This hyperbolic cosine function describes the shape of a catenary. A chain that supports only its own weight forms a catenary; the chain is purely in tension. Likewise, an inverted catenary arch that supports only its own weight is purely in compression, with no shear. The catenary arch is the stablest of all arches since the thrust passes through the legs and is absorbed in the foundations, instead of forcing the legs apart. The Gateway Arch itself is not a common catenary, but a more general curve of the form y=Acosh (Bx). This makes it an inverted weighted catenary. Saarinen chose a weighted catenary over a normal catenary curve because it looked less pointed and less steep. In 1959, he caused some confusion about the actual shape of the arch when he wrote, "This arch is not a true parabola, as is often stated. Instead it is a catenary curve—the curve of a hanging chain—a curve in which the forces of thrust are continuously kept within the center of the legs of the arch." William V. Thayer, a professor of mathematics at St. Louis Community College, later wrote to the St. Louis Post-Dispatch calling attention to the fact that the structure was a weighted catenary.
This hyperbolic cosine function describes the shape of a catenary. A chain that supports only its own weight forms a catenary; the chain is purely in tension. Likewise, an inverted catenary arch that supports only its own weight is purely in compression, with no shear. The catenary arch is the stablest of all arches since the thrust passes through the legs and is absorbed in the foundations, instead of forcing the legs apart The Gateway Arch itself is not a common catenary, but a more general curve of the form y=Acosh (Bx). This makes it an inverted weighted catenary Saarinen chose a weighted catenary over a normal catenary curve because it looked less pointed and less steep. In 1959, he caused some confusion about the actual shape of the arch when he wrote, "This arch is not a true parabola, as is often stated Instead it is a catenary curve—the curve of a hanging chain—a curve in which the forces of thrust are continuously kept within the center of the legs of the arch." William V. Thayer, a professor of mathematics at St. Louis Community College, later wrote to the St. Louis Post-Dispatch calling attention to the fact that the structure was a weighted catenary.