Solar power is constantly gaining popularity and can provide benefits to building owners and operators due to lower energy costs as well as to the general public due to reduced emissions. A possible installation option is to leave the solar array unattached, instead ballasting it with added weight and depending on friction to provide lateral resistance. This is done to reduce installation costs and to reduce the chance of water ingress by maintaining the integrity of the roof membrane. This strategy was problematic due to provisions in the building code and an inability to predict performance. This scenario has been studied by Schellenberg et al. (2012) using shake table tests and Maffei et al. (2013) using SAP 2000. Both of these studies considered varying coefficients of friction, slope angles, and roof motions. These studies produced data essential for the publication of a SEAOC standard (2012).
This paper contributes to this line of work by providing closed-form equations that can be used to generate simulation results much quicker than with commercial finite element software. The proposed governing equations are presented, then validated by comparison to an equivalent analysis with SAP 2000. Once validated, the equations are used to produce parametric plots of slip (maximum and residual) as a function of friction coefficient, roof slope, and intensity of roof shaking. This study is a proof of concept using a single earthquake record scaled to various intensity levels. Other assumptions and limitations and planned future work will also be detailed. One of the most important expected benefits of this work is to provide a fast-running tool that will allow design engineers to quickly predict the slip of ballasted solar arrays on angled roofs.