(b)

Rigid diaphragms.

When rigid

thus be expressed by the formula Ft = *M * T kd/Σ *kd *,

2

diaphragms rotate, they develop shears in all of the

where *k *is the stiffness of a vertical-resisting element,

vertical-resisting elements. In the example (Figure 7-

50) there is an eccentricity in both directions, and all

five walls develop resisting forces via the diaphragm.

inertia. For the wall forces, the direct components

due to *F*px at the *cr *are combined with the torsional

(c) Deformational compatibility. When a

components due to *M*Τ. In the example shown on

diaphragm rotates, whether it is rigid or flexible, it

Figure

7-50,

the

torsional

moment

is

causes displacements in all elements attached to it.

counterclockwise, and the diaphragm rotation will be

For example, the top of a column will be displaced

counterclockwise around the *cr*.

The direct

with respect to the bottom. Such displacements must

component of the load is shared by walls A and B,

be recognized and addressed.

while the torsional component of the load is resisted

by walls A, B, D, C, and E. Where the direct and

(d) Analysis for torsion. The method of

torsional components of wall force are the same

determining torsional forces is indicated in Figure 7-

direction, as in wall A, the torsional component adds

50. The diaphragm load, *F*px, which acts through the

to the direct component; where the torsional

component is opposite to the direct component, as in

By adding equal and opposite forces at the cr, the

wall B, the torsional component subtracts from the

diaphragm load can now be described as a

direct.

Walls C, D, and E carry only torsional

combination of a force component, *F*px (which acts

components; in fact, their design will most likely be

through the *cr*) and a moment component (which is

governed by direct forces in the east-west direction.

formed by the couple of the two remaining forces *F*px

separated by the eccentricity *e*). The moment, called

(e) Accidental torsion. Accidental torsion is

the torsional moment, *M*T, is equal to *F*px times *e*.

intended to account for uncertainties in the

The torsional moment is often called the "calculated"

calculation of the locations of the *cm *and the *cr*. The

torsion, because it is based on a calculated

accidental torsional moment, *M*A, is obtained using an

eccentricity; also this name distinguishes it from the

eccentricity, *e*acc, equal to 5 percent of the building

"accidental" torsion, which is described below. In

dimension perpendicular to the direction of the lateral

the modified loading, the force *F*px acts through the *cr*

forces; in other words, *M*A = *F*px x *e*acc.

For the

instead of *cm*; therefore, it causes no rotation and it is

example of Figure 7-50, the accidental torsion for

distributed to the walls, which are parallel to *F*px in

forces in the north-south direction is *M*T = *F*px x

proportion to their relative rigidities. The torsional

0.05*L*. In hand calculations, *M*A is treated like *M*T,

moment is resolved into a set of equivalent wall

except that absolute values of the resulting forces are

forces by a procedure similar to that used for finding

forces on bolts in an eccentrically loaded group of

bolts.

The formula is analogous to the torsion

formula τ = *Tc*/*J*. The torsional shear forces can

7 -118

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