Page 382 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch08.qxd 9/29/05 5:21 PM Page 8.36

LATERAL-FORCE DESIGN

8.36 CHAPTER EIGHT

the frame. The frame has two interior columns. So one-third of the shear in each story is distributed
to the interior columns and half of this, or one-sixth, is distributed to the exterior columns (Fig. 8.17).
The other member forces are computed by equations of equilibrium on each subassemblage. For
example, for the subassemblage at the top of the frame in Fig. 8.17, setting the sum of the moments
equal to zero yields

l h h
417
417
S = . or S = . (8.34)
1
1
2 2 l
Setting the sum of the vertical forces equal to zero gives
A =− S =− 417 h (8.35)
.
4
1
l
Setting the sum of the horizontal forces equal to zero results in
A = 25 417 = 2083 (8.36)
−
.
.
1
For the central top subassemblage:
l h h h
833 417)−
S ( 1 + S ) = 833 or S = ( . . = 416 (8.37)
.
.
2
2
2 2 l l
The remaining axial and shear forces can be determined by this procedure, and bending moments
can be determined directly from these forces from equilibrium equations.
The cantilever method is used for tall build-
ings. It is based on the recognition that axial short-
ening of the columns contributes to much of the
lateral deflections of such buildings (Fig. 8.18). In
this method, the floors are assumed to remain plane,
and the axial force in each column is assumed to be
proportional to the distance of the column from the
centroid of the columns. Inflection points are
assumed to occur at midheight of the columns and
at midspan of the beams. The internal moments and
forces are determined from equations of equilibri-
um, as with the portal method. The determination
of the forces and moments in the members at the
top floors of the frame in Fig. 8.16 is illustrated in
Fig. 8.19. The lateral forces cause overturning
moments, which induce axial tensile and compres-
sive forces in the columns. Therefore,
and (8.38)
A 4 =−A 7 A 5 =−A 6
Since the exterior columns are three times as far
from the centroid of the columns as the interior
columns,
FIGURE 8.18 Drift of a moment-resisting frame
assumed for analysis by the cantilever method. A 4 = 3A 5 (8.39)

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