{"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":20,"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":29,"n_cols":8,"rows_kept":29,"cut":false,"hidden":false,"merged":[[6,1,6,11],[3,1,3,11],[4,1,4,11],[2,1,2,11]]}
[]
[]
[null,"Structural Methods and Ratiocination Techniques"]
[null,"(SMART)"]
[null,"Beam-Columns"]
[]
[null,"TABLE  OF  CONTENTS"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,"Click on Button to go to sheet"]
[]
[]
[]
[null,"Note:  This Workbook is intended to provide simplified and automated methods of airframe structural analysis."]
[]
[]
[null,"Rev A - Previous method found V, M, q, and y at b and then used equations for going from b to L to get unknown quantities.  However, this"]
[null,null,"gives slightly incorrect answers.  Revised to correctly use formulas for finding quantities at point b going from A for each q and y,"]
[null,null,"and from B back to b to for each q and y to find unknown quantities."]

{"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}]
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[]
[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 (+)",{"$f":"MAX(J12:K12)","v":30303.5}]
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[]
[null,null,null,"RA",{"$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 (+)",{"$f":"MAX(J17:L17)","v":30303.5}]
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[null,null,null,"RA",{"$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 (+)",{"$f":"MAX(I24:I25)","v":0}]
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[]
[null,null,null,"RB",0]
[null,null,null,"qA",{"$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",10,null,null,null,null,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",0,"Case 1",null,null,null,null,null,null,"W",{"$f":"B12*(B6+B7)/2","v":2000},null,"Q",{"$f":"B13/B12","v":0},"(wb-wa)/(b - a)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"B4+B12/2","v":5},{"$f":"N$5*AE4","v":0.26984353611043294},{"$f":"N$5*SIN(AF4)","v":1.4387012407693729E-2},{"$f":"COS(AF4)","v":0.96381261840676147},{"$f":"AE4-B$4","v":5},{"$f":"N$5*AI4","v":0.26984353611043294},{"$f":"COS(AJ4)","v":0.96381261840676147},{"$f":"SIN(AJ4)","v":0.26658063808143012},{"$f":"AC$9*AH4-B$6*AL4/N$5-N$4*(1-AK4)/N$5^2","v":0},{"$f":"-AC$9*AG4-B$6*AK4-N$4*AL4/N$5","v":-207.50921515284961}]
["b",10,null,null,null,null,null,null,null,"RA",{"$f":"K4*(B3-B14)/B3","v":1000},null,"k",{"$f":"SQRT(B8/(B9*B10))","v":5.396870722208659E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AE4-AM4/AN4","v":5},0.26984353611043294,1.4387012407693729E-2,0.96381261840676147,5,0.26984353611043294,0.96381261840676147,{"$f":"SIN(AJ5)","v":0.26658063808143012},{"$f":"AC$9*AH5-B$6*AL5/N$5-N$4*(1-AK5)/N$5^2","v":0},{"$f":"-AC$9*AG5-B$6*AK5-N$4*AL5/N$5","v":-207.50921515284961}]
["wa",200,null,null,null,null,null,null,null,"RB",{"$f":"K4-K5","v":1000},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5,0.26984353611043294,1.4387012407693729E-2,0.96381261840676147,5,0.26984353611043294,0.96381261840676147,0.26658063808143012,0,-207.50921515284961]
["wb",200,null,null,null,null,null,null,null,"qA",{"$f":"Calcs1!S39","v":-1.6666840601839976E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5,0.26984353611043294,1.4387012407693729E-2,0.96381261840676147,5,0.26984353611043294,0.96381261840676147,0.26658063808143012,0,-207.50921515284961]
["P",1500,null,null,null,null,null,null,null,"qB",{"$f":"Calcs1!S40","v":-1.6666840601840094E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5,0.26984353611043294,1.4387012407693729E-2,0.96381261840676147,5,0.26984353611043294,0.96381261840676147,0.26658063808143012,0,-207.50921515284961]
["E",10300000,"psi",null,null,null,null,null,null,"Mmax",{"$f":"AC11","v":2578.1638691450325},"@ x =",{"$f":"AC12","v":5},null,null,null,null,null,null,null,null,null,null,null,null,null,"(RA - qA*P)",null,{"$f":"K5-K7*B8","v":1025.0002609027599},null,5,0.26984353611043294,1.4387012407693729E-2,0.96381261840676147,5,0.26984353611043294,0.96381261840676147,0.26658063808143012,0,-207.50921515284961]
["I",0.05,"in4",null,null,null,null,null,null,null,null,null,null,"wa/k",{"$f":"B6/N5","v":3705.8512292499454},null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AC9*SIN(AF10)/N5-B6*(1-AK10)/N5^2-N4*(AJ10-AL10)/N5^3","v":2578.1638691450325},null,5,0.26984353611043294,1.4387012407693729E-2,0.96381261840676147,5,0.26984353611043294,0.96381261840676147,0.26658063808143012,0,-207.50921515284961]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Q/k2",{"$f":"N4/N5^2","v":0},null,null,null,null,null,null,null,null,null,null,null,null,"Mmax",{"$f":"IF(AC9<0,\"NA\",AC10)","v":2578.1638691450325}]
["b - a",{"$f":"B5-B4","v":10},null,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",{"$f":"IF(AC2<0,\"NA\",AE10)","v":5}]
["wb-wa",{"$f":"B7-B6","v":0},"Case 2"]
["Xcg",{"$f":"(B6*(B5+2*B4)+B7*(2*B5+B4))*B12/(6*K4)","v":5},null,null,null,null,null,null,null,"RA",{"$f":"Calcs1!K53","v":747.5395204726118},null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"T14-V14-X14","v":0}]
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[null,null,"Case 3","  Both ends fixed",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.7473347197783884,0.20223881035487973,1.084031720903971E-2,0.97961933907881105,3.7473347197783884,0.20223881035487973,0.97961933907881105,0.20086301427289574,1.1368683772161603E-13,-204.16093478521037]
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[]
[null,null,"Case 4","  Cantilever (right end fixed)"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x","kx","k*sin","cos","x-a","k(x-a)","cos","sin","V","V'"]
[null,null,null,null,null,null,null,null,null,"RB",{"$f":"K4","v":2000},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"B4+B12/2","v":5},{"$f":"N$5*AE34","v":0.26984353611043294},{"$f":"N$5*SIN(AF34)","v":1.4387012407693729E-2},{"$f":"COS(AF34)","v":0.96381261840676147},{"$f":"AE34-B$4","v":5},{"$f":"N$5*AI34","v":0.26984353611043294},{"$f":"COS(AJ34)","v":0.96381261840676147},{"$f":"SIN(AJ34)","v":0.26658063808143012},{"$f":"AC$35*AH34-K$25*N$5*SIN(AF34)-B$6*AL34/N$5-N$4*(1-AK34)/N$5^2","v":-3.0695446184836328E-12},{"$f":"-AC$35*N$5*SIN(AF34)-K$25*N$5^2*AH34-B$6*AK34-N$4*AL34/N$5","v":-202.44796325230951}]
[null,null,null,null,null,null,null,null,null,"qA",{"$f":"Calcs1!P82","v":7.4357267095852941E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(RA - qA*P)",null,{"$f":"K23","v":999.99999999999693},null,{"$f":"AE34-AM34/AN34","v":4.9999999999999849},0.26984353611043216,1.4387012407693691E-2,{"$f":"COS(AF35)","v":0.96381261840676169},{"$f":"AE35-B$4","v":4.9999999999999849},0.26984353611043216,{"$f":"COS(AJ35)","v":0.96381261840676169},{"$f":"SIN(AJ35)","v":0.2665806380814294},-2.2737367544323206E-13,-202.44796325230951]
[null,null,null,null,null,null,null,null,null,"yA",{"$f":"Calcs1!P83","v":-0.54774949688472718},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AE35-AM35/AN35","v":4.999999999999984},0.2698435361104321,1.4387012407693687E-2,{"$f":"COS(AF36)","v":0.96381261840676169},4.999999999999984,0.2698435361104321,0.96381261840676169,{"$f":"SIN(AJ36)","v":0.26658063808142934},0,-202.44796325230951]
