Conservation-Oriented Structural Analysis of the Spire of Barcelona Cathedral
Ahmed Elyamani
Archaeological Conservation Department, Faculty of Archaeology, Cairo University, Giza, Egypt
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To cite this article:
Ahmed Elyamani. Conservation-Oriented Structural Analysis of the Spire of Barcelona Cathedral. International Journal of Materials Science and Applications. Special Issue: New Strategies for Conservation of Historical Objects, Principles and Practical Applications. Vol. 5, No. 6-2, 2016, pp. 1-9. doi: 10.11648/j.ijmsa.s.2016050602.11
Received: May 13, 2016; Accepted: July 22, 2016; Published: September 3, 2016
Abstract: The spire of Barcelona cathedral suffered from severe problems due to the corrosion of the steel ties used in reinforcing its stone masonry beams. Wide visible cracks were noticed in the stone beams and large parts were detached. Therefore, the full spire was dismantled and reconstructed using titanium ties to eliminate the corrosion problem. A finite element model of the spire was created and analyzed using DIANA software to support this decision. This analysis helped in understanding the role and strength contributions of these ties in resisting the applied loads on the spire, specifically, the lateral loads of earthquakes and wind. A nonlinear static (pushover) analysis was carried out to assess the spire capacity under the lateral loads. A number of constitutive models for modeling the masonry behavior were tried. Also, a number of seismic actions patterns were considered. As a main conclusion of this study, the ties were highly needed to carry the tensile stresses caused by earthquakes and wind loads. Therefore, in the reconstruction of the spire, such ties must be kept in the masonry beams.
Keywords: Conservation, Structural Analysis, Spire, Corrosion, Ties, Pushover, Wind, Earthquake
1. Introduction
Structural analysis plays an important role in conservation of historical structures. In the assessment phase, it helps in understanding the structural behavior under different loads. As well, it is an efficient tool for identifying the weakness places where intervention is possibly needed. In designing the intervention, a numerical model may work is a virtual laboratory in which different intervention proposals could be simulated to reveal its efficiency. There are many successful cases in the literature in which structural analysis have been used as an efficient tool for restoration of historical structures [1-8].
This paper deals with the structural analysis of the spire of Barcelona cathedral (Fig. 1) as a useful tool for its conservation. The builders of the spire reinforced all of its stone masonry beams with steel ties. Due to the coastal weather of Barcelona city which is full of rains and also because of sea spray and pollution products these ties were corroded and the spire faced severe problems. Wide visible cracks were noticed in the stone beams and large parts were detached. This situation led to carry out a complete project for the restoration of the spire. In this project, the entire spire was dismantled and reconstructed and the steel ties were replaced by titanium ones to eliminate the corrosion problem.
To understand the role and strength contributions of the steel ties, a finite element (FE) model of the spire was created and analyzed using DIANA software [10]. Specific concern was given to the analysis of the spire under lateral loads because it reaches a height of 90 m over the ground level which makes it vulnerable when subjected to such type of loads. The earthquake and wind loads were estimated using the Eurocodes [11, 12].
A FE nonlinear static (pushover) analysis was performed using the estimated lateral loads. To reveal the dependency of the results on the used constitutive models, a number of constitutive models for modeling the stone masonry were tried. As well, a number of load patterns were tried to study the dependency of the results on the used load pattern.
2. Barcelona Cathedral
The construction of the cathedral (Fig. 2) started in 1298 and continued for more than a century. The apse and the entire nave were finished in 1327 and 1417, respectively. The span of central nave is 12.80 m and the maximum high is 25.6 m. The span of the side aisles is equal to one half the span of the nave. The total length of the cathedral is 93 m. The plan of the temple is not conventional because the cimborio was not constructed over the crossing but over the first bay of the nave close to the façade. A similar distribution can be observed in very few cases, such as the German cathedrals of Ulm and Friburg [14].
3. Spire of Barcelona Cathedral
3.1. Description
The spire of Barcelona cathedral is a symmetrical stone masonry structure built at the beginning of the 20^{th} century. It has an octagonal shape in plan, Fig. 3. It consists of 8 columns connected together by 8 beams. The columns have irregular shapes with an average cross sectional area of about 0.3 m^{2}. The beam section can be approximated as a rectangle of 25 cm × 60 cm reinforced at the center with a steel tie of 1 cm × 4 cm. The shortest beam span is about 1 m (at the last level of the spire) and the longest one is about 2.5 m (at the first level of the spire). The eight columns rise up to the top of the spire until they are attached together forming a base for a stone statue (Fig. 1) which has a height of 5 meters and a weight of 6.25 t.
