Friction is much needed for the equilibrium of masonry arches as it transfers load between the voussoirs. In this paper, applying an analytical formulation of the problem, the angle of friction as a geometric constraint on the stereotomy (bricklaying pattern) is investigated to find the possible range of minimum thickness values of circular and elliptical masonry arches under static loads based on the lower bound theorem of limit state analysis. The Heymanian assumptions regarding material qualities are adopted; however, limited capacity in friction is accounted for. It has been shown earlier that considering stereotomies a-priori unknown, a considerably wide range of minimum thickness values is obtained for fixed loading and global geometry conditions. It is found that a stereotomy constrained by an angle of friction, characteristic of masonry, renders the effect of stereotomy on the minimum thickness value negligible because the range of minimum thickness values is significantly reduced in this case. Hence, the present study ultimately justifies the intuitive assumption of radial stereotomy, widely used in the literature, whenever the safety of masonry arches is studied.

平衡砌体拱时非常需要摩擦，因为摩擦会在各拱室之间转移载荷。在本文中，使用问题的解析表示法，研究了摩擦角作为立体约束（砌砖图案）的几何约束，以基于静载荷在圆形和椭圆砌体拱的最小厚度值的范围内寻找可能的范围。极限状态分析的下界定理。采用关于材料质量的Heymanian假设；但是，摩擦的能力有限。先前已经表明，考虑到先验未知的定型学，对于固定载荷和整体几何条件，可以获得相当宽的最小厚度值范围。发现立体结构受摩擦角的限制，即砌体的特征，由于在这种情况下最小厚度值的范围显着减小，因此对最小厚度值的定型效果可忽略不计。因此，无论何时研究砌体拱的安全性，本研究最终证明了在文学中广泛使用的放射状立体定位的直观假设。