A1^H (in./kip, mm/kN) Mtop (kin., kN m) Mbottom (kin., kN m) M


Equation 31.96

31.6.3 Essa Method

Considering different story drafts, different stiffness parameters, L P/EI, for columns, and different girder connections for the structural models shown in Figure 31.3, Essa (1998) presented a general effective length factor equation for column C2 by solving five equations. Those five equations are obtained by considering the equilibrium of joints A and B and story shear for columns C1, C2, and C3.

31.6.4 Cheong-Siat-Moy Method

Considering an individual end-restrained column as shown in Figure 31.1a, Equation 31.2 was presented in detail by Cheong-Siat-Moy (1999). When the beams bend in exact double curvature, RkA and Rb are directly related to GA and GB, respectively (Rk = 6/G). Equation 31.2 will become Equation 31.5 for braced frames when Tk = 1 and Equation 31.6 for unbraced frames when Tk = 0.

Tk is the difference between the final lateral stiffness (Tkf) and the initial lateral stiffness (Tki) of a column as follows:

where Tstory is the first-order lateral story stiffness and T0i is the first-order lateral stiffness of column i.

An improved lateral stiffness Tk associated with g, P, and h and the first-order stiffness property was proposed by Hellesland (2000) as follows:

Ti " Tif — Tii " / ! I Tstory — Tq, (31. 98)

The term g is the flexibility parameter and can be expressed as g = 1 + CL. A rather simple, yet fairly accurate expression was developed by Hellesland (1998):

TABLE 31.6 Comparison of K-factors for Frame in Figure 31.14a
0 0

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