3.2. Damage
The steel ties used in reinforcing the spire beams suffered from severe corrosion due to the rainy weather of Barcelona city, Fig. 4. Due to corrosion products the steel ties increased in volume (the volumetric increase may reach ten times the original volume) which caused pressure on the surrounding stone masonry and led it to crack (Fig. 5) or furthermore to fall down (Fig. 6). Big parts of some of the stone masonry beams were about to fail due to corrosion products and were temporary kept in position by some ropes (Fig. 7).
3.3. Restoration Project
The spire was completely dismantled and reconstructed. Before doing so, the spire and the supporting cimborio were documented using 3D laser scanning (Fig. 8).
In order to execute the restoration works, complete scaffolding started from the roof level and extended to the last top part of the spire was employed (Fig. 9). Another steel structure was constructed inside the spire (Figs. 10-11). This steel structure was used to support the spire during the dismantling and as well as scaffolding for the reconstruction process.
The different parts of the spire were numbered and then were cut at the locations of the mortar joints using electrical saw, Fig. 12. The spire pieces were stored on the roof of the cathedral, Fig. 13. The stone was cleaned and then the spire was reconstructed again.
4. Numerical Model
The spire was modeled using the DIANA FE code [10]. The model (Fig. 14) consisted of 4011 nodes and 5055 elements. The maximum element size was 0.1 m. Both of the columns and the beams were modeled using frame elements, in specific, the element type L13BE was used. The arches supporting the spire and the base of the statue were modeled using shell elements. The statue was not modeled; instead, it was taken as a concentrated load at the top of the spire. The steel ties were modeled as reinforcement for the beams from B1 to B9.
To simulate the nonlinear behavior of the masonry, both cracking (tensile regime) and crashing (compressive regime) were considered. The two regimes were modeled using smeared cracking, in specific; the Total Strain Fixed Crack Model was used. This model proved its efficiency in many previous studies, see for instance [5] and [6]. Two softening models were tried. The first was the ideal softening in both tension and compression (Fig. 15). This model in tension does not represent the masonry nonlinear behavior, but it is an approximation to obtain an idea about the model nonlinear behavior with less computational troubles.
The second model was linear softening in tension and parabolic softening in compression (Fig. 16). The steel nonlinear behavior was modeled using Von Misses model. The used properties of the stone masonry and steel are summarized in Tab. 1. The values were taken as recommended by some previous studies carried out using the same stone masonry [16].
Density (kg/m^{3}) | Modulus of Elasticity (E) (GPa) | Poisson’s ratio | Compressive Strength (f_{c}) (MPa) |
2200 | 12 | 0.30 | 8 |
Tensile Strength (f_{t}) (MPa) | Fracture Energy in Tension (G_{f}^{I}) (N. mm/mm^{2}) | Fracture Energy in Compression (G_{c}) (N. mm/mm^{2}) | Steel Yield Strength (F_{y}) (MPa) |
0.60 | 0.1 | 17.8 | 280 |
5. Earthquake Analysis
A pushover analysis was performed to assess the behavior of the spire under seismic actions. Two seismic actions were tried. The first was forces at the nodes of each level of the spire, and the second was prescribed displacements at the same nodes.
The tried combinations of the aforementioned constitutive models and the seismic actions are summarized in Tab. 2. For the ideal softening model, two seismic actions were tried: (1) forces proportional to the mass of each level of the spire, (2) displacements proportional to the 1^{st} mode which had the highest mass participation (49%). For the second softening model, two seismic actions were tried: (1) displacements proportional to the 1^{st} mode and (2) displacements proportional to the Square Root of Sum of Squares (SRSS) of the modes number 1, 3, 10 and 13. These modes had mass participation ratios of 49%, 11%, 10% and 13%, respectively which were the highest of all the modes.
