"Explore earthquake analysis of linear Multiple Degrees of Freedom (MDoF) systems in the field of civil engineering. Learn about dynamic phenomena, mathematical modeling, response calculations, and more."
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a home base to excellence Mata Kuliah Kode SKS : Dinamika Struktur & Pengantar Rekayasa Kegempaan : CIV - 308 : 3 SKS Earthquake Analysis of Linear MDoF System Pertemuan 11
a home base to excellence TIU : Mahasiswa dapat menjelaskan fenomena-fenomena dinamik secara fisik. Mahasiswa dapat membuat model matematik dari masalah teknis yang ada serta mencari solusinya TIK : Mahasiswa dapat menghitung respon struktur MDoF akibat beban gempa bumi
a home base to excellence Sub Pokok Bahasan : Persamaan Gerak Sistem MDoF Akibat Beban Gempa Bumi Analisis Riwayat Waktu Analisis Spektrum Respon
a home base to excellence Equation of Motion u m + ( ) t m 1 + = c u k u u g 1 With 1 1 = 1 1 Introducing the modal analysis equation , q u = and pre-multiply with [ ]T
a home base to excellence c q m + ( ) t m + = T T T T 1 q k q u (1) g Kn Cn Mn Ln Mn Cn Kn Ln = Generalized Mass = Generalized Damping = Generalized Stiffness = Earthquake Excitation Factor L = Modal = Participat ion Factor n M n 2 L effective modal mass n M n Dividing Eq.(1) by Mn, gives : q n ( ) t + + = 2 2 q q u (2) n n n n n n g
a home base to excellence ( ) t ( ) t = q D Let (3) n n n Eq. (2) becomes : D SDoF ( ) t D + + = 2 2 D u (4) n n n n n n g The qn(t) is readily available once Eq.(4) has been solved for Dn(t), utilizing numerical time stepping methods for SDF systems.
a home base to excellence ( ) t ( ) t = q D Response History Analysis ( ) ( ) t u n = n n n ( ) t D n = q t (5) n n n n ( ) t m n ( ) t = f A (6) n n n An(t) = n2Dn(t) Response Spectrum Analysis = u D (7) jn n jn n = j f m A (8) jn n jn n An= n2Dn
a home base to excellence BS Response from each mode can be combine using either SRSS 1 2 / n 2 V V b bn 1 or CQC Method 1 2 / N N = = . n , i V . i , b V n , b V b = 1 1 i n
a home base to excellence Example 1 Determine maximum Base Shear due to El Centro Acc. Use Respon Spectrum Method Use SRSS Method to combine BS from each mode W2= 24.000 kgf u2 W10x21 W10x21 3 m W1= 11.600 kgf u1 W10x45 W10x45 4,5 m = = 10 76 , 38 28 , 1 2 0 6809 , 3 0385 , = = 11 12 1 1 21 22
a home base to excellence Mode 1, 1= 10,76 rad/dt T1= 2 / 1 = 0,58 det Sd1= 2,5 inch = 6,35 cm Hitung L1= { 1}T[M]{1} M1= { 1}T[M]{ 1} 1= L1/M1 {uj} = { 1} 1.Sd1 {fj} = [M]{uj} 12 = = 10 76 , 38 28 , 1 2 0 6809 , 3 0385 , = = 11 12 1 1 21 22 Mode 2, 2= 38,28 rad/dt T2= 2 / 2 = 0,16 det Sd2= 0,18 inch = 0,4572 cm Hitung L2= { 2}T[M]{1} M2= { 2}T[M]{ 1} 2= L2/M2 {uj} = { 2} 2.Sd2 {fj} = [M]{uj} 22 = u D jn n jn n = j f m A jn n jn n
a home base to excellence W2= 24.000 kgf 19.525,21 kg 19.525,21 kg u2 W10x21 W10x21 3 m W1= 11.600 kgf u1 6.424,51 kg 28.669,23 kg W10x45 W10x45 4,5 m BS2= 9.144,02 kg BS1= 25.949,72 kg Cara SRSS BS = ((BS1)2+ (BS2)2)0,5= 27.513,65 kg
a home base to excellence Tugas 8 Determine maximum Base Shear due to El Centro Acc. Use Respon Spectrum Method Use SRSS Method to combine BS from each mode W3= 20.000 kgf u3 W10x21 W10x21 3 m W2= 24.000 kgf u2 W10x21 W10x21 3 m W1= 11.600 kgf = = = 7,934 26 65 , 39 53 , u1 1 2 3 0 5546 , 1 004 , 5 3431 , W10x45 W10x45 11 12 13 = = 0 8526 , 0 662 , 2 6574 , 4,5 m 21 22 23 1 1 1 31 32 33
