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The Lisbon Cathedral (Sé De Lisboa)

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The Lisbon Cathedral (Sé De Lisboa) STRUCTURES AND THE 1755 LISBON EARTHQUAKE CASE STUDY - THE LISBON CATHEDRAL (SÉ DE LISBOA) Zélia Beatriz Machado Fernandes, Instituto Superior Técnico, 2010 ABSTRACT The aim of this thesis was to evaluate the structural safety of the Lisbon Cathedral, Sé de Lisboa, in the event of an earthquake. A 3D model was developed with the commercial program SAP 2000® (2005), based on the geometrical characteristics of the various parts of the building. The dimensions which could not be measured in situ were obtained from drawings of the cathedral (available at IHRU - Instituto da Habitação e da Reabilitação Urbana). Simplifying assumptions were introduced in the model. Due to the absence of reliable information on the building foundations, these were simulated as restrained embedded supports. The model was calibrated with the values of the natural frequencies of vibration of the structure taken from in situ measurements. By means of static analysis, the model demonstrated that the building satisfies the loads imposed by the Code (RSA, 1983). An earthquake was simulated by response spectrum analysis defined by Portuguese safety code RSA (Regulamento de Segurança e Acções). The value of 1.0 (Lisbon Area A) was taken for the seismicity of the region. Soil type III and damping coefficient of 5% were considered. Some discrepancy was found between the linear analysis model and the damage effects attributed to the 1755 earthquake. It was concluded that a linear dynamic analysis is not sufficient to evaluate the safety of the building in case of earthquake, since, for instance it does not take into account the nonlinear behaviour of materials. However, this model provides valid information on the monument parts where the cracking probability will be greater in case of occurrence of an earthquake with the characteristics defined by RSA. Key-words: Sé de Lisboa, 1755 Lisbon Earthquake, Dynamic Analysis, Seismic Behaviour 1. INTRODUCTION The Lisbon Cathedral was classified as National Monument in 1907 (Sucena, 2004). The monument was built in late Romanesque style (as can be seen in the narthex, naves and transept) but saw later 1 addictions of Gothic style. The construction started in 1148, and it suffered several modifications until the 20 th century. Some of these were of decorative nature reflecting the taste of each period, while others were reconstructions after the damages caused by repeated earthquakes, and especially the one in 1755. Several rooms were also added, as the Vestry and the Chapel dedicated to St. Bartholomew (Bartolomeu Joanes) at late 13 th century and the Sacristy at early 18 th century (Castilho, 1936). Although most of the documents about the monument were lost on the fire following the Lisbon earthquake of 1755, there are many descriptions on what happened to the building, such as the fall down of the south tower of the main front and the upper two levels of an original bell tower standing above the main dome. The Lisbon earthquake of 1755 is a well documented event. The main goal of this work is the analysis of the seismic vulnerability of the Lisbon Cathedral, Sé de Lisboa, as it stands today. 2. METHODS A simplified linear material behaviour analysis was carried out using SAP 2000® (2005). Based on plans (Figure 1), photographic material and site inspection, a three-dimensional model was created. Figure 1 – Main front photo and a ground floor plan of Lisbon Cathedral as it is today (from IHRU). The information obtained from the historical and arquitectural research was taken into account in the construction of the model. In this model were defined 20 types of frame sections for the insertion of arches and columns and 25 kinds of areas to implement the sections of walls, vaults, ceilings and stairs. In total were used 1934 frames, 7270 areas (shells) and 6330 points. 2 Nevertheless the monument has at least to types of limestone masonry construction, there was no available information on the properties and mechanical characteristics for the various types of limestone present in the structure and so the parameters for the material were uniformed. The material properties considered for the structural components, such as density and modulus of elasticity, are presented in Table 1, according to Reis et al ., 2006 and Oliveira, 2003. Table 1 – Materials’ properties Material ρ [KN/ m 3] E [GPa] ν Limestone Masonry 24 4.5 0.2 Bricks Masonry 15 2.5 0.2 Wood (oak) 5 11 0.3 All internal and external walls were of limestone masonry. Ceilings are of wood (Sacristy, Chancel and St. Vincent Chapel) and brick masonry vaults (lateral aisles). The remaining parts are limestone masonry (Dionísio, 2002). Although the soil upon which the cathedral was built is mainly