Articles Conservation

Structural performance of shells of historical constructions

17 June, 2021 11 min reading
Based on the thesis by: Marina Polónia Rios, M.Sc. in advanced masters in Structural Analysis of Monuments and Historical Constructions

Structural performance of shells of historical constructions

The main aim of this thesis, by the author Marina Polónia Rios, is to evaluate the structural behavior of shell elements in the Municipal Theatre of Rio de Janeiro, identifying the possible causes of previous damage, evaluate the structural capacity and the effectiveness of reinforcement intervention applied on the shells.




Vaults and domes can be defined as curved structures used to provide ceilings to spaces, being especially applied in important constructions, such as palaces and churches due to their valuable aesthetic features. They can assume different shapes, which vary according to:

  • their use;
  • type of structure;
  • location;
  • a period in history;
  • and others.

Their structural behavior and construction techniques may differ according to their shape. The main characteristic of a vaulted structure is stability, provided solely by mobilizing compression forces at the cross-sections. These forces transfer the applied loads to the supports in the vault base by inclined components. 


Most vaults and domes are made of masonry, which is a complex material due to its composite character of units and mortar. It presents great strength under compression, with brittle response in tension and frictional response in shear, being characterized by its heterogeneity and anisotropy. 




Distinct cultures constructed vaults and domes using a variety of local materials such as wood, mudbrick, and stones.


The Romans

Timber centering was the most usual technique for vault construction, which could be substituted by rubble fillings and mounds or smart construction techniques that avoided the use of centering, such as the Catalan vaults. The Romans were responsible for truly spreading this technique. The use of pozzolan concrete made it easier to build this type of structure since it was adaptable to curved shapes. Its high strength also allowed large spans of up to 20m for vaults and 40m for domes.

The Basilica Nova (Figure 1) – built between 308 and 312 AD had the main nave covered by vaults of 25m span and The Pantheon (Figure 2) – built-in 125 AD with a dome of 43.3m, being the biggest span until the 15th century.



The Byzantines

The Byzantines also built several vaulted and domed constructions. They developed further the technology from the Romans, adapting the structure to the trajectory of forces with the use of ribbed domes and buttresses instead of massive walls. The main material used in byzantine construction is masonry made of rubble material with lime mortar. 

Hagia Sophia Church, with an impressive dome with 31m of span and several vaulted and arched elements.



The Romanesque construction style prevailed in Europe from the 10th to 12th centuries and is much simpler than the ones mentioned previously, with extensive use of barrel vaults and massive three-leaf walls. These structures are characterized by their redundancy and ductility. The Gothic construction is characterized by the skeletal type of construction, with the use of arches, ribs, flying arches, piers, and buttresses.



Renaissance period

During the Renaissance period (15th and 16th centuries), domes were recovered as roofing solutions for important buildings. The construction typology combines Roman and Gothic techniques, as is easily recognized in the dome of Florence (Figure 4) – the most emblematic dome in the world, with a span of 43.6m and 33m rise. It is characterized by the pointed geometry that leads to smaller horizontal thrust and ribbed structure with a double membrane.



Mechanical properties

Masonry is a composite material made by the assemblage of units – stone, brick, or adobe – usually connected by mortar joints. The global mechanical properties of masonry depend on:

  • on the dimensions and mechanical properties of each element;
  • the behavior of the interface between units and mortar joints. 
  • the constructive techniques also influence the final behavior of the material
  • the material properties depend on the conservation status, 


Structural behavior

Vaults are structures characterized by mobilizing only compression forces in order to reach stability. In general, the structural behavior of vaults can be idealized as a 2D structure with behavior similar to arches. The strength of the vault depends on the way units are assembled during its construction, which can be by arch assemblies or by enchainment of units as continuous surfaces. 


  • Barrel vault

Barrel vaults are single curved vaults, with a cylindrical shape, consisting of continuous arched sections along two parallel lines. These lines are considered the springs of the vault and usually are also defined by the supporting walls. They can have various shapes according to the different possible forms of arches presented in Figure 10.


  • Groin vaults

Groin vaults are formed by the intersection between two barrel vaults. The main difference between this type of vault and the barrel vault is the support since groin vaults are supported by piers while barrel vaults are supported by walls, leading to lighter structures. 


  • Domes

Domes can be considered doubly curved surfaces, made from the rotation of an arch around its central vertical axis. Domes are frequently used in historical architecture, especially in religious constructions, due to their visual impact. Historical domes can be made in many different shapes according to the region and culture (Figure 13).

