where *T*s 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 (*K*e) with the

(3) Equation 5-5 should be used to calculate

secant stiffness (*K*s) at the target displacement (see

the target displacement.

For velocity-dependent

Figure 8-7*)*; *C*j 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

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

procedure, displacement-controlled actions must be

(8-28)

4*π *k

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, *W*j, is work done by device in *j *in

damaging substances.

one

complete

cycle

corresponding

to

floor

displacements ***i, the summation extends over all

devices *j*, and *W*k 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

2*π*2

(8-29)

related test programs should be performed by an

independent engineering peer review panel, including

8 - 37

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