954601523},null,{"$f":"AE18-AM18/AN18","v":18.433984737271874},0.20609821484366755,2.287969980063084E-3,0.97883683367691121,8.4339847372718744,9.4294815968678072E-2,0.99555753698918459,9.4155140826342812E-2,{"$f":"AC$19*AH19-B$6*AL19/N$5-N$4*(1-AK19)/N$5^2","v":-0.18352154603481363},{"$f":"-AC$19*AG19-B$6*AK19-N$4*AL19/N$5","v":-2.2904978259006725}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,18.353861742192127,0.20520241252587157,2.2781656460189731E-3,0.97901975992029477,8.3538617421921266,9.3399013650882087E-2,0.9956414819228725,9.3263280418535238E-2,-4.8142795374062075E-4,-2.2784802972644123]
[null,null,"Case 3","  Both ends fixed",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,18.353650448746087,0.20520005019332885,2.2781397884552644E-3,0.97902024127903298,8.3536504487460874,9.3396651318339366E-2,0.99564170223897674,9.3260928382001368E-2,-3.3483420480706627E-9,-2.2784486032538638]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,18.353650447276518,0.20520005017689857,2.2781397882754221E-3,0.97902024128238085,8.3536504472765181,9.3396651301909092E-2,0.99564170224050907,9.3260928365642703E-2,2.7533531010703882E-14,-2.278448603033429]
[null,null,null,null,null,null,null,null,null,"RA",{"$f":"Calcs1!F158","v":21.456359606763257},null,"MA",{"$f":"Calcs1!J157","v":-209.01156942208391},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,18.353650447276529,0.20520005017689869,2.2781397882754234E-3,0.97902024128238085,8.3536504472765287,9.3396651301909203E-2,0.99564170224050907,9.3260928365642815E-2,1.6875389974302379E-14,-2.2784486030334303]
[null,null,null,null,null,null,null,null,null,"RB",{"$f":"K4-K23","v":28.543640393236743},null,"MB",{"$f":"Calcs1!O157","v":-250.75718515155359},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,18.353650447276536,0.20520005017689877,2.2781397882754243E-3,0.97902024128238085,8.3536504472765358,9.3396651301909286E-2,0.99564170224050907,9.3260928365642898E-2,9.7699626167013776E-15,-2.2784486030334317]
[null,null,null,null,null,null,null,null,null,"Mmax (+)",{"$f":"AC44","v":149.85558099734084},"@ x =",{"$f":"AC45","v":21.508140777352498},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,18.353650447276539,0.20520005017689882,2.2781397882754247E-3,0.97902024128238085,8.3536504472765394,9.3396651301909328E-2,0.99564170224050896,9.3260928365642939E-2,-1.2789769243681803E-13,-2.2784486030334321]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,18.353650447276483,0.20520005017689819,2.2781397882754178E-3,0.97902024128238097,8.3536504472764825,9.339665130190869E-2,0.99564170224050907,9.3260928365642301E-2,6.4837024638109142E-14,-2.2784486030334232]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AC19*SIN(AF27)/N5-B6*(1-AK27)/N5^2-N4*(AJ27-AL27)/N5^3","v":203.20828753560895},null,18.353650447276511,0.20520005017689849,2.2781397882754213E-3,0.97902024128238097,8.353650447276511,9.3396651301909009E-2,0.99564170224050907,9.326092836564262E-2,3.6415315207705135E-14,-2.2784486030334277]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Mmax",{"$f":"IF(AC19<0,\"NA\",AC27)","v":203.20828753560895}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x",{"$f":"IF(AC19<0,\"NA\",AE27)","v":18.353650447276511}]
[]
[null,null,"Case 4","  Cantilever (right end fixed)"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x","kx","k*sin","cos","x-a","k(x-a)","cos","sin","V","V'"]
[null,null,null,null,null,null,null,null,null,"RB",{"$f":"K4","v":50},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"B4+B12/2","v":20},{"$f":"N$5*AE34","v":0.22360679774997896},{"$f":"N$5*SIN(AF34)","v":2.4792186880390706E-3},{"$f":"COS(AF34)","v":0.97510399321047936},{"$f":"AE34-B$4","v":10},{"$f":"N$5*AI34","v":0.11180339887498948},{"$f":"COS(AJ34)","v":0.99375650770459845},{"$f":"SIN(AJ34)","v":0.11157062066135646},{"$f":"AC$35*AH34-N$23*N$5*SIN(AF34)-B$6*AL34/N$5-N$4*(1-AK34)/N$5^2","v":3.9689968831351994},{"$f":"-AC$35*N$5*SIN(AF34)-N$23*N$5^2*AH34-B$6*AK34-N$4*AL34/N$5","v":-2.5183524659664531}]
[null,null,null,null,null,null,null,null,null,"qA",{"$f":"Calcs1!I204","v":1.2245254965213752E-3},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(RA - qA*P)",null,{"$f":"K23","v":21.456359606763257},null,{"$f":"AE34-AM34/AN34","v":21.576029144757559},0.24122733926097276,2.670922918386805E-3,{"$f":"COS(AF35)","v":0.97104550156637304},{"$f":"AE35-B$4","v":11.576029144757559},0.12942394038598329,{"$f":"COS(AJ35)","v":0.99163640618255422},{"$f":"SIN(AJ35)","v":0.12906292238031977},{"$f":"AC$35*AH35-N$23*N$5*SIN(AF35)-B$6*AL35/N$5-N$4*(1-AK35)/N$5^2","v":-0.18669602650656358},{"$f":"-AC$35*N$5*SIN(AF35)-N$23*N$5^2*AH35-B$6*AK35-N$4*AL35/N$5","v":-2.7551355276716203}]
[null,null,null,null,null,null,null,null,null,"yA",{"$f":"Calcs1!I206","v":-3.958073875296067E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AE35-AM35/AN35","v":21.508266225426929},0.24046972679108716,2.6626970429013516E-3,{"$f":"COS(AF36)","v":0.97122621240460516},11.508266225426929,0.12866632791609767,0.99173390126453564,{"$f":"SIN(AJ36)","v":0.12831160930572202},-3.4435025659185214E-4,-2.7449718814360073]
[null,null,null,null,null,null,null,null,null,"MB",{"$f":"Calcs1!I213","v":-470.7059014380896},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.508140777782486,0.2404683242437842,2.6626818131436619E-3,0.97122654643272177,11.508140777782486,0.1286649253687947,0.99173408122666173,0.12831021835188733,-1.1803322763626056E-9,-2.7449530642920408]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.508140777352487,0.24046832423897666,2.6626818130914584E-3,0.97122654643386674,11.508140777352487,0.12866492536398716,0.99173408122727869,0.12831021834711953,1.0835776720341528E-13,-2.7449530642275404]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.508140777352526,0.2404683242389771,2.6626818130914632E-3,0.97122654643386663,11.508140777352526,0.1286649253639876,0.99173408122727857,0.12831021834711998,-6.9277916736609768E-14,-2.7449530642275466]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.508140777352502,0.24046832423897682,2.6626818130914601E-3,0.97122654643386663,11.508140777352502,0.12866492536398733,0.99173408122727857,0.1283102183471197,-4.4408920985006262E-14,-2.7449530642275426]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.508140777352484,0.24046832423897663,2.662681813091458E-3,0.97122654643386674,11.508140777352484,0.12866492536398713,0.99173408122727869,0.1283102183471195,1.1013412404281553E-13,-2.7449530642275404]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.508140777352523,0.24046832423897704,2.6626818130914627E-3,0.97122654643386663,11.508140777352523,0.12866492536398758,0.99173408122727857,0.12831021834711995,-6.5725203057809267E-14,-2.7449530642275461]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"N23*AH43+(AC35*SIN(AF43)-O10*(1-AK43)-O11*(AJ43-AL43))/N5","v":149.85558099734084},null,21.508140777352498,0.24046832423897677,2.6626818130914593E-3,0.97122654643386674,11.508140777352498,0.1286649253639873,0.99173408122727857,0.12831021834711967,-3.730349362740526E-14,-2.7449530642275421]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Mmax",{"$f":"IF(AC19<0,\"NA\",AC43)","v":149.85558099734084}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x",{"$f":"IF(AC19<0,\"NA\",AE43)","v":21.508140777352498}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,"For a =0, b = L, wL = wa",null,null,"q = wa"," - uniformly distributed load over entire length"]
[]
[null,null,null,"Case 2"]
[null,null,null,null,"1/k",{"$f":"1/N5","v":89.442719099991592},"K"]
[null,null,null,null,"a",{"$f":"B3*N5","v":0.44721359549995793}]
[null,null,null,null,"a/2",{"$f":"F73/2","v":0.22360679774997896}]
[null,null,null,null,"tan(a/2)",{"$f":"TAN(F74)","v":0.2274096529659716}]
[null,null,null,null,"M_end",{"$f":"B6*B3^2*(1/F73*F75-0.5)/(1-F73/TAN(F73))","v":201.34583612163905},"(-)"]
[]
[null,null,null,null,"U",{"$f":"B6*F72^2-F76","v":7798.6541638783619}]
[null,null,null,null,"V",{"$f":"B6*F72^2*F75+F76/TAN(F73)","v":2239.0773585543493}]
[]
[null,null,null,null,"j0",{"$f":"ATAN(F79/F78)","v":0.2795902426152847}]
[null,null,null,null,"cos(j0)",{"$f":"COS(F81)","v":0.96116859639427066}]
[]
[null,null,null,null,"M_max (+)",{"$f":"B6*F72^2*(1/F82-1)-F76/F82","v":113.721352460166}]
[]
[null,null,null,null,"@ x = ",{"$f":"B3-F72*F81","v":14.992688466662592}]

{"sheet":"Comp Special","index":4,"n_rows":73,"n_cols":33,"rows_kept":73,"cut":false,"hidden":false,"merged":[[2,20,6,24]]}
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"P",35000,"pounds",null,"k",{"$f":"SQRT(N2/(N3*N4))","v":3.1158847642487792E-2}]
[null,null,null,null,null,null,null,null,null,null,null,null,"E",10300000,"psi",null,null,null,null,null,"In \"Airframe Stress Analysis and Sizing\", M.C.Y. Niu, 3rd Ed., Hong Kong Conmilit Press Ltd., Figure 10.6.7, there are 20 Cases.  The following compares the order of the Niu cases to the order of the Special Cases.",null,null,null,null,null,"Case 1",null,"sin","cos","1-cos","kx - sin","Fa4"]
[null,null,null,null,null,null,null,null,null,null,null,null,"I",3.5,"in4",null,null,null,null,null,null,null,null,null,null,null,"kL",{"$f":"R2*N5","v":0.62317695284975583},{"$f":"SIN(AB4)","v":0.58361787747002802},{"$f":"COS(AB4)","v":0.81202843121246648},{"$f":"1-AD4","v":0.18797156878753352},{"$f":"AB4-AC4","v":3.9559075379727804E-2},{"$f":"AB4^2/2-AE4","v":6.2031884940198789E-3}]
[null,null,null,null,null,null,null,null,null,null,null,null,"L",20,"in",null,null,null,null,null,null,null,null,null,null,null,"W",{"$f":"N8*N5","v":4000},null,"(RA - qA*P)",{"$f":"P8-Q8*N2","v":2067.3413307045539}]
[]
[null,null,null,null,null,null,null,null,null,null,null,"Case",null,null,null,"R0","qL (or qR)","Mmax",null,null,null,null,null,null,null,null,"Case 3",null,"sin","cos","1-cos","kx - sin","Fa4"]
[null,null,null,null,null,null,null,null,null,null,null,1,"w",200,1,{"$f":"AB5/2","v":2000},{"$f":"(N8*AG4/R2-P8*AF4)/(AC4*N2)","v":-1.924038020130116E-3},{"$f":"AE5*AC18/R2-N8*AE18/R2^2","v":10421.156967077626},null,null,"Niu","Special",null,"Special","Niu",null,"k*(L - a)",{"$f":"R2*(N5-N11)","v":0.5297004099222925},{"$f":"SIN(AB8)","v":0.50527483008453777},{"$f":"COS(AB8)","v":0.86295848456518554},{"$f":"1-AD8","v":0.13704151543481446},{"$f":"AB8-AC8","v":2.442557983775473E-2},{"$f":"AB8^2/2-AE8","v":3.2497467011078918E-3}]
