Topology Optimization of Cold-Formed Steel Deck Diaphragms with Irregularities
Fischer, Astrid W.
Guest, James K.
Schafer, Benjamin W.
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The objective of this paper is to explore the optimization of building roofs composed of bare cold-formed steel deck profiles when subjected to lateral demands such that the diaphragm response dominates the roof design considerations. Through variation in the deck profile, deck thickness, sidelap connectors, and structural connectors the in-plane shear stiffness and strength, that may be realized by a bare steel deck acting as a diaphragm, covers a significant range. In addition, although deck orientation is not typically varied within a roof – the profiled nature of a steel deck provides starkly different in-plane rigidities along and across the deck profile. Here we consider the application of topology optimization to aid in determining an optimal layout for a cold-formed steel deck roof. The topology optimization problem is formulated employing planar orthotropic elements for the roof deck and seeks to determine the maximum stiffness (i.e. minimum compliance) under an equivalent static in-plane lateral load subject to constraints. Constraints are placed on the basic roof element properties that are consistent with ranges of available deck and connections. The optimizer considers thickness of the planar elements, in essence a proxy for in-plane stiffness, and orientation of the planar elements. Conversion of the optimization results into a realizable steel deck roof is demonstrated. A series of examples are considered, including a rectangular roof, as well as plan irregularities including non-rectangular building shape, and roof cutouts. Significant future challenges remain and are briefly enumerated.