Sheet1TUGAS MATRIKS10.60-1.000.000.000.000.000.00-0.600.0001.00[B]=x1x2x3x4x5x6x7x8x9x1020.800.000.000.000.000.001.000.800.0000.00e1000000100030.001.00-0.600.000.000.000.000.000.0090.00e2000000-101040.000.000.800.000.000.000.000.001.0000.00e300000000-1150.000.001.00-1.000.000.000.000.000.0000.00e4-101000000060.000.000.000.000.000.00-1.000.000.0000.00e500-1010000070.000.000.000.001.00-1.000.000.600.00-180.00e6010000000080.000.000.000.000.000.000.00-0.801.0000.00e7003/54/500000090.000.000.600.000.001.000.000.000.0000.00e80001000-100e900-3/54/500003/501.670.001.671.250.000.000.00-1.250.00151.67e1000000100001.00-0.752.001.500.00-0.750.00-1.500.00181.00e110000-3/54/50003/51.67-1.251.672.500.00-1.250.00-2.500.00151.671.67-1.251.672.50-1.00-1.250.00-2.500.00151.67e1e2e3e4e5e6e7e8e9e10e110.000.000.00-0.750.000.001.000.751.00-180.00[S]=F110000000000-1.000.75-1.00-1.500.000.750.001.501.00-9-1.00F2010000000000.000.000.000.000.00-1.000.000.000.0000.00F300100000000-1.671.25-1.67-1.250.001.250.001.250.00-15-1.67F400010000000-1.331.00-1.33-1.000.001.000.002.000.00-12-1.33F500001000000F6000003/800000PEMBUKTIAN INVERSF70000001/200001.000.000.000.000.000.000.000.000.00F800000003/80000.001.000.000.000.000.000.000.000.00F9000000001/2000.000.001.00-0.000.000.000.000.000.00F100000000003/800.000.000.001.000.000.000.000.000.00F1100000000000.50.000.000.000.001.000.000.000.000.00e1e2e3e4e5e6e7e8e9e100.000.000.000.000.001.000.000.000.00[C]=F10.0000.0000.0000.0000.0000.0001.0000.0000.0000.0000.000.000.000.000.000.001.000.000.00F20.0000.0000.0000.0000.0000.000-1.0000.0001.0000.0000.000.000.00-0.000.000.000.001.000.00F30.0000.0000.0000.0000.0000.0000.0000.000-1.0001.000matriks identitasF4-1.0000.0001.0000.0000.0000.0000.0000.0000.0000.000F50.0000.000-1.0000.0001.0000.0000.0000.0000.0000.000F60.0000.3750.0000.0000.0000.0000.0000.0000.0000.000F70.0000.0000.3000.4000.0000.0000.0000.0000.0000.000F80.0000.0000.0000.3750.0000.0000.000-0.3750.0000.000F90.0000.000-0.3000.4000.0000.0000.0000.0000.3000.000F100.0000.0000.0000.0000.0000.3750.0000.0000.0000.000F110.0000.0000.0000.000-0.3000.4000.0000.0000.0000.300F1F2F3F4F5F6F7F8F9F10F11[A]=P1000-10000000P200000100000P30001-100.60-0.800P40000000.810.800P50000100000-0.6P600000000010.8P71-1000000000P80000000-1000P901-1000000.600[K]=x1x2x3x4x5x6x7x8X9X10P1000100000000.6P11.0000.000-1.0000.0000.0000.0000.0000.0000.0000.000P20.0000.3750.0000.0000.0000.0000.0000.0000.0000.000P3-1.0000.0002.420-0.080-1.0000.0000.0000.000-0.2400.000P40.0000.0000.0001.0150.0000.0000.000-0.3750.2400.000P50.0000.000-1.0000.0001.180-0.2400.0000.0000.000-0.180P60.0000.0000.0000.000-0.2400.6950.0000.0000.0000.240P70.0000.0000.0000.0000.0000.0002.0000.000-1.0000.000P80.0000.0000.000-0.3750.0000.0000.0000.3750.0000.000{P}=10P1P90.0000.000-0.1800.2400.0000.000-1.0000.0002.180-1.0000P2P100.0000.0000.0000.000-0.1800.2400.0000.000-1.0001.1800P30P4123456789100P5[K]-1=13.5780.0002.578-0.0972.4590.4220.559-0.0971.1191.2370P620.0002.6670.0000.0000.0000.0000.0000.0000.0000.0000P732.5780.0002.578-0.0972.4590.4220.559-0.0971.1191.237-15P84-0.3760.000-0.3761.786-0.4040.100-0.3611.786-0.722-0.6940P952.4500.0002.450-0.1383.2660.6550.592-0.1381.1841.3680P1060.4550.0000.4550.1440.6881.838-0.1170.144-0.233-0.46670.5020.0000.502-0.2980.539-0.1330.981-0.2980.9630.9258-0.3760.000-0.3761.786-0.4040.100-0.3614.453-0.722-0.694{x}=37.237{F}=9.49191.0030.0001.003-0.5961.078-0.2660.963-0.5961.9251.8500.0009.491101.1320.0001.132-0.5561.272-0.5000.930-0.5561.8592.71927.2370.671BUKTI INVERS-30.556-10.0001.000.00-0.00-0.000.00-0.000.000.000.00-0.0026.566-0.6710.001.000.000.000.000.000.000.000.000.002.3870.0000.000.001.00-0.000.00-0.000.000.000.00-0.009.491-4.0510.000.000.001.00-0.000.000.000.00-0.000.00-70.55615.0000.000.00-0.000.001.00-0.000.000.000.00-0.0018.982-14.6990.000.000.00-0.00-0.001.000.000.00-0.000.0019.6530.8950.000.00-0.00-0.000.00-0.001.000.000.00-0.000.000.000.00-0.00-0.000.000.001.00-0.000.000.000.00-0.00-0.000.00-0.000.000.001.00-0.000.000.000.000.00-0.000.000.000.000.001.00

