analisis struktrur dengan metode matriks
DESCRIPTION
okTRANSCRIPT
BEAM
1X5AB3.45Y4BC4.72.35Z3CD2.8611.01mEbeton2100000Ebaja20000000Angka
Poison0.134P12.45P28.35b400.4P34.54h600.6Q11.44I0.0072Q22.45M4.33a.
Elemen 1 (arah orientasi
AB)E=2100000ton/m^2I=0.0072m^4L=3.45mDayRazDbyRbz4418.517621.93-4418.517621.93Day[k]17621.9317530.43-7621.938765.22Raz-4418.51-7621.934418.51-7621.9281663516Dby7621.938765.22-7621.9317530.4347826087Rbzb.
Elemen 2 (arah orientasi
BC)E=2100000ton/m^2I=0.0072m^4L=4.7mDbyRbzDcyRcz1747.594106.84-1747.594106.84Dby[k]24106.8412868.09-4106.846434.04Rbz-1747.59-4106.841747.59-4106.8356722499Dcy4106.846434.04-4106.8412868.085106383Rczc.
Elemen 3 (arah orientasi
CD)E=2100000ton/m^2I=0.0072m^4L=2.86mDcyRczDdyRdz7755.9511091.01-7755.9511091.01Dcy[k]311091.0121146.85-11091.0110573.43Rcz-7755.95-11091.017755.95-11091.0068952027Ddy11091.0110573.43-11091.0121146.8531468531RdzLangkah
3: Perakitan Matriks Kekakuan Struktur TereduksiKontribusi dari
elemen
1RazRbz[k]117530.438765.22Raz8765.2217530.4347826087RbzKontribusi
dari elemen
2RbzRcz[k]212868.096434.04Rbz6434.0412868.09RczKontribusi dari
elemen 23RczRdz[k]321146.850.00Rcz0.000.00RdzHASIL PERAKITAN
MATRIKS [k]
STRUKTUR-TEREDUKSIRazRbzRcz[K]17530.438765.220Raz8765.2230398.526434.04Rbz06434.0434014.94RczLangkah
4: Menyusun Vektor Gaya-Luara. Vektor "span loading" masing-masing
elemen: (ingat rumus balok
jepit-jepit)q1=1.44AB3.45Q2=2.45P1=2.45BC=4.7P2=8.35CD=2.86-2.484Day-6.9825Dby-4.175Dcy{fo}1=-1.4283Raz{fo}2=-5.9494166667Rbz{fo}2=-2.985125Rcz-2.484Dby-6.9825Dcy-4.175Ddy1.4283Rbz5.9494166667Rcz2.985125Rdzb.
Perakitan vektor "span loading" struktur
tereduksi:-1.4283Raz-2.484Day{Fo}=-4.5211166667Rbz-1.4283Raz2.9642916667Rcz-9.4665Dby-4.5211166667Rbzc.
Vektor "Joint Loading" (F)-11.1575Dcy{F}
=0Raz2.9642916667Rcz-4.33Rbz-4.175Ddy0Rcz2.985125Rdzd. Vektor
"beban Total"
(F)+Fo-1.4283Raz-8.8511166667Rbz2.9642916667RczLangkah 5: Persamaan
Global Struktur >> {F}
+{Fo}=[K]{D}-1.428317530.43478260878765.21739130430Raz-8.8511166667
=8765.217391304330398.51988899176434.0425531915Rbz2.964291666706434.042553191534014.9382532361RczRaz0.0000671247-0.00002016220.0000038137-1.42830.00009389RadianRbz
=-0.00002016220.0000403244-0.0000076275-8.8511166667=-0.00035073RadianRcz0.0000038137-0.00000762750.00003084162.96429166670.00015349RadianLangkah
6: Menyusun Vektor Perpindahan bagi Masing-Masing
Elemen0Day0Dby0Dcy{d}1=0.00009389Raz{d}2=-0.000351Rbz{d}3=0.000153Rcz0Dby0Dcy0Ddy-0.000351Rbz0.0001534882Rcz0RdzLangkah
7: Menghitung Masing-Masing GAYA-ELEMEN (Elemen Forces) dengan
Rumus: {f} = [k] {d} - {fo}a. Elemen 1 (Segmen
AB)f1-1.9576129739-2.4840.5263870261tonf2-1.4283--1.4283=0ton
meterf3=1.9576129739-2.4844.4416129739tonf4-5.32546475991.4283-6.7537647599ton
meterRav0.5263870261Rbv10.614080378b. Elemen 2 (Segmen
BC)Rcv13.6698715611f1-0.8100325959-6.98256.1724674041tonRdv2.4726610347f2-3.5256519068--5.9494166667=2.4237647599ton
meterf3=0.8100325959-6.98257.7925325959tonMa0f4-0.28150129385.9494166667-6.2309179605ton
meterMb-6.7537647599-33.76882379932.4237647599Mc-6.2309179605-31.15458980236.2309179605b.
