To calculate his structures, Gaudí innovated with the empirical, experimental method of suspended chains. By inverting the image in a mirror, these gave him not only the best geometry for the project, meaning the angle the columns and walls should have to withstand compression forces, but also a way to measure the force on each chain or string pulled taut with a dynamometer, which gave him the diameter for the columns or nerves depending on the scale used.
He applied this technique in a study for the church at Colònia Güell with the collaboration of a full team of professionals, including his right-hand man Francesc Berenguer, architects Josep Canaleta and Joan Rubió, Alsatian engineer Eduard Goetz, and photographer Vicens Villarrubias. Gaudí’s method consisted in modifying the weight on the strings to see how the project’s arches and vaults changed. This way, the inverted model was used to design the project, with drawings from the photos he coloured himself. This experience with the funicular model at Colònia Güell served as the basis for the calculations for the Sagrada Família, as Gaudí himself recognised.
Nevertheless, with all this attention paid to structural behaviour through the weight of different materials, meaning the building’s permanent vertical and gravitational loads, the wind loads and seismic forces were somewhat forgotten. While the first loads are vertical and static, like gravity, the latter are horizontal and dynamic. So, the method using strings and weights didn’t work.
The texts of Gaudí’s disciples tell us that the master took wind forces into account when building the Temple. However, we believe these considerations must have been calculations or tests done in addition to the funicular model, which is essentially static and gravity based. The truth is that structural calculations in Gaudí’s time weren’t regulated as they are now. Today’s requirements for tall buildings, like the Temple, are much stricter than Gaudí could ever have imagined. In fact, nowadays it is unthinkable to calculate the wind resistance of a building that stands 170 metres tall with just complementary verifications, as the calculations to ensure a building withstands horizontal forces from wind loads are as important in designing and fitting out the structure as the building’s own gravitational loads.
VERTICAL AND HORIZONTAL FORCES
We can see, then, that weight is a vertical force that Gaudí tested with the hanging models and that earthquakes and wind loads are horizontal forces that push the building from the side, trying to bend it. For example, for wind calculations, the dynamic force is normally equated to a static force, the maximum foreseeable, acting horizontally and spread throughout the exposed part of the building.
For an earthquake, the horizontal forces don’t hit the part of the building above ground, but act directly on its base, meaning the foundations. It is a horizontal jerk that can change directions in just seconds, moving back and forth several times. This shaking makes the whole building vibrate, bending it like a rope being shaken from one end, which means the opposite end is the one that moves the most.
If we consider that the wind can blow from any direction, it becomes clear that the calculations of wind loads and seismic forces are closely related. This is why earthquake loads are normally calculated as if they were a static horizontal force, increasing the level according to the seismic degree of the area where the building is located.
These calculations often show that the taller the building, the more the movement is increased at the very top. From this standpoint, we can say that the part of the building furthest from the base is most at risk.
To better understand this, we can imagine a pyramid: horizontal vibrations won’t move the tip much, because the base is so wide in comparison. However, an inverted pyramid, with a higher mass on top of a weak mast, would easily start vibrating like a pendulum and the weakest part, the mast, could fail.
Given this fact, it is understandable that this must be taken into account in the calculations for the Sagrada Família, as the Temple has an open ground floor, with only the tree trunks that branch into numerous smaller arms to hold up much heavier vaults. Plus, on top of these vaults are the central towers, which are three times taller than the vaults they sit on. The mass is far from the ground and, therefore, the effect of the vibration from an earthquake must be taken into account.
WHAT IS THE RISK OF EARTHQUAKES IN BARCELONA AND CATALONIA?
The earth’s crust is made up of tectonic plates that move around and interact. Scientists have established a number of main plates, which more or less correspond with the continents, as well as smaller ones, like the Iberian plate. This plate is moving away from the American plate on one side and pushing up against Italy and Sicily, the African Atlas Mountains, on the other, and rubbing against European plate at the Pyrenees. This explains why the Pyrenees region is quite active, with volcanoes and a higher probability of seismic activity.
