The Dome of the Temple of Diana in Baiae: Opus Caementicium, Geometry and Mechanics

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.

KEYWORDS:

• Baiae
• Building techniques
• domes
• geometry
• membrane theory
• opus caementicium
• structural analysis

Notes

¹ “It is one of the most difficult Problems there is in Architecture, that of knowing the strength that the abutments of the Vaults should have to withstand the thrust, and Architects have not yet found any certain rule to determine it. (…) This problem belongs to Mechanics, and it is by its means that we can resolve it”. (…) “It was thought that one had to search in Geometry for a rule on which one could rely to determine the strength with which the abutments should be made”.