[null,null,null,null,null,null,null,null,null,null,null,2,"W",500,2,{"$f":"N9/2","v":250},{"$f":"-N9/N2*(AC18/AC4-0.5)","v":-3.613438615491555E-4},{"$f":"(P9-Q9*N2)*AC18/R2","v":2584.1766633806928},null,null,1,1,null,1,1,null,null,null,null,"(RA - qA*P)",{"$f":"P11-Q11*N2","v":432.88155622896113}]
[null,null,null,null,null,null,null,null,null,null,null,3,"W",500,null,null,null,null,null,null,2,17,null,2,5,null,{"$f":"IF(N11>PI()/(2*R2),PI()/(2*R2),N11)","v":3},{"$f":"R2*AA10","v":9.347654292746338E-2},{"$f":"SIN(AB10)","v":9.3340471501992775E-2},{"$f":"COS(AB10)","v":0.99563424829592195},{"$f":"1-AD10","v":4.3657517040780469E-3},{"$f":"AB10-AC10","v":1.3607142547060469E-4},{"$f":"AB10^2/2-AE10","v":3.1803347569046847E-6}]
[null,null,null,null,null,null,null,null,null,null,null,null,"a",3,3,{"$f":"N10*(N5-N11)/N5","v":425},{"$f":"-N10/N2*(AC8/AC4-(N5-N11)/N5)","v":-2.2518732082746113E-4},{"$f":"(AE9*AC10-N10*AC11)/R2","v":1296.7542646805525},null,null,3,"DL Case 1",null,3,7,null,{"$f":"AA10-N11","v":0},{"$f":"R2*AA11","v":0},{"$f":"SIN(AB11)","v":0},{"$f":"COS(AB11)","v":1},{"$f":"1-AD11","v":0},{"$f":"AB11-AC11","v":0},{"$f":"AB11^2/2-AE11","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,4,"w",200,4,{"$f":"AC13*(N5-AE13)/N5","v":666.66666666666663},{"$f":"-N12/(R2*N2)*(AF4/(AB4*AC4)-R2*N5/6)","v":-8.9980066658166278E-4},{"$f":"N12/R2^2*(AC15/AC4-AB15/N5)","v":8026.5769925488421},null,null,4,15,null,4,8]
[null,null,null,null,null,null,null,null,null,null,null,5,"w",200,5,{"$f":"AB19/2","v":1000},{"$f":"(N13*N5/(4*N2)-(P13/N2+2*N13/(N5*R2^2*N2))*AE18)/AD18","v":-1.2033056202218257E-3},{"$f":"((P13-Q13*N2)*AC18-2*N13/(N5*R2^2)*AF18)/R2","v":6936.1570625691102},null,null,5,2,null,4,9,null,"Case 4","W",{"$f":"N12*N5/2","v":2000},"Xcg",{"$f":"(N12*(2*N5))*N5/(6*AC13)","v":13.333333333333334}]
[null,null,null,null,null,null,null,null,null,null,null,6,"w",200,6,{"$f":"N14*N5/2","v":2000},"ML = MR =",{"$f":"-N14*(1-AB18/TAN(AB18))/R2^2","v":-6710.2195071050355},null,null,6,16,null,5,17,null,null,null,null,"(RA - qA*P)",{"$f":"P12-Q12*N2","v":698.15968999702477}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"+M =",{"$f":"N14*(AB18/AC18-1)/R2^2","v":3371.4799319769945},null,null,7,3,null,6,12,null,null,{"$f":"ACOS(AC4/AB4)/R2","v":11.496763716884093},{"$f":"R2*AB15","v":0.3582259090360731}]
[null,null,null,null,null,null,null,null,null,null,null,7,"W",500,7,{"$f":"N16/2","v":250},"ML = MR =",{"$f":"-N16*TAN(AB4/4)/(2*R2)","v":-1260.2124298852575},null,null,8,4,null,7,13]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"+M =",{"$f":"-R16","v":1260.2124298852575},null,null,9,4,null,8,14,null,"Case 5",null,"sin","cos","1-cos","kx - sin"]
[null,null,null,null,null,null,null,null,null,null,null,8,"M1",1000,8,{"$f":"-N18/N5","v":-50},{"$f":"N18*(AB4*AD22/AC4-1)/(N2*N5)","v":-1.1221148140280952E-4},null,null,null,10,14,null,9,15,null,"kL/2",{"$f":"R2*N5/2","v":0.31158847642487791},{"$f":"SIN(AB18)","v":0.30657101036100393},{"$f":"COS(AB18)","v":0.95184779014621512},{"$f":"1-AD18","v":4.8152209853784878E-2},{"$f":"AB18-AC18","v":5.0174660638739876E-3}]
[null,null,null,null,null,null,null,null,null,null,null,null,"a",3,null,null,"MaL =",{"$f":"(P18-Q18*N2)*AC23/R2","v":-138.01659432561883},null,null,11,13,null,10,16,null,"W",{"$f":"N5*N13/2","v":2000}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"MaR =",{"$f":"R19+N18","v":861.98340567438117},null,null,12,6,null,11,18]
[null,null,null,null,null,null,null,null,null,null,null,9,"W",500,9,{"$f":"N21*(AC4*AE26-AD4*AF26)/(AC4*AE4-AD4*AF4)","v":15.709087279063199},{"$f":"-N21*(AF4*AE26-AE4*AF26)/(AC4*AE4-AD4*AF4)/N2","v":-2.709215231635884E-5},null,null,null,13,7,null,12,19,null,"Case 8",null,"sin","cos","1-cos","kx - sin"]
[null,null,null,null,null,null,null,null,null,null,null,null,"a",3,null,null,"M0 =",{"$f":"-N21/R2*(AB4*AC27-AB27*AC4)/(AC4-AB4*AD4)","v":-1185.8182544187316},null,null,14,8,null,13,11,null,"k*(L - a)",{"$f":"R2*(N5-N19)","v":0.5297004099222925},{"$f":"SIN(AB22)","v":0.50527483008453777},{"$f":"COS(AB22)","v":0.86295848456518554},{"$f":"1-AD22","v":0.13704151543481446},{"$f":"AB22-AC22","v":2.442557983775473E-2}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Ma =",{"$f":"(P21-Q21*N2)*AC27/R2","v":270.1165619255674},null,null,15,9,null,14,10,null,"k*a",{"$f":"R2*N19","v":9.347654292746338E-2},{"$f":"SIN(AB23)","v":9.3340471501992775E-2}]
[null,null,null,null,null,null,null,null,null,null,null,10,"w",200,10,{"$f":"N24*N5-N24/R2*(AB4*AC4-1+(1-AB4^2/2)*AD4)/(AC4-AB4*AD4)","v":2506.5914453092514},{"$f":"N24/(R2*N2)*(4-2*AB4*AC4-(2-AB4^2/2)*(1+AD4))/(AC4-AB4*AD4)","v":9.4295140040191196E-4},{"$f":"-N24*N5/R2*(TAN(AB4)*(TAN(AB4/2)-AB4/2))/(TAN(AB4)-AB4)","v":-10131.828906184879},null,null,16,10,null,15,4]
[null,null,null,null,null,null,null,null,null,null,null,11,"w",200,11,{"$f":"N25*N5","v":4000},{"$f":"N25/(R2*N2)*(AB4/AD4-TAN(AB4))","v":8.9341956858614343E-3},{"$f":"-N25/(R2^2)*(1+AB4*TAN(AB4)-1/AD4)","v":-44579.082213738249},null,null,17,5,null,16,6,null,"Case9",null,"sin","cos","1-cos","kx - sin"]
[null,null,null,null,null,null,null,null,null,null,null,12,"W",500,12,{"$f":"N26","v":500},{"$f":"N26/N2*AE4/AD4","v":3.3069139236007669E-3},{"$f":"-N26/R2*TAN(AB4)","v":-11533.097624007662},null,null,18,11,null,17,2,null,"k*a",{"$f":"R2*N22","v":9.347654292746338E-2},{"$f":"SIN(AB26)","v":9.3340471501992775E-2},{"$f":"COS(AB26)","v":0.99563424829592195},{"$f":"1-AD26","v":4.3657517040780469E-3},{"$f":"AB26-AC26","v":1.3607142547060469E-4}]
[null,null,null,null,null,null,null,null,null,null,null,13,"M1",500,13,0,{"$f":"-N27*R2/N2*AE4/AC4","v":-1.4336625039560016E-4},{"$f":"N27*AD18-Q27*N2/R2*AC18","v":525.29407030844084},null,null,19,12,null,18,20,null,"k*(L-a)",{"$f":"R2*(N5-N22)","v":0.5297004099222925},{"$f":"SIN(AB27)","v":0.50527483008453777},{"$f":"COS(AB27)","v":0.86295848456518554},{"$f":"1-AD27","v":0.13704151543481446},{"$f":"AB27-AC27","v":2.442557983775473E-2}]
[null,null,null,null,null,null,null,null,null,null,null,14,"M1",500,null,null,null,null,null,null,20,18,null,"DL Case 1",3]
[null,null,null,null,null,null,null,null,null,null,null,null,"M2",250,14,{"$f":"(N29-N28)/N5","v":-12.5},{"$f":"-(N28*R2*AE4+P29*AF4)/(AC4*N2)","v":-1.191582167618614E-4},{"$f":"AD29","v":500},null,null,null,null,null,null,null,null,"Case14",{"$f":"ATAN((P29-Q29*N2)/(N28*R2))/R2","v":-15.757258982661067},{"$f":"IF(AB29>N5,N5,IF(AB29<0,0,AB29))","v":0},{"$f":"N28*COS(R2*AC29)+(P29-Q29*N2)*SIN(R2*AC29)/R2","v":500}]
[null,null,null,null,null,null,null,null,null,null,null,15,"w",200]
[null,null,null,null,null,null,null,null,null,null,null,null,"a",2.5,15,{"$f":"N30*(N5-2*N31)/2","v":1500},{"$f":"(N30*AF32/R2-P31*AE18)/(N2*AD18)","v":-1.7593639515112054E-3},{"$f":"(P31-Q31*N2)*AC18/R2-N30*AE32/R2^2","v":9764.8713395436571},null,null,null,null,null,null,null,null,"Case15",null,"sin","cos","1-cos","kx - sin"]
[null,null,null,null,null,null,null,null,null,null,null,16,"W",500,null,null,null,null,null,null,null,null,null,null,null,null,"kb/2",{"$f":"R2*(N5-2*N31)/2","v":0.23369135731865845},{"$f":"SIN(AB32)","v":0.23157011272328953},{"$f":"COS(AB32)","v":0.97281821677707236},{"$f":"1-AD32","v":2.7181783222927636E-2},{"$f":"AB32-AC32","v":2.1212445953689152E-3}]
[null,null,null,null,null,null,null,null,null,null,null,null,"a",2,16,{"$f":"N32","v":500},{"$f":"-N32/N2*((AC35+AC36)/AC4-1)","v":-2.588166743467703E-4},{"$f":"(P33-Q33*N2)*AC18/R2-N32*AC37/R2","v":1049.908280317994}]
[null,null,null,null,null,null,null,null,null,null,null,17,"w",100,null,null,null,null,null,null,null,null,null,null,null,null,"Case16",null,"sin","cos","1-cos","kx - sin"]
[null,null,null,null,null,null,null,null,null,null,null,null,"M1",5000,null,null,null,null,null,null,null,null,null,null,null,null,"k(L - a)",{"$f":"R2*(N5-N33)","v":0.56085925756478028},{"$f":"SIN(AB35)","v":0.53191401210110489},{"$f":"COS(AB35)","v":0.8467983725365239},{"$f":"1-AD35","v":0.1532016274634761},{"$f":"AB35-AC35","v":2.8945245463675384E-2}]
[null,null,null,null,null,null,null,null,null,null,null,null,"M2",1000,17,{"$f":"AE52","v":799.99999999999989},{"$f":"AF53","v":-2.0083529758812401E-3},{"$f":"AB73","v":8553.2655064529372},null,{"$f":"(N36-N35)/N5+N34*N5/2","v":800},null,null,null,null,null,null,"ka",{"$f":"R2*N33","v":6.2317695284975584E-2},{"$f":"SIN(AB36)","v":6.2277368038451041E-2},{"$f":"COS(AB36)","v":0.99805888074311688},{"$f":"1-AD36","v":1.941119256883117E-3},{"$f":"AB36-AC36","v":4.0327246524543559E-5}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"k(L/2 - a)",{"$f":"R2*(N5/2-N33)","v":0.24927078113990234},{"$f":"SIN(AB37)","v":0.24669734432566792}]
