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

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 ]{...
View Full Document

## 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.

Ask a homework question - tutors are online