AISC LRFD 1.pdf

166 TYPES OF CONSTRUCTION [Comm. A2.comes into contact with the supporting column. However, it would not be appropriateto rely on these extremely large rotations (typically more than 0.1 radians) fordesign.The available ductility, u , should be compared with the required rotational ductilityunder the full factored loads, as determined by an analysis that takes into accountthe nonlinear behavior of the connection. In the absence of accurate analyses of therequired rotation capacity, the connection ductility may be considered adequatewhen the available ductility is greater than 0.03 radians. This rotation is equal to theminimum beam-to-column connection ductility as specified in the AISC seismicprovisions for special moment frames (AISC, 1997 and 1999). Many types of partialstrength PR connections, such as top and seat-angle details, meet this criterion.Connection Stiffness. Because many PR connections manifest nonlinear behavioreven at low force levels, the initial stiffness of the connection, K i , does not characterizethe connection response adequately. Short of modeling the nonlinearresponse, a better measure of behavior is the secant stiffness, K s (see FigureC-A2.1). The secant stiffness is defined on the basis of either the moment, M s ,ortherotation, s , that would occur under the applied loads. Generally, two distinct valuesof secant stiffness should be considered in design, with one corresponding to thebehavior under service loads and the other to the behavior under factored loads.The ratio of connection stiffness to beam stiffness can be defined as =K s L/EI,where L and EI are the length and bending rigidity, respectively, of the connectedbeam. Limiting values of are approximate ways of categorizing connection stiffnessin order to simplify the analysis. The limits are not exact values, and generallydepend on the structural geometry and the limit state used to establish the criterion.For continuous beams in braced frames, for example, limits based on achieving acertain percentage of the fixed-end moment or reaching a deflection limit can beused to establish stiffness criteria (Leon, 1994).Following such an approach, where is defined using the secant stiffness for theserviceability limit state, it is reasonable to classify connections as fully restrainedif > 20. On the other hand, connections with < 2 may be approximated assimple.Structural Analysis and Design. When the secant stiffness falls below the fullyrestrained limit, engineers should account for the PR behavior in determining memberand connection forces, displacements, and frame stability effects. This requires,first, that the moment-rotation characteristics of the connection be known, and second,that these characteristics be incorporated in analysis and member design.Typical moment-rotation curves for many PR connections are available from severaldatabases: Goverdhan (1983); Ang and Morris (1984); Nethercot (1985); andKishi and Chen (1986), for example. Care should be exercised when utilizing tabulatedmoment-rotation curves not to extrapolate to sizes or conditions beyond thoseused to develop the database, since other failure modes may control (ASCE TaskCommittee on Effective Length, 1997). When the connections to be modeled do notfall within the range of the databases, it is possible to derive the characteristics fromtests, simple component modeling, or finite element studies (FEMA, 1995). Examplesof how to model connection behavior are given in numerous references(Bjorhovde, Brozzetti, and Colson, 1988; Bjorhovde, Colson, Haaijer, and Stark,1992; Bjorhovde, Colson, and Zandonini, 1996; Chen and Lui, 1991; Lorenz, Kato,LRFD Specification for Structural Steel Buildings, December 27, 1999AMERICAN INSTITUTE OF STEEL CONSTRUCTION