where Ts is the secant fundamental period of the
expected at the target displacement, and (2) a
frequency equal to the inverse of the effective period.
building, including the stiffness of the velocity-
dependent devices (if any), calculated using Equation
5-3, but replacing the effective stiffness (Ke) with the
(3) Equation 5-5 should be used to calculate
secant stiffness (Ks) at the target displacement (see
the target displacement.
For velocity-dependent
Figure 8-7); Cj is the damping constant for device j;
energy-dissipation devices, the spectral acceleration
in Equation 5-5 should be reduced to account for the
and *rj is the relative displacement between the ends
damping afforded by the viscous dampers.
of device j along the axis of device j at a roof
displacement
corresponding
to
the
target
(a)
Displacement-dependent
devices.
displacement.
Equations 5-5 should be used to calculate the target
displacement.
The stiffness characteristics of the
g.
Acceptance Criteria. The acceptance criteria
energy dissipation devices should be included in the
for all performance objectives, prescribed in Chapter
mathematical model.
6, and provided for building systems and components
in Chapter 5, apply to buildings incorporating energy
(b) Velocity-dependent devices. The target
dissipation devices.
The benefits of energy
displacement of Equation 5-5 should be reduced to
dissipation are realized by the reduced demand
account for the damping added by the velocity-
response spectrum using the damping coefficients in
dependent
energy-dissipation
devices.
The
Table 8-2.
Checking for force-controlled actions
calculation of the damping effect is estimated as:
should use the component actions calculated for three
limit states: maximum drift, maximum velocity, and
∑W
maximum acceleration. In the nonlinear elastic static
j
β eff = β +
procedure, displacement-controlled actions must be
i
(8-28)
4π k
W
checked for deformations corresponding to the target
displacement. Maximum actions are to be used for
where $ is the damping in the structural frame and is
design, temperature, and exposure to moisture and
set equal to 0.05, Wj, is work done by device in j in
damaging substances.
one
complete
cycle
corresponding
to
floor
displacements *i, the summation extends over all
h.
Design and Construction Reviews. Design
devices j, and Wk is the maximum strain energy in the
and construction review will be performed on all
frame, determined using Equation 8-19. The work
buildings incorporating energy-dissipation devices.
done by device j in one complete cycle of loading
The type and scope of the review will be in
may be calculated as:
accordance with the requirements of Paragraph 1-9,
unless modified by the requirements of this chapter.
Design review of the energy-dissipation system and
2π2
Wj =
C jd2
(8-29)
j
related test programs should be performed by an
Ts
independent engineering peer review panel, including
8 - 37
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