[null,null,null,null,null,null,null,null,null,null,null,18,"a",0.02,18,{"$f":"N38*N2*R2*AC46/(AE46^2-AC46*AF46)","v":1039.4804983452136},0,{"$f":"N38*N2*AC57/(2*(AC57-AB57))","v":10744.80498345215}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Case17",null,"sin","cos",null,"wk^2"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"kL",{"$f":"R2*N5","v":0.62317695284975583},{"$f":"SIN(AB40)","v":0.58361787747002802},{"$f":"COS(AB40)","v":0.81202843121246648},null,{"$f":"N34*R2^2","v":9.7087378640776711E-2}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"M1",{"$f":"IF(N35>N36,N35,N36)","v":5000}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"M2",{"$f":"IF(N35>N36,N36,N35)","v":1000}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"kx",{"$f":"ATAN(((AB42-AF40)-(AB41-AF40)*AD40)/((AB41-AF40)*AC40))","v":-0.80916803975820095},null,{"$f":"COS(AB43)","v":0.69010077239409418}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Fa3"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"sin","cos","1-cos","kx - sin","(kx)^2/2-Fa3"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"kL",{"$f":"R2*N5","v":0.62317695284975583},{"$f":"SIN(AB46)","v":0.58361787747002802},{"$f":"COS(AB46)","v":0.81202843121246648},{"$f":"1-AD46","v":0.18797156878753352},{"$f":"AB46-AC46","v":3.9559075379727804E-2},{"$f":"AB46^2/2-AE46","v":6.2031884940198789E-3}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AC46/R2","v":18.730406341286333},{"$f":"-AC46/R2","v":-18.730406341286333},null,{"$f":"N34*AE46/R2^2","v":19361.071585115951},{"$f":"-AD46*N35","v":-4060.1421560623326},{"$f":"AE48+AF48+N36","v":16300.929429053618}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AF46/R2","v":1.2695936587136674},{"$f":"AB48","v":18.730406341286333},null,{"$f":"N34*AG46/R2^2","v":638.92841488404747},{"$f":"-N35*AE46","v":-939.85784393766755},{"$f":"AE49+AF49","v":-300.92942905362008}]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MINVERSE(AB48:AC49)","v":4.9999999999999996E-2},0.05,null,{"$f":"MMULT(AB52:AC53,AG48:AG49)","v":799.99999999999989}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-3.3891247087234214E-3,0.05,null,-70.292354155843398,{"$f":"AE53/N2","v":-2.0083529758812401E-3}]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Case18",null,"tan"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Lk/2",{"$f":"N5*R2/2","v":0.31158847642487791},{"$f":"TAN(AB57)","v":0.32207986774220587}]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Ra - qa*P",{"$f":"AE52-AE53","v":870.29235415584333}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"w/k+M1/k",{"$f":"N34/R2+N35*R2","v":3365.1555453886813}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"kx",{"$f":"ATAN(AB63/AB64)","v":0.25307384342604861}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x",{"$f":"AB66/R2","v":8.12205400949939}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"cos(kx)",{"$f":"COS(AB66)","v":0.96814736448708083}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"sin(kx)",{"$f":"SIN(AB66)","v":0.25038107084346334}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AB63*AB70/R2","v":6993.3501418482074},{"$f":"-N34*(1-AB69)/R2^2","v":-3280.8214578306743},{"$f":"N35*AB69","v":4840.7368224354041}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Mmax",{"$f":"AB72+AC72+AD72","v":8553.2655064529372}]

{"sheet":"Tens Force","index":5,"n_rows":29,"n_cols":13,"rows_kept":29,"cut":false,"hidden":false,"merged":[]}
["Concentrated Intermediate Load"]
[]
["L",20,null,null,null,null,null,null,1,2,3,4]
["a",8,null,null,null,null,null,null,"cosh","sinh","cosh - 1","sinh - kx"]
["P",5000,null,null,null,null,"k",{"$f":"SQRT(B5/(B7*B8))","v":1.17769374287677E-2}]
["W",12000,null,null,null,null,"kL",{"$f":"H5*B3","v":0.23553874857535401},{"$f":"COSH(H6)","v":1.0278677327768291},{"$f":"SINH(H6)","v":0.23772268735604313},{"$f":"I6-1","v":2.7867732776829079E-2},{"$f":"J6-H6","v":2.1839387806891208E-3},"C"]
["E",10300000,"psi",null,null,null,"k(L-a)",{"$f":"H5*(B3-B4)","v":0.14132324914521238},{"$f":"COSH(H7)","v":1.0100027619100129},{"$f":"SINH(H7)","v":0.14179414327063761},{"$f":"I7-1","v":1.0002761910012925E-2},{"$f":"J7-H7","v":4.7089412542522524E-4},"Ca"]
["I",3.5,"in4",null,null,null,"ka",{"$f":"H5*B4","v":9.4215499430141597E-2},{"$f":"COSH(H8)","v":1.0044415641931368},{"$f":"SINH(H8)","v":9.4354946233650858E-2}]
[]
["Point A at left end",null,null,null,null,null,null,{"$f":"B4","v":8},{"$f":"(E11+E12*B5)*J8/H5","v":57345.746650086221},{"$f":"IF(I10=I13,H10,0)","v":8}]
[null,null,null,"RA",{"$f":"B6*(B3-B4)/B3","v":7200}]
[null,null,null,"qA",{"$f":"-B6/(B5*H5*B3)*(L6/J6*J7-L7)","v":-8.4751100771222922E-3}]
[null,null,null,"Mmax",{"$f":"I13","v":57345.746650086221},"@ x =",{"$f":"J13","v":8},null,{"$f":"MAX(I10:I11)","v":57345.746650086221},{"$f":"J10+J11","v":8}]
[]
[]
[null,null,null,"RA",{"$f":"B6*(J6*K7-I6*L7)/(J6*K6-I6*L6)","v":5188.6848520711519}]
[null,null,null,"qA",{"$f":"-B6/B5*(L6*K7-K6*L7)/(J6*K6-I6*L6)","v":-4.7795527026001068E-3}]
[null,null,null,"MB",{"$f":"(E16+E17*B5)/H5*J6-B6/H5*J7","v":-40226.30295857694}]
[null,null,null,"Ma",{"$f":"(E16+E17*B5)*J8/H5","v":41379.451236513065}]
[]
[null,null,null,"RA",{"$f":"B6*(K6*K7-J6*L7)/(K6^2-J6*L6)","v":7775.6168059282136},null,null,null,null,"MA",{"$f":"-B6/H5*(L6*K7-K6*L7)/(K6^2-J6*L6)","v":-34524.256111327231}]
[null,null,null,"qA",0,null,null,{"$f":"B4","v":8},{"$f":"K21*COSH(H5*H22)+E21*SINH(H$5*H22)/H$5","v":27619.405131709878},"MB",{"$f":"K21*I6+E21/H5*J6-B6/H5*J7","v":-23011.919992762909}]
[null,null,null,"Mmax (-)",{"$f":"MIN(K21:K22)","v":-34524.256111327231},null,null,{"$f":"B3/2","v":10},{"$f":"K21*COSH(H5*H23)+E21*SINH(H5*H23)/H5-B6*SINH(H5*(H23-B4))/H5","v":19169.862822592513}]
[null,null,null,"Mmax (+)",{"$f":"MAX(I22:I24)","v":27619.405131709878},null,null,{"$f":"B3-B4","v":12},{"$f":"K21*COSH(H5*H24)+E21*SINH(H5*H24)/H5-B6*SINH(H5*(H24-B4))/H5","v":10730.956157914385}]
[]
[]
[null,null,null,"RB",{"$f":"B6","v":12000}]
[null,null,null,"qA",{"$f":"B6/B5*K7/I6","v":2.3355756600293383E-2}]
[null,null,null,"Mmax",{"$f":"E28*B5/H5*J6-B6/H5*J7","v":-142122.58180448803}]

{"sheet":"Tens Moment","index":6,"n_rows":31,"n_cols":13,"rows_kept":31,"cut":false,"hidden":false,"merged":[]}
["Concentrated Intermediate Moment"]
[]
["L",10,null,null,null,null,null,null,1,2,3,4]
["a",3,null,null,null,null,null,null,"cosh","sinh","cosh - 1","sinh - kx"]
["P",1500,null,null,null,null,"k",{"$f":"SQRT(B5/(B7*B8))","v":5.396870722208659E-2}]
["M0",1000,null,null,null,null,"kL",{"$f":"H5*B3","v":0.53968707222086587},{"$f":"COSH(H6)","v":1.1492002995022603},{"$f":"SINH(H6)","v":0.56626966047642446},{"$f":"I6-1","v":0.14920029950226033},{"$f":"J6-H6","v":2.6582588255558592E-2},"C"]
["E",10300000,"psi",null,null,null,"k(L-a)",{"$f":"H5*(B3-B4)","v":0.37778095055460614},{"$f":"COSH(H7)","v":1.0722119608549161},{"$f":"SINH(H7)","v":0.38683134438711664},{"$f":"I7-1","v":7.2211960854916102E-2},{"$f":"J7-H7","v":9.0503938325104949E-3},"Ca"]
["I",0.05,"in4",null,null,null,"ka",{"$f":"H5*B4","v":0.16190612166625978},{"$f":"COSH(H8)","v":1.0131354524966443},{"$f":"SINH(H8)","v":0.16261440620553821}]
[]
[null,null,null,null,null,null,null,{"$f":"B4","v":3},{"$f":"(E11+E12*B5)*J8/H5","v":-307.90473781379103},{"$f":"IF(I10=I13,H10,0)","v":0}]
[null,null,null,"RA",{"$f":"-B6/B3","v":-100}]
[null,null,null,"qA",{"$f":"B6*H5/B5*(1/H6-I7/J6)","v":-1.4585834679464974E-3}]
[null,null,null,"Mmax (-)",{"$f":"(E11+E12*B5)/H5*J8","v":-307.90473781379109}]
[null,null,null,"Mmax (+)",{"$f":"E13+B6","v":692.09526218620886}]
[]
[]
[null,null,null,"RA",{"$f":"-B6*H5*(J6*J7-I6*K7)/(J6*K6-I6*L6)","v":-136.14007689506985}]
[null,null,null,"qA",{"$f":"-B6*H5/B5*(K6*K7-L6*J7)/(J6*K6-I6*L6)","v":-3.2755956340180248E-4}]
[null,null,null,"Mmax (-)",{"$f":"(E17+E18*B5)/H5*J8","v":-411.6873974669644}]
[null,null,null,"Mmax (+)",{"$f":"B6+E19","v":588.3126025330356}]
[]
[]
[null,null,null,"RA",{"$f":"-B6*H5*(K6*J7-J6*K7)/(K6^2-J6*L6)","v":-125.96945434217768},"MA",{"$f":"-B6*(K6*K7-L6*J7)/(K6^2-J6*L6)","v":-68.129905799325314}]
[null,null,null,"qA",0,"MB",{"$f":"E23*B3+G23+B6","v":-327.82444922110221}]
[null,null,null,"Mmax (-)",{"$f":"MIN(G25:G26)","v":-448.58640727855379},{"$f":"B4","v":3},{"$f":"G23*I8+E23/H5*J8","v":-448.58640727855379}]
[null,null,null,"Mmax (+)",{"$f":"MAX(G25:G26)","v":551.41359272144621},{"$f":"F25","v":3},{"$f":"G25+B6","v":551.41359272144621}]
[]
[]
[null,null,null,"RB",0]
[null,null,null,"qA",{"$f":"-B6*H5/B5*J7/I6","v":-1.2110907372484192E-2}]
[null,null,null,"Mmax",{"$f":"E30*B5/H5*J6+B6*I7","v":881.60040763603297}]

{"sheet":"Tens Distributed","index":7,"n_rows":49,"n_cols":40,"rows_kept":49,"cut":false,"hidden":false,"merged":[]}
["Distributed Load"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"(K14+K16*B8)/N5*T5-B6/N5^2*(COSH(N5*(B3-B4))-1)-N4/N5^3*(SINH(N5*(B3-B4))-N5*(B3-B4))","v":-1133.0416632422337},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x","kx","k*sinh","cosh","x-a","k(x-a)","cosh","sinh","V","V'"]
["L",40,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"B4+B12/2","v":20},{"$f":"N$5*AE3","v":0.22360679774997896},{"$f":"N$5*SINH(AF3)","v":2.5208854787137133E-3},{"$f":"COSH(AF3)","v":1.0251043404328739},{"$f":"AE3-B$4","v":10},{"$f":"N$5*AI3","v":0.11180339887498948},{"$f":"COSH(AJ3)","v":1.0062565131299459},{"$f":"SINH(AJ3)","v":0.11203646824332211},{"$f":"AC$9*AH3-O$10*AL3-O$11*(AK3-1)","v":4.9785207270378873},{"$f":"AC$9*AG3-(O$10*AK3+O$11*AL3)*N$5","v":-2.4540349250803684}]
["a",10,"Case 1",null,null,null,null,null,null,"W",{"$f":"B12*(B6+B7)/2","v":50},null,"Q",{"$f":"B13/B12","v":0.15},"(wb-wa)/(b - a)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AE3-AM3/AN3","v":22.028708180212572},0.24628844473730499,2.7815109351991452E-3,{"$f":"COSH(AF4)","v":1.0304826173502684},12.028708180212572,0.13448504586231552,{"$f":"COSH(AJ4)","v":1.0090567516510551},{"$f":"SINH(AJ4)","v":0.13489080047423285},{"$f":"AC$9*AH4-O$10*AL4-O$11*(AK4-1)","v":-0.3078337105164497},{"$f":"AC$9*AG4-(O$10*AK4+O$11*AL4)*N$5","v":-2.7577359158195378}]
["b",30,null,null,null,null,null,null,null,"RA",{"$f":"K4*(B3-B14)/B3","v":22.5},null,"k",{"$f":"SQRT(B8/(B9*B10))","v":1.1180339887498949E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.917082658439227,0.24504043346375959,2.7671345776332516E-3,1.0301729321652111,11.917082658439227,0.13323703458877009,1.0088891921869276,0.13363159099401359,-9.3467922508416734E-4,-2.7409899355750311]
["wa",1,null,null,null,null,null,null,null,"RB",{"$f":"K4-K5","v":27.5},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.916741657834681,0.24503662096109891,2.7670906664542805E-3,1.030171988578134,11.916741657834681,0.13323322208610944,1.0088886827234635,0.13362774460225524,-8.7210416666039237E-9,-2.7409387854644285]
["wb",4,null,null,null,null,null,null,null,"qA",{"$f":"Calcs2!F43","v":-5.4400786020339365E-4},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.91674165465291,0.24503662092552564,2.7670906660445587E-3,1.0301719885693297,11.91674165465291,0.13323322205053614,1.00888868271871,0.13362774456636572,-5.6843418860808015E-14,-2.7409387849871627]
