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