constituted of sands and clays (Pereira de Sousa, 1923), there is not enough data on the characteristics of the building foundations. Therefore, for simplicity, these were simulated as restrained embedded supports. The earthquake action used in the analysis was the response spectrum defined by the Portuguese safety code (RSA, Regulamento de Segurança e Acções). The value of 1.0 (Lisbon, Area A) was taken for the seismicity of the region. Soil type III and damping coefficient of 5% were considered. Both seismic action Types I and II were analysed. They were applied simultaneously to the x and y directions. The CQC (complete quadratic combination) algorithm was used for the combination of the modal participation while the SRSS (square-root of sum-of-squares) combination was used for the directional combination. The vertical seismic action was not considered. The standard values of ultimate stresses (Reis et al ., 2006; Tassios, 2010) (Table 2), were used for the safety verification of the building under self-weight (static analysis) or seismic conditions (dynamic analysis). Table 2 – Ultimate strength Material σ Compression [MPa] σ Tension [MPa] Limestone Masonry ~ -6 +0.2 Bricks Masonry -3 up to -8 +0.1 Wood (oak) -50 +90 3 3. RESULTS AND DISCUSSION To analyse the seismic model simulation it was helpful to compare it with what happed in the earthquake of 1755. An historical investigation about what happened to the structure was performed and Table 3 presents a summary of the main conclusions. The lapidary signatures method was used to confront the information taken from pictures and testimonials. This method allows to determine the age of each part of the monument. These signatures are fine traits written on one side of each stone, made by the medieval stonemason and that identifies him as part of a school or even as an individual. It is thus possible to place each part of the building, almost exactly, in every generation of schools and therefore in different construction periods. Table 3 – Damages on the cathedral in the 1755 Lisbon earthquake North South Facade Bell Transept Chancel, ambulatory tower tower Portal tower and nave and apse chapels Pictures - ± - + ± ± Written testimonials (1) + (1) + ± (1) Lapidary signatures ± (2) ± (2) - ± (3) ± (4) - (5) method (Van de Winckel,1964) - did not fall + fall completely ± partially fall (1) there are no references (2) did not fall from the ground floor to the first floor (3) what remains today of the tower didn’t fall (4) did not fall from the ground floor to women’s gallery (5) neither the ambulatory nor the gothic apse chapels had no problem; no reference to the chancel The modal analysis results are given in Table 4. The first mode corresponds mainly to translation in x direction; the second mode corresponds to translation in y direction. The third mode corresponds to torsion. Table 4 – Modal frequencies and modal mass participation ratios Mode Freq. UX UY UZ RX RY RZ ∑UX ∑UY ∑UZ ∑RX ∑RY ∑RZ Hz N-S (%) E-W (%) % % % % % % % % % % 1 2.59 0.32 0.00 0.00 0.00 0.21 0.02 0.32 0.00 0.00 0.00 0.21 0.02 2 3.59 0.00 0.40 0.00 0.12 0.00 0.05 0.33 0.40 0.00 0.12 0.21 0.07 3 3.85 0.17 0.01 0.00 0.00 0.04 0.25 0.49 0.41 0.00 0.13 0.25 0.32 4 Measurements made at the site showed that, the first natural frequency on NS direction ( x) occurs at 2.5 Hz, the second on EW ( y) direction occurs at 3.5 Hz, and the third frequency (corresponding to torsion) occurs at 4 Hz (Oliveira, 1997). Figure 2– First mode, corresponds to translation in x direction (N-S), view from the top Figure 3– Second mode, corresponds mainly to translation in y direction (E-W), view from the south facade Figure 4– Third mode, corresponds mainly to torsion, view from the top. 5 STATIC ANALISYS Since the measured values of natural frequencies were similar to the ones of the model, analysis of structural safety was made for dead-loads and permanent and variable loads. Modelation results of ultimate limit states, taking into account dead-loads and variable imposed loads, are shown in 3D graphics with coloured areas representing the tensions and compressions to which the structure is submitted. The software used assigns positive values to tension (towards the blue colour) and negative values to compression (towards the fuccia colour). For comparative effects, all graphics are presented with the same scale of colours. Figure 5 – South view of the maxim stress ( σmax) under self-weight and variable imposed loads. Under self-weight structural safety is assured, since no main structural damages can be detected on the simulation. The values of tension and compression are lower than the ultimate strength for each material. DYNAMIC ANALYSIS After the determination of the most relevant vibration modes, a dynamic analysis of the structure behaviour under a seismic simulation was made.
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