Ei I

Figure 3.22. Outrigger at quarter-height, z = 0.25L.

where M4 and K4 represent the moment and stiffness of the spring at z = L/4. Noting that K4 = 4Kj, M4 in Eq. (3.19) can be expressed in terms of M{.

The drift for this case is given by the expression

Equations (3.6), (3.13), (3.18), and (3.22) give the building drift for four different locations of the belt and outrigger trusses.

The value of K1, which corresponds to stiffness of the spring when it is located at z = L, can be derived as follows.

A unit rotation given to the core at the top results in extension and compression of all perimeter columns, the magnitudes of which are given by their respective distances from the center of gravity of the core. The resulting force multiplied by the lever arm gives the value for stiffness K1. Thus, if p1 is measured in kips and the distance in feet, K1 has units of kip feet. The force p in each exterior column is given by the relation p = AE d/L since, by definition, d corresponds to column extension or compression due to unit rotation of the core, d = d/2, where d is the distance between the exterior columns. Therefore,

and its contribution to the stiffness K1 is given by the relation

AiE d2 L 2

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