[null,null,null,null,null,null,null,null,null,"MB",{"$f":"Calcs1!L66","v":-10000},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.999999999999984,0.2698435361104321,1.4387012407693687E-2,0.96381261840676169,4.999999999999984,0.2698435361104321,0.96381261840676169,0.26658063808142934,0,-202.44796325230951]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.999999999999984,0.2698435361104321,1.4387012407693687E-2,0.96381261840676169,4.999999999999984,0.2698435361104321,0.96381261840676169,0.26658063808142934,0,-202.44796325230951]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.999999999999984,0.2698435361104321,1.4387012407693687E-2,0.96381261840676169,4.999999999999984,0.2698435361104321,0.96381261840676169,0.26658063808142934,0,-202.44796325230951]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.999999999999984,0.2698435361104321,1.4387012407693687E-2,0.96381261840676169,4.999999999999984,0.2698435361104321,0.96381261840676169,0.26658063808142934,0,-202.44796325230951]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.999999999999984,0.2698435361104321,1.4387012407693687E-2,0.96381261840676169,4.999999999999984,0.2698435361104321,0.96381261840676169,0.26658063808142934,0,-202.44796325230951]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.999999999999984,0.2698435361104321,1.4387012407693687E-2,0.96381261840676169,4.999999999999984,0.2698435361104321,0.96381261840676169,0.26658063808142934,0,-202.44796325230951]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"K25*AH43+(AC35*SIN(AF43)-O10*(1-AK43)-O11*(AJ43-AL43))/N5","v":840.4673832929268},null,4.999999999999984,0.2698435361104321,1.4387012407693687E-2,0.96381261840676169,4.999999999999984,0.2698435361104321,0.96381261840676169,0.26658063808142934,0,-202.44796325230951]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Mmax",{"$f":"IF(AC19<0,\"NA\",AC43)","v":840.4673832929268}]
[null,null,null,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",{"$f":"IF(AC19<0,\"NA\",AE43)","v":4.999999999999984}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,"For a =0, b = L, wL = wa",null,null,"q = wa"," - uniformly distributed load over entire length"]
[]
[null,null,null,"Case 2"]
[null,null,null,null,"1/k",{"$f":"1/N5","v":18.529256146249729},"K"]
[null,null,null,null,"a",{"$f":"B3*N5","v":0.53968707222086587}]
[null,null,null,null,"a/2",{"$f":"F73/2","v":0.26984353611043294}]
[null,null,null,null,"tan(a/2)",{"$f":"TAN(F74)","v":0.27658969491611712}]
[null,null,null,null,"M_end",{"$f":"B6*B3^2*(1/F73*F75-0.5)/(1-F73/TAN(F73))","v":2524.6047952738859},"(-)"]
[]
[null,null,null,null,"U",{"$f":"B6*F72^2-F76","v":66142.061871392783}]
[null,null,null,null,"V",{"$f":"B6*F72^2*F75+F76/TAN(F73)","v":23207.161038217746}]
[]
[null,null,null,null,"j0",{"$f":"ATAN(F79/F78)","v":0.33744826186598625}]
[null,null,null,null,"cos(j0)",{"$f":"COS(F81)","v":0.94360256702568379}]
[]
[null,null,null,null,"M_max (+)",{"$f":"B6*F72^2*(1/F82-1)-F76/F82","v":1428.5876095888957}]
[]
[null,null,null,null,"@ x = ",{"$f":"B3-F72*F81","v":3.7473347197783866}]

{"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}]
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["I",3.5,"in4",null,null,null,null,null,null,null,null,null,null,"wa/k",{"$f":"B6/N5","v":6418.7226143524849},null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AC9*SINH(AF15)/N$5-B$6*(AK15-1)/N$5^2-N$4*(AL15-AJ15)/N$5^3","v":5622.0764932538059},null,8.1668073208766572,0.25446830503674966,8.0147885412424538E-3,1.0325521490082989,5.1668073208766572,0.16099176210928628,1.012987187957209,0.16168810397012504,2.2737367544323206E-13,-194.54167330752054]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Q/k2",{"$f":"N4/N5^2","v":0},null,null,null,null,null,null,null,null,null,null,null,null,"Mmax",{"$f":"IF(AC9<0,\"NA\",AC10)","v":5622.0764932538059},null,8.1668073208766589,0.25446830503674972,8.0147885412424572E-3,1.0325521490082989,5.1668073208766589,0.16099176210928634,1.0129871879572092,0.16168810397012512,-4.5474735088646412E-13,-194.5416733075206]
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["wb-wa",{"$f":"B7-B6","v":0},"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,8.1668073208766589,0.25446830503674972,8.0147885412424572E-3,1.0325521490082989,5.1668073208766589,0.16099176210928634,1.0129871879572092,0.16168810397012512,-4.5474735088646412E-13,-194.5416733075206]
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[null,null,null,null,null,null,null,null,null,"qA",{"$f":"Calcs2!N53","v":-5.8868367725416172E-4}]
[null,null,null,null,null,null,null,null,null,"MB",{"$f":"Calcs2!N54","v":-4614.4539218342925},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'"]
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[null,null,"Case 3","  Both ends fixed",null,null,null,null,null,"RA",{"$f":"Calcs2!R60","v":1129.6627044256634},null,"MA",{"$f":"Calcs2!M62","v":-4299.0759853865575},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7.027706781442439,0.21897524487904321,6.8776746234046476E-3,1.0240710329231009,4.027706781442439,0.12549870195157983,1.0078853033615824,0.12582839398271511,0,-196.15282181351836]
[null,null,null,null,null,null,null,null,null,"RB",{"$f":"K4-K20","v":470.33729557433662},null,"MB",{"$f":"Calcs2!P62","v":-2505.821896873289},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7.027706781442439,0.21897524487904321,6.8776746234046476E-3,1.0240710329231009,4.027706781442439,0.12549870195157983,1.0078853033615824,0.12582839398271511,0,-196.15282181351836]
[null,null,null,null,null,null,null,null,null,"Mmax (+)",{"$f":"AC48","v":6692.9989805723671},"@ x =",{"$f":"AC49","v":8.8313762220408076},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7.027706781442439,0.21897524487904321,6.8776746234046476E-3,1.0240710329231009,4.027706781442439,0.12549870195157983,1.0078853033615824,0.12582839398271511,0,-196.15282181351836]
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[null,null,null,null,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$5^3","v":3962.5935320760846},null,7.027706781442439,0.21897524487904321,6.8776746234046476E-3,1.0240710329231009,4.027706781442439,0.12549870195157983,1.0078853033615824,0.12582839398271511,0,-196.15282181351836]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Mmax",{"$f":"IF(AC19<0,\"NA\",AC27)","v":3962.5935320760846},null,7.027706781442439,0.21897524487904321,6.8776746234046476E-3,1.0240710329231009,4.027706781442439,0.12549870195157983,1.0078853033615824,0.12582839398271511,0,-196.15282181351836]
[null,null,"Case 4","  Cantilever (right end fixed)",null,null,null,null,null,"RB",{"$f":"K4","v":1600},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x",{"$f":"IF(AC19<0,\"NA\",AE27)","v":7.027706781442439},null,7.027706781442439,0.21897524487904321,6.8776746234046476E-3,1.0240710329231009,4.027706781442439,0.12549870195157983,1.0078853033615824,0.12582839398271511,0,-196.15282181351836]
