EQUIVALENT TIME-VARYING STIFFNESS OF BRACED FRAMES USING WAVELET ANALYSIS.

The results of a series of shake table tests on full-scale single storey concentrically braced steel frames are analysed to evaluate the stiffness of the frames at different stages of their response. Each frame possessed a pair of 3.3m long diagonal bracing members with hollow or filled rectangular steel sections that experienced alternating tensile yielding and compressive buckling when subjected to earthquake loading. Consequently, the lateral stiffness of the frame varied continuously as the combined resistance of the braces changed. In all, eight frames with a wide range of brace slendernesses were investigated.   A wavelet-based equivalent linearisation technique is employed to determine the temporal equivalent natural frequency of the frames. The equivalence is established by minimising the difference in local response energy for the nonlinear and equivalent linear systems. This allows the time-varying stiffness of a frame to be calculated throughout its response. It is observed that frame stiffness reduces significantly in later stages of the tests due to the extensive yielding and elongation experienced by the brace members.   These observed frame stiffnesses are compared with initial values determined from the elastic properties of the braces and the measured natural frequencies of the test frames, and with equivalent energy and secant stiffness values. The initial frequencies are shown to be closely correlated with the initial lateral deformations of the braces upon installation in the test frame. Agreement between expected and actual stiffness is best during the first strong ground motion stage of the tests. In later stages, response energy is shown to shift to lower frequency bands and frame stiffness is strongly influenced by the residual lateral deformations in the post-bucked brace members.