∑W

determined from Equations 8-23 and 8-24 using *$*eff-m

for the *m*-th mode.

(8-25)

4*π *mk

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, *W*mj 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

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

= ∑ Fmi dmi

(8-26)

2 i

The

nonlinear

static

procedure,

described

in

Paragraph 5-4, should be followed unless explicitly

where *F*mi 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

2*π*2

=

(8-27)

characteristics of the components supporting the

devices. Stiffness characteristics should be consistent

with the deformations corresponding to the target

where *T*m 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 *T*e, as defined in Paragraph 5-4(e)(4).

dependent devices, *C*j is the damping constant for

device *j*, and ***mrj is the *m-t*h 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 *CF*1 and *CF*2 should be

8 - 36

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