["P",1000,null,null,null,null,null,null,null,"Mmax",{"$f":"AC11","v":372.57970568619015},"@ x =",{"$f":"AC12","v":21.916741654652974},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.916741654652888,0.24503662092552539,2.7670906660445561E-3,1.0301719885693297,11.916741654652888,0.13323322205053592,1.0088886827187098,0.1336277445663655,2.2915003228263231E-13,-2.7409387849871591]
["E",80000,"psi",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(RA +qA*P)",null,{"$f":"K5+K7*B8","v":21.955992139796606},null,21.916741654652974,0.24503662092552633,2.767090666044567E-3,1.0301719885693299,11.916741654652974,0.13323322205053686,1.00888868271871,0.13362774456636645,-1.1368683772161603E-13,-2.7409387849871725]
["I",100,"in4",null,null,null,null,null,null,null,null,null,null,"wa/k",{"$f":"B6/N5","v":89.442719099991592},null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AC9*SINH(AF15)/N$5-B$6*(AK15-1)/N$5^2-N$4*(AL15-AJ15)/N$5^3","v":372.57970568619015},null,21.916741654652931,0.24503662092552586,2.7670906660445609E-3,1.0301719885693297,11.916741654652931,0.13323322205053639,1.00888868271871,0.13362774456636597,-7.815970093361102E-14,-2.7409387849871663]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Q/k2",{"$f":"N4/N5^2","v":1200},null,null,null,null,null,null,null,null,null,null,null,null,"Mmax",{"$f":"IF(AC9<0,\"NA\",AC10)","v":372.57970568619015},null,21.916741654652903,0.24503662092552556,2.7670906660445574E-3,1.0301719885693297,11.916741654652903,0.13323322205053606,1.00888868271871,0.13362774456636564,-4.9737991503207013E-14,-2.7409387849871614]
["b - a",{"$f":"B5-B4","v":20},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x",{"$f":"IF(AC2<0,\"NA\",AE9)","v":21.916741654652974},null,21.916741654652885,0.24503662092552536,2.7670906660445557E-3,1.0301719885693297,11.916741654652885,0.13323322205053587,1.00888868271871,0.13362774456636545,-3.1974423109204508E-14,-2.7409387849871587]
["wb-wa",{"$f":"B7-B6","v":3},"Case 2",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.916741654652874,0.24503662092552522,2.7670906660445544E-3,1.0301719885693297,11.916741654652874,0.13323322205053575,1.0088886827187098,0.13362774456636534,2.4513724383723456E-13,-2.7409387849871574]
["Xcg",{"$f":"(B6*(B5+2*B4)+B7*(2*B5+B4))*B12/(6*K4)","v":22},null,null,null,null,null,null,null,"RA",{"$f":"Calcs2!F102","v":13.681206768706469},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.916741654652963,0.24503662092552622,2.7670906660445652E-3,1.0301719885693299,11.916741654652963,0.13323322205053675,1.0088886827187102,0.13362774456636636,-3.730349362740526E-13,-2.7409387849871716]
[null,null,null,null,null,null,null,null,null,"RB",{"$f":"K4-K14","v":36.318793231293533},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.916741654652828,0.24503662092552472,2.7670906660445479E-3,1.0301719885693297,11.916741654652828,0.13323322205053523,1.0088886827187098,0.13362774456636481,2.9132252166164108E-13,-2.7409387849871507]
[null,null,null,null,null,null,null,null,null,"qA",{"$f":"Calcs2!J101","v":-2.5665219560581503E-4}]
[null,null,null,null,null,null,null,null,null,"MB",{"$f":"Calcs2!T103","v":-350.61880319270784},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x","kx","k*sinh","cosh","x-a","k(x-a)","cosh","sinh","V","V'"]
[null,null,null,null,null,null,null,null,null,"Mmax (+)",{"$f":"AC28","v":198.62767713415343},"@ x =",{"$f":"AC29","v":18.400616114174678},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"B4+B12/2","v":20},{"$f":"N$5*AE18","v":0.22360679774997896},{"$f":"N$5*SINH(AF18)","v":2.5208854787137133E-3},{"$f":"COSH(AF18)","v":1.0251043404328739},{"$f":"AE18-B$4","v":10},{"$f":"N$5*AI18","v":0.11180339887498948},{"$f":"COSH(AJ18)","v":1.0062565131299459},{"$f":"SINH(AJ18)","v":0.11203646824332211},{"$f":"AC$19*AH18-O$10*AL18-O$11*(AK18-1)","v":-3.7670929527142096},{"$f":"AC$19*AG18-(O$10*AK18+O$11*AL18)*N$5","v":-2.4755417021548052}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(RA + qA*P)",null,{"$f":"K14+K16*B8","v":13.424554573100654},null,{"$f":"AE18-AM18/AN18","v":18.478275300539195},0.20659339839480498,{"$f":"N$5*SINH(AF19)","v":2.3262500986215764E-3},{"$f":"COSH(AF19)","v":1.0214164264249401},8.4782753005391953,9.4789999519815496E-2,{"$f":"COSH(AJ19)","v":1.004495936879342},{"$f":"SINH(AJ19)","v":9.4932013605036808E-2},{"$f":"AC$19*AH19-O$10*AL19-O$11*(AK19-1)","v":-0.17404112327925603},{"$f":"AC$19*AG19-(O$10*AK19+O$11*AL19)*N$5","v":-2.2469136794504991}]
[null,null,"Case 3","  Both ends fixed",null,null,null,null,null,"RA",{"$f":"Calcs2!F158","v":21.175531320664568},null,"MA",{"$f":"Calcs2!J157","v":-203.93170517709987},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,18.40081744140069,0.20572739320267849,2.3163613784785869E-3,1.0212366230632632,8.4008174414006902,9.3923994327688998E-2,1.0044141019208026,9.4062150397342698E-2,-4.5002253201076314E-4,-2.235294156573997]
[null,null,null,null,null,null,null,null,null,"RB",{"$f":"K4-K20","v":28.824468679335432},null,"MB",{"$f":"Calcs2!O157","v":-256.91045235051718},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,18.400616115534614,0.20572514231106762,2.3163356783160037E-3,1.0212361567223898,8.4006161155346142,9.392174343607812E-2,1.0044138901996418,9.4059889570305144E-2,-3.039872353838291E-9,-2.2352639576884235]
[null,null,null,null,null,null,null,null,null,"Mmax (+)",{"$f":"AC48","v":355.42132490925223},"@ x =",{"$f":"AC49","v":21.621250830143218},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,18.400616114174653,0.20572514229586278,2.3163356781423987E-3,1.0212361567192396,8.4006161141746531,9.3921743420873297E-2,1.0044138901982116,9.4059889555033194E-2,3.0198066269804258E-14,-2.2352639574844289]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,18.400616114174667,0.20572514229586294,2.3163356781424004E-3,1.0212361567192396,8.4006161141746674,9.3921743420873449E-2,1.0044138901982116,9.4059889555033346E-2,1.5987211554602254E-14,-2.2352639574844311]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,18.400616114174674,0.20572514229586303,2.3163356781424013E-3,1.0212361567192396,8.4006161141746745,9.3921743420873532E-2,1.0044138901982116,9.4059889555033444E-2,7.1054273576010019E-15,-2.2352639574844324]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,18.400616114174678,0.20572514229586306,2.3163356781424021E-3,1.0212361567192396,8.400616114174678,9.3921743420873574E-2,1.0044138901982116,9.4059889555033471E-2,0,-2.2352639574844329]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,18.400616114174678,0.20572514229586306,2.3163356781424021E-3,1.0212361567192396,8.400616114174678,9.3921743420873574E-2,1.0044138901982116,9.4059889555033471E-2,0,-2.2352639574844329]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AC19*SINH(AF29)/N$5-B$6*(AK29-1)/N$5^2-N$4*(AL29-AJ29)/N$5^3","v":198.62767713415343},null,18.400616114174678,0.20572514229586306,2.3163356781424021E-3,1.0212361567192396,8.400616114174678,9.3921743420873574E-2,1.0044138901982116,9.4059889555033471E-2,0,-2.2352639574844329]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Mmax",{"$f":"IF(AC19<0,\"NA\",AC27)","v":198.62767713415343},null,18.400616114174678,0.20572514229586306,2.3163356781424021E-3,1.0212361567192396,8.400616114174678,9.3921743420873574E-2,1.0044138901982116,9.4059889555033471E-2,0,-2.2352639574844329]
[null,null,"Case 4","  Cantilever (right end fixed)",null,null,null,null,null,"RB",{"$f":"K4","v":50},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x",{"$f":"IF(AC19<0,\"NA\",AE27)","v":18.400616114174678},null,18.400616114174678,0.20572514229586306,2.3163356781424021E-3,1.0212361567192396,8.400616114174678,9.3921743420873574E-2,1.0044138901982116,9.4059889555033471E-2,0,-2.2352639574844329]
[null,null,null,null,null,null,null,null,null,"qA",{"$f":"Calcs2!I204","v":1.0028880923087214E-3}]
[null,null,null,null,null,null,null,null,null,"yA",{"$f":"Calcs2!I206","v":-3.3664530470319441E-2}]
[null,null,null,null,null,null,null,null,null,"MB",{"$f":"Calcs2!I213","v":-395.75566627478048}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x","kx","k*sinh","cosh","x-a","k(x-a)","cosh","sinh","V","V'"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"B4+B12/2","v":20},{"$f":"N$5*AE34","v":0.22360679774997896},{"$f":"N$5*SINH(AF34)","v":2.5208854787137133E-3},{"$f":"COSH(AF34)","v":1.0251043404328739},{"$f":"AE34-B$4","v":10},{"$f":"N$5*AI34","v":0.11180339887498948},{"$f":"COSH(AJ34)","v":1.0062565131299459},{"$f":"SINH(AJ34)","v":0.11203646824332211},{"$f":"AC$35*AH34-O$10*AL34-O$11*(AK34-1)","v":4.1784669538078401},{"$f":"AC$35*AG34-(O$10*AK34+O$11*AL34)*N$5","v":-2.4560023774260236}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(RA + qA*P)",null,{"$f":"K20","v":21.175531320664568},null,{"$f":"AE34-AM34/AN34","v":21.701328546019983},0.24262822915478677,{"$f":"N$5*SINH(AF35)","v":2.7393595954702857E-3},{"$f":"COSH(AF35)","v":1.0295789080718198},11.701328546019983,0.1308248302797973,{"$f":"COSH(AJ35)","v":1.0085697804028493},{"$f":"SINH(AJ35)","v":0.13119833056045876},{"$f":"AC$35*AH35-O$10*AL35-O$11*(AK35-1)","v":-0.21659149515564557},{"$f":"AC$35*AG35-(O$10*AK35+O$11*AL35)*N$5","v":-2.7107726994964487}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AE35-AM35/AN35","v":21.621428266960852},0.24173491687779966,2.7290777318579977E-3,1.0293604432521126,11.621428266960852,0.12993151800281019,1.0084529817306618,0.13029741502218198,-4.7886173990896452E-4,-2.6987865744357813]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.621250831018177,0.24173293308365232,2.7290549011707928E-3,1.0293599590176581,11.621250831018177,0.12992953420866282,1.0084527232493969,0.13029541445931531,-2.3614390443071898E-9,-2.6987599590390698]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.621250830143168,0.24173293307386942,2.7290549010582053E-3,1.0293599590152702,11.621250830143168,0.12992953419887993,1.0084527232481222,0.1302954144494497,1.1368683772161603E-13,-2.6987599589078184]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.621250830143211,0.24173293307386989,2.729054901058211E-3,1.0293599590152702,11.621250830143211,0.1299295341988804,1.0084527232481224,0.1302954144494502,-1.971756091734278E-13,-2.6987599589078251]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.621250