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End-fixity factor, r

FIGURE 23.8 Deflection of a uniformly loaded beam versus end-fixity factor.

End-fixity factor, r

FIGURE 23.8 Deflection of a uniformly loaded beam versus end-fixity factor.

demonstrated subsequently, the formulations of stiffness matrices and effective-length factors of beam-columns can all be expressed in terms of the end-fixity factors. The end-fixity factor has further value in design because it provides a physical interpretation of the extent of rigidity available in a connection. It also provides designers with a convenient way to compare the structural responses of a member with semirigid connections to that with rigid or pinned connections.

By Equation 23.7, the relationship between the end-fixity factor and the connection stiffness is nonlinear, as shown in Figure 23.9. It is observed from the figure that when the connection stiffness is large, very significant changes in stiffness produce only very small changes in the end-fixity factor. Consequently, from Figure 23.7 and Figure 23.8, such changes have a negligible influence on both moments and deflection of the beam. Conversely, from Figure 23.9, with low values of connection stiffness, small increases in the stiffness result in appreciable increases in the end-fixity factor. In this case, as Figure 23.7 and Figure 23.8 show, there is a considerable effect on the bending moments and the deflection. Thus, in practice, when a real pinned connection has some stiffness, a considerable restraining moment may develop to the benefit of the structure. At the other extreme, attempting to achieve further increase in connection stiffness beyond that of a nearly rigid connection is not efficient and economical because it involves only a small change in the end-fixity factor and, consequently, has little effect on the response of structure.

TABLE 23.3 End-Reactions of a Semirigid Member

Member span loads

Member end-reactions

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