[null,null,null,null,null,null,null,null,null,"qA",{"$f":"Calcs2!P82","v":3.706821470442336E-3}]
[null,null,null,null,null,null,null,null,null,"yA",{"$f":"Calcs2!P83","v":-5.8736618631244353E-2}]
[null,null,null,null,null,null,null,null,null,"MB",{"$f":"Calcs2!L66","v":-20800}]
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{"sheet":"Calcs1","index":8,"n_rows":152,"n_cols":41,"rows_kept":152,"cut":false,"hidden":false,"merged":[]}
["Distributed Load"]
[]
["L",{"$f":"'Comp Distributed'!B3","v":10},null,null,null,null,null,null,"wa",{"$f":"B6","v":200}]
["a",{"$f":"'Comp Distributed'!B4","v":0},null,null,null,null,null,null,"Q",{"$f":"(B7-B6)/(B5-B4)","v":0},"(wb-wa)/(b - a)"]
["b",{"$f":"'Comp Distributed'!B5","v":10},null,null,null,null,null,null,"k",{"$f":"SQRT(B8/(B9*B10))","v":5.396870722208659E-2}]
["wa",{"$f":"'Comp Distributed'!B6","v":200},null,null,null,null,null,null,null,null,null,"wa/k",{"$f":"J3/J5","v":3705.8512292499454},"Z1"]
["wb",{"$f":"'Comp Distributed'!B7","v":200},null,null,null,null,null,null,null,null,null,"Q/k2",{"$f":"J4/J5^2","v":0},"Z2"]
["P",{"$f":"'Comp Distributed'!B8","v":1500}]
["E",{"$f":"'Comp Distributed'!B9","v":10300000},"psi"]
["I",{"$f":"'Comp Distributed'!B10","v":0.05},"in4"]
[]
["b - a",{"$f":"B5-B4","v":10}]
["wb-wa",{"$f":"B7-B6","v":0}]
["W",{"$f":"(B6+B7)*(B5-B4)/2","v":2000}]
["Xcg",{"$f":"(B6*(B5+2*B4)+B7*(2*B5+B4))*B12/(6*B14)","v":5},null,null,"CASE 1 ss/ss",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"qA*P*F1"]
[null,null,null,null,"yA = yL = 0",null,null,null,"RA",{"$f":"B14*(1-B15/B3)","v":1000},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AI$5*Z16","v":0}]
[null,null,null,null,"MA = ML = 0",null,null,null,"RB",{"$f":"B14-J16","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,null,null,null,{"$f":"AI$5*Z17","v":0}]
[null,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,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,3,null,null,"Values at b for span 0 to b",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,11,null,null,"qb*P = qA*P*F1 + RA*F3 - Z1*Fa4 - Z2*Fa5",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,200,null,null,"yb*k*P = qA*P*F2 + RA*F4 - Z1*Fa5 - Z2*Fa6",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,200,null,null,null,null,null,null,null,null,null,"Going from B toward A to b",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,"Values at b for span L to b",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,"qb*P = qB*P*F1 + RB*F3",null,null,null,null,null,null,"qb*P = qB*P*F1 + MB*k*F2 + RB*F3",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,"yb*k*P = qB*P*F2 + RB*F4",null,null,null,null,null,null,"yb*k*P = yB*k*P + qB*P*R2 + MB*k*F3 + RB*F4",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,"qB*P*F1"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,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":"Q$40*Z26","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,"see below",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"Q$40*Z27","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,"T1","T2",null,null,null,null,null,null,"C1 = RA*F3b - (Z1*Fa4 + Z2*Fa5)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,null,null,"F1b","F1d","=","-(C1 + RB*F3d)",null,{"$f":"-(U30+J17*O36)","v":-46.447222893292249},null,null,"C2 = RA*F4b - (Z1*Fa5 + Z2*Fa6)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,null,null,"F2b","-F2d","=","-C2 + RB*F4d",null,{"$f":"-U31+J17*P36","v":-12.846823209756545},null,null,"C1",{"$f":"J16*O35 -(M6*P37+M7*Q37)","v":46.447222893292249},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C2",{"$f":"J16*P35 -(M6*Q37+M7*R37)","v":12.846823209756545},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,null,null,null,"F1","F2","F3","F4",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,null,"x","kx","cos","sin","1 - cos","kx - sin","Fa5","Fa6",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,"b",{"$f":"B5","v":10},{"$f":"J$5*K35","v":0.53968707222086587},{"$f":"COS(L35)","v":0.85786952680019513},{"$f":"SIN(L35)","v":0.51386756561161684},{"$f":"1-M35","v":0.14213047319980487},{"$f":"L35-N35","v":2.5819506609249032E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,"d = L-b",{"$f":"B3-B5","v":0},{"$f":"J$5*K36","v":0},1,0,0,0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,"c = b-a",{"$f":"B12","v":10},{"$f":"J$5*K37","v":0.53968707222086587},0.85786952680019513,0.51386756561161684,0.14213047319980487,2.5819506609249032E-2,{"$f":"L37^2/2-O37","v":3.5005947613601651E-3},{"$f":"L37^3/6-P37","v":3.7889495487066979E-4}]
[]
[null,null,null,null,null,null,null,null,null,"Matrix",{"$f":"M35","v":0.85786952680019513},{"$f":"M36","v":1},"Inverse",{"$f":"MINVERSE(K39:L40)","v":0},1.946026694270492,null,{"$f":"MMULT(N39:O40,Q29:Q30)","v":-25.000260902759962},"qA*P",{"$f":"Q39/B8","v":-1.6666840601839976E-2},"qA",{"$f":"Q39+H28","v":-25.000260902759962},"qb"]
[null,null,null,null,null,null,null,null,null,null,{"$f":"N35","v":0.51386756561161684},{"$f":"-N36","v":0},null,1,-1.669436999354375,null,-25.000260902760143,"qB*P",{"$f":"Q40/B8","v":-1.6666840601840094E-2},"qB"]
[]
[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,null,null,null,null,null,null,null,null,null,null,"T1","T2"]
[null,null,null,null,"RB = W-RA",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"F1b","(F3b + C5)","=","C1 + C3"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"F2b","(F4b - C6)","=","C2 - C4"]
[null,null,null,null,"Values at b for span 0 to b",null,null,null,null,null,"see below"]
[null,null,null,null,"qb*P = qA*P*F1 + RA*F3 - Z1*Fa4 - Z2*Fa5",null,null,null,null,"Matrix",{"$f":"M35","v":0.85786952680019513},{"$f":"O35+W52","v":0.14213047319980487},"Inverse",{"$f":"MINVERSE(K48:L49)","v":-0.50739431167552107},2.7930895314435529,null,{"$f":"W48+W50","v":95.683250306512619},{"$f":"MMULT(N48:O49,Q48:Q49)","v":-12.315270730295531},"qA*P","C1 = Z1*Fa4 + Z2*Fa5",null,null,{"$f":"M6*P37+M7*Q37","v":95.683250306512619}]
[null,null,null,null,"yb*k*P = qA*P*F2 + RA*F4 - Z1*Fa5 - Z2*Fa6",null,null,null,null,null,{"$f":"N35","v":0.51386756561161684},{"$f":"P35-W53","v":2.5819506609249032E-2},null,10.098313793977859,-16.858498678757293,null,{"$f":"W49-W51","v":12.972683399492487},747.5395204726118,"RA","C2 = Z1*Fa5 + Z2*Fa6",null,null,{"$f":"M6*Q37+M7*R37","v":12.972683399492487}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C3 = W*((L-Xcg)*k*F2d - F3d)",null,null,{"$f":"B14*((B3-B15)*J5*N36-O36)","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C4 = W*((L-Xcg)*k*F3d - F4d)",null,null,{"$f":"B14*((B3-B15)*J5*O36-P36)","v":0}]
[null,null,null,null,"Values at b for span L to b",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C5 = L*k*F2d - F3d",null,null,{"$f":"B3*J5*N36-O36","v":0}]
[null,null,null,null,"qb*P = MB*k*F2 + RB*F3",null,null,null,null,"RA",{"$f":"R49","v":747.5395204726118},null,"qA",{"$f":"R48/B8","v":-8.2101804868636875E-3},null,null,null,null,null,"C6 = L*k*F3d - F4d",null,null,{"$f":"B3*J5*O36-P36","v":0}]
