The study focuses on using trigonometric series to calculate cable stress in stiffened suspension bridges, particularly those spanning uniformly distributed loads. This method provides a more accurate and practical alternative to the traditional deflection method, especially when the bridge's truss has minimal rigidity. Trigonometric series allow for precise computation of cable stress, even when loads are concentrated, bypassing the complexities of older methods such as the trial and error approach proposed by Melan in 1888 and amplified by Moisseiff in 1926. Stiffened suspension bridges, ideal for spanning considerable lengths like the Delaware River and Florianapolis bridges, are increasingly favored in modern engineering. The trigonometric series method promises to facilitate simpler and more accurate stress calculations, suitable for both single and multi-span bridges. The research extends the application of this series to bridge engineering, noting its underutilization in existing literature. The study's plan included applying the trigonometric series to deflection problems, calculating uniform and non-uniform load effects, assessing temperature changes, and evaluating real-world data from the Manhattan and Delaware River Bridges. The findings underscore the method's efficacy in addressing various stress scenarios, setting a foundation for broader application in future bridge designs.