Abstract
Spherically voided biaxial slabs (SVBS) present structural advantages for static loading which can lead to economic solutions. There exist however lacunae, in the knowledge on the behaviour of SVBS diaphragm systems when subject to seismic induced ground motion which, if overlooked, would restrict their future advancement and proliferation into seismic regions. The assertion, of lower floor seismic accelerations due to the 25-30% SVBS mass reduction, should factor the response uncertainty due to the diaphragm stiffness, higher natural frequency and floor acceleration magnification. The present research presents an innovative structural modellisation approach to facilitate the nonlinear transient dynamic analysis (NLTDA) of SVBS diaphragms by the transmutation of their in-plane diaphragm bending behaviour into 3D Kirchhoff beam finite elements. The SVBS diaphragm in-plane flexural response is captured using a novel adaptation of the 2D static-nonlinear moment-curvature analysis (2D-SNLMCA) procedure on partially-perforated RC diaphragms. A method is proposed for the 2D-plane stress (2D-PS) models to directly emulate the 3D-SVBS diaphragm behaviour by converting their 3D morphology into a 2D-PS diaphragm configuration without the need of using 3D-solid-continuum nonlinear finite element analysis. The numerical tools adopted were validated using available experimental data and verified using the closed-form differential equation of motion for a dynamic system and RUAUMOKO dynamic finite element suite. The 3D-NLTDA model accurately captured the global diaphragm demands in terms of force, deformation, floor acceleration magnification and ductility levels which are compared to the diaphragm 2D-SNLMCA capacity levels. Diaphragm energy dissipation optimisation is possible through an iterative matching approach of the seismic demands using the 3D-NLTDA with the diaphragm designed moment-curvature response from the 2D-SNLMCA. This shows that the proposed methodology could be adopted in the design towards increasing energy absorption and therefore reducing structural damage. The 3D-NLTDA shows that the better performance of SVBS diaphragms during a seismic event, compared to a solid diaphragm, is not by default due to their lighter mass, as sometimes claimed in the literature, but is conditional on the diaphragm stiffness, floor acceleration magnification and reinforcement levels which can be assessed using the proposed methods.