[null,null,null,null,"yb*k*P = MB*k*F3 + RB*F4",null,null,null,null,"RB",{"$f":"B14-K53","v":1252.4604795273881},null,"MB",{"$f":"K53*B3-B14*(B3-B15)","v":-2524.6047952738818},null,"MB = RA*L - W*(L - Xcg)"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"T1","T2"]
[null,null,null,null,"CASE 3 fixed/fixed",null,null,null,null,null,"see below",null,null,null,null,null,null,null,null,"(F2b + F2d)","(F3b + C5)","=","C1 + C3"]
[null,null,null,null,"yA = yB = 0",null,null,null,null,null,{"$f":"N35+N36","v":0.51386756561161684},{"$f":"O35+(B3*J5*N36-O36)","v":0.14213047319980487},null,{"$f":"MINVERSE(K59:L60)","v":-3.7240043217005394},20.499791279970189,null,{"$f":"W61+W63","v":95.683250306512619},{"$f":"MMULT(N59:O60,Q59:Q60)","v":-90.387535625077362},"MA*k","(F3b - F3d)","(F4b - C6)","=","C2 - C4"]
[null,null,null,null,"qA = qB = 0",null,null,null,null,null,{"$f":"O35-O36","v":0.14213047319980487},{"$f":"P35-(B3*J5*O36-P36)","v":2.5819506609249032E-2},null,20.499791279970189,-74.116251099619873,null,{"$f":"W62-W64","v":12.972683399492487},999.99999999999693,"RA"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C1 = Z1*Fa4 + Z2*Fa5",null,null,{"$f":"M6*P37+M7*Q37","v":95.683250306512619}]
[null,null,null,null,null,null,null,null,null,null,null,"MA",{"$f":"R59/J5","v":-1674.8138000253309},null,"MB",{"$f":"(R59+R60*J5*B3-B14*J5*(B3-B15))/J5","v":-1674.8138000253625},null,null,null,"C2 = Z1*Fa5 + Z2*Fa6",null,null,{"$f":"M6*Q37+M7*R37","v":12.972683399492487}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"RB",{"$f":"B14-R60","v":1000.0000000000031},null,null,null,"C3 = W*((L-Xcg)*k*F2d - F3d)",null,null,{"$f":"B14*((B3-B15)*J5*N36-O36)","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C4 = W*((L-Xcg)*k*F3d - F4d)",null,null,{"$f":"B14*((B3-B15)*J5*O36-P36)","v":0}]
[null,null,null,null,"CASE4 free/fixed (cantilever)"]
[null,null,null,null,"yB = qB = 0",null,null,null,null,"MB =  W*(L - Xcg)",null,{"$f":"-B14*(B3-B15)","v":-10000},null,"RB = W",{"$f":"B14","v":2000},null,"MB*k",{"$f":"L66*J5","v":-539.68707222086584}]
[null,null,null,null,"RA = MA = 0"]
[null,null,null,null,null,null,null,null,null,"yb*k*P = yA*k*P + qA*P*F2 - Z1*Fa5 - Z2*Fa6"]
[null,null,null,null,null,null,null,null,null,"qb*P = qA*P*F1 - Z1*Fa4 - Z2*Fa5"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"at b"]
[null,null,null,null,null,null,null,null,null,"yb*k*P = RB*F4d + Mb*k*F3d",null,null,null,null,"F4d",{"$f":"P36","v":0},"RB",{"$f":"O66","v":2000},{"$f":"P72*R72","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"F3d",{"$f":"O36","v":0},"MB*k",{"$f":"R66","v":-539.68707222086584},{"$f":"P73*R73","v":0}]
[null,null,null,null,null,null,null,null,null,"qb*P = MB*k*F2d + RB*F3d",null,null,null,null,null,null,null,"C1 =",{"$f":"S72+S73","v":0}]
[]
[null,null,null,null,null,null,null,null,null,"- Z1*FA5 - Z2*FA6",null,"S1",{"$f":"-M6*Q37-M7*R37","v":-12.972683399492487},null,"F2d",{"$f":"N36","v":0},"MB*k",{"$f":"R73","v":-539.68707222086584},{"$f":"P76*R76","v":0}]
[null,null,null,null,null,null,null,null,null,"- Z1*FA4 - Z2*FA5",null,"S2",{"$f":"-M6*P37-M7*Q37","v":-95.683250306512619},null,"F3d",{"$f":"P73","v":0},"RB",{"$f":"R72","v":2000},0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C2 =",{"$f":"S76+S77","v":0}]
[null,null,null,null,null,null,null,null,null,"Let T1 = yA*k*P",null,null,"T1 + T2*F2b + S1 = C1"]
[null,null,null,null,null,null,null,null,null,"T2 = qA*P",null,null,"T2*F1b + S2 = C2"]
[]
[null,null,null,null,null,null,null,null,null,"T2 = (C2 - S2)/F1b",null,{"$f":"(-S78-M77)/M35","v":111.53590064377941},"qA*P",null,"qA",{"$f":"L82/B8","v":7.4357267095852941E-2}]
[null,null,null,null,null,null,null,null,null,"T1 = C1 - T2*F2b - S1",null,{"$f":"S74-L82*N35-M76","v":-44.341998342625608},"yA*k*P",null,"yA",{"$f":"L83/(J5*B8)","v":-0.54774949688472718}]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,"Case 1"]
[null,null,null,null,null,null,null,null,null,"qb*P = qA*P*F1b + RA*F3b - Z1*Fa4 - Z2*Fa5"]
[null,null,null,null,null,null,null,null,null,"yb*k*P = qA*P*F2b + RA*F4b - Z1*Fa5 - Z2*Fa6"]
[]
[null,null,null,null,null,null,null,null,null,"qb*P = qB*P*F1d + RB*F3d",null,null,null,null,"RB = W - RA"]
[null,null,null,null,null,null,null,null,null,"yb*k*P = qB*P*F2d + RB*F4d",null,null,null,null,"RA and RB are known"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"qA and qB are unknown"]
[null,null,null,null,null,null,null,null,"Let","C1 = RA*F3b - (Z1*Fa4 + Z2*Fa5)",null,null,null,"T1 = qA*P"]
[null,null,null,null,null,null,null,null,null,"C2 = RA*F4b - (Z1*Fa5 + Z2*Fa6)",null,null,null,"T2 = qB*P"]
[]
[null,null,null,null,null,null,null,null,null,"T1*F1b + C1 = -(T2*F1d + RB*F3d)",null,null,null,"T1*F1b + T2*F1d = -(C1 + RB*F3d)"]
[null,null,null,null,null,null,null,null,null,"T1*F2b + C2 = T2*F2d + RB*F4d",null,null,null,"T1*F2b - T2*F2d = -C2 + RB*F4d"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"T1","T2"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"F1b","F1d","=","-(C1 + RB*F3d)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"F2b","-F2d","=","-C2 + RB*F4d"]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,"Case 2"]
[null,null,null,null,null,null,null,null,null,"qb*P = qA*P*F1b + RA*F3b - Z1*Fa4 - Z2*Fa5"]
[null,null,null,null,null,null,null,null,null,"yb*k*P = qA*P*F2 + RA*F4 - Z1*Fa5 - Z2*Fa6"]
[]
[null,null,null,null,null,null,null,null,null,"qb*P = MB*k*F2 + RB*F3",null,null,null,null,"MB = RA*L - W*(L - Xcg)"]
[null,null,null,null,null,null,null,null,null,"yb*k*P = MB*k*F3 + RB*F4",null,null,null,null,"RB = W - RA"]
[]
[null,null,null,null,null,null,null,null,null,"qb*P = [RA*L - W*(L - Xcg)]*k*F2d + [W - RA]*F3d",null,null,null,null,null,"RA*(L*k*F2d - F3d) - W*[(L-Xcg)*k*F2d - F3d)"]
[null,null,null,null,null,null,null,null,null,"yb*k*P = [RA*L - W*(L - Xcg)]*k*F3d + [W - RA]*F4d",null,null,null,null,null,"RA*(L*k*F3d - F4d) - W*((L-Xcg)*k*F3d - F4d)"]
[]
[null,null,null,null,null,null,null,null,"Let","C1 = Z1*Fa4 + Z2*Fa5",null,null,"T1 = qA*P",null,"qb*P = T1*F1b + T2*F3b - C1",null,null,null,"qb*P[L] = -qb*P[R]"]
[null,null,null,null,null,null,null,null,null,"C2 = Z1*Fa5 + Z2*Fa6",null,null,"T2 = RA",null,"yb*k*P = T1*F2b + T2*F4b - C2",null,null,null,"yb*k*P[L] = yb*k*P[R]"]
[]
[null,null,null,null,null,null,null,null,null,"C3 = W*((L-Xcg)*k*F2d - F3d)",null,null,null,null,"qb*P = T2*C5 - C3"]
[null,null,null,null,null,null,null,null,null,"C4 = W*((L-Xcg)*k*F3d - F4d)",null,null,null,null,"yb*k*P = T2*C6 - C4"]
[]
[null,null,null,null,null,null,null,null,null,"C5 = L*k*F2d - F3d",null,null,null,null,"T1*F1b + T2*F3b - C1 = -(T2*C5 - C3)"]
[null,null,null,null,null,null,null,null,null,"C6 = L*k*F3d - F4d",null,null,null,null,"T1*F2b + T2*F4b - C2 = T2*C6 - C4"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"T1","T2"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"F1b","(F3b + C5)","=","C1 + C3"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"F2b","(F4b - C6)","=","C2 - C4"]