Elemen 3 (Segmen
CD)Md-1.3622285198-6.8111425989f11.7023389653-4.1755.8773389653tonf23.2457929605--2.985125=6.2309179605ton
meterMe9.643812548.2190625f3=-1.7023389653-4.1752.4726610347tonMf5.9702529.85125f41.62289648022.985125-1.3622285198ton
meterMx0.09620947960.481047398x0.5263870261sfd(3.14-x)4.4416da10tonx0.3655465459da20.5264ton2.63193513065.26390.2db1-4.4416ton-22.2080648694Me
superx3.8071532006db26.1725ton30.86233702072.354.7de10.4150ton2.0748370207x1.90357660036.7650625de2-2.0350ton-10.1751629793x'4.3273413602dc1-7.7925ton-38.9626629793Me
super5.316471139826.5823556992dc25.8773ton29.3866948264df15.8773ton29.3866948264Mf
superx1.43df2-2.4727ton-12.36330517364.86868944072.86dd1-2.4727ton-12.3633051736x2.4343447203dd10tonx'3.7965732401Mf
super2.173676759910.8683837994DayRazDbyRbzDcyRczDdyRdz4418.517621.93-4418.517621.930.000.000.000.00Day0.007621.9317530.43-7621.938765.220.000.000.000.00Raz93.89E-6-4418.51-7621.936166.10-3515.09-1747.594106.840.000.00Dby07621.938765.22-3515.0930398.52-4106.846434.040.000.00Rbz-350.7E-60.000.00-1747.59-4106.849503.546984.17-7755.9511091.01Dcy00.000.004106.846434.046984.1734014.94-11091.0110573.43Rcz153.5E-60.000.000.000.00-7755.95-11091.017755.95-11091.01Ddy00.000.000.000.0011091.0110573.43-11091.0121146.85Rdz0-1.9576129739-2.48400.5264Day-1.4283-1.42830.0000Raz1.147580378-9.466510.6141Dby-8.8511166667-4.5211-4.3300Rbz2.5123715611-11.157513.6699Dcy2.96429166672.96430.0000Rcz-1.7023389653-4.17502.4727Ddy1.62289648022.9851-1.3622Rdz
BEAM 2MATRIKS KEKAKUAN STRUKTURRBZDCYRCZ KIRCZ
KARDZREZX1ELEMEN 1
(A-B)58153.85-37278.1119384.620.000.000.00RBZPERAKITAN SPAN
LOADINGPERSAMAAN GLOBAL STRUKTURmenghitung masing-masing gaya
elemenDIPEROLEH
:Y4E2100000-37278.1195584.89-37278.1137278.1137278.110.00DCY{f} =
[K] * {d} -
{fo}RAV-2.7551Z2I0.007219384.62-37278.1138769.230.000.000.00RCZ
KI-2.2464DAY0DAY0DAY0DAY{F} + {fo} = [K] *
[D]RBV16.5452L3.120.0037278.110.0038769.2319384.620.00RCZ
KA-1.168128RAZ0RAZ0RAZ0RAZ[D] = [K]^(-1) * {F} + {fo}ELEMEN 1
(AB)ELEMEN 2
(BC)RCV-8.2100P12.41ton0.0037278.110.0019384.6252483.526857.14RDZ-2.2464DBY-1.8798DBY0DBY0DBYRDV8.0422P28.21tonDAYRAZDBYRBZ0.000.000.000.006857.1413714.29REZ{fo}
11.168128RBZ{fo} 2-0.488748RBZ{fo} 30RBZ{fo}
40RBZ39.36E-648.68E-627.13E-6-35.28E-6-23.05E-611.52E-6RAV=-5.0015234043--2.2464RBV=7.4174978723--1.8798REV-1.6103P34.14ton5974.069319.53-5974.069319.53DAYRBZDCYRCZ
KIRCZ
KARDZREZ0DCY-1.8798DCY-1.8798DCY0DCY[K]^(-1)48.68E-6126.6E-697.35E-6-91.73E-6-59.93E-629.96E-6MA-5.2015843404-1.168128MB11.0825486809-0.488748Q11.44ton/m[k]19319.5319384.62-9319.539692.31RAZ19384.6154RBZ0RCZ
KI0.488748RCZ KI0RCZ KI0RCZ
KI27.13E-697.35E-6105.8E-6-70.56E-6-46.1E-623.05E-6RBV5.0015234043-2.2464RCV-7.4174978723-1.8798Q22.41ton/m-5974.06-9319.535974.06-9319.53DBYDCYMENYUSUN
VEKTOR GAYA LUAR0RCZ KA0RCZ KA-0.488748RCZ KA0RCZ
KA-35.28E-6-91.73E-6-70.56E-698.63E-630.73E-6-15.37E-6MB-10.40316868091.168128MC
KI0.4887480.488748MA-4.0335-20.1672817021M4.22ton
m9319.539692.31-9319.5319384.62RBZRCZ
KI0DDY0DDY-1.8798DDY0DDY-23.05E-6-59.93E-6-46.1E-630.73E-653.78E-6-26.89E-6MB
ki-11.5713-57.8564834043RCZ KAELEMEN
AB0RDZ0RDZ0.488748RDZ0RDZ11.52E-629.96E-623.05E-6-15.37E-6-26.89E-686.36E-6MB
ka11.571357.8564834043DIMENSI BALOKELEMEN 2
(B-C)RDZRA-2.2464DAY0DEY0DEY0DEY0DEYRAV=-2.7551tonRBV=9.2973tonMC-0.0000-0B0.4mE2100000REZMA{fo}
1-1.168128RAZ0REZ0REZ0REZ0REZRBZ-0.0005366714RADIANSMA-4.0335ton
mMB11.5713ton
mMD-7.1013-35.5063965957H0.6mI0.00721.44RB-2.2464DBY[D]DCY-0.0014186841RADIANSRBV7.2479tonRCV-5.5377tonL1.56MB1.168128RBZRCZ
KI-0.001083177RADIANSMB-11.5713ton mMC KI-0.0000ton
mDa10inersia0.0072m^4AB-2.2464DAYSETELAH TEREDUKSIRCZ
KA0.0010063116RADIANSDa2-2.7551-13.77560.2210000kg/cm^2DBYRBZDCYRCZ
