The objective of this study was to develop design equations that predict lateral restraint forces in two commonly used Z-purlin supported roof systems. These are quarter point bracing and third point plus support bracing. To that end, a stiffness model used in the past has been reintroduced. This model has been modified slightly to better represent roof system behavior. The updated stiffness model was then used to estimate lateral restraint forces for a number of roof systems with a varying cross sectional dimensions of the purlin, number of purlin lines, number of spans, and span length. A regression analysis was then performed on the data to obtain empirical design equations similar to those found in the 1996 Edition of the American Iron and Steel Institute's Specification for the Design of Cold-Formed Steel Members, Section D.3.2.1. <i>Vita removed April 4, 2011. GMc</i> / Master of Science

Supplement No. 1 to Section D3.1 of the 1999 AISI Cold-Form Specification contains the current provisions for predicting required lateral restraint forces in Z-purlin supported, sloped metal roof systems under gravity loads. A proposed prediction equation, relying heavily on engineering principles, has been developed because the current provisions in the specification are empirical and based on statistical analysis. The provisions treat roof slope and system effects incorrectly, which necessitates refinement. Also, an assumed roof panel stiffness value was used for the development of the current design provisions, ignoring the effect that varying stiffness values have on the required restraint forces. To determine the validity of the new restraint force prediction equation, experimental testing was conducted on single span and multiple span metal roof systems. Z-purlins were used extensively with through-fastened and standing seam roof panel. Two, four, and six purlin lines were used for the single span tests while only four purlin lines were used for the multiple span tests. Restraint forces were measured at five restraint locations in each span: support, third-point, midpoint, quarter-point, and third-point plus support. Each restraint configuration was tested at six roof slopes: 0:12, 0.5:12, 1:12, 2:12, 3:12, and 4:12. For each restraint configuration and roof slope, the restraint forces were measured and compared to predicted forces using the proposed design equation. The proposed equation contains the term "δ" which is the resultant eccentricity of the applied gravity load acting on the top flange of a purlin. A value of 1/3 was assumed for d in the development of the proposed equation and many of the test results were in agreement with this value. However, other results were in better agreement with a value of 0 for d and some of the measured forces were between the predicted forces with d = 0 and d = 1/3. No consistent correlation between the results and the proposed prediction equation was found. / Master of Science