[]
[]
[null,null,null,null,null,null,null,null,null,"Case 3"]
[null,null,null,null,null,null,null,null,null,"qb*P = MA*k*F2b + RA*F3b - Z1*Fa4 - Z2*Fa5"]
[null,null,null,null,null,null,null,null,null,"yb*k*P = MA*k*F3b + RA*F4b - Z1*Fa5 - Z2*Fa6"]
[]
[null,null,null,null,null,null,null,null,null,"qb*P = MB*k*F2d + RB*F3d",null,null,null,null,"MB = MA + RA*L - W*(L - Xcg)"]
[null,null,null,null,null,null,null,null,null,"yb*k*P = MB*k*F3d + RB*F4d",null,null,null,null,"RB = W - RA"]
[]
[null,null,null,null,null,null,null,null,null,"qb*P = [MA + RA*L - W*(L - Xcg)]*k*F2d + [W - RA]*F3d",null,null,null,null,null,"MA*k*F2d + RA*(L*k*F2d - F3d) - W*[(L-Xcg)*k*F2d - F3d)"]
[null,null,null,null,null,null,null,null,null,"yb*k*P = [MA + RA*L - W*(L - Xcg)]*k*F3d + [W - RA]*F4d",null,null,null,null,null,"MA*k*F3d + RA*(L*k*F3d - F4d) - W*((L-Xcg)*k*F3d - F4d)"]
[]
[]
[null,null,null,null,null,null,null,null,"Let","C1 = Z1*Fa4 + Z2*Fa5",null,null,"T1 = MA*k",null,"qb*P = T1*F2b + T2*F3b - C1",null,null,null,"qb*P[L] = -qb*P[R]",null,null,"T1*F2b + T2*F3b - C1 = -(T1*F2d + T2*C5 - C3)"]
[null,null,null,null,null,null,null,null,null,"C2 = Z1*Fa5 + Z2*Fa6",null,null,"T2 = RA",null,"yb*k*P = T1*F3b + T2*F4b - C2",null,null,null,"yb*k*P[L] = yb*k*P[R]"]
[]
[null,null,null,null,null,null,null,null,null,"C3 = W*((L-Xcg)*k*F2d - F3d)",null,null,null,null,"qb*P = T1*F2d + T2*C5 - C3"]
[null,null,null,null,null,null,null,null,null,"C4 = W*((L-Xcg)*k*F3d - F4d)",null,null,null,null,"yb*k*P = T1*F3d + T2*C6 - C4"]
[]
[null,null,null,null,null,null,null,null,null,"C5 = L*k*F2d - F3d",null,null,null,null,"T1*(F2b + F2d) + T2*(F3b + C5) = C1 + C3"]
[null,null,null,null,null,null,null,null,null,"C6 = L*k*F3d - F4d",null,null,null,null,"T1*(F3b - F3d) + T2*(F4b - C6) = C2 - C4"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"T1","T2"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(F2b + F2d)","(F3b + C5)","=","C1 + C3"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(F3b - F3d)","(F4b - C6)","=","C2 - C4"]

{"sheet":"Calcs2","index":9,"n_rows":83,"n_cols":41,"rows_kept":83,"cut":false,"hidden":false,"merged":[]}
["Distributed Load"]
[]
["L",{"$f":"'Tens Distributed'!B3","v":20},null,null,null,null,null,null,"wa",{"$f":"B6","v":200}]
["a",{"$f":"'Tens Distributed'!B4","v":3},null,null,null,null,null,null,"Q",{"$f":"(B7-B6)/(B5-B4)","v":0},"(wb-wa)/(b - a)",null,null,null,null,null,null,null,null,null,null,null,null,"x","kx","F1","F2","F3",null,null,null,null,null,null,{"$f":"J16","v":1040}]
["b",{"$f":"'Tens Distributed'!B5","v":11},null,null,null,null,null,null,"k",{"$f":"SQRT(B8/(B9*B10))","v":3.1158847642487792E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,0,{"$f":"X5*J$5","v":0},{"$f":"COS(Y5)","v":1},{"$f":"SIN(Y5)","v":0},{"$f":"1-Z5","v":0},null,"k(x-a)",null,null,null,null,{"$f":"Q39","v":-34.887482998714837}]
["wa",{"$f":"'Tens Distributed'!B6","v":200},null,null,null,null,null,null,null,null,null,"wa/k",{"$f":"J3/J5","v":6418.7226143524849},"Z1",null,null,null,null,null,null,null,null,null,{"$f":"X5+B$4/10","v":0.3},{"$f":"X6*J$5","v":9.347654292746338E-3},{"$f":"COS(Y6)","v":0.99995631099773685},{"$f":"SIN(Y6)","v":9.3475181624533242E-3},{"$f":"1-Z6","v":4.3689002263147536E-5},null,null,null,null,null,null,{"$f":"AI$5*Z6+AI$4*AB6","v":-34.840522237037476}]
["wb",{"$f":"'Tens Distributed'!B7","v":200},null,null,null,null,null,null,null,null,null,"Q/k2",{"$f":"J4/J5^2","v":0},"Z2",null,null,null,null,null,null,null,null,null,{"$f":"X6+B$4/10","v":0.6},1.8695308585492676E-2,0.9998252478084052,1.8694219557422342E-2,1.7475219159479582E-4,null,null,null,null,null,null,{"$f":"AI$5*Z7+AI$4*AB7","v":-34.699644055343001}]
["P",{"$f":"'Tens Distributed'!B8","v":35000},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.89999999999999991,2.804296287823901E-2,0.99960682188404504,2.8039287488790251E-2,3.9317811595496188E-4,null,null,null,null,null,null,-34.464860763285827]
["E",{"$f":"'Tens Distributed'!B9","v":10300000},"psi",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.2,3.7390617170985352E-2,0.99930105231027777,3.7381905403169054E-2,6.9894768972222909E-4,null,null,null,null,null,null,-34.136192875761544]
["I",{"$f":"'Tens Distributed'!B10","v":3.5},"in4",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.5,4.673827146373169E-2,0.99890796580463859,4.6721256961248334E-2,1.0920341953614132E-3,null,null,null,null,null,null,-33.713669111114278]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.8,5.6085925756478028E-2,0.99842759671424197,5.6056526109125385E-2,1.5724032857580283E-3,null,null,null,null,null,null,-33.197326388627481]
["b - a",{"$f":"B5-B4","v":8},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.1,6.5433580049224366E-2,0.99785998701278045,6.5386897149610337E-2,2.1400129872195528E-3,null,null,null,null,null,null,-32.587209825297855]
["wb-wa",{"$f":"B7-B6","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.4,7.4781234341970704E-2,0.99720518629685706,7.4711554813500183E-2,2.7948137031429399E-3,null,null,null,null,{"$f":"M$6","v":6418.7226143524849},null,-31.883372731893211]
["W",{"$f":"(B6+B7)*(B5-B4)/2","v":1600},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.6999999999999997,8.4128888634717028E-2,0.99646325178165174,8.4029684330815368E-2,3.5367482183482624E-3,null,null,"Fa4","Fa5",{"$f":"M$7","v":0},null,-31.085876608294285]
["Xcg",{"$f":"(B6*(B5+2*B4)+B7*(2*B5+B4))*B12/(6*B14)","v":7},null,null,"CASE 1 ss/ss",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.9999999999999996,9.3476542927463366E-2,0.99563424829592206,9.3340471501992761E-2,4.3657517040779359E-3,null,0,{"$f":"AD15-SIN(AD15)","v":0},{"$f":"AD15^2/2-(1-COS(AD15))","v":0},null,null,-30.194791138121154,null,"RA*F3-Z1*Fa4-Z2*Fa5",null,null,"qA*P*F1"]
[null,null,null,null,"yA = yL = 0",null,null,null,"RA",{"$f":"B14*(1-B15/B3)","v":1040},null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"X15+B$12/10","v":3.8},0.11840362104145361,0.99299847677220143,0.11812715660714,7.0015232277985673E-3,null,{"$f":"J$5*(X16-B$4)","v":2.4927078113990229E-2},{"$f":"AD16-SIN(AD16)","v":2.5813647836318843E-6},{"$f":"AD16^2/2-(1-COS(AD16))","v":1.608663696385992E-8},null,null,{"$f":"AI$5*Z16+AI$4*AB16-AG$13*AE16-AG$14*AF16","v":-27.378202383741989},null,{"$f":"AI$4*AB16-AG$13*AE16-AG$14*AF16","v":7.2650150923979187},null,null,{"$f":"AI$5*Z16","v":-34.64321747613991}]
[null,null,null,null,"MA = ML = 0",null,null,null,"RB",{"$f":"B14-J16","v":560},null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"X16+B$12/10","v":4.5999999999999996},0.14333069915544383,0.9897457284342267,0.14284044611454444,1.0254271565773299E-2,null,4.9854156227980458E-2,2.0648993605855426E-5,2.5737019947332483E-7,null,null,{"$f":"AI$5*Z17+AI$4*AB17-AG$13*AE17-AG$14*AF17","v":-23.997835007617013},null,{"$f":"AI$4*AB17-AG$13*AE17-AG$14*AF17","v":10.531902266182707},null,null,{"$f":"AI$5*Z17","v":-34.529737273799718}]