830143136,0.24173293307386906,2.729054901058201E-3,1.02935995901527,11.621250830143136,0.12992953419887956,1.0084527232481222,0.13029541444944936,1.4033219031261979E-13,-2.6987599589078144]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.62125083014319,0.24173293307386964,2.7290549010582079E-3,1.0293599590152702,11.62125083014319,0.12992953419888018,1.0084527232481224,0.13029541444944998,-1.758593271006248E-13,-2.6987599589078219]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.621250830143126,0.24173293307386895,2.7290549010582001E-3,1.02935995901527,11.621250830143126,0.12992953419887945,1.0084527232481222,0.13029541444944925,1.5099033134902129E-13,-2.6987599589078126]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.621250830143182,0.24173293307386959,2.7290549010582075E-3,1.0293599590152702,11.621250830143182,0.12992953419888009,1.0084527232481222,0.13029541444944986,9.9475983006414026E-14,-2.6987599589078202]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.621250830143218,0.24173293307386998,2.7290549010582118E-3,1.0293599590152702,11.621250830143218,0.12992953419888048,1.0084527232481224,0.13029541444945028,-2.042810365310288E-13,-2.6987599589078259]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.621250830143143,0.24173293307386914,2.7290549010582023E-3,1.02935995901527,11.621250830143143,0.12992953419887965,1.0084527232481222,0.13029541444944942,1.3500311979441904E-13,-2.6987599589078144]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.621250830143193,{"$f":"N$5*AE46","v":0.2417329330738697},2.7290549010582088E-3,1.0293599590152702,{"$f":"AE46-B$4","v":11.621250830143193},{"$f":"N$5*AI46","v":0.1299295341988802},1.0084527232481224,0.13029541444944998,-1.758593271006248E-13,-2.6987599589078219]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21.621250830143129,{"$f":"N$5*AE47","v":0.24173293307386898},2.7290549010582006E-3,1.02935995901527,{"$f":"AE47-B$4","v":11.621250830143129},{"$f":"N$5*AI47","v":0.12992953419887951},1.0084527232481222,0.13029541444944931,1.4566126083082054E-13,-2.6987599589078131]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Mmax",{"$f":"AC35*SINH(AF49)/N$5-B$6*(AK49-1)/N$5^2-N$4*(AL49-AJ49)/N$5^3","v":355.42132490925223},null,21.621250830143182,{"$f":"N$5*AE48","v":0.24173293307386959},2.7290549010582075E-3,1.0293599590152702,{"$f":"AE48-B$4","v":11.621250830143182},{"$f":"N$5*AI48","v":0.12992953419888009},1.0084527232481222,0.13029541444944986,9.9475983006414026E-14,-2.6987599589078202]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x",{"$f":"AE49","v":21.621250830143218},null,21.621250830143218,{"$f":"N$5*AE49","v":0.24173293307386998},2.7290549010582118E-3,1.0293599590152702,{"$f":"AE49-B$4","v":11.621250830143218},{"$f":"N$5*AI49","v":0.12992953419888048},1.0084527232481224,0.13029541444945028,-2.042810365310288E-13,-2.6987599589078259]

{"sheet":"Calcs1","index":8,"n_rows":213,"n_cols":24,"rows_kept":213,"cut":false,"hidden":false,"merged":[]}
["Distributed Load"]
[]
["L",{"$f":"'Comp Distributed'!B3","v":40},null,null,null,null,null,null,"wa",{"$f":"B6","v":1}]
["a",{"$f":"'Comp Distributed'!B4","v":10},null,null,null,null,null,null,"Q",{"$f":"(B7-B6)/(B5-B4)","v":0.15},"(wb-wa)/(b - a)"]
["b",{"$f":"'Comp Distributed'!B5","v":30},null,null,null,null,null,null,"k",{"$f":"SQRT(B8/(B9*B10))","v":1.1180339887498949E-2}]
["wa",{"$f":"'Comp Distributed'!B6","v":1},null,null,null,null,null,null,null,null,null,"wa/k",{"$f":"J3/J5","v":89.442719099991592},"Z1"]
["wb",{"$f":"'Comp Distributed'!B7","v":4},null,null,null,null,null,null,null,null,null,"Q/k2",{"$f":"J4/J5^2","v":1200},"Z2"]
["P",{"$f":"'Comp Distributed'!B8","v":1000}]
["E",{"$f":"'Comp Distributed'!B9","v":80000},"psi"]
["I",{"$f":"'Comp Distributed'!B10","v":100},"in4"]
[]
["b - a",{"$f":"B5-B4","v":20}]
["wb-wa",{"$f":"B7-B6","v":3}]
["W",{"$f":"(B6+B7)*(B5-B4)/2","v":50}]
["Xcg",{"$f":"(B6*(B5+2*B4)+B7*(2*B5+B4))*B12/(6*B14)","v":22},null,null,"CASE 1 ss/ss"]
[null,null,null,null,"yA = yL = 0",null,null,null,"RA",{"$f":"B14*(1-B15/B3)","v":22.499999999999996}]
[null,null,null,null,"MA = ML = 0"]
[null,null,null,null,"Based on length (L - b)"]
[null,null,null,null,"yL = yb +qb/k*F2 + Mb/P*F3 + Vb/(kP)*F4 = 0"]
[null,null,null,"or","yb*k*P + qb*P*F2 + Mb*k*F3 + Vb*F4 = 0"]
[null,null,null,null,"F2, F3, F4 are F2b, F3b, F4b (span b to L)"]
[]
[null,null,null,null,"Values at b for span 0 to b"]
[null,null,null,null,"Vb = (RA-qA*P)*F1 - Z1*Fa2 - Z2*Fa3"]
[null,null,null,null,"Mb*k = (RA-qA*P)*F2 - Z1*Fa3 - Z2*Fa4"]
[null,null,null,null,"qb*P = qA*P*F1 + RA*F3 - Z1*Fa4 - Z2*Fa5"]
[null,null,null,null,"yb*k*P = qA*P*F2 + RA*F4 - Z1*Fa5 - Z2*Fa6"]
[]
[null,null,null,null,"(qA*P*F2 + RA*F4 - Z1*Fa5 - Z2*Fa6)"]
[null,null,null,null,"+ (qA*P*F1 + RA*F3 - Z1*Fa4 - Z2*Fa5)*F2b"]
[null,null,null,null,"+ [(RA-qA*P)*F2 - Z1*Fa3 - Z2*Fa4]*F3b"]
[null,null,null,null,"+ [(RA-qA*P)*F1 - Z1*Fa2 - Z2*Fa3]*F4b = 0"]
[]
[]
[null,null,null,null,"qA*P","F2 + F1*F2b - F2*F3b - F1*F4b",null,null,null,{"$f":"Q39+P39*Q38-Q39*R38-P39*S38","v":0.43223503222002213}]
[]
[null,null,null,null,"RA","F4 + F3*F2b + F2*F3b + F1*F4b",null,null,null,{"$f":"S39+R39*Q38+Q39*R38+P39*S38","v":1.474578506630278E-2},{"$f":"J37*N42","v":0.33178016399181254},null,null,"x","kx","F1","F2","F3","F4","F5","F6"]
[null,null,null,null,null,null,null,null,null,null,null,null,"L-b",{"$f":"B3-B5","v":10},{"$f":"J$5*N38","v":0.11180339887498948},{"$f":"COS(O38)","v":0.99375650770459845},{"$f":"SIN(O38)","v":0.11157062066135646},{"$f":"1-P38","v":6.2434922954015537E-3},{"$f":"O38-Q38","v":2.3277821363301698E-4}]
[null,null,null,null,"Z1","Fa5 + Fa4*F2b + Fa3*F3b + Fa2*F4b",null,null,null,{"$f":"T40+S40*Q38+R40*R38+Q40*S38","v":5.1842980062231654E-4},{"$f":"-J39*N43","v":-4.6369771030126503E-2},null,"b",{"$f":"B5","v":30},{"$f":"J$5*N39","v":0.33541019662496846},{"$f":"COS(O39)","v":0.94427537017871055},{"$f":"SIN(O39)","v":0.32915653612507711},{"$f":"1-P39","v":5.5724629821289451E-2},{"$f":"O39-Q39","v":6.2536604998913448E-3}]
[null,null,null,null,null,null,null,null,null,null,null,null,"b-a",{"$f":"B12","v":20},{"$f":"J$5*N40","v":0.22360679774997896},{"$f":"COS(O40)","v":0.97510399321047936},{"$f":"SIN(O40)","v":0.22174806070172826},{"$f":"1-P40","v":2.4896006789520642E-2},{"$f":"O40-Q40","v":1.8587370482507082E-3},{"$f":"O40^2/2-R40","v":1.0399321047935631E-4},{"$f":"O40^3/6-S40","v":4.6529329991162882E-6}]
[null,null,null,null,"Z2","Fa6 + Fa5*F2b + Fa4*F3b + Fa3*F4b",null,null,null,{"$f":"U40+T40*Q38+S40*R38+R40*S38","v":3.3655778463855947E-5},{"$f":"-J41*N44","v":-4.0386934156627134E-2}]
[null,null,null,null,null,null,null,null,null,null,null,null,"RA",{"$f":"B14*(B3-B15)/B3","v":22.5}]
[null,null,null,null,"qA*P",{"$f":"-(K37+K39+K41)/J35","v":-0.56687552035424493},null,null,null,null,null,null,"Z1",{"$f":"M$6","v":89.442719099991592},"wa/k"]
[null,null,null,null,"qA",{"$f":"F43/B8","v":-5.6687552035424493E-4},null,null,null,null,null,null,"Z2",{"$f":"M$7","v":1200},"Q/k2"]
[]
[]
[]
[null,null,null,null,"CASE 2 ss/fixed"]
[null,null,null,null,"yA = yL = 0"]
[null,null,null,null,"MA = qL = 0"]
[null,null,null,null,"Based on length (L - b)"]
[null,null,null,null,"yL = yb +qb/k*F2 + Mb/P*F3 + Vb/(kP)*F4 = 0"]
[null,null,null,null,"yb*k*P + qb*P*F2 + Mb*k*F3 + Vb*F4 = 0"]
[null,null,null,null,"F2, F3, F4 are F2b, F3b, F4b (span b to L)"]
[]
[null,null,null,null,"qL = qb*F1 + Mb*k/P*F2 + Vb/P*F3 = 0"]
[null,null,null,null,"qb*P*F1 + Mb*k*F2 + Vb*F3 = 0"]
[]
[null,null,null,null,"Values at b for span 0 to b"]
[null,null,null,null,"Vb = (RA-qA*P)*F1 -  Z1*Fa2 - Z2*Fa3"]
[null,null,null,null,"Mb*k = (RA-qA*P)*F2 - Z1*Fa3 - Z2*Fa4"]
[null,null,null,null,"qb*P = qA*P*F1 + RA*F3 - Z1*Fa4 - Z2*Fa5"]
[null,null,null,null,"yb*k*P = qA*P*F2 + RA*F4 - Z1*Fa5 - Z2*Fa6"]
[]
[null,null,null,null,"y equation",null,"yb*k*P + qb*P*F2 + Mb*k*F3 + Vb*F4 = 0"]
[null,null,null,null,"(qA*P*F2 + RA*F4 - Z1*Fa5 - Z2*Fa6)"]
[null,null,null,null,"+ (qA*P*F1 + RA*F3 - Z1*Fa4 - Z2*Fa5)*F2b"]
[null,null,null,null,"+ [(RA-qA*P)*F2 - Z1*Fa3 - Z2*Fa4]*F3b"]
[null,null,null,null,"+ [(RA-qA*P)*F1 - Z1*Fa2 - Z2*Fa3]*F4b = 0"]
[]
[null,null,null,null,"y equation"]
[null,null,null,null,"qA*P","F2 + F1*F2b - F2*F3b - F1*F4b",null,null,null,{"$f":"Q76+P76*Q75-Q76*R75-P76*S75","v":0.43223503222002213}]
[]
[null,null,null,null,"RA","F4 + F3*F2b + F2*F3b + F1*F4b",null,null,null,{"$f":"S76+R76*Q75+Q76*R75+P76*S75","v":1.474578506630278E-2},null,null,null,"x","kx","F1","F2","F3","F4","F5","F6"]
[null,null,null,null,null,null,null,null,null,null,null,null,"L-b",{"$f":"B$3-B$5","v":10},{"$f":"J$5*N75","v":0.11180339887498948},{"$f":"COS(O75)","v":0.99375650770459845},{"$f":"SIN(O75)","v":0.11157062066135646},{"$f":"1-P75","v":6.2434922954015537E-3},{"$f":"O75-Q75","v":2.3277821363301698E-4}]
[null,null,null,null,"Z1","Fa5 + Fa4*F2b + Fa3*F3b + Fa2*F4b",null,null,null,{"$f":"T77+S77*Q75+R77*R75+Q77*S75","v":5.1842980062231654E-4},{"$f":"-J76*N80","v":-4.6369771030126503E-2},null,"b",{"$f":"B$5","v":30},{"$f":"J$5*N76","v":0.33541019662496846},{"$f":"COS(O76)","v":0.94427537017871055},{"$f":"SIN(O76)","v":0.32915653612507711},{"$f":"1-P76","v":5.5724629821289451E-2},{"$f":"O76-Q76","v":6.2536604998913448E-3}]
[null,null,null,null,null,null,null,null,null,null,null,null,"b-a",{"$f":"B$5-B$4","v":20},{"$f":"J$5*N77","v":0.22360679774997896},{"$f":"COS(O77)","v":0.97510399321047936},{"$f":"SIN(O77)","v":0.22174806070172826},{"$f":"1-P77","v":2.4896006789520642E-2},{"$f":"O77-Q77","v":1.8587370482507082E-3},{"$f":"O77^2/2-R77","v":1.0399321047935631E-4},{"$f":"O77^3/6-S77","v":4.6529329991162882E-6}]
[null,null,null,null,"Z2","Fa6 + Fa5*F2b + Fa4*F3b + Fa3*F4b",null,null,null,{"$f":"U77+T77*Q75+S77*R75+R77*S75","v":3.3655778463855947E-5},{"$f":"-J78*N81","v":-4.0386934156627134E-2}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Z1",{"$f":"M$6","v":89.442719099991592},"wa/k"]
[null,null,null,null,"q equation",null,"qb*P*F1 + Mb*k*F2 + Vb*F3 = 0",null,null,null,null,null,"Z2",{"$f":"M$7","v":1200},"Q/k2"]
[null,null,null,null,"(qA*P*F1 + RA*F3 - Z1*Fa4 - Z2*Fa5)*F1b"]