KI3.12-1.168128RAZRDZ0.0006904022RADIANSDb1-7.2479234043-36.2396E2100000ton/m^247792.4437278.11-47792.4437278.11DBYRBZDCYRCZ
KIRCZ KARDZREZ-4.1262DBY0.67938RBZREZ-0.0003452011RADIANSELEMEN
3ELEMEN
4Db29.297346.4865[k]137278.1138769.23-37278.1119384.62RBZ38769.2308-37278.106519384.6154RBZ{fo}0.67938RBZ{fo}-3.7596DCYDc15.537697872327.6885LAB3.12m-47792.44-37278.1147792.44-37278.11DCY-37278.106547792.4442-37278.1065DCYELEMEN
BC-3.7596DCY0.488748RCZ KIVEKTOR PERPINDAHAN MASING-MASING
ELEMENRCV=-4.5521021277--1.8798RCV=1.6102674193-0Dc2-2.6723021277-13.3615LBC1.563.12m37278.1119384.62-37278.1138769.23RCZ
KI19384.6154-37278.106538769.2308RCZ KIRB-1.8798ton0.488748RCZ
KI-0.488748RCZ
KAMC-0.488748-0.488748MC7.10127931910Dd1-6.4319021277-32.1595LCD1.56RCZ
KAMA-0.488748ton m-0.488748RCZ
KA0.488748RDZ0DAYRDV4.5521021277-1.8798RDV-1.61026741930Dd21.61038.0513LDE4.41mELEMEN
3 (C-D)RDZ2.41RC-1.8798ton-1.8798DDY0REZ{d}
10RAZMD-6.61253131910.488748MD00De11.61038.0513E2100000REZMC0.488748ton
m0.488748RDZ0DBYDe2-0.0000-0.0000I0.0072BC0DEY-0.0005366714RBZRCV=-2.6723tonRDV=1.6103tonL1.561.560REZMC0.0000ton
mMD7.1013ton m-1.8798DBY0DBYRDV6.4319tonREV-1.6103tonDCYRCZ
KADDYRDZ{fo} 2-0.488748RBZVEKTOR JOINT LOAD TEREDUKSIVEKTOR SPAN +
JOINT LOAD TEREDUKSI{d} 1-0.0005366714RBZMD-7.1013ton mME0.0000ton
m47792.444237278.1065-47792.444237278.1065DCYRBZDCYRCZ KIRCZ
KARDZREZ-1.8798DCY0RBZ0.67938RBZ-0.0014186841DCY[k]137278.106538769.2308-37278.106519384.6154RCZ
KARBZ0.488748RCZ KI{F}-8.21DCY{F} + {fo}-11.9696DCY-0.001083177RCZ
KI-47792.4442-37278.106547792.4442-37278.1065DDY47792.444237278.106537278.1065DCYELEMEN
CD0RCZ KI0.488748RCZ
KI37278.106519384.6154-37278.106538769.2308RDZRCZ
KIRB-1.8798ton0RCZ KA-0.488748RCZ
KA-0.0014186841DCY37278.106538769.230819384.6154RCZ
KAMA-0.488748ton m0RDZ0.488748RDZ{d} 10.0010063116RCZ KAELEMEN 4
(D-E)37278.106519384.615438769.2308RDZ2.41RC-1.8798ton0REZ0REZ0DDYE2100000REZMC0.488748ton
m0.0006904022RDZI0.0072CDL4.411.560DDY-1.8798DCY{d}
10.0006904022RDZDDYRDZDEYREZ{fo} 3-0.488748RCZ
KA0DEZ2115.524664.72-2115.524664.72DDYRBZDCYRCZ KIRCZ
KARDZREZ-1.8798DDY-0.0003452011REZ[k]14664.7213714.29-4664.726857.14RDZRBZ0.488748RDZ-2115.52-4664.722115.52-4664.72DEYDCYELEMEN
DE4664.726857.14-4664.7213714.29REZRCZ KIRCZ
KA0DCY13714.28576857.1429RDZ{fo}
40RCZ6857.142913714.2857REZ0DDYDE0RDZ4.41
TRUSS 3BPENYELESAIAN SOAL TUGAS 1 ANALISIS STRUKTUR METODE
MATRIKSP34.14q22.41x1.0000y4.0000z2.0000DIKETAHUIE20000000ton/m2L44.1400A10.0019cm2L57.4100L1
= L38.4881mL18.4881L57.4100mL2 = L44.1400mcos alpha0.4877STEP
PENYELESAIAN60.8077beta29.19232.07002.07001. Diskritisasi (lihat
gambar di atas)-2.07002. Matriks kekakuan batang9.4482DOF SEBELUM
TEREDUKSIDOF SETELAH
TERREDUKSIv2v3v2v3P3P3u2u2u32u3135u1u4u44v1v4Mencari Matriks
Kekakuan BatangMencari Gaya BatangBATANG 1E20000000ton/m2Rumus :
{f} = [k] {d} = [k] { [T]*[D]}Diketahui
PerpindahanA0.0019m2sudut60.80770.0088u2L8.4881mcos0.4877a.batang
10.0000u1-0.0028v2sin0.87300.0000v10.0092u3k14387.3230-4387.3230u1v1u2v2f1x4387.3230-4387.32300.48770.87300.00000.00000.0088u2-0.0075v3-4387.32304387.3230[K1]=1043.71081868.0910-1043.7108-1868.0910u1f2x-4387.32304387.32300.00000.00000.48770.8730-0.0028v2-0.0004u41868.09103343.6122-1868.0910-3343.6122v1-1043.7108-1868.09101043.71081868.0910u2-1868.0910-3343.61221868.09103343.6122v2f1x4387.3230-4387.32300.0000=-8.0857tontekanf2x-4387.32304387.32300.0018=8.0857tonBATANG
2CEK
BUHULE20000000ton/m2A0.0019m2sudut0.00002.0000600000.00008.5061L4.1400mcos1.0000b.batang
20.0088u2sin0.0000-0.0028v2k28995.1691-8995.1691u2v2u3v3f2x8995.1691-8995.16911.00000.00000.00000.00000.0092u31.0000-5.7174-8995.16918995.1691[K2]=8995.16910.0000-8995.16910.0000u2f3x-8995.16918995.16910.00000.00001.00000.00000.0000v30.00000.00000.00000.0000v23.00002.7886-8995.16910.00008995.16910.0000u30.00000.00000.00000.0000v3f2x8995.1691-8995.16910.0088=-3.9437tonf3x-8995.16918995.16910.0092=3.9437tonBATANG
