Track 1: DOCUMENTATION AND DIAGNOSTICS – UNDERSTANDING HISTORIC PLACES / Volet 1 : Documentation et diagnostic – Comprendre les lieux historiques

# A parametric model for ribbed masonry vaults and the development of structural simulations

Friday, October 13
3:00 PM - 4:30 PM

The structure of a historic building is composed by various structural elements, such as foundation, pier, buttress, wall, vault, and other. One of the most complex parts to be analyzed in an historic masonry building are the ribbed vaults. Challenging geometry and structural complexity defines a barrier for the analyst.
The aim of the research is to define a procedure to generate in a semi-automatic way the structural three-dimensional finite element model of a ribbed masonry vault. Furthermore, use the generated model to analyze the vault behavior in relation to the observed damage.
The members that compose the structural geometry of the ribbed vault are: tas-de-charge, arch, rib, web, crown, rubber-fill, etc. Point cloud measurement represent only the surface of the vault (mainly the intrados or in some cases the extrados either) and cannot be used to directly obtain the 3D solid model of the vault. Moreover, thickening of this surface does not result in the real structural geometry. The result is to generate the geometry of the structure using a parametric model. In this study, the point cloud was used to extract the radius of the arch and rib, and identify the web curvature. The geometric construction considers individual members (arch, rib, web) and connection nodes (tas-de-charge, boss). The objective is to have a good approximation of real geometry and a good possibility of creating its discretization in a finite element model. Approximations made on the construction geometry, aim not to alter the structural behavior. There are analogies between the geometrical divisions considered by the builders and those needed to draw the geometry and to create the finite element mesh. The relative position of the members (super-position, interfaces, connection) is controlled, considering the construction process. The model is finalized for use in a three-dimensional numerical finite element analysis to study the structural response. Results of the parametric model show that different ribbed masonry vault such as quadripartite (with square, rectangular, or trapezoidal shape in plan) or sexpartite can be generated just by changing the input parameters of the parametric model.
Based on the generated numerical model using the parametric procedure, detailed finite element analysis were carried out for a vault of the Cathedral of Milan where damage was observed in the past. Complex damage phenomena such as tensile damage in the arch voussoir, sliding at the joints of the arch or rib and detachment of the web from the rib was predicted during the analysis of the developed model.

## Learning Objectives:

• Understand the technology of the construction of historic masonry vaulted structures.
• Describe the complexity of correct modelling of ribbed masonry vaults.
• List methods and techniques that can help to overcome difficulties in the study of the structural behavior of ribbed masonry vaults.
• Demonstrate the need of deepening the knowledge on the structure of historic vaulted system, in order to define a correct diagnosis of active phenomena.

# Grigor Angjeliu, PhD Student

Ph.D. Student
Politecnico di Milano

Grigor Angjeliu is a Ph.D student at Politecnico di Milano, in Italy. Recently, he was a visiting scholar at the Department of Architectural Engineering, at the Pennsylvania State University. His research focues on the integration of experimental observations and numerical methods in historic buildings. Grigor is author of arround 10 publications in this field and has actively participated in many restoration and conservations projects including the Mother Teresa Square in honor of the visit of Pope Francis in Albania and the Cathedral of Milan in Italy.

# Assets

## Attendees who have favorited this

• Ronald Staley
Senior VP
The Christman Company