Shear Racking Component

This response in a rigid frame, shown in Fig. 3.4b, is similar to the shear deflection component of the cantilever column. As the frame displaces laterally, by virtue of the rigid beam-to-column connections, bending moments and shears are developed in the beams and columns. The horizontal shear above a given level due to lateral loads is resisted by shear in each of the columns of that story (Fig. 3.4b). This shear in turn causes the story-height columns to bend in double curvature with points of contraflexure at approximately midstory levels. To satisfy equilibrium, the sum of column moments above and below a joint must equal the sum of beam moments on either side of the column. In resisting the bending, the beams also bend in a double curvature, with points of contraflexure at approximately midspan. The cumulative bending of the columns and beams results in the overall shear racking of the frame. The deflected shape due to this component has a shear deflection configuration, as shown in Fig. 3.4b.

The shear mode of deformation accounts for about 70% of the total sway of a moment frame, with the beam flexure contributing about 10 to 15%, and the column

Points of contrail exu re

^ Column shear forces

Beam moment diagram

Column moment diagram (b)

Figure 3.4. Rigid frame deflections: (a) forces and deformations caused by external overturning moment; (b) forces and deformations caused by external shear.

Figure 3.4. Rigid frame deflections: (a) forces and deformations caused by external overturning moment; (b) forces and deformations caused by external shear.

bending furnishing the remainder. This is because in a rigid frame, typically, the column stiffness, as measured by the Ic/Lc ratio, is substantially greater than the beam stiffness ratio, Ib/Lb, moment of inertia of beam moment of inertia of column length of beam length of column

Therefore, in general, to reduce lateral deflection, the place to start adding stiffness is in the beams. However, in nontypical frames, such as for those in framed tubes with column spacing approaching floor-to-floor height, it is prudent to study the relative beam and column stiffnesses before making adjustments to the member stiffnesses.

Because of the cumulative effect of building rotation up the height, the story drift increases with height, while that due to shear racking tends to stay the same up the height. The contribution to story drift due to cantilever bending in the uppermost stories exceeds that from shear racking. However, the bending effect usually does not exceed 10 to 20% of that due to shear racking, except in very tall and slender rigid frames. Therefore, the overall deflected shape of a medium-rise frame usually has a shear deflection configuration. Thus, the total lateral deflection of a rigid frame may be considered a combination of the following factors:

• Cantilever deflection due to axial deformation of columns (15 to 20%).

• Frame shear racking due to bending of beams (50 to 60%).

• Frame racking due to bending of columns (15 to 20%).

In addition to the preceding factors, the deformations of the panel zone of a beam-column joint, defined as the rectangular segment of the column web within the column flanges and beam continuity plates, also contributes to the total lateral deflection of the frame. Its effect, however, rarely exceeds 5% of the total deflection.

where

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