This analytical note shall provide a contribution to the understanding of general principles in the Mechanics of (symmetric circular) masonry arches. Within a mainstream of previous research work by the authors (and competent framing in the dedicated literature), devoted to investigate the classical structural optimization problem leading to the least-thickness condition under self-weight (“Couplet-Heyman problem”), and the relevant characteristics of the purely rotational five-hinge collapse mode, new and complementary information is here analytically derived. Peculiar extremal conditions are explicitly inspected, as those leading to the maximum intrinsic non-dimensional horizontal thrust and to the foremost wide angular inner-hinge position from the crown, both occurring for specific instances of over-complete (horseshoe) arches. The whole is obtained, and confronted, for three typical solution cases, i.e., Heyman, “CCR” and Milankovitch instances, all together, by full closed-form explicit representations, and elucidated by relevant illustrations.

该分析说明将有助于对（对称圆形）砌体拱的力学中的一般原理的理解。在作者先前的主流研究工作中（以及专门文献中的胜任框架），致力于研究导致自重作用下厚度最小的经典结构优化问题（“ Couplet-Heyman问题”），以及纯粹旋转的五铰合塌陷模式的相关特征，此处通过分析得出新的补充信息。明确检查了特殊的极端情况，因为这些情况导致最大的固有无量纲水平推力和从冠部到最宽的内角铰链位置，这两种情况都发生在过完整（马蹄形）足弓的特定情况下。