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contoh soal analisa matriks (portal) 02-07-15

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Data properties penampang balok Mutu beton fc' = 25 M.Pa Dimensi penampang Lebar balok 1, b1 = 0.25 m Tinggi balok 1, h1 = 0.3 m Luas pnp balok 1, A1 = 0.075 m2 Lebar balok 2, b2 = 0.3 m Tinggi balok 2, h2 = 0.6 m Luas pnp balok 2, A2 = 0.18 m2 Lebar balok 3, b3 = 0.3 m Tinggi balok 3, h3 = 0.4 m Luas pnp balok 3, A3 = 0.12 m2 Lebar balok 4, b4 = 0.3 m Tinggi balok 4, h4 = 0.4 m Luas pnp balok 4, A4 = 0.12 m2 Panjang bentang Panjang bentang 1, L1 = 1.8 m Jarak beban, a1 = 0.9 m Jarak beban, b1 = 0.9 m Panjang bentang 2, L2 = 4.8 m Jarak beban, a2 = 2.4 m Jarak beban, b2 = 2.4 m Panjang bentang 3, L3 = 3.8 m Jarak beban, a3 = 1.9 m Jarak beban, b3 = 1.9 m Panjang bentang 4, L4 = 4.8 m Jarak beban, a4 = 2.4 m Jarak beban, b4 = 2.4 m Modulus Elastisitas, Ec = 23500000 Inersia Inersia balok 1, = 1/12 x b1 x h1^3 = 0.001 Inersia balok2, = 1/12 x b2 x h2^3 = 0.005 Inersia balok3, = 1/12 x b3 x h3^3 = 0.002 Inersia balok4, = 1/12 x b4 x h4^3 = 0.002 I1 I2 I3 I4

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Sheet1Data properties penampang balokMutu betonfc'=25M.PaDimensi penampangLebar balok 1,b1=0.25mTinggi balok 1,h1=0.3mLuas pnp balok 1,A1=0.075m2Lebar balok 2,b2=0.3mTinggi balok 2,h2=0.6mLuas pnp balok 2,A2=0.18m2Lebar balok 3,b3=0.3mTinggi balok 3,h3=0.4mLuas pnp balok 3,A3=0.12m2Lebar balok 4,b4=0.3mTinggi balok 4,h4=0.4mLuas pnp balok 4,A4=0.12m2Panjang bentangPanjang bentang 1,L1=1.8mJarak beban,a1=0.9mJarak beban,b1=0.9mPanjang bentang 2,L2=4.8mJarak beban,a2=2.4mJarak beban,b2=2.4mPanjang bentang 3,L3=3.8mJarak beban,a3=1.9mJarak beban,b3=1.9mPanjang bentang 4,L4=4.8mJarak beban,a4=2.4mJarak beban,b4=2.4mModulus Elastisitas,Ec=23500000InersiaInersia balok 1,I1=1/12 x b1 x h1^3=0.001Inersia balok2,I2=1/12 x b2 x h2^3=0.005Inersia balok3,I3=1/12 x b3 x h3^3=0.002Inersia balok4,I4=1/12 x b4 x h4^3=0.002Hitung matriks kekakuan batang 1 (SM1)Akibat displacement arah 1 --> D1 (translasi arah sb lokal 1)SM11 =Ec.A1=979166.666666667SM41 =- Ec.A1=-979166.666666667L1L1SM21 =0=0SM51 =0=0SM31 =0=0SM61 =0=0Akibat displacement arah 2 --> D2 (translasi arah sb lokal 2)SM12 =0=0SM42 =0=0SM22 =12.Ec.I1=27199.0740740741SM52 =- 12.Ec.I1=-27199.0740740741L13L13SM32 =6.Ec.I1=24479.1666666667SM62 =6.Ec.I1=24479.1666666667L12L12Akibat displacement arah 3 --> D3 (rotasi arah sb lokal 3)SM13 =0=0SM43 =0=0SM23 =6.Ec.I1=24479.1666666667SM53 =- 6.Ec.I1=-24479.1666666667L12L12SM33 =4.Ec.I1=29375SM63 =2.Ec.I1=14687.5L1L1Akibat displacement arah 4 --> D4 (translasi arah sb lokal 4)SM14 =- Ec.A1=-979166.666666667SM44 =Ec.A1=979166.666666667L1L1SM24 =0=0SM54 =0=0SM34 =0=0SM64 =0=0Akibat displacement arah 5 --> D5 (translasi arah sb lokal 5)SM15 =0=0SM45 =0=0SM25 =-12.Ec.I1=-27199.0740740741SM55 =12.Ec.I1=27199.0740740741L13L13SM35 =- 6.Ec.I1=-24479.1666666667SM65 =- 6.Ec.I1=-24479.1666666667L12L12Akibat displacement arah 6 --> D6 (rotasi arah sb lokal 6)SM16 =0=0SM46 =0=0SM26 =6.Ec.I1=24479.1666666667SM56 =- 6.Ec.I1=-24479.1666666667L12L12SM36 =2.Ec.I1=14687.5SM66 =4.Ec.I1=29375L1L1Susunan matriks kekakuan batang 1 (SM1) :--> catatan matriks kekakuan batang dalam arah sumbu