An equivalent frequency approach for determining non-linear effects on pre-tensioned-cable cross-braced structures

Pre-tensioned cable braces are widely used as bracing systems in various structural typologies.
This technology is fundamentally utilized for stiffening purposes in the case of
steel and timber structures. The pre-stressing force imparted to the braces provides to the
system a remarkable increment of stiffness. On the other hand, the pre-tensioning force in
the braces must be properly calibrated in order to satisfactorily meet both serviceability
and ultimate limit states. Dynamic properties of these systems are however affected by
non-linear behavior due to potential slackening of the pre-tensioned brace. In the recent
years the author has been working on a similar problem regarding the non-linear response
of cables in cable-stayed bridges and braced structures. In the present paper a
displacement-based approach is used to examine the non-linear behavior of a building
system. The methodology operates through linearization and allows obtaining an equivalent
linearized frequency to approximately characterize, mode by mode, the dynamic
behavior of the system. The equivalent frequency depends on both the mechanical characteristics
of the system, the pre-tensioning level assigned to the braces and a characteristic
vibration amplitude. The proposed approach can be used as a simplified technique,
capable of linearizing the response of structural systems, characterized by non-linearity
induced by the slackening of pre-tensioned braces.