This thesis examines the geometry and statics of arch structures with the aim of determining optimal arch shapes based on load type, span, and structural requirements. Various geometric forms of arches and their practical applications are presented. Special attention is given to the catenary, which represents the optimal arch shape under uniform distributed load. A mathematical derivation demonstrates the dependence of the catenary shape on the span and the inclination of the arch at the supports. The thesis also addresses the stability of the arch and the influence of a variable cross-section on uniform stress distribution. The practical part includes case studies of catenary arches, including the Golden Gate Bridge, where the main cable follows a parabolic shape due to constant vertical loading.
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