This text bases itself on common misconceptions about structural engineers. Structural engineers do not only analyze the architects drawings (computer-programs can do that). They design the supporting structural framework. The framework is like a skeleton of the building that retains it within the facades and floors to keep it from collapsing, swaying, vibrating etc. Engineers not only determine the thickens of each member that make up the framework but also their layout. It is a process that can be quite creative. But their design is not visible once the building is complete. Thus they are not recognized as designers.
Structural engineers have more input than architects on projects like bridges and dams (if architects are even involved). On bridges the engineer will determine the layout and size of the members (like pillars, cables, roadway) and thus much of the looks of the bridge. The architects will mostly work on things like textures and smoothing out some rough edges (they will provide finishing touches). Structural engineers can also work on projects like ships, offshore structures and much else.
Architects are important in providing comfort and aesthetics. Engineers are important when it comes to providing safety.