The effect of diaphragm wave propagation on the analysis of pounding structures

Abstract

Building pounding is frequently observed during earthquakes in regions of dense
\nurban populations, with damage levels ranging from cosmetic to catastrophic for buildings
\nwith insufficient separation. While the numerical modeling of pounding has significantly progressed
\nin recent years, significant uncertainty still remains in many collision properties. The
\ncollision force itself is highly dependent on the stiffness of the so called ‘collision element’,
\nyet this stiffness is not well characterized in the existing literature.
\nThis paper identifies building pounding as the collision of two distributed masses and subsequently
\nanalyses the collision in terms of the one dimensional wave equation. Collision properties
\nare derived from wave theory and numerically verified, building on the work of
\nprevious researchers. An ‘instant wave’ method is proposed as a distributed mass equivalent
\nto stereo mechanics.
\nNumerical approximations of distributed masses are assessed in terms of displacement response.
\nTwo building configurations are subjected to 10 second excitations with 5 % modal
\ndamping. The collision element stiffness in lumped mass models is also investigated to determine
\nthe most accurate response. It is found that at least three nodal masses connected by axial
\nspring elements should be used to represent each diaphragm in order to provide
\nconsistently accurate displacement results. The contact element stiffness should be calculated
\nwith y = 1 and the element stiffness of the stiffer diaphragm should be used in this calculation.