Mekanika Rekayasa 4 ( Metode Matriks )

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Sheet1E=200000MpaA=11000cm2luas 16000luas 25000A11000Batang 1L=5000mmEA/L=440000sin =0.8cos =0.6Matriks kekakuan10-104400000-4400000[KI,1]=4400000000=0000-1010-4400000440000000000000Matriks transformasi0.60.8000.6-0.80010001000[T]=-0.80.600[TT] =0.80.600[T]0100[TT] =0100000.60.8000.6-0.80010001000-0.80.6000.80.6000100012640000-2640000[TT].[K1]=3520000-3520000-264000026400004400000-4400000-35200003520000[Kg]0000-44000004400000u1v1u2v20000158400211200-158400-211200u1[Kg]=[TT][K1][T]=211200281600-211200-281600v1-158400-211200158400211200u2-211200-281600211200281600v2Batang 2L=500cmEA/L=4400000sin =0.6cos =0.8Matriks kekakuan10-104400000-4400000[KI,2]=44000000000=0000-1010-4400000440000000000000Matriks transformasi0.6-0.8000.60.800[T]=0.80.600[TT] =-0.80.600000.6-0.8000.60.8000.80.600-0.80.62640000-2640000[TT].[K2]=-35200003520000-264000026400003520000-3520000u2v2u3v3158400-211200-158400211200u2[Kg]=[TT][K2][T]=-211200281600211200-281600v2-158400211200158400-211200u3211200-281600-211200281600v3Batang 3L=800cmEA/L=2750000sin =0cos =1Matriks kekakuan10-1027500000-27500000[KI,3]=27500000000=0000-1010-275000002750000000000000Matriks transformasi10001000[T]=0100[TT] =0100001000100001000127500000-27500000[TT].[K3]=0000-27500000275000000000u1v1u3v327500000-27500000u1[Kg]=[TT][K3][T]=0000v1-2750000027500000u30000v3Overall Stiffnessu1v1u2v2u3v3F12908400211200-158400-211200-27500000u10G1211200281600-211200-28160000v100=-158400-2112003168000-158400211200u2U2-4-211200-2816000563200211200-281600v2V20-27500000-1584002112002908400-211200u3U3G300211200-281600-211200281600v30Rearrangementu2v2u3u1v1v303168000-158400-158400-211200211200U2-40563200211200-211200-281600-281600V20=-1584002112002908400-27500000-211200U3F1-158400-211200-2750000290840021120000G1-211200-281600021120028160000G3211200-281600-211200002816000Unknown Displacement and Reaction03168000-158400U2-4=0563200211200V20-1584002112002908400U3U20.0000032475-0.00000006820.00000018180V2=-0.00000006820.0000018267-0.0000001364-4U30.0000001818-0.00000013640.00000036360U20.0000002727V2=-0.0000073068U30.0000005455F1-158400-211200-27500000.0000002727F10G1=-211200-2816000-0.0000073068G1=2G3211200-281600-2112000.0000005455G32Gaya BatangBatang 1f1g1=[T1][Kg1][U1]f2g2f10.60.800158400211200-158400-2112000g1=-0.80.600211200281600-211200-2816000f2000.60.8-158400-2112001584002112000.0000002727u2g200-0.80.6-211200-281600211200281600-0.0000073068v2264000352000-264000-352000000000-264000-3520002640003520000.00000027270000-0.0000073068f12.5g1=0f2-2.5g20Batang 2f2g2=[T2][Kg2][U2]f3g3f20.6-0.800158400-211200-1584002112000.0000002727g2=0.80.600-211200281600211200-281600-0.0000073068f3000.6-0.8-158400211200158400-2112000.0000005455g3000.80.6211200-281600-2112002816000264000-352000-2640003520000.00000027270000-0.0000073068-264000352000264000-3520000.000000545500000f22.5g2=0f3-2.5g30Batang 3f1g1=[T3][Kg3][U3]f3g3f1100027500000-275000000g1=010000000f30010-27500000275000000.0000005455g300010000027500000-27500000000000-27500000275000000.000000545500000f1-1.5g1=0f31.5g30