[null,20,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.3999999999999995,0.16825777726943406,0.98587802430252702,0.16746498498894,1.4121975697472977E-2,null,7.478123434197069E-2,6.9679528470520391E-5,1.3028017114284814E-6,null,null,-20.15520165144024,null,14.239601160220749,null,null,-34.394802811660988]
[null,3,null,null,"Values at b for span 0 to b",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.1999999999999993,0.19318485538342428,0.98139776748630114,0.19198547333822955,1.8602232513698858E-2,null,9.9708312455960915E-2,1.6513037329037028E-4,4.1168998508650176E-6,null,null,-15.952102175263581,null,18.286395752891448,null,null,-34.238497928155027]
[null,11,null,null,"qb*P = qA*P*F1 + RA*F3 - Z1*Fa4 - Z2*Fa5",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.9999999999999991,0.21811193349741451,0.97630774169029988,0.21638667591972183,2.369225830970012E-2,null,0.12463539056995114,3.224300897839566E-4,1.004915166877892E-5,null,null,-11.49056040648987,null,22.570359333244141,null,null,-34.060919739734011]
[null,200,null,null,"yb*k*P = qA*P*F2 + RA*F4 - Z1*Fa5 - Z2*Fa6",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7.7999999999999989,0.24303901161140473,0.97061110948523566,0.24065343160619976,2.9388890514764343E-2,null,0.14956246868394138,5.5696881129280174E-4,2.0833174116165545E-5,null,null,-6.8727607497091183,null,26.989417830820788,null,null,-33.862178580529907]
[null,200,null,null,null,null,null,null,null,null,null,"Going from B toward A to b",null,null,null,null,null,null,null,null,null,null,null,8.6,0.26796608972539498,0.96431141034279155,0.26477066280593897,3.5688589657208447E-2,null,0.17448954679793163,8.8408868047532008E-4,3.8585636900977105E-5,null,null,-2.2009846967640669,null,31.441413237036798,null,null,-33.642397933800865]
[null,null,null,null,"Values at b for span L to b",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,9.4,0.29289316783938524,0.9574125584364519,0.28872338483082327,4.2587441563548101E-2,null,0.19941662491192189,1.319074316818547E-3,6.5804947343685305E-5,null,null,2.4224527235074689,null,35.824167078715263,null,null,-33.401714355207794]
[null,null,null,null,"qb*P = qB*P*F1 + RB*F3",null,null,null,null,null,null,"q*P = qB*P*F1 + MB*k*F2 + RB*F3",null,null,null,null,null,null,null,null,null,null,null,10.200000000000001,0.31782024595337549,0.94991884020952,0.31249671520673683,5.0081159790480001E-2,null,0.22434370302591214,1.877143319890584E-3,1.05369698049574E-4,null,null,6.8952665163682632,null,40.035543904336805,null,null,-33.140277387968545]
[null,null,null,null,"yb*k*P = qB*P*F2 + RB*F4",null,null,null,null,null,null,"y*k*P = yB*k*P + qB*P*R2 + MB*k*F3 + RB*F4",null,null,null,null,null,null,null,null,null,null,null,11.000000000000002,0.34274732406736574,0.94183491171183575,0.33607588292044788,5.8165088288164246E-2,null,0.24927078113990239,2.5734368142344144E-3,1.6053687836131356E-4,null,null,11.115265273614401,null,43.973514743557161,"RB*F3",null,-32.858249469942763,"qB*P*F1"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"K36","v":9},0.28042962878239014,0.96093661927739127,0.276768520124197,3.9063380722608732E-2,null,null,null,null,null,null,{"$f":"AO26-AL26","v":-49.859207418106593},null,null,{"$f":"J$17*AB26","v":21.875493204660891},null,null,{"$f":"Q$40*Z26","v":-27.983714213445701}]
[null,null,null,null,null,null,null,null,null,null,null,"see bottom of Calcs1 worksheet",null,null,null,null,null,null,null,null,null,null,null,{"$f":"B$3-(X25+K$36/10)","v":8.0999999999999979},0.25238666590415104,0.9683191921314811,0.24971572267247386,3.1680807868518901E-2,null,null,null,null,null,null,{"$f":"AO27-AL27","v":-45.939956666781242},null,null,{"$f":"J$17*AB27","v":17.741252406370585},null,null,{"$f":"Q$40*Z27","v":-28.198704260410654}]
[null,null,null,null,null,null,null,null,null,null,null,"T1","T2",null,null,null,null,null,null,"C1 = RA*F3b - (Z1*Fa4 + Z2*Fa5)",null,null,null,{"$f":"X27-K$36/10","v":7.1999999999999975},0.22434370302591203,0.97494032115436025,0.22246655970602144,2.5059678845639755E-2,null,null,null,null,null,null,-42.424940234106913,null,null,14.033420153558263,null,null,-28.391520080548649]
[null,null,null,null,null,null,null,null,null,null,null,"F1b","F1d","=","-(C1 + RB*F3d)",null,{"$f":"-(U30+J17*O36)","v":-67.230713491690949},null,null,"C2 = RA*F4b - (Z1*Fa5 + Z2*Fa6)",null,null,null,6.2999999999999972,0.19630074014767301,0.98079479977995954,0.19504245877395265,1.9205200220040464E-2,null,null,null,null,null,null,-39.31692217516057,null,null,10.75491212322266,null,null,-28.562010051937911]
[null,null,null,null,null,null,null,null,null,null,null,"F2b","-F2d","=","-C2 + RB*F4d",null,{"$f":"-U31+J17*P36","v":-3.9191610291735124},null,null,"C1",{"$f":"J16*O35 -(M6*P37+M7*Q37)","v":45.066615209169406},null,null,5.3999999999999968,0.16825777726943397,0.98587802430252702,0.16746498498893991,1.4121975697472977E-2,null,null,null,null,null,null,-36.618346499311826,null,null,7.9083063905848672,null,null,-28.710040108726957]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C2",{"$f":"J16*P35 -(M6*Q37+M7*R37)","v":5.9855685342489551},null,null,4.4999999999999964,0.14021481439119496,0.99018599749678127,0.13975582406935444,9.8140025032187328E-3,null,null,null,null,null,null,-34.331335248360617,null,null,5.4958414018024904,null,null,-28.835493846558126]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.5999999999999965,0.11217185151295594,0.9937153317611539,0.11193676528656631,6.2846682388461028E-3,null,null,null,null,null,null,-32.457686827856669,null,null,3.5194142137538176,null,null,-28.938272614102853]
[null,null,null,null,null,null,null,null,null,null,null,null,"F1","F2","F3","F4",null,null,null,null,null,null,null,2.6999999999999966,8.4128888634716931E-2,0.99646325178165174,8.4029684330815271E-2,3.5367482183482624E-3,null,null,null,null,null,null,-30.998874592911797,null,null,1.9805790022750269,null,null,-29.018295590636772]
[null,null,null,null,null,null,null,null,null,null,"x","kx","cosh","sinh","cosh - 1","sinh - kx","Fa5","Fa6",null,null,null,null,null,1.7999999999999967,5.6085925756477924E-2,0.99842759671424197,5.6056526109125281E-2,1.5724032857580283E-3,null,null,null,null,null,null,-29.956045689618087,null,null,0.88054584002449587,null,null,-29.075499849593591]
[null,null,null,null,null,null,null,null,null,"b",{"$f":"B5","v":11},{"$f":"J$5*K35","v":0.34274732406736569},{"$f":"COSH(L35)","v":1.0593151432941545},{"$f":"SINH(L35)","v":0.34949760058162804},{"$f":"M35-1","v":5.9315143294154549E-2},{"$f":"N35-L35","v":6.7502765142623544E-3},null,null,null,null,null,null,null,0.89999999999999669,2.804296287823891E-2,0.99960682188404504,2.803928748879015E-2,3.9317811595496188E-4,null,null,null,null,null,null,-29.330020152982563,null,null,0.22017974493477865,null,null,-29.109840408047784]
[null,null,null,null,null,null,null,null,null,"d = L-b",{"$f":"B3-B5","v":9},{"$f":"J$5*K36","v":0.28042962878239014},{"$f":"COSH(L36)","v":1.0395787469330742},0.28411964218431057,{"$f":"M36-1","v":3.9578746933074171E-2},{"$f":"N36-L36","v":3.6900134019204334E-3},null,null,null,null,null,null,null,0,0,1,0,0,null,null,null,null,null,null,-29.121290262087211,null,null,0,null,null,-29.121290262087211]