3E20000000ton/m2A0.0019m2sudut60.8077L8.4881mcos0.4877c.batang
30.0092u3sin0.8730-0.0075v3k34387.3230-4387.3230u3v3u4v4f3x4387.3230-4387.32300.48770.87300.00000.0000-0.0004u4-4387.32304387.3230[K3]=1043.71081868.0910-1043.7108-1868.0910u3f4x-4387.32304387.32300.00000.00000.48770.87300.0000v41868.09103343.6122-1868.0910-3343.6122v3-1043.7108-1868.09101043.71081868.0910u4-1868.0910-3343.61221868.09103343.6122v4f3x4387.3230-4387.3230-0.0021=-8.0857tonf4x-4387.32304387.3230-0.0002=8.0857tonBATANG
4E20000000ton/m2sudut0.0000d. batang
40.0000u1A0.0019m2cos1.00000.0000v1L4.1400msin0.0000f1x8995.1691-8995.16911.00000.00000.00000.0000-0.0004u4u1v1u4v4f4x-8995.16918995.16910.00000.00001.00000.00000.0000v4k48995.1691-8995.1691[K3]=8995.16910.0000-8995.16910.0000u1-8995.16918995.16910.00000.00000.00000.0000v1f1x8995.1691-8995.16910.0000=3.9437ton-8995.16910.00008995.16910.0000u4f4x-8995.16918995.1691-0.0004=-3.9437ton0.00000.00000.00000.0000v4e.
batang 50.0088u2BATANG
5-0.0028v2E20000000ton/m2sudut90.0000f2x5025.6410-5025.64100.00001.00000.00000.0000-0.0004u4A0.0019m2cos0.0000f4x-5025.64105025.64100.00000.00000.00001.00000.0000v4L7.4100msin1.0000u2v2u4v4f2x5025.6410-5025.6410-0.0028=-14.1174tonk45025.6410-5025.6410[K3]=0.00000.0000-0.0000-0.0000u2f4x-5025.64105025.6410-0.0000=14.1174ton-5025.64105025.64100.00005025.6410-0.0000-5025.6410v2-0.0000-0.00000.00000.0000u4-0.0000-5025.64100.00005025.6410v4u2v2u3v3u4DIDAPATKAN10038.87991868.0910-8995.16910.0000-0.0000u2MATRIKS
KEKAKUAN GLOBAL
=1868.09108369.25330.00000.0000-0.0000v2-8995.16910.000010038.87991868.0910-1043.7108u30.00000.00001868.09103343.6122-1868.0910v3-0.0000-0.0000-1043.7108-1868.091010038.8799u4diperoleh
Perpindahan : {D} = [K]-1 . {F} [K]-1
{F}{D}0.0016-0.00040.0016-0.0009-0.00000.00000.0088u2m-0.00040.0002-0.00040.00020.0000-7.0587=-0.0028v2m0.0016-0.00040.0017-0.00100.00000.00000.0092u3m-0.00090.0002-0.00100.00090.0001-7.0587-0.0075v3m-0.00000.00000.00000.00010.00010.0000-0.0004u4mdiperoleh
Reaksi perletakan : {F} = [K] . {D} - {fo} [K]{D}-
{fo}u1v1u2v2u3v3u4v410038.881868.09-1043.71-1868.090.000.00-8995.170.00u10.00000.00001868.093343.61-1868.09-3343.610.000.000.000.00v10.00000.0000-1043.71-1868.0910038.881868.09-8995.170.00-0.00-0.00u20.00880.0000-1868.09-3343.611868.098369.250.000.00-0.00-5025.64v2-0.0028--7.05870.000.00-8995.170.0010038.881868.09-1043.71-1868.09u30.00920.00000.000.000.000.001868.093343.61-1868.09-3343.61v3-0.0075-7.0587-8995.170.00-0.00-0.00-1043.71-1868.0910038.881868.09u4-0.00040.00000.000.00-0.00-5025.64-1868.09-3343.611868.098369.25v40.00000.0000[K]
. {D}
{fo}0.00000.00000.0000u1ton-7.05870.0000-7.0587v1ton0.00000.00000.0000u2ton-7.0587--7.0587=0.0000v2ton-0.00000.0000-0.0000u3ton-7.0587-7.05870.0000v3ton-0.00000.0000-0.0000u4ton21.17610.000021.1761v4ton14.117414.1174ok
2
Q2
Q2
3
4
3
2
4
1
1
1
4
3
2
5
PORTALX110.5610.64Y47.443.123.427.223.14Z2P1 = 2.41P2
=8.21Q11.44Q22.41M =4.227.1110.41A =0.008008m2A =0.008008m2IX
=8.920E-05m4IX =8.9205E-05m4E =20000000ton/m2E
=20000000ton/m2LANGKAH 1 : Deskretisasi
D.O.FDBXDBYRBZDFXDFYRFZDGXDGYRGZLANGKAH 2: Matriks Kekakuan Masing
- Masing Elemen Dalam Sumbu Lokal A. Elemen 1 (AB)E
=20000000ton/m2Sudut ( q ) =90.0000Sin2 q =1.0000A =0.008008m2Sin q
=1.0000Cos2 q =0.0000I =8.920E-05m4Cos q =0.0000L
=10.4100mDAXDAYRAZDBXDBYRBZ15385.20650.00000.0000-15385.20650.00000.0000DAX0.00001.000000000.000018.977898.77950.0000-18.977898.7795DAY-1.00000.00000000[k]
1 =0.000098.7795685.52960.0000-98.7795342.7648RAZ[T] 1
=001000-15385.20650.00000.000015385.20650.00000.0000DBX0000.00001.000000.0000-18.9778-98.77950.000018.9778-98.7795DBY000-1.00000.000000.000098.7795342.76480.0000-98.7795685.5296RBZ000001B.
