TOPIC 6 Structural Dynamics III Analysis of Elastic MDOF ...

TOPIC 6 Structural Dynamics IIIA nalysis of Elastic MDOF SystemsTOPIC 6 Structural Dynamics IIIA nalysis of Elastic MDOF Systems Equations of Motion for MDOF Systems Uncoupling of Equations through use of Natural Mode Shapes Solution of Uncoupled Equations Recombination of Computed Response modal Response Spectrum Analysis (By Example) Use of Reduced Number of ModesuxuyrzMajority of Massis in FloorsTypical Nodal DOFM otion isPredominantlyLateralPlanar Frame with 36 Degrees of Freedom12345678910111213141516 Planar Frame with 36 Static Degrees of Freedombut with only THREE Dynamic DOFu1u2u3f11f21f31V1=1 kipfff112131 Development of Flexibility MatrixDevelopment of Flexibility Matrixf12f22f32V2=1 kip fff122232 Development of Flexibility Matrixf13f23f33V3=1 kip fff132333 UfffVfffVfffV= + + 112131112223321323333 UfffffffffVVV= 111213212223313233123 FVU=KUV=KF= 1 Concept of Linear Combination of Shapes (Flexibility)m1m3m2k1k2k3V1(t), u1(t)V2(t), u2(t)V3(t), u3(t)Kkkkkkkkkk= + + 11112222300 Mmmm= 123000000 Utututut()()()()= 123 VtVtVtVt()()()()= 123 Idealized Structural Property MatricesNote.

TOPIC 6 Structural Dynamics III Analysis of Elastic MDOF Systems • Equations of Motion for MDOF Systems • Uncoupling of Equations through use of Natural Mode Shapes • Solution of Uncoupled Equations • Recombination of Computed Response • Modal Response Spectrum Analysis (By Example) • Use of Reduced Number of Modes

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