E0-190-2008_(8)Chapter_6(Substructure_Method)

B xb xs s f xf q that is the index b refers to

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Unformatted text preview: XS} S F {XF} {Q} That is, the index B refers to the Building-Foundation, F to the interface and S to the soil. The stiffness matrix in Eq.(1) includes [ 0 ] matrix, (1) which means that the B region does not touch directly the S region but touches the S region through the F region. Dynamic stiffness matrix [KIJ] , which includes the mass, the damping and stiffness, is expressed by: (2) where, [kIJ] , [mIJ] and [cIJ] are stiffness, mass and damping matrix. And δIJ=1 when I is equals to J, while δIJ=0 when I is not equal to J. Because the index F indicates the interface between B and S region, the dynamic stiffness matrix [KFF] consists of the dynamic stiffness [KFFB] for B region and [KFFS] for S region as shown in Fig.2. That is: (3) In Eq.(1) : (1) The second equation in Eq.(1) (expressed by Eq.(1-2)) is: (4) Substituting Eq.(3) : (3) into Eq.(4) gives: [K FB ]{ XB } + ([K FFB ] + [K FFS ]){ XF } + [K FS ]{ X S } = {0} ∴ ([K FB ]{ XB } + [K FFB ]{ XF }) + ([K FFS ]{ XF } + [K FS ]{ X S ) = {0} (5) Expressing the first parenthesis in Eq.(5): ∴ ([K FB ]{...
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This note was uploaded on 03/14/2014 for the course CE 5680 taught by Professor Drgrd during the Summer '14 term at Indian Institute of Technology, Chennai.

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