Elemen 2 (BF)E =20000000ton/m2Sudut ( q ) =0Sin2 q =0A
=0.008008m2Sin q =0Cos2 q =1I =0.000089m4Cos q =1L
=21.2mDBXDBYRBZDFXDFYRFZ7554.71700.00000.0000-7554.71700.00000.0000DBX1.00000.000000000.00002.246923.81750.0000-2.246923.8175DBY0.00001.00000000[k]
2 =0.000023.8175336.62090.0000-23.8175168.3105RBZ[T] 2
=001000-7554.71700.00000.00007554.71700.00000.0000DFX0001.00000.000000.0000-2.2469-23.81750.00002.2469-23.8175DFY0000.00001.000000.000023.8175168.31050.0000-23.8175336.6209RFZ000001C.
Elemen 3 (FG)E =20000000ton/m2Sudut ( q ) =0Sin2 q =0A
=0.008008m2Sin q =0Cos2 q =1I =0.000089m4Cos q =1L
=3.14mDFXDFYRFZDGXDGYRGZ51006.369426751600-51006.369426751600DFX1.00000.000000000691.52718175931085.69767536210-691.52718175931085.6976753621DFY0.00001.00000000[k]
3
=01085.69767536212272.7271337580-1085.69767536211136.363566879RFZ[T]
3
=001000-51006.36942675160051006.369426751600DGX0001.00000.000000-691.5271817593-1085.69767536210691.5271817593-1085.6976753621DGY0000.00001.0000001085.69767536211136.3635668790-1085.69767536212272.727133758RGZ000001D.
Elemen 4 (FH)E =20000000ton/m2Sudut ( q ) =66.1722Sin2 q =0.8368A
=0.008008m2Sin q =-0.9148Cos2 q =0.1632I =0.000089m4Cos q =0.4040L
=7.7725mDFXDFYRFZDHXDHYRHZ20605.99220.00000.0000-20605.99220.00000.0000DFX0.4040-0.914800000.000045.5949177.19320.0000-45.5949177.1932DFY0.91480.40400000[k]
4 =0.0000177.1932918.15590.0000-177.1932459.0779RFZ[T] 4
=001000-20605.99220.00000.000020605.99220.00000.0000DHX0000.4040-0.914800.0000-45.5949-177.19320.000045.5949-177.1932DHY0000.91480.404000.0000177.1932459.07790.0000-177.1932918.1559RHZ000001LANGKAH
3: Matriks Kekakuan Masing - Masing Elemen Dalam Sumbu GlobalA.
Elemen 1
(AB)DAXDAYRAZDBXDBYRBZDFXDFYRFZDGXDGYRGZDHXDHYRHZ0.0000-18.9778-98.7795-0.000018.9778-98.77950.00001.00000.00000.00000.00000.000018.97780.0000-98.7795-18.9778-0.0000-98.7795DAX15385.20650.00000.0000-15385.2065-0.00000.0000-1.00000.00000.00000.00000.00000.00000.000015385.20650.0000-0.0000-15385.20650.0000DAY[T]T
. [k] =0.000098.7795685.52960.0000-98.7795342.7648[T] 1
=0.00000.00001.00000.00000.00000.0000-98.77950.0000685.529698.7795-0.0000342.7648RAZ-0.000018.977898.77950.0000-18.977898.77950.00000.00000.00000.00001.00000.0000-18.9778-0.000098.779518.97780.000098.7795DBX-15385.2065-0.0000-0.000015385.20650.0000-0.00000.00000.00000.0000-1.00000.00000.0000-0.0000-15385.2065-0.00000.000015385.2065-0.0000DBY0.000098.7795342.76480.0000-98.7795685.52960.00000.00000.00000.00000.00001.0000-98.77950.0000342.764898.7795-0.0000685.5296RBZDFX[K]1
=DFYDAXDAYRAZDBXDBYRBZRFZ18.97780.0000-98.7795-18.9778-0.0000-98.7795DAX0.0000-1.00000000DGX0.000015385.20650.0000-0.0000-15385.20650.0000DAY1.00000.00000000DGY[K]1
=-98.77950.0000685.529698.7795-0.0000342.7648RAZ[T]T 1
=001000RGZ-18.9778-0.000098.779518.97780.000098.7795DBX0000.0000-1.00000DHX-0.0000-15385.2065-0.00000.000015385.2065-0.0000DBY0001.00000.00000DHY-98.77950.0000342.764898.7795-0.0000685.5296RBZ000001RHZB.