[null,null,null,null,null,null,null,null,null,"c = b-a",{"$f":"B12","v":8},{"$f":"J$5*K37","v":0.24927078113990234},{"$f":"COSH(L37)","v":1.0312291644297402},0.25186025802111012,{"$f":"M37-1","v":3.1229164429740219E-2},{"$f":"N37-L37","v":2.5894768812077806E-3},{"$f":"O37-L37^2/2","v":1.6120326469167348E-4},{"$f":"P37-L37^3/6","v":8.0318985291802369E-6}]
[]
[null,null,null,null,null,null,null,null,null,"Matrix",{"$f":"M35","v":1.0593151432941545},{"$f":"M36","v":1.0395787469330742},"Inverse",{"$f":"MINVERSE(K39:L40)","v":0.42769616982139347},1.5649176694463409,null,{"$f":"MMULT(N39:O40,Q29:Q30)","v":-34.887482998714837},"qA*P",{"$f":"Q39/B8","v":-9.9678522853470963E-4},"qA",{"$f":"Q39+H28","v":-34.887482998714837},"qb"]
[null,null,null,null,null,null,null,null,null,null,{"$f":"N35","v":0.34949760058162804},{"$f":"-N36","v":-0.28411964218431057},null,0.52611211242326406,-1.5946276221437863,null,-29.121290262087211,"qB*P",{"$f":"Q40/B8","v":-8.3203686463106312E-4},"qB"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Slope"]
[null,null,null,null,"CASE 2 ss/fixed"]
[null,null,null,null,"yA = yL = 0",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x","kx","F1","F2","F3",null,null,null,null,null,null,{"$f":"Q56*B8","v":0}]
[null,null,null,null,"MA = qL = 0",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"T1","T2",null,null,0,{"$f":"X44*J$5","v":0},{"$f":"COS(Y44)","v":1},{"$f":"SIN(Y44)","v":0},{"$f":"1-Z44","v":0},null,null,null,null,null,null,{"$f":"K54","v":790.72269609171462}]
[null,null,null,null,"RB = W-RA",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"F1b","(F3b + C5)","=","C1 + C3",{"$f":"X44+B$4/10","v":0.3},{"$f":"X45*J$5","v":9.347654292746338E-3},{"$f":"COS(Y45)","v":0.99995631099773685},{"$f":"SIN(Y45)","v":9.3475181624533242E-3},{"$f":"1-Z45","v":4.3689002263147536E-5},null,null,null,null,null,null,{"$f":"AI$44*Z45+AI$43*AB45","v":790.68815020605552}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"F2b","(F4b - C6)","=","C2 - C4",{"$f":"X45+B$4/10","v":0.6},1.8695308585492676E-2,0.9998252478084052,1.8694219557422342E-2,1.7475219159479582E-4,null,null,null,null,null,null,{"$f":"AI$44*Z46+AI$43*AB46","v":790.58451556762884}]
[null,null,null,null,"Values at b for span 0 to b",null,null,null,null,null,"see bottom of Calcs1 worksheet",null,null,null,null,null,null,null,null,null,null,null,null,0.89999999999999991,2.804296287823901E-2,0.99960682188404504,2.8039287488790251E-2,3.9317811595496188E-4,null,null,null,null,null,null,790.41180123182244]
[null,null,null,null,"qb*P = qA*P*F1 + RA*F3 - Z1*Fa4 - Z2*Fa5",null,null,null,null,"Matrix",{"$f":"M35","v":1.0593151432941545},{"$f":"O35+W52","v":0.19679320922226198},"Inverse",{"$f":"MINVERSE(K48:L49)","v":0.16964610214485604},2.3470585023531263,null,{"$f":"W48+W50","v":137.43422409946152},{"$f":"MMULT(N48:O49,Q48:Q49)","v":-20.603928703895662},"qA*P","C1 = Z1*Fa4 + Z2*Fa5",null,null,{"$f":"M6*P37+M7*Q37","v":16.621133816751325},1.2,3.7390617170985352E-2,0.99930105231027777,3.7381905403169054E-2,6.9894768972222909E-4,null,null,null,null,null,null,790.17002229007039]
[null,null,null,null,"yb*k*P = qA*P*F2 + RA*F4 - Z1*Fa5 - Z2*Fa6",null,null,null,null,null,{"$f":"N35","v":0.34949760058162804},{"$f":"P35-W53","v":-1.4224272995181992E-2},null,4.1682907567744092,-12.633945162873584,null,{"$f":"W49-W51","v":-18.712404944162785},809.27730390828538,"RA","C2 = Z1*Fa5 + Z2*Fa6",null,null,{"$f":"M6*Q37+M7*R37","v":1.034719040583894},1.5,4.673827146373169E-2,0.99890796580463859,4.6721256961248334E-2,1.0920341953614132E-3,null,null,null,null,null,null,789.85919986853412]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C3 = W*((L-Xcg)*k*F2d - F3d)",null,null,{"$f":"B14*((B3-B15)*J5*N36-O36)","v":120.81309028271019},1.8,5.6085925756478028E-2,0.99842759671424197,5.6056526109125385E-2,1.5724032857580283E-3,null,null,null,null,null,null,789.47936112625655]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C4 = W*((L-Xcg)*k*F3d - F4d)",null,null,{"$f":"B14*((B3-B15)*J5*O36-P36)","v":19.747123984746679},2.1,6.5433580049224366E-2,0.99785998701278045,6.5386897149610337E-2,2.1400129872195528E-3,null,null,null,null,null,null,789.03053925278914]
[null,null,null,null,"Values at b for span L to b",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C5 = L*k*F2d - F3d",null,null,{"$f":"B3*J5*N36-O36","v":0.13747806592810743},2.4,7.4781234341970704E-2,0.99720518629685706,7.4711554813500183E-2,2.7948137031429399E-3,null,null,null,null,{"$f":"M$6","v":6418.7226143524849},null,788.51277346529139]
[null,null,null,null,"qb*P = MB*k*F2 + RB*F3",null,null,null,null,"RA",{"$f":"R49","v":809.27730390828538},null,"qA",{"$f":"R48/B8","v":-5.8868367725416172E-4},null,null,null,null,null,"C6 = L*k*F3d - F4d",null,null,{"$f":"B3*J5*O36-P36","v":2.0974549509444346E-2},2.6999999999999997,8.4128888634717028E-2,0.99646325178165174,8.4029684330815368E-2,3.5367482183482624E-3,null,null,"Fa4","Fa5",{"$f":"M$7","v":0},null,787.92610900510476]
[null,null,null,null,"yb*k*P = MB*k*F3 + RB*F4",null,null,null,null,"RB",{"$f":"B14-K53","v":790.72269609171462},null,"MB",{"$f":"K53*B3-B14*(B3-B15)","v":-4614.4539218342925},null,"MB = RA*L - W*(L - Xcg)",null,null,null,null,null,null,null,2.9999999999999996,9.3476542927463366E-2,0.99563424829592206,9.3340471501992761E-2,4.3657517040779359E-3,null,0,{"$f":"AD54-SIN(AD54)","v":0},{"$f":"AD54^2/2-(1-COS(AD54))","v":0},null,null,787.27059713379913]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"X54+B$12/10","v":3.8},0.11840362104145361,0.99299847677220143,0.11812715660714,7.0015232277985673E-3,null,{"$f":"J$5*(X55-B$4)","v":2.4927078113990229E-2},{"$f":"AD55-SIN(AD55)","v":2.5813647836318843E-6},{"$f":"AD55^2/2-(1-COS(AD55))","v":1.608663696385992E-8},null,null,{"$f":"AI$44*Z55+AI$43*AB55-AG$13*AE55-AG$14*AF55","v":785.16986370376833}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"X55+B$12/10","v":4.5999999999999996},0.14333069915544383,0.9897457284342267,0.14284044611454444,1.0254271565773299E-2,null,4.9854156227980458E-2,2.0648993605855426E-5,2.5737019947332483E-7,null,null,{"$f":"AI$44*Z56+AI$43*AB56-AG$13*AE56-AG$14*AF56","v":782.48187067054823}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"T1","T2",null,null,5.3999999999999995,0.16825777726943406,0.98587802430252702,0.16746498498894,1.4121975697472977E-2,null,7.478123434197069E-2,6.9679528470520391E-5,1.3028017114284814E-6,null,null,779.10887582891598]
[null,null,null,null,"CASE 3 fixed/fixed",null,null,null,null,null,"see bottom of Calcs1 worksheet",null,null,null,null,null,null,null,null,"(F2b + F2d)","(F3b + C5)",null,"C1 + C3",6.1999999999999993,0.19318485538342428,0.98139776748630114,0.19198547333822955,1.8602232513698858E-2,null,9.9708312455960915E-2,1.6513037329037028E-4,4.1168998508650176E-6,null,null,774.95356258380241]