Domes have similar behavior to vaults, with the meridian forces responsible for the vertical transfer of thrusts. However, they also develop internal horizontal thrusts – the hoop forces (Figure 14), which form parallel rings responsible for resisting the out-of-plane bending moment from the meridians, acting as lateral support.



Typical damage and collapse mechanisms

One of the main tools to identify causes and mechanisms of decay in historical buildings is visual inspection, with a detailed mapping of existing cracks together with a geometric survey.

Through the analysis of crack maps, it is possible to highlight major structural problems and acquire information about the present level of safety of the building. 



Structural analysis

The main challenge in the structural analysis of arches is to define the horizontal thrust acting on the supports in order to properly design the buttresses. Existing deformations and cracks together with the presence or not of infill are crucial in the analysis of such structures.


Different techniques used to evaluate the behavior of masonry vaults along with history:

  • Ancient geometrical rules
  • Rational approaches and limit analysis
  • Finite element method (FEM)
  • Discrete element method (DEM)





The Municipal Theatre of Rio de Janeiro, with a total of 4220 m2, is a masterpiece in eclectic style and is considered an icon of the modernization plan for Rio de Janeiro's city center at the beginning of the 20th century. The design of the theatre is the result of the works from Oliveira Passos and Albert Guilbert, strongly based in the Paris Opera.



The façade (Figure 35) is characterized by the six main columns in the central body, which are made of marble in Corinthian style. The design lines are of classic style, but the varied decorative elements of the façade resemble the baroque.



The lateral façade (Figure 36) is marked by balusters made of six columns in marble with golden capitals. Arched windows over the columns allow the light to come into this part of the Theatre.


Interior of the theatre

The interior of the theatre is divided into three parts, namely the main body, the showroom, and the stage, as presented in Figure 37.




The roof is the most impressive part of the building, extensively ornamented, made of noble materials, and morphology of high complexity (Figure 39). The original tiles were made of zinc. However, they were replaced later by copper tiles. The main parts are a barrel vault, two small domes on both sides of the main façade, and half a dome in the middle of the building.



The great dome (Grande Cúpula) is the central element of the theatre, covering the showroom. It has a half-elliptical shape in the front part and a regular shape in the back. 



The structure of the Theatre is supported by 1180 woodpiles with a length between 4 and 11m. It is known that the piles are immersed in water, once the water table in this region is close to the surface. The ground in this location is the result of a landfill over a lagoon. The structural system consists of load-bearing walls with an internal structure made of metallic beams and columns made of cast iron and marble, respectively. The roof is made of wood and metallic trusses that reach a span of 30m in some parts of the building, supporting the metallic tiles and wooden plates. 


The roof is characterized by three main parts:


  • The roof over the foyer

The foyer is covered by a roof made of copper tiles, supported over composite trusses of wood and steel. 

  • Lateral domes of the roof 

The domes of the roof have a varying curvature making a peak shape and are made of copper tiles with a globe of glass on its top

  • Great dome

The great dome is part of the roof over the elliptical ceiling in the showroom. It is made of copper tiles in the shape of half a sphere in the front part and by a regular triangular roof in the back part.




Intervention in 1934

In 1934, a great renovation was performed in the theatre to increase its capacity. Aiming at increasing the visibility, the cast-iron piers in the noble balcony were removed and replaced by three reinforced concrete trusses with six meters height to cross a span of 30m, which are supported by masonry walls. On the opposite side of the stage, cantilever trusses were built to support the new arrangement of the space with spans of 6m.


Construction of metro station at the end of 1970s

Figure 48 shows the construction of the station and the proximity of the ditch to the theatre can be observed. These excavations led to instability issues in the structure of the theatre, causing the appearance of cracks. It is notable especially the cracks in the vault over the foyer, which had to be reinforced.



Intervention in 1977-1979

The intervention that carried out between 1977 and 1979 included the restoration of the theatre as a whole, from the replacement of damaged copper tiles at the roof to the recovery of artistic elements. Hydraulic and electrical installations were also reviewed and updated when necessary.


Intervention in 1987-1989

Even though the last intervention in the roof had been only ten years before, the roof presented poor conditions of conservation leading to some leakage issues. This was due to a lack of a maintenance plan. Therefore, the main goal of the intervention between 1987 and 1989 was to cover the areas that present leakage problems.


Intervention in 2008-2010

The restoration work carried out between 2008 and 2010 was one of the greatest interventions in heritage buildings ever made in Brazil. It included works to recover and modernize the installations and restoration of artistic elements.




