Structural performance of shells of historical constructions: The Municipal Theatre of Rio de Janeiro
The main objective of this thesis of the author Marina Polónia Rios is to evaluate the structural behaviour 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.
Respecting the authenticity
Heritage construction must be object of special care due to its historical and cultural value. In the modern concept, conservation of these structures should mainly respect their authenticity. With this in view, prior to any intervention on the structure, a detailed study should be carried out to guarantee full understanding on the structure conditions, allowing the minimum intervention to be applied.

Structural analysis
The analysis of the historic buildings’s structures should gather most information as possible on the structural conditions, involving historical research, visual inspection, non-or minor destructive tests, monitoring and numerical modelling.
The structural analysis by numerical simulation is crucial for understanding the structural behaviour under different conditions, allowing evaluate causes of damages, capacity of the structure and the efficiency of strengthening techniques.
Case Study: Municipal Theatre of Rio de Janeiro
The object of this thesis is the Municipal Theatre of Rio de Janeiro, built in the beginning of the 20th century and considered a masterpiece of the Brazilian eclectic style. This work is mainly focused on the structural analysis of the shells located on the front part of the theatre, namely a barrel vault and two lateral domes. In general, the structure presents itself in good conditions. However, important damages were reported in the 1970s, that led to an intervention in order to guarantee the structural safety.
The study is divided in four main parts, namely (i) a study on the state of the art of structural analysis of shell elements made of masonry together with a historic and architectonic review on the theatre, (ii) in-situ investigation by NDT tests, such as dynamic identification tests, (iii) preparation of the numerical model, including its calibration and validation by comparison with experimental data,(iv) non-linear structural analysis, aiming at identifying the possible cause of reported damage and evaluation on the structural capacity.

Historical overview of the Municipal Theatre of Rio de Janeiro
In 1902, the Rio de Janeiro's mayor Pereira Passos remodeled the city center of Rio de Janeiro, especially the Central Avenue – known nowadays as Rio Branco Avenue – where the theatre is located. The need for modernizing the city came from the changes in the politics, since Brazil had just become a republic and wanted to be noted internationally. Besides, the rich population of the city wanted a place for socialization, and supported the construction of a new theatre. Pereira Passos included the construction of the theatre as part of this renovation plan, hence the design of 'Theatro Municipal do Rio de Janeiro' was opened to competition in 1903.
The final layout was result of a merge between the two winners of the competition: Oliveira Passos (Figure 30) and Albert Guilbert (Figure 31).

The two models had the same typology and were both inspired in the design of Paris' Opera from Charles Garnier.

Some renowned artists were invited to work in the decoration of the theatre, namely Eliseu Visconti, Rodolfo Amoedo and the Bernardelli brothers. Stained glasses windows and mosaic finishing were imported from European artists.
The Municipal Theatre of Rio de Janeiro was built between 1905 and 1909 (Figure 32), being inaugurated in July 14, 1909 by Brazil's president Nilo Peçanha and Rio de Janeiro's mayor Sousa Aguiar. It is considered nowadays one of the most important concert halls not only in Brazil but also in South America.
The theatre was one of the first constructions made with electricity, phone connection, firefighting system and air conditioning. Therefore, it is also considered an example of the technological advances in the period after the industrial revolution.

Architecture
The Municipal Theatre of Rio de Janeiro is a masterpiece in eclectic style and is considered an ikon of the modernization plan for the Rio de Janeiro's city center in the beginning of 20th century. The eclectic style is predominant in the main buildings from the end of 19th century and beginning of 20th century in Brazil, and symbolizes the end of colonial period by the construction based on the foreign architecture as a way to present the city as one of the main capitals of the world. The design of the theatre is result of the works from Oliveira Passos and Albert Guilbert, strongly based in the Paris' Opera, as mentioned previously (Figures 38 and 39).


Interventions
Intervention in 1934
In 1934, a great renovation work was performed in the theatre to increase its capacity with design by Paulo Fragoso and Bjarne Ness.

