maximum resistance of the energy-dissipation

devices.

(8-22)

*w *

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, *N*rj 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, *w*i is the reactive weight of floor level *i*, *N*i

is the first mode displacement at floor level *i*, and

∑W

other terms are as defined above.

Equation 8-22

applies to linear viscous devices only.

(8-20)

4*π *k

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

action should be used for design.

corresponding

to

floor

displacements

the

summation extends over all devices *j*, and *W*k 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

2*π*2

each energy dissipation device should be calculated

(8-21)

by Equations 8-14 or 8-17, where the relative

velocity D is given by 2B*f*1D, 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, *C*j is the damping constant for device *j*, and

calculated viscous forces should be applied to the

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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