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.