Curved structural members are widely seen in our surroundings, such as railway supports in playgrounds resembling a c-ring structure. The common geometry of the curved member consists of a segment of a circular ring with a uniform width. The curved section is of constant width in most cardiovascular stents. This study focuses on curved strut members whose width changes along the curved segment. The location of the maximum equivalent stress varies depending on the manner in which the width changes. When the width is constant or larger toward the top, the maximum equivalent stress is developed at the top. Meanwhile, when the area is reduced toward the bottom, the largest equivalent stress is developed some distance from the top. Simple equations, based on the mechanics of materials and the theory of elasticity, were compared favorably with the results from finite element analysis. Included are elaborations of the distribution of the change of stress. The suggested strategy of changing the width, with refinements, could be applied to the optimal design of structural members, including pipes and medical devices such as stents.