between each end of the device, D is the relative
and where forces in the device, F+ and F-, are
velocity between each end of the device, and keff is
evaluated at displacements D and D , respectively.
the effective stiffness of the device calculated as:
(4) Velocity-dependent devices.
F+ + F-
D + D
The force-displacement response of a velocity-
dependent device is primarily a function of the
relative velocity between each end of the device.
where K1 is the so-called storage stiffness.
(a) Solid viscoelastic devices. The cyclic
3. The damping coefficient for the device
response of viseoelastic solids is generally dependent
shall be calculated as:
on the frequency and amplitude of the motion, and
the operation temperature (including temperature rise
due to excitation).
π 1 Da2ve
Solid viseoelastic devices may be
where K11 is the loss stiffness, the angular frequency
modeled using a spring and dashpot in parallel
T1 is equal to 2Bf1, Dave is the average of the absolute
(Kelvin model). The spring and dashpot constants
values of displacements D+ and D-, and WD is the
selected should adequately capture the frequency and
area enclosed by one complete cycle of the force-
temperature dependence on the device consistent
displacement response of the device.
with fundamental frequency of the building (f1), and
the operating temperature range.
If the cyclic
(b) Fluid viscoelastic devices. The cyclic
response of a viseoelastic solid device cannot be
response of viscoelastic fluid devices is generally
adequately captured by single estimates of the spring
dependent on the frequency and amplitude of the
and dashpot constants, the response of the building
motion, and the operation temperature (including
should be estimated by multiple analyses of the
temperature rise due to excitation). Fluid viscoelastic
building frame, using limited values for the spring
devices may be modeled using a spring and dashpot
and dashpot constants.
in series (Maxwell model). The spring and dashpot
constants selected should adequately capture the
2. The force in a viseoelastic device may
frequency and temperature dependence of the device
be expressed as:
consistent with fundamental frequency of the
F = keff D + C D
If the cyclic response of a
viscoelastic fluid device cannot be adequately
where C is the damping coefficient for the
captured by single estimate of the spring and dashpot
viscoelastic device, D is the relative displacement
constants, the response of the building should be
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