lokalSM11SM12SM13SM14SM15SM16979166.66666666700-979166.66666666700SM1=SM21SM22SM23SM24SM25SM26SM1=027199.074074074124479.16666666670-27199.074074074124479.1666666667SM31SM32SM33SM34SM35SM36024479.1666666667293750-24479.166666666714687.5SM41SM42SM43SM44SM45SM46-979166.66666666700979166.66666666700SM51SM52SM53SM54SM55SM560-27199.0740740741-24479.1666666667027199.0740740741-24479.1666666667SM61SM62SM63SM64SM65SM66024479.166666666714687.50-24479.166666666729375Sudut batang 1 :a1=90degMatriks transformasi rotasi :cos a1sin a100000.010000R=- sin a1cos a10000R=-10.00000001000001000000cos a1sin a100000.010000- sin a1cos a10000-10.00000001000001Transpose matrik Rotasi [R]0-10000RT=1000000010000000-10000100000001Matriks kekakuan struktur menjadi :SMS = RT. SM . R0-10000979166.66666666700-979166.66666666700010000100000027199.074074074124479.16666666670-27199.074074074124479.1666666667-100000SMS 1=001000x024479.1666666667293750-24479.166666666714687.5x0010000000-10-979166.66666666700979166.666666667000000100001000-27199.0740740741-24479.1666666667027199.0740740741-24479.1666666667000-100000001024479.166666666714687.50-24479.1666666667293750000010-27199.0740740741-24479.1666666667027199.0740740741-24479.166666666701000027199.07407407410-24479.1666666667-27199.07407407410-24479.1666666667979166.66666666700-979166.66666666700-1000000979166.66666666700-979166.6666666670SMS 1=024479.1666666667293750-24479.166666666714687.5x001000=-24479.166666666702937524479.1666666667014687.5027199.074074074124479.16666666670-27199.074074074124479.1666666667000010-27199.0740740741024479.166666666727199.0740740741024479.1666666667-979166.66666666700979166.66666666700000-1000-979166.66666666700979166.6666666670024479.166666666714687.50-24479.166666666729375000001-24479.1666666667014687.524479.1666666667029375SM11SM12SM13SM14SM15SM16SM22SM21SM23SM25SM24SM26SM1=SM21SM22SM23SM24SM25SM26SMS1=SM12SM11SM13SM15SM14SM16SM31SM32SM33SM34SM35SM36Setelah tranfromasi menjadiSM32SM31SM33SM35SM34SM36SM41SM42SM43SM44SM45SM46SM52SM51SM53SM55SM54SM56SM51SM52SM53SM54SM55SM56SM42SM41SM43SM45SM44SM46SM61SM62SM63SM64SM65SM66SM62SM61SM63SM65SM64SM66Hitung matriks kekakuan batang 2 (SM2)Akibat displacement arah 1 --> D1 (translasi arah sb lokal 1)SM11 =Ec.A2=881250SM41 =- Ec.A2=-881250L2L2SM21 =0=0SM51 =0=0SM31 =0=0SM61 =0=0Akibat displacement arah 2 --> D2 (translasi arah sb lokal 2)SM12 =0=0SM42 =0=0SM22 =12.Ec.I2=13769.53125SM52 =- 12.Ec.I2=-13769.53125L23L23SM32 =6.Ec.I2=33046.875SM62 =6.Ec.I2=33046.875L22L22Akibat displacement arah 3 --> D3 (rotasi arah sb lokal 3)SM13 =0=0SM43 =0=0SM23 =6.Ec.I2=33046.875SM53 =- 6.Ec.I2=-33046.875L22L22SM33 =4.Ec.I2=105750SM63 =2.Ec.I2=52875L2L2Akibat displacement arah 4 --> D4 (translasi arah sb lokal 4)SM14 =- Ec.A2=-881250SM44 =Ec.A2=881250L2L2SM24 =0=0SM54 =0=0SM34 =0=0SM64 =0=0Akibat displacement arah 5 --> D5 (translasi arah sb lokal 5)SM15 =0=0SM45 =0=0SM25 =-12.Ec.I2=-13769.5SM55 =12.Ec.I2=13769.5L23L23SM35 =- 6.Ec.I2=-33046.9SM65 =- 6.Ec.I2=-33046.9L22L22Akibat displacement arah 6 --> D6 (rotasi arah sb lokal 6)SM16 =0=0SM46 =0=0SM26 =6.Ec.I2=33046.875SM56 =- 6.Ec.I2=-33046.875L22L22SM36 =2.Ec.I2=52875SM66 =4.Ec.I2=105750L2L2Susunan matriks kekakuan batang 2 (SM2) :--> catatan matriks kekakuan batang dalam arah sumbu