(4) Torsion, in a general sense, occurs in a
(A, B, C, and D); a rigidity analysis is needed in
building whenever the location of the resultant of the
order to determine the forces in the walls.
lateral forces, i.e., the center of mass, cm, at and
above a given level does not coincide with the center
(b) Building with walls on three sides (an
of rigidity, cr, of the vertical-resisting elements at
example is shown in Figure 7-49). For transverse
that level. If the resisting elements have different
(north-south) forces (Figure 7-49, part a), this is a
deflections, the diaphragm will rotate. Torsion, in
simple case: because of symmetry of load and
this general sense of rotation, occurs regardless of the
reactions, the end walls share the load equally. For
stiffness properties of the diaphragms and the walls
longitudinal (east-west) forces (Figure 7-49, part b),
or frames.
For purposes of design, however, the
there is an eccentricity between the resultant of the
procedure for dealing with torsion does depend on
load and the centerline of the one east-west resisting
these stiffness properties.
wall, wall C. The analysis is simplified by treating
the load as a combination of the load, W, acting
(a)
Flexible
diaphragms.
Flexible
directly on the wall, and the couple M = WD/2
diaphragms such as wooden diaphragms can rotate,
(Figure 7-49, part c).
The direct force induces a
but cannot develop torsional shears. For example, a
direct shear, W, on the diaphragm and a reaction, W,
single-span diaphragm with a relatively stiff shear
in Wall C (Figure 7-49, part d); the moment, M, is
wall at one end and a more flexible frame at the other
resisted by walls A and B (Figure 7-49, part e),
end will rotate because the two resisting elements
causing
a
counterclockwise
rotation
of
the
have different deflections.
Flexible diaphragms,
diaphragm. A particular concern with this type of
however, are considered incapable of inducing forces
building is the deflection on the corners at the open
in the walls or frames that are perpendicular to the
side. If this is excessive, it can lead to vertical
direction
of
the
design
forces;
i.e.,
flexible
instability in the southwest and southeast corners.
diaphragms are said to be incapable of taking
torsional moments. All of the lateral load is taken by
1. Flexible diaphragm. In an all-wood
the walls that are parallel to the lateral forces; none is
building, the concern about rotation is met by
taken by the other walls. (The building with walls on
limitations on the size and proportions of the
three sides is a special case and entails special
diaphragm. In buildings with walls of concrete or
limitations, as discussed above.) Lateral loads are
masonry, the greater weight causes greater concern
usually distributed to the resisting walls by using the
for rotation, and there are special limitations on the
continuous beam analogy.
There is no rigidity
span/width ratio of the diaphragms.
analysis, no calculation of the cm and the cr. If there
are uncertainties about the locations of the loads and
2. Rigid diaphragm. If the diaphragm is
the rigidities of the structural elements, the design
rigid, the design of the building will consider the
can be adjusted to bracket the range of possibilities.
effects of torsion. The concept of orthogonality does
not apply.
7 -116
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