Elemen 2
(BF)DAXDAYRAZDBXDBYRBZDFXDFYRFZDGXDGYRGZDHXDHYRHZ7554.71700.00000.0000-7554.71700.00000.00001.00000.00000.00000.00000.00000.0000DAX0.00002.246923.81750.0000-2.246923.81750.00001.00000.00000.00000.00000.0000DAY[T]T
. [k] =0.000023.8175336.62090.0000-23.8175168.3105[T] 2
=0.00000.00001.00000.00000.00000.0000RAZ-7554.71700.00000.00007554.71700.00000.00000.00000.00000.00001.00000.00000.00007554.71700.00000.0000-7554.71700.00000.0000DBX0.0000-2.2469-23.81750.00002.2469-23.81750.00000.00000.00000.00001.00000.00000.00002.246923.81750.0000-2.246923.8175DBY0.000023.8175168.31050.0000-23.8175336.62090.00000.00000.00000.00000.00001.00000.000023.8175336.62090.0000-23.8175168.3105RBZ-7554.71700.00000.00007554.71700.00000.0000DFX[K]2
=0.0000-2.2469-23.81750.00002.2469-23.8175DFYDBXDBYRBZDFXDFYRFZ0.000023.8175168.31050.0000-23.8175336.6209RFZ7554.717000-7554.717000DBX1.00000.00000000DGX02.246923.81750-2.246923.8175DBY0.00001.00000000DGY[K]2
=023.8175336.62090-23.8175168.3105RBZ[T]T 2
=001000RGZ-7554.7170007554.717000DFX0001.00000.00000DHX0-2.2469-23.817502.2469-23.8175DFY0000.00001.00000DHY023.8175168.31050-23.8175336.6209RFZ000001RHZC.
Elemen 3
(FG)DAXDAYRAZDBXDBYRBZDFXDFYRFZDGXDGYRGZDHXDHYRHZ51006.36940.00000.0000-51006.36940.00000.00001.00000.00000.00000.00000.00000.0000DAX0.0000691.52721085.69770.0000-691.52721085.69770.00001.00000.00000.00000.00000.0000DAY[T]T
. [k] =0.00001085.69772272.72710.0000-1085.69771136.3636[T] 3
=0.00000.00001.00000.00000.00000.0000RAZ-51006.36940.00000.000051006.36940.00000.00000.00000.00000.00001.00000.00000.0000DBX0.0000-691.5272-1085.69770.0000691.5272-1085.69770.00000.00000.00000.00001.00000.0000DBY0.00001085.69771136.36360.0000-1085.69772272.72710.00000.00000.00000.00000.00001.0000RBZ51006.36940.00000.0000-51006.36940.00000.0000DFX[K]3
=0.0000691.52721085.69770.0000-691.52721085.6977DFYDFXDFYRFZDGXDGYRGZ0.00001085.69772272.72710.0000-1085.69771136.3636RFZ51006.369400-51006.369400DFX1.00000.00000000-51006.36940.00000.000051006.36940.00000.0000DGX0691.52721085.69770-691.52721085.6977DFY0.00001.000000000.0000-691.5272-1085.69770.0000691.5272-1085.6977DGY[K]3
=01085.69772272.72710-1085.69771136.3636RFZ[T]T 3
=0010000.00001085.69771136.36360.0000-1085.69772272.7271RGZ-51006.36940051006.369400DGX0001.00000.00000DHX0-691.5272-1085.69770691.5272-1085.6977DGY0000.00001.00000DHY01085.69771136.36360-1085.69772272.7271RGZ000001RHZD.
Elemen 4
(FH)DAXDAYRAZDBXDBYRBZDFXDFYRFZDGXDGYRGZDHXDHYRHZ8324.586141.7086162.0900-8324.5861-41.7086162.09000.4040-0.91480.00000.00000.00000.0000DAX-18849.620218.419871.584118849.6202-18.419871.58410.91480.40400.00000.00000.00000.0000DAY[T]T
. [k] =0.0000177.1932918.15590.0000-177.1932459.0779[T] 4
=0.00000.00001.00000.00000.00000.0000RAZ-8324.5861-41.7086-162.09008324.586141.7086-162.09000.00000.00000.00000.4040-0.91480.0000DBX18849.6202-18.4198-71.5841-18849.620218.4198-71.58410.00000.00000.00000.91480.40400.0000DBY0.0000177.1932459.07790.0000-177.1932918.15590.00000.00000.00000.00000.00001.0000RBZ3401.1915-7598.1820162.0900-3401.19157598.1820162.0900DFX[K]4
=-7598.182017250.395771.58417598.1820-17250.395771.5841DFYDFXDFYRFZDHXDHYRHZ162.090071.5841918.1559-162.0900-71.5841459.0779RFZ3401.1915-7598162.0900-3401.19157598162.0900DFX0.40400.91480000DGX-759817250.3957727598-17250.395772DFY-0.91480.40400000DGY[K]4
=162.090072918.1559-162.0900-72459.0779RFZ[T]T 4