For the estimation of the applied forces on the spire, the lateral force method of analysis described in Eurocode 8 [12] was employed. The base shear was estimated as 30 tons which represented about 11.5% of the spire weight. More details can be consulted at [15].
For the all examined cases, a phased analysis was followed. In the first phase, the self-weight of the spire was applied in two load increments, each of 50% of the spire weight. In the second phase, the seismic action was applied incrementally at a chosen control points at each level. These points were the corners of the octagonal section of the spire.
The obtained capacity curves for the four cases are shown in Fig. 17. The displacement is for the top point of the spire. For the effect of the used constitutive model, it was found that the ideal softening model gave higher capacities than the
Case no. | Softening model | Seismic action pattern |
1 | Ideal (tension and compression) | Forces proportional to mass |
2 | Displacements proportional to 1^{st} mode | |
3 | Linear (tension) and Parabolic (compression) | Displacements proportional to 1^{st} mode |
4 | Displacements proportional to SRSS of 1^{st}, 3^{rd}, 10^{th} & 13^{th} modes |
second softening model. Case 2 was around 35% higher than case 3 (0.23 compared to 0.15). For the effect of the used seismic action pattern, it was noticed that representing the seismic action in the form of prescribed displacements resulted in a lower capacity than the case of using forces. Case 2 was about 13% lower than case 1. For the second softening model, changing the pattern of the prescribed displacements didn’t result in a significant effect neither in the capacity nor in the maximum displacement. Regarding to the maximum displacement at failure, all the cases gave near values from about 4 cm to about 5.5 cm.
For the failure mechanism, the two cases 1 and 2 showed that the damaged places at collapse were at: (1) the columns of the first level of the spire, (2) almost half the span of almost all the beams at all the levels and (3) at the connections between the columns and the beams, Fig. 18. For the two cases 3 and 4, less damaged locations were noticed, as the middle span of the beams were damaged at collapse, see Fig. 18 for case 3.
The role of reinforcement in resisting the seismic actions was investigated. It was found that at failure, the steel reached its yield strength as shown in Figs. 19 and 20 for the cases 2 and 3. The highest stresses were noticed at the beams corners, i.e. at the connections with the columns.
6. Wind Analysis
The wind loads were estimated using the Eurocode 1 [11]. The total wind load was estimated as 60 tons. Full details are found in [15]. The ideal softening model was employed in the nonlinear static analysis under wind loads. The same phased analysis used for the earthquake analysis was also followed here. The load-displacement diagram is presented in Fig. 21 for the top point of the spire. The spire was able to resist the wind loads with a maximum displacement at failure of about 4.2 cm.
The damage at collapse is plotted in Fig. 22. It can be noticed that it is quiet similar to that found for the cases 1 and 2 of the seismic analysis. The stress in the reinforcement is depicted in Fig. 23. Again for the wind analysis, the steel ties were found to resist high values of stresses at failure that were near to its yield strength, Fig. 23.
7. Conclusions
The spire of Barcelona cathedral was subjected to a complete restoration project in which the spire was totally dismantled and reconstructed. This was due to the corrosion of the steel ties used to reinforce its stone masonry beams. The steel ties corrosion led to sever problems like the developing of wide visible cracks in the stone beams and detaching of large parts of the beams stones.
It was necessary for the restoration to understand the behavior of the spire under lateral loads and the role of the steel ties in resisting these loads.
The spire was modeled using the FE code DIANA and analyzed under the effect of earthquakes and wind. Different constitutive models and load patterns were tried. It was found that:
• The seismic capacity and the damage pattern depended significantly on the employed constitutive model.
• Using the same seismic action pattern, the ideal softening model in tension and compression gave about 35% higher capacity than the model of linear softening in tension and parabolic softening in compression. For the ideal softening model, the spire manifested more extended damage than the other softening model.
• Using the same constitutive model, lower seismic capacity was obtained when applying the seismic action in the form of prescribed displacements according to the first mode shape than that obtained one when applying forces proportional to mass.
• The steel ties were highly needed to resist both of the wind and the earthquakes. The stresses in the ties were found to be near to the steel yield strength.
Acknowledgement
I would like to express my gratitude to the MSc SAHC Consortium and the Erasmus Mundus Programme for the financial support. Heartfelt thanks for Prof. Pere Roca the supervisor of my MSc and PhD.
References