[null,null,null,null," + [(RA-qA*P)*F2 - Z1*Fa3 - Z2*Fa4]*F2b"]
[null,null,null,null," + [ (RA-qA*P)*F1 - Z1*Fa2 - Z2*Fa3]*F3b = 0"]
[]
[null,null,null,null,"qA*P","F1*F1b - F2*F2b - F1*F3b",null,null,null,{"$f":"P76*P75-Q76*Q75-P76*R75","v":0.89576001915159698}]
[]
[null,null,null,null,"RA","F3*F1b + F2*F2b + F1*F3b",null,null,null,{"$f":"R76*P75+Q76*Q75+P76*R75","v":9.7996488553001415E-2}]
[]
[null,null,null,null,"Z1","Fa4*F1b + Fa3*F2b + Fa2*F3b",null,null,null,{"$f":"S77*P75+R77*Q75+Q77*R75","v":6.0092772758184162E-3},{"$f":"-J90*N80","v":-0.53748609937498926}]
[]
[null,null,null,null,"Z2","Fa5*F1b + Fa4*F2b + Fa3*F3b",null,null,null,{"$f":"T77*P75+S77*Q75+R77*R75","v":4.6616240236718048E-4},{"$f":"-N81*J92","v":-0.55939488284061656},null,null,{"$f":"T77","v":1.0399321047935631E-4}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"S77*Q75","v":2.073804461195892E-4}]
[null,null,null,null,null,"qA*P","RA",null,null,null,null,null,null,{"$f":"R77*R75","v":1.554380265766369E-4},null,{"$f":"R77","v":2.4896006789520642E-2},{"$f":"R75","v":6.2434922954015537E-3}]
[null,null,null,null,"y",{"$f":"J72","v":0.43223503222002213},{"$f":"J74","v":1.474578506630278E-2},null,null,{"$f":"-K76-K78","v":8.675670518675363E-2},null,null,null,{"$f":"SUM(N92:N94)","v":4.6681168317558243E-4}]
[null,null,null,null,"q",{"$f":"J86","v":0.89576001915159698},{"$f":"J88","v":9.7996488553001415E-2},null,null,{"$f":"-K90-K92","v":1.0968809822156058}]
[]
[null,null,null,null,"inverse",{"$f":"MINVERSE(F95:G96)","v":3.3619354975094193},-0.50587912878363261,null,null,null,null,null,null,"Mb*k = [(RA - qA*P)*F2 - Z1*Fa3 - Z2*Fa4]",null,null,null,null,null,{"$f":"J102*Q76-N80*R77-N81*S77","v":0.10561431926987819}]
[null,null,null,null,null,-30.730564432486862,14.828554773181343,null,null,null,null,null,null,"qb*P = qA*P*F1 + RA*F3 - [Z1*Fa4 + Z2*Fa5]",null,null,null,null,null,{"$f":"F101*P76+F102*R76-(N80*S77+N81*T77)","v":0.21821021343240565}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Vb = (RA - qA*P)*F1 - [Z1*Fa2 + Z2*Fa3]",null,null,null,null,null,{"$f":"J102*P76-(N80*Q77+N81*R77)","v":-36.619133007679139}]
[null,null,null,null,"qA*P",{"$f":"MMULT(F98:G99,J95:J96)","v":-0.2632187488482593},null,null,"qA",{"$f":"F101/B8","v":-2.6321874884825929E-4}]
[null,null,null,null,"RA",13.599077205753263,null,null,"RA - qA*P",{"$f":"F102-F101","v":13.862295954601523},null,null,null,"ML*k = Mb*k*F1b + (Vb - qb*P)*F2b",null,null,null,null,null,{"$f":"T98*P75+(T100-T99)*Q38","v":-4.0050103296135946}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"ML",null,null,null,null,null,{"$f":"T102/J5","v":-358.21901390419345}]
[]
[null,null,null,null,"CASE 3 fixed/fixed"]
[null,null,null,null,"yA = yL = 0"]
[null,null,null,null,"qA = qL = 0"]
[null,null,null,null,"Based on length (L - b)"]
[null,null,null,null,"yL = yb +qb/k*F2 + Mb/P*F3 + Vb/(kP)*F4 = 0"]
[null,null,null,null,"yb*k*P + qb*P*F2 + Mb*k*F3 + Vb*F4 = 0"]
[null,null,null,null,"F2, F3, F4 are F2b, F3b, F4b (span b to L)"]
[]
[null,null,null,null,"qL = qb*F1 + Mb*k/P*F2 + Vb/P*F3 = 0"]
[null,null,null,null,"qb*P*F1 + Mb*k*F2 + Vb*F3 = 0"]
[]
[null,null,null,null,"Values at b for span 0 to b"]
[null,null,null,null,"Vb = RA*F1 - MA*k*F2 - Z1*Fa2 - Z2*Fa3"]
[null,null,null,null,"Mb*k = MA*k*F1 + RA*F2 - Z1*Fa3 - Z2*Fa4"]
[null,null,null,null,"qb*P = MA*k*F2 + RA*F3 - Z1*Fa4 - Z2*Fa5"]
[null,null,null,null,"yb*k*P = MA*k*F3 + RA*F4 - Z1*Fa5 - Z2*Fa6"]
[]
[null,null,null,null,"y equation",null,"yb*k*P + qb*P*F2 + Mb*k*F3 + Vb*F4 = 0"]
[null,null,null,null,"(MA*k*F3 + RA*F4 - Z1*Fa5 - Z2*Fa6)"]
[null,null,null,null,"+ (MA*k*F2 + RA*F3 - Z1*Fa4 - Z2*Fa5)*F2b"]
[null,null,null,null,"+ (MA*k*F1 + RA*F2 - Z1*Fa3 - Z2*Fa4)*F3b"]
[null,null,null,null,"+(RA*F1 - MA*k*F2 - Z1*Fa2 - Z2*Fa3)*F4b = 0"]
[]
[null,null,null,null,"y equation"]
[null,null,null,null,"MA*k","F3 + F2*F2b + F1*F3b - F2*F4b",null,null,null,{"$f":"R133+Q133*Q132+P133*R132-Q133*S132","v":9.8267784379469911E-2}]
[]
[null,null,null,null,"RA","F4 + F3*F2b + F2*F3b + F1*F4b",null,null,null,{"$f":"S133+R133*Q132+Q133*R132+P133*S132","v":1.474578506630278E-2},null,null,null,"x","kx","F1","F2","F3","F4","F5","F6"]
[null,null,null,null,null,null,null,null,null,null,null,null,"L-b",{"$f":"B$3-B$5","v":10},{"$f":"J$5*N132","v":0.11180339887498948},{"$f":"COS(O132)","v":0.99375650770459845},{"$f":"SIN(O132)","v":0.11157062066135646},{"$f":"1-P132","v":6.2434922954015537E-3},{"$f":"O132-Q132","v":2.3277821363301698E-4}]
[null,null,null,null,"Z1","Fa5 + Fa4*F2b + Fa3*F3b + Fa2*F4b",null,null,null,{"$f":"T134+S134*Q132+R134*R132+Q134*S132","v":5.1842980062231654E-4},{"$f":"-J133*N137","v":-4.6369771030126503E-2},null,"b",{"$f":"B$5","v":30},{"$f":"J$5*N133","v":0.33541019662496846},{"$f":"COS(O133)","v":0.94427537017871055},{"$f":"SIN(O133)","v":0.32915653612507711},{"$f":"1-P133","v":5.5724629821289451E-2},{"$f":"O133-Q133","v":6.2536604998913448E-3}]
[null,null,null,null,null,null,null,null,null,null,null,null,"b-a",{"$f":"B$5-B$4","v":20},{"$f":"J$5*N134","v":0.22360679774997896},{"$f":"COS(O134)","v":0.97510399321047936},{"$f":"SIN(O134)","v":0.22174806070172826},{"$f":"1-P134","v":2.4896006789520642E-2},{"$f":"O134-Q134","v":1.8587370482507082E-3},{"$f":"O134^2/2-R134","v":1.0399321047935631E-4},{"$f":"O134^3/6-S134","v":4.6529329991162882E-6}]
[null,null,null,null,"Z2","Fa6 + Fa5*F2b + Fa4*F3b + Fa3*F4b",null,null,null,{"$f":"U134+T134*Q132+S134*R132+R134*S132","v":3.3655778463855947E-5},{"$f":"-J135*N138","v":-4.0386934156627134E-2}]
[]
[null,null,null,null,"q equation",null,"qb*P*F1 + Mb*k*F2 + Vb*F3 = 0",null,null,null,null,null,"Z1",{"$f":"M$6","v":89.442719099991592},"wa/k"]
[null,null,null,null,"(MA*k*F2 + RA*F3 - Z1*Fa4 - Z2*Fa5)*F1b",null,null,null,null,null,null,null,"Z2",{"$f":"M$7","v":1200},"Q/k2"]
[null,null,null,null," + (MA*k*F1 + RA*F2 - Z1*Fa3 - Z2*Fa4)*F2b"]
[null,null,null,null," + (RA*F1 - MA*k*F2 - Z1*Fa2 - Z2*Fa3)*F3b = 0"]
[]
[null,null,null,null,"MA*k","(F2*F1b + F1*F2b - F2*F3b)",null,null,null,{"$f":"Q133*P132+P133*Q132-Q133*R132","v":0.43039975265659208}]
[]
[null,null,null,null,"RA","F3*F1b + F2*F2b + F1*F3b",null,null,null,{"$f":"R133*P132+Q133*Q132+P133*R132","v":9.7996488553001415E-2}]
[]
[null,null,null,null,"Z1","Fa4*F1b + Fa3*F2b + Fa2*F3b",null,null,null,{"$f":"S134*P132+R134*Q132+Q134*R132","v":6.0092772758184162E-3},{"$f":"-J146*N137","v":-0.53748609937498926}]
[]
[null,null,null,null,"Z2","Fa5*F1b + Fa4*F2b + Fa3*F3b",null,null,null,{"$f":"T134*P132+S134*Q132+R134*R132","v":4.6616240236718048E-4},{"$f":"-J148*N138","v":-0.55939488284061656}]
[]
[null,null,null,null,null,"MA*k","RA"]
[null,null,null,null,"y",{"$f":"J129","v":9.8267784379469911E-2},{"$f":"J131","v":1.474578506630278E-2},null,null,{"$f":"-K133-K135","v":8.675670518675363E-2}]
[null,null,null,null,"q",{"$f":"J142","v":0.43039975265659208},{"$f":"J144","v":9.7996488553001415E-2},null,null,{"$f":"-K146-K148","v":1.0968809822156058}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"V157+W153+X153","v":-0.92715786457549365},{"$f":"F158*Q133","v":7.0625010060162152},{"$f":"-(N137*R134+N138*S134)","v":-4.4572509998874281}]
[null,null,null,null,"inverse",{"$f":"MINVERSE(F151:G152)","v":29.846807810045487},-4.4911263595342188]
[null,null,null,null,null,-131.08692861055553,29.929436427783084]
[]
[null,null,null,null,"MA*k",{"$f":"MMULT(F154:G155,J151:J152)","v":-2.3368203865584802},null,null,"MA",{"$f":"F157/J5","v":-209.01156942208391},null,null,null,"ML",{"$f":"J157+F158*B3-B14*(B3-B15)","v":-250.75718515155359},null,null,null,null,null,null,{"$f":"V158*J5","v":-3.5324078707042808}]
[null,null,null,null,"RA",21.456359606763257,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-315.94816492600239]
[]
[]
[null,null,null,null,"CASE 4 free/fixed"]
[null,null,null,null,"MA = 0, RA = 0"]
[null,null,null,null,"yL= qL = 0"]
[null,null,null,null,"Based on length (L - b)"]
[null,null,null,null,"yL = yb +qb/k*F2 + Mb/P*F3 + Vb/(kP)*F4 = 0"]
[null,null,null,null,"yb*k*P + qb*P*F2 + Mb*k*F3 + Vb*F4 = 0"]
[null,null,null,null,"F2, F3, F4 are F2b, F3b, F4b (span b to L)"]
[]
[null,null,null,null,"qL = qb*F1 + Mb*k/P*F2 + Vb/P*F3 = 0"]
[null,null,null,null,"qb*P*F1 + Mb*k*F2 + Vb*F3 = 0"]
[]
[null,null,null,null,"Values at b for span 0 to b"]
[null,null,null,null,"Vb = -qA*P*F1 -  Z1*Fa2 - Z2*Fa3"]
[null,null,null,null,"Mb*k = -qA*P*F2 - Z1*Fa3 - Z2*Fa4"]
[null,null,null,null,"qb*P = qA*P*F1 - Z1*Fa4 - Z2*Fa5"]
[null,null,null,null,"yb*k*P = yA*k*P + qA*P*F2 - Z1*Fa5 - Z2*Fa6"]
[]
[null,null,null,null,"y equation",null,"yb*k*P + qb*P*F2 + Mb*k*F3 + Vb*F4 = 0"]
[null,null,null,null,"(yA*k*P + qA*P*F2 - Z1*Fa5 - Z2*Fa6)"]
[null,null,null,null," + (qA*P*F1 - Z1*Fa4 - Z2*Fa5)*F2b"]
[null,null,null,null," + (-qA*P*F2 - Z1*Fa3 - Z2*Fa4)*F3b"]
[null,null,null,null," + (-qA*P*F1 - Z1*Fa2 - Z2*Fa3)*F4b = 0"]
[]
[null,null,null,"yA*k*P",null,null,null,null,null,1]
[]
[null,null,null,"qA*P","F2 + F1*F2b - F2*F3b - F1*F4b",null,null,null,null,{"$f":"Q188+P188*Q187-Q188*R187-P188*S187","v":0.43223503222002213},null,null,null,"x","kx","F1","F2","F3","F4","F5","F6"]
[null,null,null,null,null,null,null,null,null,null,null,null,"L-b",{"$f":"B$3-B$5","v":10},{"$f":"J$5*N187","v":0.11180339887498948},{"$f":"COS(O187)","v":0.99375650770459845},{"$f":"SIN(O187)","v":0.11157062066135646},{"$f":"1-P187","v":6.2434922954015537E-3},{"$f":"O187-Q187","v":2.3277821363301698E-4}]
[null,null,null,"Z1","Fa5 + Fa4*F2b + Fa3*F3b + Fa2*F4b",null,null,null,null,{"$f":"T189+S189*Q187+R189*R187+Q189*S187","v":5.1842980062231654E-4},{"$f":"-J188*N192","v":-4.6369771030126503E-2},null,"b",{"$f":"B$5","v":30},{"$f":"J$5*N188","v":0.33541019662496846},{"$f":"COS(O188)","v":0.94427537017871055},{"$f":"SIN(O188)","v":0.32915653612507711},{"$f":"1-P188","v":5.5724629821289451E-2},{"$f":"O188-Q188","v":6.2536604998913448E-3}]
[null,null,null,null,null,null,null,null,null,null,null,null,"b-a",{"$f":"B$5-B$4","v":20},{"$f":"J$5*N189","v":0.22360679774997896},{"$f":"COS(O189)","v":0.97510399321047936},{"$f":"SIN(O189)","v":0.22174806070172826},{"$f":"1-P189","v":2.4896006789520642E-2},{"$f":"O189-Q189","v":1.8587370482507082E-3},{"$f":"O189^2/2-R189","v":1.0399321047935631E-4},{"$f":"O189^3/6-S189","v":4.6529329991162882E-6}]
