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

# 5 k fb xb k ffb xf k ffs xf k

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Unformatted text preview: XB } + [K FFB ]{ XF }) + ([K FFS ]{ XF } + [K FS ]{ X S ) = {0} (5) by: (6) Then, the second parenthesis must be: (7) where, {F} denotes "Interaction Force Vector" between B and S region, and is applied on the interface F. {F} Joining Eq.(1-1): (1) with Eq.(6) : (6) gives: (8) Also, joining Eq.(7) : (7) with Eq.(1-3) : (1) leads to: (9) All entries in the dynamic stiffness matrix of Eq.(8) : (8) can be determined by the material constants of B region, while that of Eq.(9): (9) by S region. You can see that Eq.(1): (1) is separated into Eq.(8) : (8) and Eq.(9): (9) Eq.(8) and Eq.(9) are jointed by the interaction force vector {F} on the interface F. The mechanics for Eq.(8) : (8) can be expressed by Fig.3: which governs the B region including the F region. And also, the mechanics of Eq.(9) : (9) is illustrated by Fig.4: The equation governs the S region including the F region with a void. The void indicates the soil part which is excavated. In Eq.(9): (9) the external force term vector can be decomposed into: (10) The corresponding displacement vector are defined by: (11) The first vector {{XFf} {{XSf}}T in the right hand side is due to the interaction force vector {{F} {0}}T, while the second {{XFq} {{XSq}}T to the earthquake disturbance vector {{0} {Q}}T. That is, the fir...
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