A Comparison of Approximate Methods for Period Determination in Rack Structures

The seismic design of rack structures according to the Rack Manufacturers Institute (RMI) MH16.1-08 standard requires calculation of the fundamental period in both the down-aisle and cross-aisle directions using “the structural properties and deformation characteristics of the resisting elements in a properly substantiated analysis” for seismic load determination. A detailed finite element model provides accurate calculation of the rack structure’s natural periods but can be tedious for large rack structures. The additional accuracy provided by the finite element approach can be impractical for evaluating large facilities containing several thousand storage racks. Approximate methods for computing the natural period of rack structures can provide simplifications that enable tractable solutions for large facilities. A discussion of approximate methods for period calculation, including approximate analytical methods and a reduced direct stiffness model, is presented with a comparison of periods computed using the approximate methods and the finite element method. The accuracy of each period calculation procedure is compared and the implications for the resulting design calculations are discussed for various rack structures. An analysis framework for systematically evaluating rack structures in large facilities using organized information about the rack structures with the approximate methods is also discussed.