[null,null,null,"Z2","Fa6 + Fa5*F2b + Fa4*F3b + Fa3*F4b",null,null,null,null,{"$f":"U189+T189*Q187+S189*R187+R189*S187","v":3.3655778463855947E-5},{"$f":"-J190*N193","v":-4.0386934156627134E-2}]
[]
[null,null,null,null,"q equation",null,null,null,null,null,null,null,"Z1",{"$f":"M$6","v":89.442719099991592},"wa/k"]
[null,null,null,null,"(qA*P*F1 - Z1*Fa4 - Z2*Fa5)*F1b",null,null,null,null,null,null,null,"Z2",{"$f":"M$7","v":1200},"Q/k2"]
[null,null,null,null," + (-qA*P*F2 - Z1*Fa3 - Z2*Fa4)*F2b"]
[null,null,null,null," + (-qA*P*F1 -  Z1*Fa2 - Z2*Fa3)*F3b"]
[]
[null,null,null,"qA*P","F1*F1b - F2*F2b - F1*F3b",null,null,null,null,{"$f":"P188*P187-Q188*Q187-P188*R187","v":0.89576001915159698}]
[]
[null,null,null,"Z1","Fa4*F1b + Fa3*F2b + Fa2*F3b",null,null,null,null,{"$f":"S189*P187+R189*Q187+Q189*R187","v":6.0092772758184162E-3},{"$f":"-J199*N192","v":-0.53748609937498926}]
[]
[null,null,null,"Z2","Fa5*F1b + Fa4*F2b + Fa3*F3b",null,null,null,null,{"$f":"T189*P187+S189*Q187+R189*R187","v":4.6616240236718048E-4},{"$f":"-J201*N193","v":-0.55939488284061656}]
[]
[]
[null,null,null,"qA*P",{"$f":"-(K199+K201)/J197","v":1.2245254965213752},null,null,"qA",{"$f":"E204/B8","v":1.2245254965213752E-3}]
[]
[null,null,null,"yA*k*P",{"$f":"-E204*J186-(K188+K190)","v":-0.44252611225640159},null,null,"yA",{"$f":"E206/(B8*J5)","v":-3.958073875296067E-2}]
[]
[]
[null,null,null,"Mb = [- qA*P*F2 - Z1*Fa3 - Z2*Fa4]/k",null,null,null,null,{"$f":"-(E204*Q188+N192*R189+N193*S189)/J5","v":-434.71948255828022}]
[null,null,null,"qb*P = qA*P*F1 - [Z1*Fa4 + Z2*Fa5]",null,null,null,null,{"$f":"E204*P188-(N192*S189+N193*T189)","v":0.86524691825832778}]
[null,null,null,"Vb = -qA*P*F1 - [Z1*Fa2 + Z2*Fa3]",null,null,null,null,{"$f":"-E204*P188-(N192*R189+N193*Q189)","v":-269.48072865058151}]
[]
[null,null,null,"ML =Mb*F1b + Vb/k*F2b - qb*P/k*F2b",null,null,null,null,{"$f":"I209*P187+I211*Q187-I210*Q187/J5","v":-470.7059014380896}]

{"sheet":"Calcs2","index":9,"n_rows":213,"n_cols":21,"rows_kept":213,"cut":false,"hidden":false,"merged":[]}
[]
[]
["L",{"$f":"'Tens Distributed'!B3","v":40},null,null,null,null,null,null,"wa",{"$f":"B6","v":1}]
["a",{"$f":"'Tens Distributed'!B4","v":10},null,null,null,null,null,null,"Q",{"$f":"(B7-B6)/(B5-B4)","v":0.15},"(wb-wa)/(b - a)"]
["b",{"$f":"'Tens Distributed'!B5","v":30},null,null,null,null,null,null,"k",{"$f":"SQRT(B8/(B9*B10))","v":1.1180339887498949E-2}]
["wa",{"$f":"'Tens Distributed'!B6","v":1},null,null,null,null,null,null,null,null,null,"wa/k",{"$f":"J3/J5","v":89.442719099991592},"Z1"]
["wb",{"$f":"'Tens Distributed'!B7","v":4},null,null,null,null,null,null,null,null,null,"Q/k2",{"$f":"J4/J5^2","v":1200},"Z2"]
["P",{"$f":"'Tens Distributed'!B8","v":1000}]
["E",{"$f":"'Tens Distributed'!B9","v":80000},"psi"]
["I",{"$f":"'Tens Distributed'!B10","v":100},"in4"]
[]
["b - a",{"$f":"B5-B4","v":20}]
["wb-wa",{"$f":"B7-B6","v":3}]
["W",{"$f":"B12*(B6+B7)/2","v":50}]
["Xcg",{"$f":"(B6*(B5+2*B4)+B7*(2*B5+B4))*B12/(6*B14)","v":22},null,null,"CASE 1 ss/ss"]
[null,null,null,null,"yA = yL = 0"]
[null,null,null,null,"MA = ML = 0"]
[null,null,null,null,"Based on length (L - b)"]
[null,null,null,null,"yL = yb +qb/k*F2 + Mb/P*F3 + Vb/(kP)*F4 = 0"]
[null,null,null,null,"yb*k*P + qb*P*F2 + Mb*k*F3 + Vb*F4 = 0"]
[null,null,null,null,"F2, F3, F4 are F2b, F3b, F4b (length L-b)"]
[]
[null,null,null,null,"Values at b:"]
[null,null,null,null,"Vb = (RA+qA*P)*F1 - Z1*Fa2 - Z2*Fa3"]
[null,null,null,null,"Mb*k = (RA+qA*P)*F2 - Z1*Fa3 - Z2*Fa4"]
[null,null,null,null,"qb*P = qA*P*F1 + RA*F3 - Z1*Fa4 - Z2*Fa5"]
[null,null,null,null,"yb*k*P = qA*P*F2 + RA*F4 - Z1*Fa5 - Z2*Fa6"]
[]
[null,null,null,null,"(qA*P*F2 + RA*F4 - Z1*Fa5 - Z2*Fa6)"]
[null,null,null,null,"+ (qA*P*F1 + RA*F3 - Z1*Fa4 - Z2*Fa5)*F2b"]
[null,null,null,null,"+ [(RA+qA*P)*F2 - Z1*Fa3 - Z2*Fa4]*F3b"]
[null,null,null,null,"+ [(RA+qA*P)*F1 - Z1*Fa2 - Z2*Fa3]*F4b = 0"]
[]
[null,null,null,null,"qA*P","F2 + F1*F2b + F2*F3b + F1*F4b",null,null,null,{"$f":"Q39+P39*Q38+Q39*R38+P38*S38","v":0.46250502595663334}]
[]
[null,null,null,null,"RA","F4 + F3*F2b + F2*F3b + F1*F4b",null,null,null,{"$f":"S39+R39*Q38+Q39*R38+P39*S38","v":1.507013640825389E-2},{"$f":"J36*N42","v":0.33907806918571254}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"x","kx","F1","F2","F3","F4","F5","F6"]
[null,null,null,null,"Z1","Fa5 + Fa4*F2b + Fa3*F3b + Fa2*F4b",null,null,null,{"$f":"T40+S40*Q38+R40*R38+Q40*S38","v":5.2324752298873285E-4},{"$f":"-J38*N43","v":-4.6800681218447625E-2},null,"L-b",{"$f":"B$3-B$5","v":10},{"$f":"J$5*N38","v":0.11180339887498948},{"$f":"COSH(O38)","v":1.0062565131299459},{"$f":"SINH(O38)","v":0.11203646824332211},{"$f":"P38-1","v":6.2565131299459065E-3},{"$f":"Q38-O38","v":2.330693683326307E-4}]
[null,null,null,null,null,null,null,null,null,null,null,null,"b",{"$f":"B$5","v":30},{"$f":"J$5*N39","v":0.33541019662496846},{"$f":"COSH(O39)","v":1.0567793252667674},{"$f":"SINH(O39)","v":0.34173460800932076},{"$f":"P39-1","v":5.6779325266767433E-2},{"$f":"Q39-O39","v":6.324411384352302E-3}]
[null,null,null,null,"Z2","Fa6 + Fa5*F2b + Fa4*F3b + Fa3*F4b",null,null,null,{"$f":"U40+T40*Q38+S40*R38+R40*S38","v":3.389251538606818E-5},{"$f":"-J40*N44","v":-4.0671018463281819E-2},null,"b-a",{"$f":"B$12","v":20},0.22360679774997896,1.0251043404328739,0.22547485175583848,2.5104340432873906E-2,1.8680540058595152E-3,{"$f":"R40-O40^2/2","v":1.0434043287390823E-4},{"$f":"S40-O40^3/6","v":4.6640246096907312E-6}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K36+K38+K40","v":0.25160636950398313}]
[null,null,null,null,"qA*P",{"$f":"-K41/J34","v":-0.54400786020339365},null,null,null,null,null,null,"RA",{"$f":"B14*(B3-B15)/B3","v":22.5}]
[null,null,null,null,"qA",{"$f":"F42/B8","v":-5.4400786020339365E-4},null,null,null,null,null,null,"Z1",{"$f":"M$6","v":89.442719099991592},"wa/k"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Z2",{"$f":"M$7","v":1200},"Q/k2"]
[]
[]
[]
[null,null,null,null,"CASE 2 ss/fixed"]
[null,null,null,null,"yA = yL = 0"]
[null,null,null,null,"MA = qL = 0"]
[null,null,null,null,"Based on length (L - b)"]
[null,null,null,null,"yL = yb +qb/k*F2 + Mb/P*F3 + Vb/(kP)*F4 = 0"]
[null,null,null,null,"yb*k*P + qb*P*F2 + Mb*k*F3 + Vb*F4 = 0"]
[null,null,null,null,"F2, F3, F4 are F2b, F3b, F4b (length L-b)"]
[]
[null,null,null,null,"qL = qb*F1 + Mb*k/P*F2 + Vb/P*F3 = 0"]
[null,null,null,null,"qb*P*F1 + Mb*k*F2 + Vb*F3 = 0"]
[]
[null,null,null,null,"Values at b:"]
[null,null,null,null,"Vb = (RA+qA*P)*F1 - Z1*Fa2 - Z2*Fa3"]
[null,null,null,null,"Mb*k = (RA+qA*P)*F2 - Z1*Fa3 - Z2*Fa4"]
[null,null,null,null,"qb*P = qA*P*F1 + RA*F3 - Z1*Fa4 - Z2*Fa5"]
[null,null,null,null,"yb*k*P = qA*P*F2 + RA*F4 - Z1*Fa5 - Z2*Fa6"]
[]
[null,null,null,null,"y equation",null,"yb*k*P + qb*P*F2 + Mb*k*F3 + Vb*F4 = 0"]
[null,null,null,null,"(qA*P*F2 + RA*F4 - Z1*Fa5 - Z2*Fa6)"]
[null,null,null,null,"+ (qA*P*F1 + RA*F3 - Z1*Fa4 - Z2*Fa5)*F2b"]
[null,null,null,null,"+ [(RA+qA*P)*F2 - Z1*Fa3 - Z2*Fa4]*F3b"]
[null,null,null,null,"+ [(RA+qA*P)*F1 - Z1*Fa2 - Z2*Fa3]*F4b = 0"]
[]
[null,null,null,null,"y equation"]
[null,null,null,null,"qA*P","F2 + F1*F2b + F2*F3b + F1*F4b",null,null,null,{"$f":"Q76+P76*Q75+Q76*R75+P76*S75","v":0.46251680127654449}]
[]
[null,null,null,null,"RA","F4 + F3*F2b + F2*F3b + F1*F4b",null,null,null,{"$f":"S76+R76*Q75+Q76*R75+P76*S75","v":1.507013640825389E-2},null,null,null,"x","kx","F1","F2","F3","F4","F5","F6"]
[null,null,null,null,null,null,null,null,null,null,null,null,"L-b",{"$f":"B$3-B$5","v":10},{"$f":"J$5*N75","v":0.11180339887498948},{"$f":"COSH(O75)","v":1.0062565131299459},{"$f":"SINH(O75)","v":0.11203646824332211},{"$f":"P75-1","v":6.2565131299459065E-3},{"$f":"Q75-O75","v":2.330693683326307E-4}]
[null,null,null,null,"Z1","Fa5 + Fa4*F2b + Fa3*F3b + Fa2*F4b",null,null,null,{"$f":"T77+S77*Q75+R77*R75+Q77*S75","v":5.2324752298873285E-4},{"$f":"-J76*N80","v":-4.6800681218447625E-2},null,"b",{"$f":"B$5","v":30},{"$f":"J$5*N76","v":0.33541019662496846},{"$f":"COSH(O76)","v":1.0567793252667674},0.34173460800932076,{"$f":"P76-1","v":5.6779325266767433E-2},{"$f":"Q76-O76","v":6.324411384352302E-3}]
[null,null,null,null,null,null,null,null,null,null,null,null,"b-a",{"$f":"B$12","v":20},0.22360679774997896,1.0251043404328739,0.22547485175583848,2.5104340432873906E-2,1.8680540058595152E-3,{"$f":"R77-O77^2/2","v":1.0434043287390823E-4},{"$f":"S77-O77^3/6","v":4.6640246096907312E-6}]
[null,null,null,null,"Z2","Fa6 + Fa5*F2b + Fa4*F3b + Fa3*F4b",null,null,null,{"$f":"U77+T77*Q75+S77*R75+R77*S75","v":3.389251538606818E-5},{"$f":"-J78*N81","v":-4.0671018463281819E-2}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Z1",{"$f":"M$6","v":89.442719099991592},"wa/k"]
[null,null,null,null,"q equation",null,"qb*P*F1 + Mb*k*F2 + Vb*F3 = 0",null,null,null,null,null,"Z2",{"$f":"M$7","v":1200},"Q/k2"]
[null,null,null,null,"(qA*P*F1 + RA*F3 - Z1*Fa4 - Z2*Fa5)*F1b"]
[null,null,null,null," + [(RA+qA*P)*F2 - Z1*Fa3 - Z2*Fa4]*F2b"]
[null,null,null,null," + [ (RA+qA*P)*F1 - Z1*Fa2 - Z2*Fa3]*F3b = 0"]
[]
[null,null,null,null,"qA*P","F1*F1b + F2*F2b + F1*F3b",null,null,null,{"$f":"P76*P75+Q76*Q75+P76*R75","v":1.1082895712726217}]
[]
[null,null,null,null,"RA","F3*F1b + F2*F2b + F1*F3b",null,null,null,{"$f":"R76*P75+Q76*Q75+P76*R75","v":0.10203305814267573}]
[]
[null,null,null,null,"Z1","Fa4*F1b + Fa3*F2b + Fa2*F3b",null,null,null,{"$f":"S77*P75+R77*Q75+Q77*R75","v":6.1030295204348578E-3},{"$f":"-J90*N80","v":-0.54587155505521134}]
[]
[null,null,null,null,"Z2","Fa5*F1b + Fa4*F2b + Fa3*F4b",null,null,null,{"$f":"T77*P75+S77*Q75+R77*R75","v":4.7134904900336585E-4},{"$f":"-N81*J92","v":-0.56561885880403906}]
[]
[null,null,null,null,null,"qA*P","RA"]
[null,null,null,null,"y",{"$f":"J72","v":0.46251680127654449},{"$f":"J74","v":1.507013640825389E-2},null,null,{"$f":"-K76-K78","v":8.7471699681729437E-2}]
[null,null,null,null,"q",{"$f":"J86","v":1.1082895712726217},{"$f":"J88","v":0.10203305814267573},null,null,{"$f":"-K90-K92","v":1.1114904138592503}]