=001000RGZ-3401.19157598-162.09003401.1915-7598-162.0900DHX0000.40400.91480-3401.19157598.1820-162.09003401.1915-7598.1820-162.0900DHX7598-17250.3957-72-759817250.3957-72DHY000-0.91480.404007598.1820-17250.3957-71.5841-7598.182017250.3957-71.5841DHY162.090072459.0779-162.0900-72918.1559RHZ000001162.090071.5841459.0779-162.0900-71.5841918.1559RHZLANGKAH
4: Menyusun Matriks Kekakuan GLOBAL yang sudah
TereduksiDAXDAYRAZDBXDBYRBZDFXDFYRFZDGXDGYRGZDHXDHYRHZ18.97780.0000-98.7795-18.9778-0.0000-98.77950.00000.00000.00000.00000.00000.00000.00000.00000.0000DAX0.000015385.20650.0000-0.0000-15385.20650.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000DAY-98.77950.0000685.529698.7795-0.0000342.76480.00000.00000.00000.00000.00000.00000.00000.00000.0000RAZ-18.9778-0.000098.77957573.69480.000098.7795-7554.71700.00000.00000.00000.00000.00000.00000.00000.0000DBX-0.0000-15385.2065-0.00000.000015387.453523.81750.0000-2.246923.81750.00000.00000.00000.00000.00000.0000DBY-98.77950.0000342.764898.779523.81751022.15050.0000-23.8175168.31050.00000.00000.00000.00000.00000.0000RBZ[K]S
=0.00000.00000.0000-7554.71700.00000.000061962.2779-7598.1820162.0900-51006.36940.00000.0000-3401.19157598.1820162.0900DFX0.00000.00000.00000.0000-2.2469-23.8175-7598.182017944.16981133.46420.0000-691.52721085.69777598.1820-17250.395771.5841DFY0.00000.00000.00000.000023.8175168.3105162.09001133.46423527.50390.0000-1085.69771136.3636-162.0900-71.5841459.0779RFZ0.00000.00000.00000.00000.00000.0000-51006.36940.00000.000051006.36940.00000.00000.00000.00000.0000DGX0.00000.00000.00000.00000.00000.00000.0000-691.5272-1085.69770.0000691.5272-1085.69770.00000.00000.0000DGY0.00000.00000.00000.00000.00000.00000.00001085.69771136.36360.0000-1085.69772272.72710.00000.00000.0000RGZ0.00000.00000.00000.00000.00000.0000-3401.19157598.1820-162.09000.00000.00000.00003401.1915-7598.1820-162.0900DHX0.00000.00000.00000.00000.00000.00007598.1820-17250.3957-71.58410.00000.00000.0000-7598.182017250.3957-71.5841DHY0.00000.00000.00000.00000.00000.0000162.090071.5841459.07790.00000.00000.0000-162.0900-71.5841918.1559RHZDBXDBYRBZDFXDFYRFZDGXDGYRGZ7573.69480.000098.7795-7554.71700.000.000.000.000.00DBX0.000015387.453523.81750.0000-2.2523.820.000.000.00DBY98.779523.81751022.15050.0000-23.82168.310.000.000.00RBZ[K]S
=-7554.71700.00000.000061962.2779-7598.18162.09-51006.370.000.00DFX0.0000-2.2469-23.8175-7598.182017944.171133.460.00-691.531085.70DFY0.000023.8175168.3105162.09001133.463527.500.00-1085.701136.36RFZ0.00000.00000.0000-51006.36940.000.0051006.370.000.00DGX0.00000.00000.00000.0000-691.53-1085.700.00691.53-1085.70DGY0.00000.00000.00000.00001085.701136.360.00-1085.702272.73RGZLANGKAH
5a : Menghitung Persamaan Span Loading Setiap Elemen Pada SUMBU
LOKALA. Elemen 1 (AB)B. Elemen 2 (BF)C. Elemen 3 (FG)D. Elemen 4
(FH)0FAX0FBX0FFX0FFX-1.19817927770FAY-12.5119618805FBY0FFY0FFY-15.7256932908{f0}1
=0MA{f0}2 =-40.6893MB{f0}3 =0MF{f0}4
=0MF-1.08796555110FBX0FFX0FGX0FHX6.36230939980FBY-18.0118381195FFY-30.52380FGY0FHY37.93409722150MB51.1666MF30.52380MG0MH6.8701995508LANGKAH
5b : Menghitung Persamaan Span Loading Setiap Elemen Pada SUMBU
GLOBALA. Elemen 1 (AB)B. Elemen 2 (BC)C. Elemen 3 (CD)D. Elemen 4
(CE)0FAX0FBX0FFX0FFX0FAY-12.5119618805FBY0FFY0FFY{f0}1 =0MA{f0}2
=-40.6893MB{f0}3 =0MF{f0}4
=0MF0FBX0FFX0FGX0FHX0FBY-18.0118381195FFY0FGY0FHY0MB51.1666MF0MG0MHLANGKAH
5c : Menyusun Matriks Span Loading Setiap Elemen Pada SUMBU
GLOBAL0FAX0FAY0FBX0MA-12.5119618805FBY0FBX-40.6893MB-12.5119618805FBY0FFX-40.689348038MB{f0}
=-18.0118381195FFY0FFX51.1666MF-18.0118381195FFY0FGX51.1666061721MF0FGY0FGX0MG0FGY0MGLANGKAH