Sheet2E=200000MpaA=11000cm2Batang 1L=3000mmEA/L=733333.333333333sin =0cos =1Matriks kekakuan10-10733333.30-733333.30[KI,1]=733333.300000000-1010-733333.30733333.300000000010001000[T]=0100[TT] =01000010001000010001733333.30-733333.30733333.30-733333.30[TT].[K1]0000[Kg]0000-733333.30733333.30-733333.30733333.3000000000Batang 2L=5000EA/L=440000sin =0cos =1matriks kekakuan10-104400000-4400000[KI,2]=4400000000=0000-1010-440000044000000000000010001000[T]=0100[TT] =010000100010000100014400000-44000004400000-4400000[TT].[K2]=0000[Kg]0000-44000004400000-4400000440000000000000Batang 3L=3000EA/L=733333.333333333sin =0cos =1matriks kekakuan10-10733333.3333333330-733333.3333333330[KI,3]=733333.3333333330000=0000-1010-733333.3333333330733333.33333333300000000010001000[T]=0100[TT] =01000010001000010001733333.3333333330-733333.3333333330733333.3333333330-733333.3333333330[TT].[K3]=0000[Kg]0000-733333.3333333330733333.3333333330-733333.3333333330733333.333333333000000000Batang 4L=5000EA/L=440000sin =0.8cos =0.6matriks kekakuan10-104400000-4400000[KI,4]=4400000000=0000-1010-44000004400000000000000.60.8000.6-0.800[T]=-0.80.600[TT] =0.80.600000.60.8000.6-0.800-0.80.6000.80.62640000-2640000158400211200-158400-211200[TT].[K4]=3520000-3520000[Kg]211200281600-211200-281600-26400002640000-158400-211200158400211200-35200003520000-211200-281600211200281600Batang 5L=4000EA/L=550000sin =1cos =0matriks kekakuan10-105500000-5500000[KI,5]=5500000000=0000-1010-550000055000000000000001000-100[T]=-1000[TT] =10000001000-100-10001000000000[TT].[K5]=5500000-5500000[Kg]05500000-55000000000000-550000055000000-5500000550000Batang 6L=5385.16EA/L=408530.108669009sin =0.37cos =0.93matriks kekakuan10-10408530.1086690090-408530.1086690090[KI,6]=408530.1086690090000=0000-1010-408530.1086690090408530.1086690090000000000.930.37000.93-0.3700[T]=-0.370.9300[TT] =0.370.9300000.930.37000.93-0.3700-0.370.93000.370.93379933.0010621780-379933.0010621780353337.690987826140575.210393006-353337.690987826-140575.210393006[TT].[K6]=151156.1402075330-151156.1402075330[Kg]140575.21039300655927.7718767873-140575.210393006-55927.7718767873-379933.0010621780379933.0010621780-353337.690987826-140575.210393006353337.690987826140575.210393006-151156.1402075330151156.1402075330-140575.210393006-55927.7718767873140575.21039300655927.7718767873Batang 7L=5385.16EA/L=408530.108669009sin =0.37cos =0.93matriks kekakuan10-10408530.1086690090-408530.1086690090[KI,7]=408530.1086690090000=0000-1010-408530.1086690090408530.1086690090000000000.93-0.37000.930.3700[T]=0.370.9300[TT] =-0.370.9300000.93-0.37000.930.37000.370.9300-0.370.93379933.0010621780-379933.0010621780353337.690987826-140575.210393006-353337.690987826140575.210393006[TT].[K7]=-151156.1402075330151156.1402075330[Kg]-140575.21039300655927.7718767873140575.210393006-55927.7718767873-379933.0010621780379933.0010621780-353337.690987826140575.210393006353337.690987826-140575.210393006151156.1402075330-151156.1402075330140575.210393006-55927.7718767873-140575.21039300655927.7718767873Batang 8L=4000EA/L=550000sin =1cos =0matriks kekakuan10-105500000-5500000[KI,8]=5500000000=0000-1010-550000055000000000000001000-100[T]=-1000[TT] =10000001000-100-10001000000000[TT].[K8]=5500000-5500000[Kg]05500000-55000000000000-550000055000000-5500000550000