lokalSM11SM12SM13SM14SM15SM1688125000-88125000SM2=SM21SM22SM23SM24SM25SM26SM2=013769.5312533046.8750-13769.5312533046.875SM31SM32SM33SM34SM35SM36033046.8751057500-33046.87552875SM41SM42SM43SM44SM45SM46-8812500088125000SM51SM52SM53SM54SM55SM560-13769.53125-33046.875013769.53125-33046.875SM61SM62SM63SM64SM65SM66033046.875528750-33046.875105750Sudut batang 2 :a2=90degMatriks transformasi rotasi :cos a1sin a10000010000R=- sin a1cos a10000R=-100000001000001000000cos a1sin a10000010000- sin a1cos a10000-100000001000001Transpose matrik Rotasi [R]0-10000RT=1000000010000000-10000100000001Matriks kekakuan struktur menjadi :SMS = RT. SM . R0-1000088125000-88125000010000100000013769.5312533046.8750-13769.5312533046.875-100000SMS 2=001000x033046.8751057500-33046.87552875x0010000000-10-88125000881250000000100001000-13769.53125-33046.875013769.53125-33046.875000-100000001033046.875528750-33046.8751057500000010-13769.53125-33046.875013769.53125-33046.87501000013769.531250-33046.875-13769.531250-33046.87588125000-88125000-100000088125000-8812500SMS 2=033046.8751057500-33046.87552875x001000=-33046.875010575033046.875052875013769.5312533046.8750-13769.5312533046.875000010-13769.53125033046.87513769.53125033046.875-8812500088125000000-1000-881250008812500033046.875528750-33046.875105750000001-33046.87505287533046.8750105750Hitung matriks kekakuan batang 3 (SM3)Akibat displacement arah 1 --> D1 (translasi arah sb lokal 1)SM11 =Ec.A3=742105.263157895SM41 =- Ec.A3=-742105.263157895L3L3SM21 =0=0SM51 =0=0SM31 =0=0SM61 =0=0Akibat displacement arah 2 --> D2 (translasi arah sb lokal 2)SM12 =0=0SM42 =0=0SM22 =12.Ec.I3=8222.7729989794SM52 =- 12.Ec.I3=-8222.7729989794L33L33SM32 =6.Ec.I3=15623.2686980609SM62 =6.Ec.I3=15623.2686980609L32L32Akibat displacement arah 3 --> D3 (rotasi arah sb lokal 3)SM13 =0=0SM43 =0=0SM23 =6.Ec.I3=15623.2686980609SM53 =- 6.Ec.I3=-15623.2686980609L32L32SM33 =4.Ec.I3=39578.9473684211SM63 =2.Ec.I3=19789.4736842105L3L3Akibat displacement arah 4 --> D4 (translasi arah sb lokal 4)SM14 =- Ec.A3=-742105.263157895SM44 =Ec.A3=742105.263157895L3L3SM24 =0=0SM54 =0=0SM34 =0=0SM64 =0=0Akibat displacement arah 5 --> D5 (translasi arah sb lokal 5)SM15 =0=0SM45 =0=0SM25 =-12.Ec.I3=-8222.7729989794SM55 =12.Ec.I3=8222.7729989794L33L33SM35 =- 6.Ec.I3=-15623.2686980609SM65 =- 6.Ec.I3=-15623.2686980609L32L32Akibat displacement arah 6 --> D6 (rotasi arah sb lokal 6)SM16 =0=0SM46 =0=0SM26 =6.Ec.I3=15623.2686980609SM56 =- 6.Ec.I3=-15623.2686980609L32L32SM36 =2.Ec.I3=19789.4736842105SM66 =4.Ec.I3=39578.9473684211L3L3Susunan matriks kekakuan batang 3 (SM3) :--> catatan matriks kekakuan batang dalam arah sumbu lokalSM11SM12SM13SM14SM15SM16742105.26315789500-742105.26315789500SM3=SM21SM22SM23SM24SM25SM26SM3=08222.772998979415623.26869806090-8222.772998979415623.2686980609SM31SM32SM33SM34SM35SM36015623.268698060939578.94736842110-15623.268698060919789.4736842105SM41SM42SM43SM44SM45SM46-742105.26315789500742105.26315789500SM51SM52SM53SM54SM55SM560-8222.7729989794-15623.268698060908222.7729989794-15623.2686980609SM61SM62SM63SM64SM65SM66015623.268698060919789.47368421050-15623.268698060939578.9473684211Sudut batang 3 :a3=0degMatriks transformasi rotasi :cos a1sin a10000100000R=- sin a1cos a10000R=010000001000001000000cos a1sin a10000100000- sin a1cos a10000010000001000001Transpose matrik Rotasi [R]100000RT=010000001000000100000010000001Matriks kekakuan struktur menjadi :SMS = RT. SM . R100000742105.26315789500-742105.2631578950010000001000008222.772998979415623.26869806090-8222.772998979415623.2686980609010000SMS 3=001000x015623.268698060939578.94736842110-15623.268698060919789.4736842105x001000000100-742105.26315789500742105.263157895000001000000100-8222.7729989794-15623.268698060908222.7729989794-15623.2686980609000010000001015623.268698060919789.47368421050-15623.268698060939578.9473684211000001742105.26315789500-742105.26315789500100000742105.26315789500-742105.2631578950008222.772998979415623.26869806090-8222.772998979415623.268698060901000008222.772998979415623.26869806090-8222.772998979415623.2686980609SMS 3=015623.268698060939578.94736842110-15623.268698060919789.4736842105x001000=015623.268698060939578.94736842110-15623.268698060919789.4736842105-742105.26315789500742105.26315789500000100-742105.26315789500742105.263157895000-8222.7729989794-15623.268698060908222.7729989794-15623.26869806090000100-8222.7729989794-15623.268698060908222.7729989794-15623.2686980609015623.268698060919789.47368421050-15623.268698060939578.9473684211000001015623.268698060919789.47368421050-15623.268698060939578.9473684211Hitung matriks kekakuan batang 4 (SM4)Akibat displacement arah 1 --> D1 (translasi arah sb lokal 1)SM11 =Ec.A4=587500SM41 =- Ec.A4=-587500L4L4SM21 =0=0SM51 =0=0SM31 =0=0SM61 =0=0Akibat displacement arah 2 --> D2 (translasi arah sb lokal 2)SM12 =0=0SM42 =0=0SM22 =12.Ec.I4=4079.8611111111SM52 =- 12.Ec.I4=-4079.8611111111L43L43SM32 =6.Ec.I4=9791.6666666667SM62 =6.Ec.I4=9791.6666666667L42L42Akibat displacement arah 3 --> D3 (rotasi arah sb lokal 3)SM13 =0=0SM43 =0=0SM23 =6.Ec.I4=9791.6666666667SM53 =- 6.Ec.I4=-9791.6666666667L42L42SM33 =4.Ec.I4=31333.3333333333SM63 =2.Ec.I4=15666.6666666667L4L4Akibat displacement arah 4 --> D4 (translasi arah sb lokal 4)SM14 =- Ec.A4=-587500SM44 =Ec.A4=587500L4L4SM24 =0=0SM54 =0=0SM34 =0=0SM64 =0=0Akibat displacement arah 5 --> D5 (translasi arah sb lokal 5)SM15 =0=0SM45 =0=0SM25 =-12.Ec.I4=-4079.8611111111SM55 =12.Ec.I4=4079.8611111111L43L43SM35 =- 6.Ec.I4=-9791.6666666667SM65 =- 6.Ec.I4=-9791.6666666667L42L42Akibat displacement arah 6 --> D6 (rotasi arah sb lokal 6)SM16 =0=0SM46 =0=0SM26 =6.Ec.I4=9791.6666666667SM56 =- 6.Ec.I4=-9791.6666666667L42L42SM36 =2.Ec.I4=15666.6666666667SM66 =4.Ec.I4=31333.3333333333L4L4Susunan matriks kekakuan batang 4 (SM4) :--> catatan matriks kekakuan batang dalam arah sumbu lokalSM11SM12SM13SM14SM15SM1658750000-58750000SM4=SM21SM22SM23SM24SM25SM26SM4=04079.86111111119791.66666666670-4079.86111111119791.6666666667SM31SM32SM33SM34SM35SM3609791.666666666731333.33333333330-9791.666666666715666.6666666667SM41SM42SM43SM44SM45SM46-5875000058750000SM51SM52SM53SM54SM55SM560-4079.8611111111-9791.666666666704079.8611111111-9791.6666666667SM61SM62SM63SM64SM65SM6609791.666666666715666.66666666670-9791.666666666731333.3333333333Sudut batang 4 :a4=0degMatriks transformasi rotasi :cos a1sin a10000100000R=- sin a1cos a10000R=010000001000001000000cos a1sin a10000100000- sin a1cos a10000010000001000001Transpose matrik Rotasi [R]100000RT=010000001000000100000010000001Matriks kekakuan struktur menjadi :SMS = RT. SM . R10000058750000-5875000010000001000004079.86111111119791.66666666670-4079.86111111119791.6666666667010000SMS 