Wood Diaphragm Deflections. I: Generalizing Standard Equations Using Mechanics-Based Derivations for Panel Construction

Abstract

Horizontal wood diaphragm systems, whether decked with conventional or mass timber panels, transfer wind and seismic loads to vertical elements of a lateral force-resisting system (LFRS), in flexible, rigid, or semirigid fashion. Characterizing and calculating the resulting diaphragm deflections determines the distribution of forces to critically loaded components and a significant portion of lateral building translations and rotations. Deflection equations for sheathed wood structural panel (WSP) diaphragms are well established in US design standards in a four-term expression that models flexural, shear, and fastener-slip deformations, and its full derivation using principles of mechanics is provided herein. Derivations of similar equations for cross-laminated timber (CLT) diaphragms have yet to unfold, despite growing industry consensus that CLT panels make efficient slabs and decks. In this first of two companion papers, the corrected full derivation of the current four-term WSP diaphragm deflection expression is provided and assessed, and two ways to quantify the cumulative contribution of fastener slip are presented to expand its usage to a wider variety of WSP and CLT configurations in current use. Building on this generalized mechanics-based derivation, the authors are able to propose and assess in the companion paper a unified diaphragm deflection model to compute both WSP and CLT diaphragm deflections as implemented under current practice and guide further development.