[]
[null,null,null,null,"inverse",{"$f":"MINVERSE(F95:G96)","v":3.3464511933825105},-0.49426604363184629,null,null,null,null,null,null,"Mb*k = [(RA + qA*P)*F2 - Z1*Fa3 - Z2*Fa4]",null,null,null,null,null,{"$f":"J102*Q76-N80*R77-N81*S77","v":0.10056961817876608}]
[null,null,null,null,null,-36.349365841926286,15.169494375313491,null,null,null,null,null,null,"qb*P = qA*P*F1 + RA*F3 - [Z1*Fa4 + Z2*Fa5]",null,null,null,null,null,{"$f":"F101*P76+F102*R76-(N80*S77+N81*T77)","v":0.21329260590334076}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Vb = (RA + qA*P)*F1 - [Z1*Fa2 + Z2*Fa3]",null,null,null,null,null,{"$f":"J102*P76-(N80*Q77+N81*R77)","v":-36.105500625390192}]
[null,null,null,null,"qA*P",{"$f":"MMULT(F98:G99,J95:J96)","v":-0.25665219560581504},null,null,"qA",{"$f":"F101/B8","v":-2.5665219560581503E-4}]
[null,null,null,null,"RA",13.681206768706469,null,null,"RA + qA*P",{"$f":"F102+F101","v":13.424554573100654},null,null,null,"ML*k = Mb*k*F1b + (Vb + qb*P)*F2b",null,null,null,null,null,{"$f":"T98*P75+(T100+T99)*Q38","v":-3.9200373906425749}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"ML",null,null,null,null,null,{"$f":"T102/J5","v":-350.61880319270784}]
[]
[null,null,null,null,"CASE 3 fixed/fixed"]
[null,null,null,null,"yA = yL = 0"]
[null,null,null,null,"qA = qL = 0"]
[null,null,null,null,"Based on length (L - b)"]
[null,null,null,null,"yL = yb +qb/k*F2 + Mb/P*F3 + Vb/(kP)*F4 = 0"]
[null,null,null,null,"yb*k*P + qb*P*F2 + Mb*k*F3 + Vb*F4 = 0"]
[null,null,null,null,"F2, F3, F4 are F2b, F3b, F4b (length L-b)"]
[]
[null,null,null,null,"qL = qb*F1 + Mb*k/P*F2 + Vb/P*F3 = 0"]
[null,null,null,null,"qb*P*F1 + Mb*k*F2 + Vb*F3 = 0"]
[]
[null,null,null,null,"Values at b:"]
[null,null,null,null,"Vb = RA*F1 - MA*k*F2 - Z1*Fa2 - Z2*Fa3"]
[null,null,null,null,"Mb*k = MA*k*F1 + RA*F2 - Z1*Fa3 - Z2*Fa4"]
[null,null,null,null,"qb*P = MA*k*F2 + RA*F3 - Z1*Fa4 - Z2*Fa5"]
[null,null,null,null,"yb*k*P = MA*k*F3 + RA*F4 - Z1*Fa5 - Z2*Fa6"]
[]
[null,null,null,null,"y equation",null,"yb*k*P + qb*P*F2 + Mb*k*F3 + Vb*F4 = 0"]
[null,null,null,null,"(MA*k*F3 + RA*F4 - Z1*Fa5 - Z2*Fa6)"]
[null,null,null,null,"+ (MA*k*F2 + RA*F3 - Z1*Fa4 - Z2*Fa5)*F2b"]
[null,null,null,null,"+ (MA*k*F1 + RA*F2 - Z1*Fa3 - Z2*Fa4)*F3b"]
[null,null,null,null,"+(RA*F1 - MA*k*F2 - Z1*Fa2 - Z2*Fa3)*F4b = 0"]
[]
[null,null,null,null,"y equation"]
[null,null,null,null,"MA*k","F3 + F2*F2b + F1*F3b - F2*F4b",null,null,null,{"$f":"R133+Q133*Q132+P133*R132-Q133*S132","v":0.1015981696794086}]
[]
[null,null,null,null,"RA","F4 + F3*F2b + F2*F3b + F1*F4b",null,null,null,{"$f":"S133+R133*Q132+Q133*R132+P133*S132","v":1.507013640825389E-2},null,null,null,"x","kx","F1","F2","F3","F4","F5","F6"]
[null,null,null,null,null,null,null,null,null,null,null,null,"L-b",{"$f":"B$3-B$5","v":10},{"$f":"J$5*N132","v":0.11180339887498948},{"$f":"COSH(O132)","v":1.0062565131299459},{"$f":"SINH(O132)","v":0.11203646824332211},{"$f":"P132-1","v":6.2565131299459065E-3},{"$f":"Q132-O132","v":2.330693683326307E-4}]
[null,null,null,null,"Z1","Fa5 + Fa4*F2b + Fa3*F3b + Fa2*F4b",null,null,null,{"$f":"T134+S134*Q132+R134*R132+Q134*S132","v":5.2324752298873285E-4},{"$f":"-J133*N137","v":-4.6800681218447625E-2},null,"b",{"$f":"B$5","v":30},{"$f":"J$5*N133","v":0.33541019662496846},{"$f":"COSH(O133)","v":1.0567793252667674},0.34173460800932076,{"$f":"P133-1","v":5.6779325266767433E-2},{"$f":"Q133-O133","v":6.324411384352302E-3}]
[null,null,null,null,null,null,null,null,null,null,null,null,"b-a",{"$f":"B$12","v":20},0.22360679774997896,1.0251043404328739,0.22547485175583848,2.5104340432873906E-2,1.8680540058595152E-3,{"$f":"R134-O134^2/2","v":1.0434043287390823E-4},{"$f":"S134-O134^3/6","v":4.6640246096907312E-6}]
[null,null,null,null,"Z2","Fa6 + Fa5*F2b + Fa4*F3b + Fa3*F4b",null,null,null,{"$f":"U134+T134*Q132+S134*R132+R134*S132","v":3.389251538606818E-5},{"$f":"-J135*N138","v":-4.0671018463281819E-2}]
[]
[null,null,null,null,"q equation",null,"qb*P*F1 + Mb*k*F2 + Vb*F3 = 0",null,null,null,null,null,"Z1",{"$f":"M$6","v":89.442719099991592},"wa/k"]
[null,null,null,null,"(MA*k*F2 + RA*F3 - Z1*Fa4 - Z2*Fa5)*F1b",null,null,null,null,null,null,null,"Z2",{"$f":"M$7","v":1200},"Q/k2"]
[null,null,null,null," + (MA*k*F1 + RA*F2 - Z1*Fa3 - Z2*Fa4)*F2b"]
[null,null,null,null," + (RA*F1 - MA*k*F2 - Z1*Fa2 - Z2*Fa3)*F3b = 0"]
[]
[null,null,null,null,"MA*k","F2*F1b + F1*F2b - F2*F3b",null,null,null,{"$f":"Q133*P132+P133*Q132-Q133*R132","v":0.46013243132477033}]
[]
[null,null,null,null,"RA","F3*F1b + F2*F2b + F1*F3b",null,null,null,{"$f":"R133*P132+Q133*Q132+P133*R132","v":0.10203305814267573}]
[]
[null,null,null,null,"Z1","Fa4*F1b + Fa3*F2b + Fa2*F3b",null,null,null,{"$f":"S134*P132+R134*Q132+Q134*R132","v":6.1030295204348578E-3},{"$f":"-J146*N137","v":-0.54587155505521134}]
[]
[null,null,null,null,"Z2","Fa5*F1b + Fa4*F2b + Fa3*F3b",null,null,null,{"$f":"T134*P132+S134*Q132+R134*R132","v":4.7134904900336585E-4},{"$f":"-J148*N138","v":-0.56561885880403906}]
[]
[null,null,null,null,null,"MA*k","RA"]
[null,null,null,null,"y",{"$f":"J129","v":0.1015981696794086},{"$f":"J131","v":1.507013640825389E-2},null,null,{"$f":"-K133-K135","v":8.7471699681729437E-2}]
[null,null,null,null,"q",{"$f":"J142","v":0.46013243132477033},{"$f":"J144","v":0.10203305814267573},null,null,{"$f":"-K146-K148","v":1.1114904138592503}]
[]
[null,null,null,null,"inverse",{"$f":"MINVERSE(F151:G152)","v":29.728929326999921},-4.3909202407983363]
[null,null,null,null,null,-134.06678953782475,29.602217762876091]
[]
[null,null,null,null,"MA*k",{"$f":"MMULT(F154:G155,J151:J152)","v":-2.2800257777172055},null,null,"MA",{"$f":"F157/J5","v":-203.93170517709987},null,null,null,"ML",{"$f":"J157+F158*B3-B14*(B3-B15)","v":-256.91045235051718}]
[null,null,null,null,"RA",21.175531320664568]
[]
[]
[null,null,null,null,"CASE 4 free/fixed"]
[null,null,null,null,"MA = 0, RA = 0"]
[null,null,null,null,"yL= qL = 0"]
[null,null,null,null,"Based on length (L - b)"]
[null,null,null,null,"yL = yb +qb/k*F2 + Mb/P*F3 + Vb/(kP)*F4 = 0"]
[null,null,null,null,"yb*k*P + qb*P*F2 + Mb*k*F3 + Vb*F4 = 0"]
[null,null,null,null,"F2, F3, F4 are F2b, F3b, F4b (length L-b)"]
[]
[null,null,null,null,"qL = qb*F1 + Mb*k/P*F2 + Vb/P*F3 = 0"]
[null,null,null,null,"qb*P*F1 + Mb*k*F2 + Vb*F3 = 0"]
[]
[null,null,null,null,"Values at b:"]
[null,null,null,null,"Vb = qA*P*F1 -  Z1*Fa2 - Z2*Fa3"]
[null,null,null,null,"Mb*k = qA*P*F2 - Z1*Fa3 - Z2*Fa4"]
[null,null,null,null,"qb*P = qA*P*F1 - Z1*Fa4 - Z2*Fa5"]
[null,null,null,null,"yb*k*P = yA*k*P + qA*P*F2 - Z1*Fa5 - Z2*Fa6"]
[]
[null,null,null,null,"y equation",null,"yb*k*P + qb*P*F2 + Mb*k*F3 + Vb*F4 = 0"]
[null,null,null,null,"(yA*k*P + qA*P*F2 - Z1*Fa5 - Z2*Fa6)"]
[null,null,null,null," + (qA*P*F1 - Z1*Fa4 - Z2*Fa5)*F2b"]
[null,null,null,null," + (qA*P*F2 - Z1*Fa3 - Z2*Fa4)*F3b"]
[null,null,null,null," + (qA*P*F1 - Z1*Fa2 - Z2*Fa3)*F4b = 0"]
[]
[null,null,null,"yA*k*P",null,null,null,null,null,1]
[]
[null,null,null,"qA*P","F2 + F1*F2b + F2*F3b + F1*F4b",null,null,null,null,{"$f":"Q188+P188*Q187+Q188*R187+P188*S187","v":0.46251680127654449},null,null,null,"x","kx","F1","F2","F3","F4","F5","F6"]
[null,null,null,null,null,null,null,null,null,null,null,null,"L-b",{"$f":"B$3-B$5","v":10},{"$f":"J$5*N187","v":0.11180339887498948},{"$f":"COSH(O187)","v":1.0062565131299459},{"$f":"SINH(O187)","v":0.11203646824332211},{"$f":"P187-1","v":6.2565131299459065E-3},{"$f":"Q187-O187","v":2.330693683326307E-4}]
[null,null,null,"Z1","Fa5 + Fa4*F2b + Fa3*F3b + Fa2*F4b",null,null,null,null,{"$f":"T189+S189*Q187+R189*R187+Q189*S187","v":5.2324752298873285E-4},{"$f":"-J188*N192","v":-4.6800681218447625E-2},null,"b",{"$f":"B$5","v":30},{"$f":"J$5*N188","v":0.33541019662496846},{"$f":"COSH(O188)","v":1.0567793252667674},0.34173460800932076,{"$f":"P188-1","v":5.6779325266767433E-2},{"$f":"Q188-O188","v":6.324411384352302E-3}]
[null,null,null,null,null,null,null,null,null,null,null,null,"b-a",{"$f":"B$12","v":20},0.22360679774997896,1.0251043404328739,0.22547485175583848,2.5104340432873906E-2,1.8680540058595152E-3,{"$f":"R189-O189^2/2","v":1.0434043287390823E-4},{"$f":"S189-O189^3/6","v":4.6640246096907312E-6}]
[null,null,null,"Z2","Fa6 + Fa5*F2b + Fa4*F3b + Fa3*F4b",null,null,null,null,{"$f":"U189+T189*Q187+S189*R187+R189*S187","v":3.389251538606818E-5},{"$f":"-J190*N193","v":-4.0671018463281819E-2}]
[]
[null,null,null,null,"q equation",null,"qb*P*F1 + Mb*k*F2 + Vb*F3 = 0",null,null,null,null,null,"Z1",{"$f":"M$6","v":89.442719099991592},"wa/k"]
[null,null,null,null,"(qA*P*F1 - Z1*Fa4 - Z2*Fa5)*F1b",null,null,null,null,null,null,null,"Z2",{"$f":"M$7","v":1200},"Q/k2"]
[null,null,null,null," + (qA*P*F2 - Z1*Fa3 - Z2*Fa4)*F2b"]
[null,null,null,null," + (qA*P*F1 -  Z1*Fa2 - Z2*Fa3)*F3b"]
[]
[null,null,null,"qA*P","F1*F1b + F2*F2b +- F1*F3b",null,null,null,null,{"$f":"P188*P187+Q188*Q187+P188*R187","v":1.1082895712726217}]
[]
[null,null,null,"Z1","Fa4*F1b + Fa3*F2b + Fa2*F3b",null,null,null,null,{"$f":"S189*P187+R189*Q187+Q189*R187","v":6.1030295204348578E-3},{"$f":"-J199*N192","v":-0.54587155505521134}]
[]
[null,null,null,"Z2","Fa5*F1b + Fa4*F2b + Fa3*F3b",null,null,null,null,{"$f":"T189*P187+S189*Q187+R189*R187","v":4.7134904900336585E-4},{"$f":"-J201*N193","v":-0.56561885880403906}]
[]
[]
[null,null,null,"qA*P",{"$f":"-(K199+K201)/J197","v":1.0028880923087213},null,null,"qA",{"$f":"E204/B8","v":1.0028880923087214E-3}]
[]
[null,null,null,"yA*k*P",{"$f":"-E204*J186-(K188+K190)","v":-0.37638089281123621},null,null,"yA",{"$f":"E206/(B8*J5)","v":-3.3664530470319441E-2}]
[]
[]
[null,null,null,"Mb = [qA*P*F2 - Z1*Fa3 - Z2*Fa4]/k",null,null,null,null,{"$f":"(E204*Q188-N192*R189-N193*S189)/J5","v":-370.68137007991061}]
[null,null,null,"qb*P = qA*P*F1 - [Z1*Fa4 + Z2*Fa5]",null,null,null,null,{"$f":"E204*P188-(N192*S189+N193*T189)","v":0.76753905234968955}]
[null,null,null,"Vb = qA*P*F1 - [Z1*Fa2 + Z2*Fa3]",null,null,null,null,{"$f":"E204*P188-(N192*R189+N193*Q189)","v":-271.7553911750262}]
[]
[null,null,null,"ML =Mb*F1b + Vb/k*F2b + qb*P/k*F2b",null,null,null,null,{"$f":"I209*P187+I211*Q187+I210*Q187/J5","v":-395.75566627478048}]