T ∑ C j cos 2θ j f r2j
maximum resistance of the energy-dissipation
βeff = β +
devices.
i
(8-22)
w
π∑ i f i2
i g
2. The base shear and story forces should
be reduced, as described above, by the damping
where 2 j is the angle of inclination of device j to the
modification factors in Table 8-2 to account for the
horizontal, Nrj is the first mode relative displacement
energy dissipation (damping) afforded by the energy-
dissipation devices.
The calculation for effective
between the ends of device j in the horizontal
damping is estimated as:
direction, wi is the reactive weight of floor level i, Ni
is the first mode displacement at floor level i, and
∑W
other terms are as defined above.
Equation 8-22
j
β eff = β +
i
applies to linear viscous devices only.
(8-20)
4π k
W
4. The design actions for components of
where $ is the damping in the structural frame, and is
the building should be calculated in three distinct
set equal to 0.05 unless modified in Section 2.6.1.5,
stages of deformation, as follows.
The maximum
Wj is work done by device j in one complete cycle
action should be used for design.
*i,
corresponding
to
floor
displacements
the
summation extends over all devices j, and Wk is the
i. At the stage of maximum drift. The
maximum strain energy in the frame, determined
lateral forces at each level of the building should be
using Equation 8-19.
calculated using Equations 5.3.4-1 and 5.3.4-2 in
FEMA 302, where V is the modified equivalent base
3.
The work done by linear viscous
shear.
device j in one complete cycle of loading may be
calculated as:
ii. At the stage of maximum velocity
and zero drift. The viscous component of force in
2π2
each energy dissipation device should be calculated
Wj =
C j dr2j
(8-21)
by Equations 8-14 or 8-17, where the relative
T
velocity D is given by 2Bf1D, where D is the relative
where T is the fundamental period of the building,
displacement between the ends of the device
including the stiffness of the velocity-dependent
calculated at the stage of maximum drift.
The
devices, Cj is the damping constant for device j, and
calculated viscous forces should be applied to the
*rj is the relative displacement between the ends of
mathematical model of the building at the points of
device j along the axis of device j. An alternative
attachment of the device, and in directions consistent
equation for calculating the effective damping of
with the deformed shape of the building at maximum
Equation 8-20 is:
drift. The horizontal inertial forces at each floor level
of the building should be applied concurrently with
8 - 34
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