∑W
determined from Equations 8-23 and 8-24 using $eff-m
mj
eff -m = m +
i
for the m-th mode.
(8-25)
4π mk
W
4.
If the maximum base shear force
where $m is the m-th mode damping in the building
calculated by dynamic analysis is less than 80 percent
frame, Wmj is work done by device j in one complete
of the modified equivalent base shear of Paragraph 8-
cycle corresponding to modal floor displacements
4e(3),
component
and
element
actions
and
*mi, and Wmk is the maximum strain energy in the
deformations shall be proportionally increased to
frame in the m-th mode, determined using Equation
correspond to 80 percent of the modified equivalent
8-26.
base shear.
1
f.
Nonlinear Elastic Static Procedure.
= ∑ Fmi dmi
Wmk
(8-26)
2 i
The
nonlinear
static
procedure,
described
in
Paragraph 5-4, should be followed unless explicitly
where Fmi is the m-th mode horizontal inertia force at
modified by the following paragraphs.
floor level i and *mi is the m-th mode horizontal
displacement at floor level i.
The work done by
(1) The nonlinear mathematical model of the
linear viscous device j in one complete cycle of
building should explicitly include the nonlinear
loading in the m-th mode may be calculated as:
force-velocity-displacement characteristics of the
energy-dissipation devices, and the mechanical
2π2
=
2
Wmj
C j dmrj
(8-27)
characteristics of the components supporting the
Tm
devices. Stiffness characteristics should be consistent
with the deformations corresponding to the target
where Tm is the m-th mode period of the rehabilitated
displacement and frequency equal to the inverse of
building, including the stiffness of the velocity-
period Te, as defined in Paragraph 5-4(e)(4).
dependent devices, Cj is the damping constant for
device j, and *mrj is the m-th mode relative
(2) The nonlinear mathematical model of the
displacement between the ends of device j along the
building shall include the nonlinear force-velocity-
axis of device j.
displacement characteristics of the energy-dissipation
devices,
and
the
mechanical
characteristic
3.
Direct application of the Response
components supporting the devices.
Energy-
Spectrum Method will result in member actions at
dissipation devices with stiffness and damping
maximum drift.
Member actions at maximum
characteristics that are dependent on excitation
velocity
and
maximum
in
each
frequency and/or temperature shall be modeled with
significant mode should be determined using the
characteristics consistent with (1) the deformations
procedure described in Paragraph 8-4e(2)(b).
The
combination factors CF1 and CF2 should be
8 - 36
Previous Page