In order to have a proper understanding of any structure, it is necessary to know its elements, materials, morphology, structural features, and conservation status.



The tests with a thermographic camera were carried out on January 19, 2017, by a team from the Catholic University of Rio de Janeiro and Federal Fluminense University. The conditions in situ were 26 to 28ºC of temperature with 59% humidity. It used a camera FLIR T1020 with an infrared sensor.



A pachometer was used to identify the location of metallic beams in the main spans of the structure.


Dynamic Identification

Dynamic identification tests were performed in the Municipal Theatre of Rio de Janeiro, aiming at estimating the dynamic properties (natural frequencies and mode shapes), mainly of the global modes of the structure and the local modes of the shells.




The model was calibrated according to the results of dynamic identification tests performed in the structure and the non-linear analysis was performed.


Geometric properties

The geometry was created based on the architectural drawings provided by Fundação Theatro Municipal do Rio de Janeiro (2006), information acquired in historical and architectural research, and in-situ investigation.


Material properties

The initial mechanical properties for the masonry materials present in the structure were defined according to the Italian guideline for historic masonry (NTC-08, 2008). Due to the uncertainties, these values will be calibrated based on the results of dynamic identification tests.


Modeling strategy


  • 3D Model
    The complexity of the structural geometry of the Municipal Theatre of Rio de Janeiro leads to a high number of degrees of freedom (DOFs) for a detailed numerical model.
  • 2D Model
    Due to the high computational effort demanded by the 3D model, the use of simpler 2D models for the analysis of the effectiveness of the layer of concrete added in 1975 was adopted.

Linear static analysis

A preliminary linear elastic analysis was performed for the large 3D model in order to have an overview of the results, aiming to check that there were no irregularities in the model, such as geometric, material, or loading inconsistencies. This analysis considered only the dead-load (self-weight) of the structure as body forces.


Eigenvalue analysis

In order to evaluate the numerical model, an initial eigenvalue analysis was carried out using the linear mechanical properties defined.





  • The inspection and diagnosis campaign allowed us to identify important facets of the structural conditions. However, there are still several aspects that should be clarified, mainly regarding the soil properties, foundation elements, and steel elements embedded in the masonry. Further studies should be performed in order to confirm the hypothesis assumed in this study concerning the morphology of the shells, such as GPR, impact echo, and sonic tests.


  • The dynamic identification tests performed in this study allowed us to estimate the elastic modulus of masonry materials by the calibration of the numerical model with the experimental results. However, these results should be validated by other methods. NDT and MDT tests could be carried out for this purpose, such as sonic tests and double flat jack tests.


  • The numerical model prepared in this study considers only the front part of the theatre where the shells are located. The contact with other parts of the structure was simulated by elements with normal stiffness.  A global model of the structure should be made in order to have a full understanding of the global behavior of the structure.


  • The non-linear analysis carried out to study the soil-structure interaction presented relevant results in terms of crack pattern related to each scenario of differential settlement, identifying possible causes for the damages in the structure.


However, this analysis reached only the beginning of the damage pattern. Due to a lack of information regarding the foundation and soil conditions, a simplified approach for simulating the foundation conditions was adopted. It is recommended further studies in this assumption, including the foundation elements in the 3D model, as well as the soil characteristics, in order to properly determine the severity caused by possible differential settlements for which the structure may have been submitted.


An analysis considering differential settlement between the side facing Treze de Maio Avenue and the side facing Rio Branco Avenue should also be performed, to evaluate a possible decrease in soil stiffness due to the opening of the ditch during the construction of the metro in the 1970s.


  • The structural capacity of the shells was assessed for self-weight loading, leading to the conclusion that the structure is able of resisting high levels of vertical loads. These shells, mainly the dome, are curved elements that act mainly under compressive stresses. Distributed loads increase the confinement of these elements, increasing their behavior. Other types of loads could be applied for the shell such as horizontal forces or point loads, in order to have a full estimation of the structural capacity. 


  • The analysis of the unstrengthened and strengthened models of the dome showed that the reinforced concrete layer and beams applied in 1975 improved significantly the performance of the dome, in which an increase of about 500% on the load capacity for a prescribed horizontal displacement at the base was observed. The strengthening technique presented a different collapse mechanism with respect to the unstrengthened model, preventing the two hinges at the connection with the backing (cracking at the extrados).


  • Other types of loading should be evaluated, such as point loads.



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