[null,null,null,null,"yA = yB = 0",null,null,null,null,null,{"$f":"N35+N36","v":0.63361724276593856},{"$f":"O35+(B3*J5*N36-O36)","v":0.19679320922226198},null,{"$f":"MINVERSE(K59:L60)","v":1.1029361109232978},15.259151515809293,null,{"$f":"W61+W63","v":137.43422409946152},{"$f":"MMULT(N59:O60,Q59:Q60)","v":-133.95425363213781},"MA*k","(F3b - F3d)","(F4b - C6)",null,"C2 - C4",6.9999999999999991,0.21811193349741451,0.97630774169029988,0.21638667591972183,2.369225830970012E-2,null,0.12463539056995114,3.224300897839566E-4,1.004915166877892E-5,null,null,769.91910041572316]
[null,null,null,null,"qA = qB = 0",null,null,null,null,null,{"$f":"O35-O36","v":1.9736396361080377E-2},{"$f":"P35-(B3*J5*O36-P36)","v":-1.4224272995181992E-2},null,1.5303407248654401,-49.130056614275915,null,{"$f":"W62-W64","v":-18.712404944162785},1129.6627044256634,"RA",null,null,null,null,7.7999999999999989,0.24303901161140473,0.97061110948523566,0.24065343160619976,2.9388890514764343E-2,null,0.14956246868394138,5.5696881129280174E-4,2.0833174116165545E-5,null,null,763.90920504420183]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C1 = Z1*Fa4 + Z2*Fa5",null,null,{"$f":"M6*P37+M7*Q37","v":16.621133816751325},8.6,0.26796608972539498,0.96431141034279155,0.26477066280593897,3.5688589657208447E-2,null,0.17448954679793163,8.8408868047532008E-4,3.8585636900977105E-5,null,null,756.82819825179592]
[null,null,null,null,null,null,null,null,null,null,null,"MA",{"$f":"R59/J5","v":-4299.0759853865575},null,"MB",{"$f":"(R59+R60*J5*B3-B14*J5*(B3-B15))/J5","v":-2505.821896873289},null,null,null,"C2 = Z1*Fa5 + Z2*Fa6",null,null,{"$f":"M6*Q37+M7*R37","v":1.034719040583894},9.4,0.29289316783938524,0.9574125584364519,0.28872338483082327,4.2587441563548101E-2,null,0.19941662491192189,1.319074316818547E-3,6.5804947343685305E-5,null,null,748.58106733156274]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"RB",{"$f":"B14-R60","v":470.33729557433662},null,null,null,"C3 = W*((L-Xcg)*k*F2d - F3d)",null,null,{"$f":"B14*((B3-B15)*J5*N36-O36)","v":120.81309028271019},10.200000000000001,0.31782024595337549,0.94991884020952,0.31249671520673683,5.0081159790480001E-2,null,0.22434370302591214,1.877143319890584E-3,1.05369698049574E-4,null,null,739.07352412102387]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C4 = W*((L-Xcg)*k*F3d - F4d)",null,null,{"$f":"B14*((B3-B15)*J5*O36-P36)","v":19.747123984746679},11.000000000000002,0.34274732406736574,0.94183491171183575,0.33607588292044788,5.8165088288164246E-2,null,0.24927078113990239,2.5734368142344144E-3,1.6053687836131356E-4,null,null,728.21206358595111]
[null,null,null,null,"CASE4 free/fixed (cantilever)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"K36","v":9},0.28042962878239014,0.96093661927739127,0.276768520124197,3.9063380722608732E-2,null,null,null,null,null,null,{"$f":"-(V$67*AA65+V$66*AB65)","v":-31.62224274211637}]
[null,null,null,null,"yB = qB = 0",null,null,null,null,"MB =  W*(L - Xcg)",null,{"$f":"-B14*(B3-B15)","v":-20800},null,"RB = W",{"$f":"B14","v":1600},null,"MB*k",{"$f":"L66*J5","v":-648.10403096374603},null,null,null,{"$f":"K53","v":809.27730390828538},null,{"$f":"B$3-(X64+K$36/10)","v":8.0999999999999979},0.25238666590415104,0.9683191921314811,0.24971572267247386,3.1680807868518901E-2,null,null,null,null,null,null,-25.646801154107312]
[null,null,null,null,"RA = MA = 0",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"K48*J5","v":3.3007039155282684E-2},null,{"$f":"X66-K$36/10","v":7.1999999999999975},0.22434370302591203,0.97494032115436025,0.22246655970602144,2.5059678845639755E-2,null,null,null,null,null,null,-20.287572295453792]
[null,null,null,null,null,null,null,null,null,"yb*k*P = yA*k*P + qA*P*F2 - Z1*Fa5 - Z2*Fa6",null,null,null,null,null,null,null,null,null,null,null,null,null,6.2999999999999972,0.19630074014767301,0.98079479977995954,0.19504245877395265,1.9205200220040464E-2,null,null,null,null,null,null,-15.548770429166849]
[null,null,null,null,null,null,null,null,null,"qb*P = qA*P*F1 - Z1*Fa4 - Z2*Fa5",null,null,null,null,null,null,null,null,null,null,null,null,null,5.3999999999999968,0.16825777726943397,0.98587802430252702,0.16746498498893991,1.4121975697472977E-2,null,null,null,null,null,null,-11.434121941625929]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.4999999999999964,0.14021481439119496,0.99018599749678127,0.13975582406935444,9.8140025032187328E-3,null,null,null,null,null,null,-7.9468624123112557]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"at b",null,null,null,null,null,null,null,null,3.5999999999999965,0.11217185151295594,0.9937153317611539,0.11193676528656631,6.2846682388461028E-3,null,null,null,null,null,null,-5.089734069486135]
[null,null,null,null,null,null,null,null,null,"yb*k*P = RB*F4d + Mb*k*F3d",null,null,null,null,"F4d",{"$f":"P36","v":3.6900134019204334E-3},"RB",{"$f":"O66","v":1600},{"$f":"P72*R72","v":5.9040214430726934},null,null,null,null,2.6999999999999966,8.4128888634716931E-2,0.99646325178165174,8.4029684330815271E-2,3.5367482183482624E-3,null,null,null,null,null,null,-2.8649836338282268]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"F3d",{"$f":"O36","v":3.9578746933074171E-2},"MB*k",{"$f":"R66","v":-648.10403096374603},{"$f":"P73*R73","v":-25.651145427819372},null,null,null,null,1.7999999999999967,5.6085925756477924E-2,0.99842759671424197,5.6056526109125281E-2,1.5724032857580283E-3,null,null,null,null,null,null,-1.2743605517069794]
[null,null,null,null,null,null,null,null,null,"qb*P = MB*k*F2d + RB*F3d",null,null,null,null,null,null,null,"C1 =",{"$f":"S72+S73","v":-19.747123984746679},null,null,null,null,0.89999999999999669,2.804296287823891E-2,0.99960682188404504,2.803928748879015E-2,3.9317811595496188E-4,null,null,null,null,null,null,{"$f":"-(V$67*AA74+V$66*AB74)","v":-0.31911561949579947}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,0,1,0,0,null,null,null,null,null,null,{"$f":"-(V$67*AA75+V$66*AB75)","v":0}]
[null,null,null,null,null,null,null,null,null,"- Z1*FA5 - Z2*FA6",null,"S1",{"$f":"-M6*Q37-M7*R37","v":-1.034719040583894},null,"F2d",{"$f":"N36","v":0.28411964218431057},"MB*k",{"$f":"R73","v":-648.10403096374603},{"$f":"P76*R76","v":-184.13908537562887}]
[null,null,null,null,null,null,null,null,null,"- Z1*FA4 - Z2*FA5",null,"S2",{"$f":"-M6*P37-M7*Q37","v":-16.621133816751325},null,"F3d",{"$f":"P73","v":3.9578746933074171E-2},"RB",{"$f":"R72","v":1600},63.325995092918674]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C2 =",{"$f":"S76+S77","v":-120.81309028271019}]
[null,null,null,null,null,null,null,null,null,"Let T1 = yA*k*P",null,null,"T1 + T2*F2b + S1 = C1"]
[null,null,null,null,null,null,null,null,null,"T2 = qA*P",null,null,"T2*F1b + S2 = C2"]
[]
[null,null,null,null,null,null,null,null,null,"T2 = (C2 - S2)/F1b",null,{"$f":"(-S78-M77)/M35","v":129.73875146548176},"qA*P",null,"qA",{"$f":"L82/B8","v":3.706821470442336E-3}]
[null,null,null,null,null,null,null,null,null,"T1 = C1 - T2*F2b - S1",null,{"$f":"S74-L82*N35-M76","v":-64.055787283804847},"yA*k*P",null,"yA",{"$f":"L83/(J5*B8)","v":-5.8736618631244353E-2}]