Sheet2Diketahui :E=2100t/cm2Elemen 1Elemen 2Elemen 1Elemen 2AE/L280A (cm2)1004012EI/(L)^30.9333333333I (cm4)500010006EI/(L)^2140L(m)5003004EI/L28000cos0.802EI/L14000sin0.6-1a. Matriks kekakuan elemen (member stiffness matrix)Elemen 1Elemen 2[kl]=42000-42000[kl]=28000-2800001.0082520-1.00825200.93331400-11400252840000-252420000.0000140.000028000.00000.0000-140.000014000.0000-4200042000-280.00000.00000.0000280.00000.00000.00000-1.008-25201.008-2520.0000-0.9333-140.00000.00000.9333-140.00000252420000-252840000.0000140.000014000.00000.0000-140.000028000.0000[T]=0.80.60000[T]=0-10000-0.60.800001000000010000010000000.80.600000-10000-0.60.80000100000001000001[TT] =0.8-0.60000[kg]=0.930.00140.00-0.930.00140.000.60.800000.00280.000.000.00-280.000.00001000140.000.0028000.00-140.000.0014000.000000.8-0.60-0.930.00-140.000.930.00-140.000000.60.800.00-280.000.000.00280.000.00000001140.000.0014000.00-140.000.0028000.00[TT] [ki]=336-0.6048-151.2-3360.6048-151.2b. Overall stiffness matrix2520.8064201.6-252-0.8064201.6269.2201.1-151.2-269.2-201.1-151.20252840000-25242000201.1151.8201.6-201.1-151.8201.6-3360.6048151.2336-0.6048151.2-151.2201.684000.0151.2-201.642000.0-252-0.8064-201.62520.8064-201.6-269.2-201.1151.2269.2201.1151.20252420000-25284000-201.1-151.8-201.6201.1151.8-201.6-151.2201.642000.0151.2-201.684000.0[kg]=269.2201.1-151.2-269.2-201.1-151.2201.1151.8201.6-201.1-151.8201.6-151.2201.684000.0151.2-201.642000.0-269.2-201.1151.2269.2201.1151.2-201.1-151.8-201.6201.1151.8-201.6-151.2201.642000.0151.2-201.684000.0

269.2201.1-151.2-269.2-201.1-151.20.93333333330140-0.93333333330140201.1151.8201.6-201.1-151.8201.6028000-2800-151.2201.684000.0151.2-201.642000.0140028000-140014000-269.2-201.1151.2269.2201.1151.2-0.93333333330-1400.93333333330-140-201.1-151.8-201.6201.1151.8-201.60-280002800-151.2201.642000.0151.2-201.684000.0140014000-140028000123456789F11269.2201.1-151.2-269.2-201.1-151.20.00.00.00G12201.1151.8201.6-201.1-151.8201.60.00.00.00M13-151.2201.684000.0151.2-201.642000.00.00.00.00-44-269.2-201.1151.2270.1201.1291.2-0.90.0140.0U205-201.1-151.8-201.6201.1431.8-201.60.0-280.00.0V25006-151.2201.642000.0291.2-201.6112000.0-140.00.014000.02F370.00.00.0-0.90.0-140.00.90.0-140.00G380.00.00.00.0-280.00.00.0280.00.00M390.00.00.0140.00.014000.0-140.00.028000.00Rearrangement-4=270.0962133333201.11616291.2-269.16288-201.11616151.2-0.93333333330140U20201.11616431.84512-201.6-201.11616-151.84512-201.60-2800V2500291.2-201.6112000-151.2201.642000-1400140002F1-269.16288-201.11616-151.2269.16288201.11616-151.20.00.00.00G1-201.11616-151.84512201.6201.11616151.84512201.60.00.00.00M1151.2-201.642000-151.2201.6840000.00.00.00F3-0.93330.0-140.0-0.9333-280.0-140.00.9333280.0-140.00G30.0-280.00.0140.0-280.014000.0-140.0280.028000.00M3140.00.014000.0140.00.014000.0-140.00.028000.00Perpindahan123-4=1270.0962133333201.11616291.2U202201.11616431.84512-201.6V25003291.2-201.61120002InversU2=0.0057107444-0.0026687456-0.0000196517-4=-0.0326688163V2-0.00266874560.00356475090.000013355300.01735262752-1.97E-051.34E-059.00E-065000.0045804594

