ABSTRACT

This research is focused on one of the most ancient domes of large rise and span built in opus caementicium: the dome of the temple of Diana in Baiae. The main purpose of this paper is to prove that the geometric meridian profile adopted by the Romans for the dome is different from the polycentric profile proposed by Rakob in 1988, which presents some inconsistencies as regards the position of the centres of the upper arcs and the presumed presence of a cusp at the top, not visible at the extrados. To the aim of the research thesis, a recent architectonical survey has been performed and a methodology based on a multi-disciplinary approach has been adopted by critically examining significant aspects related to both the geometry and structural behaviour of the dome: the appropriate choice of the meridian geometric profile, related to historical context, suggestions received from Sassanid constructive traditions and geometric knowledge at the time the dome was built; the Romans’ intuitive and experimentally based understanding of the influence that geometry could have on the mechanical behaviour of a given dome’s profile; and, finally, the adoption of a very small thickness allowed by the opus caementicium constructive techniques, so that the dome can be considered as a first unaware anticipation of the modern membrane theory for thin domes. Results of the architectonic surveys performed up to now, by Rakob in 1988 and recently in 2017, are discussed. Then, after a theoretical investigation on possible profiles of the upper calotte, either circular or parabolic, a statistical regression is undertaken in order to compare theoretical and experimental data of both the surveys. Important considerations on the actual dome springing, and the demonstrated absence of any cuspidal shape at the dome’s key, confirm the Authors’ thesis: the meridian profile is well described by a parabola — the best approximation of a catenary —, which immerses itself in the tambour and continues to be fully contained in it as far as the dome springing. Moreover, mechanical analyses on the structural efficiency of both the polycentric profile proposed by Rakob and the parabolic one thus identified are performed. The analysis confirms that the dome could have been built without the aid of global centring, by demonstrating that the Romans were experimentally aware of the dome’s mechanical behaviour in relation to the various construction phases and the consequent solutions adopted. Finally, the stability of both the overall and partially collapsed structure is examined.

摘要

这项研究的重点是在 Opus caementicium 中建造的最古老的大型隆起和跨度圆顶之一：Baiae 的戴安娜神庙的圆顶。本文的主要目的是证明罗马人对穹顶采用的几何子午线剖面与拉科布在 1988 年提出的多中心剖面不同，在上圆弧的中心位置和圆顶上存在一些不一致。假定顶部存在一个尖点，在引流处不可见。To the aim of the research thesis, a recent architectonical survey has been performed and a methodology based on a multi-disciplinary approach has been adopted by critically examining significant aspects related to both the geometry and structural behaviour of the dome: the appropriate choice of the经络几何轮廓，与历史背景有关，从萨珊王朝的建设性传统和建造圆顶时的几何知识得到的建议；罗马人对几何形状可能对给定圆顶轮廓的机械行为产生的影响的直观和基于实验的理解；最后，采用了 Opus caementicium 构造技术所允许的非常小的厚度，因此圆顶可以被认为是现代薄膜理论对薄圆顶的第一个不知情的预期。讨论了 Rakob 在 1988 年和最近在 2017 年进行的建筑调查的结果。然后，在对上圆顶的可能轮廓进行理论研究之后，无论是圆形的还是抛物线的，为了比较这两项调查的理论数据和实验数据，进行了统计回归。对实际圆顶弹跳的重要考虑，以及在圆顶键处证明没有任何尖头形状，证实了作者的论点：子午线轮廓被抛物线很好地描述了——悬链线的最佳近似值——它沉浸在鼓声并继续完全包含在其中直到圆顶弹簧。此外，对 Rakob 提出的多中心剖面和由此确定的抛物线剖面的结构效率进行了力学分析。分析证实，圆顶可以在没有全球中心的帮助下建造，通过证明罗马人通过实验了解圆顶与不同施工阶段相关的机械行为以及所采用的后续解决方案。最后，检查了整体和部分倒塌结构的稳定性。