a parabolic analysis of arches under uniform vertical load

In this paper, an analytical practical–mathematical approach is presented to determine the equation of parabolic arches that exhibit funicular behavior (i.e., with negligible internal bending moments) under uniform vertical loading. the main objective of the study is to develop a systematic and applicable method for constructing and analyzing parabolas passing through three defined points: the origin (0,0), the crown point (2.5, f), and the return to the horizontal axis at (5,0). accordingly, three different values of the crown height (f) are considered, and the associated parameters including the parabolic coefficient, horizontal thrust due to uniform load, and the approximate required cross-sectional area for common construction materials are calculated and analyzed. this study aims to elucidate the geometric effects on internal force equilibrium and the structural efficiency of parabolic arches. the numerical and analytical results are presented step-by-step to provide a clear and comprehensive understanding of the structural behavior of arches subjected to uniform vertical loading.