F1=-269.2-201.1-151.2-0.0326688163=4.611G1-201.1-151.8201.60.01735262754.859M1151.2-201.642000.00.0045804594183.941F3-0.90.0-140.0-0.611G30.0-280.00.0-4.859M3140.00.014000.059.553e. Member Forces (Gaya-gaya elemen) Elemen 1 [T] [Kg][U]0.80.60000269.16288201.11616-151.2-269.16288-201.11616-151.20-0.60.80000201.11616151.84512201.6-201.11616-151.84512201.60001000-151.2201.684000151.2-201.64200000000.80.60-269.16288-201.11616151.2269.16288201.11616151.2-0.0326688163000-0.60.80-201.11616-151.84512-201.6201.11616151.84512-201.60.0173526275000001-151.2201.642000151.2-201.6840000.0045804594F16.604G11.121M1183.941F2-6.604G2-1.121M2376.321Elemen 2[T][Kg][U]0-100000.93333333330140-0.93333333330140-0.0326688163100000028000-28000.0173526275001000140028000-1400140000.00458045940000-10-0.93333333330-1400.93333333330-14000001000-2800028000000001140014000-1400280000F2-4.859G20.611M2123.679F34.859G3-0.611M359.553

Sheet3SISTEM RANGKA BATANG 3-DIMENSI (SPACE TRUSS)Diketahui :A130000mm2A240000mm2A320000mm2A430000mm2E200000MPaPx200kNPy600kNPz-800kNPenyelesaian :Koordinat titik nodal (satuan dalam mm)NodalXYZ12000400080002800000380006000040005060000Panjang batang dan cosinus sudut arahBatangNodalLxxvxLij1x20.3103448276x x-0.2068965517x vx-0.4137931034x20.1379310345vX x0.275862069vx20.551724137912110770-0.55708601450.37139067640.742781352711600000020.34615384620.1153846154-0.46153846150.0384615385-0.15384615380.615384615423110198-0.5883484054-0.19611613510.784464540610400000030.04761904760.09523809520.19047619050.19047619050.3809523810.761904761934191650.21821789020.43643578050.87287156098400000040.0555555556-0.05555555560.22222222220.0555555556-0.22222222220.888888888945184850.2357022604-0.23570226040.942809041672000000

Elemen 1Elemen 1AE/L557086.014531156AE/L784464.540552736[kl(1)] =55708600-557086.01453115600f2[kl(2)] =784464.54055273600-784464.54055273600000000g2000000000000h2000000-557086.0145311560055708600f1-784464.54055273600784464.54055273600000000g1000000000000h1000000

0.34615384620.1153846154-0.4615384615-0.3461538462-0.1153846154-0.46153846150.3103448276-0.2068965517-0.4137931034-0.31034482760.20689655170.41379310340.0384615385-0.15384615380.11538461540.0384615385-0.15384615380.13793103450.2758620690.2068965517-0.1379310345-0.2758620690.61538461540.46153846150.1538461538-0.61538461540.55172413790.4137931034-0.275862069-0.55172413790.34615384620.1153846154-0.46153846150.3103448276-0.2068965517-0.41379310340.0384615385-0.15384615380.13793103450.2758620690.88888888890.5517241379[kg(2)] =271545.41788363990515.1392945464-362060.557178186-271545.417883639-90515.1392945464-362060.557178186[kg(1)] =172888.763130359-115259.175420239-230518.350840478-172888.763130359115259.175420239230518.35084047830171.7130981822-120686.85239272990515.139294546430171.7130981822-120686.85239272976839.4502801594153678.900560319115259.175420239-76839.4502801594-153678.900560319482747.409570914362060.557178186120686.852392729-482747.409570914307357.801120638230518.350840478-153678.900560319-307357.801120638271545.41788363990515.1392945464-362060.557178186172888.763130359-115259.175420239-230518.35084047830171.7130981822-120686.85239272976839.4502801594153678.900560319697301.813824654307357.801120638