Page 358 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

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LATERAL-FORCE DESIGN

8.12 CHAPTER EIGHT

Finally, dual systems have improved inelastic performance over the individual systems acting alone.
These include special steel moment-resisting frames capable of resisting at least 25% of the design base
shear, V, combined with steel eccentric braced frames, special concentrically braced frames, or ordi-
nary braced frames. Such dual systems are consistently permitted larger R values, because of the
improved inelastic performance anticipated with the added moment-resisting connections.

Force Distribution. The seismic base shear V, Eq. (8.6), is distributed throughout the structure in
accordance with its mass and stiffness. This is accomplished by distributing the forces to individual
stories over the building height by the equation
F x = C vx V (8.11a)

where
C = wh k (8.11b)
xx
∑ n i=1 wh k
vx
ii
F x and w x are the seismic force and floor weight at the xth level, and h x is the height from the base
to the ith floor. The coefficient, k, varies between 1 and 2, and k is equal to 1.0 for short-period struc-
tures and increases to 2.0 for structures with periods longer than 2.5 s. The larger values of k cause
larger story forces in the upper floors of a building, and this accounts for contributions of higher
modes that are expected with longer-period structures. The force F x at each floor is distributed hori-
zontally in proportion to the distribution of the mass of the floor. The stiffness of the floor diaphragm
must be evaluated to determine whether the diaphragm satisfies the rigid or flexible diaphragm stiff-
ness requirements. With rigid diaphragms, the horizontal forces are distributed to vertical frames
with consideration of the horizontal mass distribution (including minimum torsion) and the relative
stiffness of the frames. With flexible diaphragms, the horizontal forces are distributed to vertical
frames with consideration of the mass distribution and the tributary area of each frame. Floor slabs
and their attachments between floor diaphragms and lateral load frames must have adequate strength
to distribute these inertial forces. The frames must be designed for a minimum torsion that is pro-
duced by a mass eccentricity of 5% of the normal maximum base dimension. This minimum is in
addition to torsion due to the computed eccentricity between the centers of mass and gravity.
Deflections and Element Design Forces. Story drifts and element forces must be adjusted to
account for P–∆ effects where appropriate. Basic elastic deflections for the seismic design forces, δ xe ,
are computed by performing an elastic analysis on the structure. These deflections do not represent
the seismic story drifts and deformations expected during the design earthquake because they do not
consider the inelastic deformation that occurs. These inelastic story drifts, δ x , are then estimated by
the equation
δ
δ = C d xe (8.12a)
x
I
where C d is the deflection amplification factor and I is the importance factor. C d is related to the
R factor, but it is invariably smaller than R because of the overstrength that is inherent in the structural
design process. Calculation of a stability coefficient, θ, is required:
P ∆
θ= x (8.12b)
Vh C
xsx d
where P x is the total vertical design load at and above the level x, h sx is the story height below level
x, V x is the shear force acting between levels x and x − 1, and ∆ is the design story drift. If θ is greater
than 0.1, the forces and deformations of the frame must be adjusted for P–∆ effects by a rational
analysis method.

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