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