To understand the behavior of an outrigger system, consider a building stiffened by a storyhigh outrigger at top, as shown in Fig. 3.18. Because the outrigger is at the top, the system is often referred to as a cap or hat truss system. The tie-down action of the cap truss generates a restoring couple at the building top, resulting in a point of contraflexure in its deflection curve. This reversal in curvature reduces the bending moment in the core and hence, the building drift.

Although the belt truss shown in Fig. 3.18 functions as a horizontal fascia stiffener mobilizing other exterior columns, for analytical simplicity we will assume that the cumulative effect of the exterior columns may be represented by two equivalent columns, one at each end of the outrigger (Fig. 3.18c). This idealization is not necessary in developing the theory, but keeps the explanation simple.

The core may be considered as a single-redundant cantilever with the rotation restrained at the top by the stretching and shortening of windward and leeward columns. The result of the tensile and compressive forces is equivalent to a restoring couple opposing the rotation of the core. Therefore, the cap truss may be conceptualized as a restraining spring located at the top of the cantilever. Its rotational stiffness may be defined as the restoring couple due to a unit rotation of the core at the top.

Figure 3.18. (a) Building plan with cap truss; (b) cantilever bending of core; (c) tie-down action of cap truss.

Assuming the cap truss is infinitely rigid, the axial elongation and shortening of columns is equal to the rotation of the core multiplied by their respective distances from the center of the core. If the distance of the equivalent column is d/2 from the center of the core, the axial deformation of the columns is then equal to QdJ2, where 0 is the rotation of the core. Since the equivalent spring stiffness is calculated for unit rotation of the core (that is, 0 = 1), the axial deformation of the equivalent columns is equal to 1 x d/2 = d/2 units. The corresponding axial load is given by

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