4=001000x09791.666666666731333.33333333330-9791.666666666715666.6666666667x001000000100-58750000587500000001000000100-4079.8611111111-9791.666666666704079.8611111111-9791.666666666700001000000109791.666666666715666.66666666670-9791.666666666731333.333333333300000158750000-5875000010000058750000-5875000004079.86111111119791.66666666670-4079.86111111119791.666666666701000004079.86111111119791.66666666670-4079.86111111119791.6666666667SMS 4=09791.666666666731333.33333333330-9791.666666666715666.6666666667x001000=09791.666666666731333.33333333330-9791.666666666715666.6666666667-5875000058750000000100-58750000587500000-4079.8611111111-9791.666666666704079.8611111111-9791.66666666670000100-4079.8611111111-9791.666666666704079.8611111111-9791.666666666709791.666666666715666.66666666670-9791.666666666731333.333333333300000109791.666666666715666.66666666670-9791.666666666731333.3333333333Susun MATRIKS KEKAKUAN STRUKTURD1D10D11D1212313141527199.07407407410-24479.1666666667-27199.07407407410-24479.166666666710979166.66666666700-979166.66666666702SMS 1=-24479.166666666702937524479.1666666667014687.53D1-27199.0740740741024479.166666666727199.0740740741024479.166666666713D100-979166.66666666700979166.666666667014D11-24479.1666666667014687.524479.166666666702937515D12D2D3D7D8D9D1D2D3D4D5D6D7D8D9D10D11D1245610111213769.531250-33046.875-13769.531250-33046.8754D2D1293750000000024479.1666666667014687.5088125000-88125005D2013769.53125-33046.875000-13769.531250-33046.875000SMS 2=-33046.875010575033046.8750528756D3D30-33046.87510575000033046.875052875000-13769.53125033046.87513769.53125033046.87510D7D4000742105.26315789500-742105.263157895000000-88125000881250011D8D500008222.7729989794-15623.26869806090-8222.7729989794-15623.2686980609000-33046.87505287533046.875010575012D9D60000-15623.268698060939578.9473684211015623.268698060919789.4736842105000D70-13769.5312533046.875-742105.263157895001343374.79440789033046.875-58750000D80000-8222.772998979415623.26869806090893552.6341100915831.60203139430-4079.8611111111-9791.6666666667D7D8D9D4D5D6D90-33046.875528750-15623.268698060919789.473684210533046.8755831.6020313943176662.28070175409791.666666666715666.6666666667101112789D1024479.166666666700000-58750000614699.074074074024479.1666666667742105.26315789500-742105.2631578950010D7D110000000-4079.86111111119791.66666666670983246.5277777789791.666666666708222.772998979415623.26869806090-8222.772998979415623.268698060911D8D1214687.5000000-9791.666666666715666.666666666724479.16666666679791.666666666760708.3333333333SMS 3=015623.268698060939578.94736842110-15623.268698060919789.473684210512D9-742105.26315789500742105.263157895007D40-8222.7729989794-15623.268698060908222.7729989794-15623.26869806098D5015623.268698060919789.47368421050-15623.268698060939578.94736842119D6D10D11D12D7D8D913141510111258750000-5875000013D1004079.86111111119791.66666666670-4079.86111111119791.666666666714D11SMS 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Sheet2

Sheet3


Matriks GROUP

Latihan Matriks

75079 A STUDY ON BIOMOLECULAR SEQUENCE ALIGNMENT … · BAB 7 ANALISA KEPUTUSAN DAN PERBINCANGAN TERHADAP PARAMETER MATRIKS PENGGANTIAN BLOSUM DAN JURANG PENALTI AFFINE DALAM PENGATURCARAAN

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library.binus.ac.idlibrary.binus.ac.id/eColls/eThesisdoc/Bab2DOC/2012-2... · Web viewMatriks IFE, EFE, Matriks IE, Matriks SWOT, Matriks Grand Strategy, Matriks QSPM Hartiwi Prabowo,

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