6 : Menyusun Matriks Joint Loading 0FHX0FHY8.21FBX0MH0FBY0MB0FFX{F}
=0FFY0MF0FGX0FGY4.22MGMATRIKS TOTAL BEBAN STRUKTUR DALAM SUMBU
GLOBAL8.21FBX-12.5119618805FBY-40.6893MB0FFX{Fo} + {F}
=-18.0118381195FFY51.1666MF0FGX0FGY4.22MGLANGKAH 7 : Menyelesaikan
Persamaan GLOBAL Struktur {D} = [K]-1 ( {Fo} + {F}
)DBXDBYRBZDFXDFYRFZDGXDGYRGZ2.33E-028.72E-06-1.49E-032.32E-021.02E-02-3.18E-032.32E-022.18E-04-3.18E-03DBX8.72E-066.50E-05-1.90E-068.72E-063.85E-06-2.25E-068.72E-06-3.22E-06-2.25E-06DBY-1.49E-03-1.90E-061.10E-03-1.48E-03-6.49E-046.85E-05-1.48E-03-4.34E-046.85E-05RBZ[K]-1
=2.32E-028.72E-06-1.48E-032.32E-021.02E-02-3.19E-032.32E-022.13E-04-3.19E-03DFX1.02E-023.85E-06-6.49E-041.02E-024.57E-03-1.41E-031.02E-021.44E-04-1.41E-03DFY-3.18E-03-2.25E-066.85E-05-3.19E-03-1.41E-031.25E-03-3.19E-032.53E-031.25E-03RFZ2.32E-028.72E-06-1.48E-032.32E-021.02E-02-3.19E-032.32E-022.13E-04-3.19E-03DGX2.18E-04-3.22E-06-4.34E-042.13E-041.44E-042.53E-032.13E-041.39E-025.29E-03DGY-3.18E-03-2.25E-066.85E-05-3.19E-03-1.41E-031.25E-03-3.19E-035.29E-033.01E-03RGZDBX-0.1089METERDBY-0.0009METERRBZ-0.0413RADIANDFX-0.1108METER{D}
=DFY-0.0501METERRFZ0.0659RADIANDGX-0.1108METERDGY0.1686METERRGZ0.0733RADIANLANGKAH
8 : Menyusun Vektor Perpindahan Setiap Elemen Dalam SUMBU
LOKALFormula : {d} = [T] . {D}ELEMENT #1 (AB)0DAX0DAX0DAY0DAY{D}#1
=0RAZ{d}#1
=0RAZ-0.1089DBX-0.0009DBX-0.0009DBY0.1089DBY-0.0413RBZ-0.0413RBZELEMENT
#2 (BF)-0.1089DBX-0.1089DBX-0.0009DBY-0.0009DBY{D}#2
=-0.0413RBZ{d}#2
=-0.0413RBZ-0.1108DFX-0.1108DFX-0.0501DFY-0.0501DFY0.0659RFZ0.0659RFZELEMENT
#3 (FG)-0.1108DFX-0.1108DFX-0.0501DFY-0.0501DFY{D}#3
=0.0659RFZ{d}#3
=0.0659RFZ-0.1108DGX-0.1108DGX0.1686DGY0.1686DGY0.0733RGZ0.0733RGZELEMENT
#4 (FH)-0.1108DFX0.0011DFX-0.0501DFY-0.1216DFY{D}#4 =0.0659RFZ{d}#4
=0.0659RFZ0DHX0DHX0DHY0DHY0RHZ0RHZLANGKAH 9 : Menghitung GAYA DALAM
Setiap Elemen Pada SUMBU LOKALFormula : {f} = {k} {d} -{fo}ELEMENT
#1
(AB)DAXDAYRAZDBXDBYRBZFAX15385.20650.00000.0000-15385.20650.00000.0000DAX00FAY0.000018.977898.77950.0000-18.977898.7795DAY00MA=0.000098.7795685.52960.0000-98.7795342.7648RAZ0-0FBX-15385.20650.00000.000015385.20650.00000.0000DBX-0.00085855870FBY0.0000-18.9778-98.77950.000018.9778-98.7795DBY0.10888623240MB0.000098.7795342.76480.0000-98.7795685.5296RBZ-0.04128504220FAX13.2091013.2091TONFAY-6.14450-6.1445TONMA=-24.9068-0=-24.9068TONMFBX-13.20910-13.2091TONFBY6.144506.1445TONMB-39.05780-39.0578TONMELEMENT
#2
(BF)DBXDBYRBZDFXDFYRFZFBX7554.71700.00000.0000-7554.71700.00000.0000DBX-0.10890.0000FBY0.00002.246923.81750.0000-2.246923.8175DBY-0.0009-12.5120MB=0.000023.8175336.62090.0000-23.8175168.3105RBZ-0.0413--40.6893FFX-7554.71700.00000.00007554.71700.00000.0000DFX-0.11080.0000FFY0.0000-2.2469-23.81750.00002.2469-23.8175DFY-0.0501-18.0118MF0.000023.8175168.31050.0000-23.8175336.6209RFZ0.065951.1666FBX14.35450.000014.3545TONFBY0.6971-12.512013.2091TONMB=-1.6315--40.6893=39.0578TONMFFX-14.35450.0000-14.3545TONFFY-0.6971-18.011817.3147TONMF16.410951.1666-34.7557TONMELEMENT
#3
(FG)DFXDFYRFZDGXDGYRGZFFX51006.36940.00000.0000-51006.36940.00000.0000DFX-0.11080FFY0.0000691.52721085.69770.0000-691.52721085.6977DFY-0.05010MF=0.00001085.69772272.72710.0000-1085.69771136.3636RFZ0.0659-0FGX-51006.36940.00000.000051006.36940.00000.0000DGX-0.11080FGY0.0000-691.5272-1085.69770.0000691.5272-1085.6977DGY0.16860MG0.00001085.69771136.36360.0000-1085.69772272.7271RGZ0.07330FFX-0.00000-0TONFFY-0.00000-0TONMF=-4.2200-0=-4.22TONMFGX0.000000TONFGY0.000000TONMG4.220004.22TONMELEMENT
#4
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