No 2aE=200000MpaA=11000cm22aBatang 1L=3000mmEA/L=733333.333333333sin =0cos =1Matriks kekakuan10-10733333.3333333330-733333.3333333330[KI,1]=733333.3333333330000=0000-1010-733333.3333333330733333.333333333000000000Matriks transformasi10001000[T]=0100[TT] =01000010001000010001733333.3333333330-733333.3333333330[TT].[K1]=0000-733333.3333333330733333.33333333300000u1v1u2v2733333.3333333330-733333.3333333330u1[Kg]=[TT][K1][T]=0000v1-733333.3333333330733333.3333333330u20000v2Batang 2L=3000mmEA/L=733333.333333333sin =0cos =1Matriks kekakuan10-10733333.3333333330-733333.3333333330[KI,2]=733333.3333333330000=0000-1010-733333.3333333330733333.333333333000000000Matriks transformasi10001000[T]=0100[TT] =01000010001000010001733333.3333333330-733333.3333333330[TT].[K2]=0000-733333.3333333330733333.33333333300000u2v2u3v3733333.3333333330-733333.3333333330u2[Kg]=[TT][K2][T]=0000v2-733333.3333333330733333.3333333330u30000v3Batang 3L=3000mmEA/L=733333.333333333sin =0cos =1Matriks kekakuan10-10733333.3333333330-733333.3333333330[KI,3]=733333.3333333330000=0000-1010-733333.3333333330733333.333333333000000000Matriks transformasi10001000[T]=0100[TT] =01000010001000010001733333.3333333330-733333.3333333330[TT].[K3]=0000-733333.3333333330733333.33333333300000u3v3u4v4733333.3333333330-733333.3333333330u3[Kg]=[TT][K3][T]=0000v3-733333.3333333330733333.3333333330u40000v4Batang 4L=5000mmEA/L=440000sin =0.8cos =0.6Matriks kekakuan10-104400000-4400000[KI,4]=4400000000=0000-1010-4400000440000000000000Matriks transformasi0.60.8000.6-0.800[T]=-0.80.600[TT] =0.80.600000.60.8000.6-0.800-0.80.6000.80.62640000-2640000[TT].[K4]=3520000-3520000-26400002640000-35200003520000u1v1u5v5158400211200-158400-211200u1[Kg]=[TT][K4][T]=211200281600-211200-281600v1-158400-211200158400211200u5-211200-281600211200281600v5Batang 5L=4000mmEA/L=550000sin =1cos =0Matriks kekakuan10-105500000-5500000[KI,5]=5500000000=0000-1010-5500000550000000000000Matriks transformasi01000-100[T]=-1000[TT] =10000001000-100-1000100000[TT].[K5]=5500000-55000000000-55000005500000u2v2u5v50000u2[Kg]=[TT][K5][T]=05500000-550000v20000u50-5500000550000v5Batang 6L=2500mmEA/L=880000sin =0.8cos =0.6Matriks kekakuan10-108800000-8800000[KI,6]=8800000000=0000-1010-8800000880000000000000Matriks transformasi0.60.8000.6-0.800[T]=-0.80.600[TT] =0.80.600000.60.8000.6-0.800-0.80.6000.80.65280000-5280000[TT].[K6]=7040000-7040000-52800005280000-70400007040000u2v2u6v6316800422400-316800-422400u2[Kg]=[TT][K6][T]=422400563200-422400-563200v2-316800-422400316800422400u6-422400-563200422400563200v6Batang 7L=2500mmEA/L=880000sin =-0.8cos =0.6Matriks kekakuan10-108800000-8800000[KI,7]=8800000000=0000-1010-8800000880000000000000Matriks transformasi0.6-0.8000.60.800[T]=0.80.600[TT] =-0.80.600000.6-0.8000.60.8000.80.600-0.80.65280000-5280000[TT].[K7]=-70400007040000-528000052800007040000-7040000u6v6u3v3316800-422400-316800422400u6[Kg]=[TT][K7][T]=-422400563200422400-563200v6-316800422400316800-422400u3422400-563200-422400563200v3Batang 8L=4000mmEA/L=550000sin =1cos =0Matriks kekakuan10-105500000-5500000[KI,8]=5500000000=0000-1010-5500000550000000000000Matriks transformasi01000-100[T]=-1000[TT] =10000001000-100-1000100000[TT].[K8]=5500000-55000000000-55000005500000u3v3u7v70000u3[Kg]=[TT][K8][T]=05500000-550000v30000u70-5500000550000v7Batang 9L=5000mmEA/L=440000sin =-0.8cos =0.6Matriks kekakuan10-104400000-4400000[KI,9]=4400000000=0000-1010-4400000440000000000000Matriks transformasi0.6-0.8000.60.800[T]=0.80.600[TT] =-0.80.600000.6-0.8000.60.8000.80.600-0.80.62640000-2640000[TT].[K9]=-35200003520000-264000026400003520000-3520000u7v7u4v4158400-211200-158400211200u7[Kg]=[TT][K9][T]=-211200281600211200-281600v7-