Intervention in 1977-1979
The intervention that carried out between 1977 and 1979 included the restoration of the theatre as a whole, from replacement of damaged copper tiles at the roof to 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 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. The intervention involved a multidisciplinary team with careful supervision by Iphan, which has detailed documentation of the works performed
SEE ALSO: Why engineers need to know construction history?
Shells
The main object of this study are the three vaults, namely the barrel vault on top of the foyer and the two spherical vaults over the lateral resting rooms. The vaults are crucial parts for the architecture and characterization of the eclectic style of the theatre, being the most important decorative feature in each room where they are located.
The vaults have artistic paintings at the intrados. The barrel vault was painted by Eliseu Visconti between 1913 and 1916 in canvas, placed on the surface of the vault. The two lateral vaults were painted by Henrique Bernardelli in 1908 directly over the regularization plaster that covers the masonry.
Non-Destructive Tests
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 Municipal Theatre of Rio de Janeiro is built in eclectic architectonic style, which is known for the extensive decoration, with no apparent parts of the structural materials. Hence, it is very difficult to identify the structural elements and conditions only by visual inspection. It is necessary to perform non-destructive tests to have a better understanding of the structure.
An investigation campaign has been carried including diverse NDT tests to gather information regarding structural conditions, morphology and materials that may affect the behaviour of the shells under study. You can download the full thesis in the end of the article, so you can see the the results of thermography tests performed in the context of this study.
Additionally, pachometry tests were carried out to identify metallic elements embedded in the masonry walls. Also, dynamic identification tests were performed in order to estimate the dynamic properties of the structure.
Numerical Modelling
Numerical modelling is a powerful tool that allows a better understanding of structural behaviour. It provides information such as stresses, damage and deformation.
For new constructions, this information is used to design the structural elements required in the construction, while for historical construction it is used for diagnosis, safety assessment and definition of intervention. Different actions can be simulated (e.g. gravity, wind, earthquake loading), helping to understand the causes of existing damage and structural capacity. Besides, different types of strengthening techniques can be evaluated, aiming at improving the structural performance of the structure.
In the case of historical structures, the numerical modelling is a challenging task since these constructions usually present highly complex shapes, such as arches and vaults, which can involve 3D analysis with solid elements. Another difficulty is the lack of data regarding the structure, such as material properties, morphology, together with information concerning the geometry and existing damage.
In cases of masonry construction, non-linear analysis is required because of the characteristics of the material, which presents high compressive strength and almost null tensile strength. This leads to a considerable increase of computational effort, which is aggravated by the use of 3D models.
A numerical model was developed for the structural analysis of shells in the Municipal Theatre of Rio de Janeiro. Three shells are analysed in this study: a barrel vault and two lateral domes, located in the front part of the theatre. Since the theatre is a massive construction with several different elements, it was decided to model only the front part of the structure, involving the foyer room, under the barrel vault and the two lateral towers, under the domes, as presented in Figure 77.
The model was calibrated according to results of dynamic identification tests performed in the structure and the non-linear analysis was performed. In order to reduce the computational cost for the non-linear analysis, the symmetry of the structure was considered for the non-linear analysis, with only half of the structure being modelled and the results mirrored for the rest of it.
Furthermore, a partial model with only the top part of the structure (shells and lintels) was prepared, aiming at evaluating the load capacity of the shells. It is noted that in this model the masonry walls and columns were replaced by rigid boundary conditions. In addition, a 2D model representing a section of the barrel vault was performed for both strengthened and unstrenghtened configurations, in order to evaluate the contribution of the concrete layer to the load carrying capacity of the vault.
The numerical analyses were carried out in the FEM software DIANA 10.1 (TNO DIANA BV., 2017). Details on the elements considered and modelling strategies are presented in the full thesis.

Structural Analysis
Once the model has been calibrated and validated, it can be considered trustworthy to describe the structural behaviour of the theatre. As mentioned previously, the linear analysis is not suitable for analysing masonry construction due to its highly non-linear behaviour, being required the use of non- linear analysis in the numerical study of such type of material.
In this study, non-linear analysis was performed to describe the structural behaviour of the shells located in the front part of the Municipal Theatre of Rio de Janeiro. The non-linear response was calculated according to the Newton-Raphson iterative method, in which a new tangent stiffness matrix is calculated within each iteration. The analysis convergence criterion was defined by the energy control with a tolerance equal to 10-3.
The non-linear analysis was carried out in three different models, aiming to analyse three distinct aspects of the structural behaviour. Firstly, the interaction between soil and structure was analyse under different soil conditions, in order to estimate the possible cause of cracks that led to the intervention in 1975. Secondly, a study of the load capacity of the structure prior to the 1975 intervention was performed. Lastly, the increase of the structural capacity due to the addition of the reinforced concrete layer was evaluated.
Conclusions and Recommendations
According to the results obtained in this study, the differential soil settlements can be one of the causes for the damages identified in the 1970s, namely settlements at the base of the main façade and towers. The shells present a considerable safety level under vertical loads and the strengthening intervention performed in 1970 increased significantly the load capacity of the barrel vault. Even though the study carried out allows a good understanding on the structural behaviour of the shell elements, further analysis is recommended in order to improve the current conclusions.