Unformatted text preview: e is given by Eq.(3-21):
λ = iωo exp(iφ) = ωo ( − sin φ + i cos φ) (3-21) where ω*o(=√k*/m) . Substituting the real and the
imaginary part of the eigenvalue of Eq.(3-21) into Eq.(3-16),
−1 K ′ ) = h
η = sin φ = sin( tan
Eq.(3-22) equals damping factor of a single degree of
freedom system with the complex spring constant.
When the damping factor is small,
the damping factor can be
approximately expressed by:
In a practical seismic design analysis,
the rigidity is often given by: K′
K + iK′ = K(1 + i2h) The figure shows the
damping factors hHH of
damping factors hHH
of the horizontal D.I.F,
slight differences in
the damping factors
are only observed
between the raft and
the pile foundations.
hHH are small and nearly constant in lower frequencies up
to the cut-off frequency 1.25Hz, the values of hHH are
around the damping factor h2=0.05 of the surface stratum.
hHH becomes larger in higher frequencies over the cut-off
frequency. The damping factors
hRR of the rotational
D.I.F for the raft
foundation are larger
than the pile
foundation. Comparing hRR to hHH , hHH is larger than hRR in all
frequencies for the both foundation types. 3.5 Foundation Input Motion
A foundation input motion (F.I.M) is an effective input
motion of earthquake disturbance, which is applied to D.I.F.
The figure shows the amplitudes of F.I.M for the horizontal
∆ and the rotational Θ components. F.I.M are depicted by the ratio to the ground surface
response amplitudes Us. The values of ∆/Us are less
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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.
- Summer '14