Nowadays, to detect earthquakes we use sophisticated electronic seismographs that can sense the smallest movement of the earth, whether at the surface or any depth. But these tools are relatively recent. In the past, Chinese civilisation also tried to quantify seismic activity, but the instrument they used was a sort of bronze sculpture, 2 metres tall, with eight dragon heads around the edges looking in towards a central bowl. There were bronze balls in each of their mouths. When there was an earthquake, the magnitude was determined by how many balls fell into the bowl.
However, it wasn’t until the 20th century that we got a more rigorous measurement technique: the seismograph. Taking into account that earthquakes can happen once every several centuries, and that this technology is very recent, we can conclude that there isn’t enough data to establish the seismic risk for each area of the globe precisely. This is why, to determine a region’s seismic level, regulations look not to scientific data but to chronicles and stories describing the damage caused by seismic activity throughout history.
So, the first earthquake on record in Catalonia was in 1373. Historians have put the epicentre between Ribagorça county and the Val d’Aran. It caused damage in several parts of Catalonia, from Barcelona and Sant Just to Lleida, La Noguera and Boí i Taüll. It was even felt in France.
Nevertheless, the magnitude of an earthquake isn’t determined solely by the area that is effected but also by the damages caused. So, we can point to the 1428 earthquake, very deadly and known popularly as the Candlemas quake, as the reason Barcelona is considered an area of important seismic activity. In fact, the map of seismic risk for Catalonia from 1997 put the Barcelona region at VI to VII out of a maximum of XII on the MSK scale.
This earthquake, based in the Catalan Pyrenees, toppled bell towers and church keystones and caused more than one thousand deaths. In Queralbs, nearly the whole population perished; in Camprodon, there were 200 casualties and between 100 and 300 in Puigcerdà, when the church collapsed. In Barcelona, where roughly thirty people died, residents sought refuge inside the church of Santa Maria del Mar when they felt the first jolts. They were unlucky, however, as the main rose window separated from the building and fell on the people inside.
Nowadays, small earthquakes are detected almost daily. Last year there were more than 250 earthquakes above a 1 in Catalonia. And if we count the ones in the French Pyrenees, Andorra, the bordering strip of Aragon, the nearby Mediterranean and Balearic Islands, the number of seismic events in just one year rises to 400. Among the most noteworthy, in Alt Urgell in February 2017, one of the 130 movements detected was a 3.2 and in March in La Selva, one was a 3.8. On the coast of the Baix Llobregat, on 7 August, there was a 2.4 earthquake. As a reference point, it is important to remember that earthquakes are measured on a logarithmic scale and the largest one in history was a 9.5 in Chile in 1960.
So, to properly analyse the behaviour of a building as complex as our Temple in a seismic event, it is important to understand and check that the building model, more or less simplified, can predict the structure’s real behaviour. Earthquakes, for their part, are also quite complex and must be simplified.
LATEST UPDATES TO CALCULATIONS
When Gaudí came on board as the architect of the Temple, the foundations for the crypt had already been laid, reflecting Villar’s project, which was much smaller. So, as the project became taller with the great lantern of the Virgin Mary above the apse, and taking into account the new weight and the effects of wind and earthquakes on the tower, these original foundations had to be seriously reinforced, with works in the crypt for two years (2007-2009).
Likewise, the issue of seismic activity was clearly present in beginning construction on the foundations for the main nave and transept in 1988. The crossing that supports the central lanterns we are now building, therefore, is within this area that sits on the new foundations, made with reinforced concrete pylons that are 20 metres below ground. For these calculations, we used static approximations of earthquakes according to the 1974 Spanish Earthquake-Resistant Construction Standards.
Later on, the structural analysis was refined. For accurate seismic calculations, it is very important to determine the acceleration the structure will be subjected to, as force = mass x acceleration. So, in recent years, dynamic analysis has been used with a series of virtual simulations of how the ground moves and makes the building vibrate.
Also in this line, a study was conducted on site of the Temple vibrations, analysing the frequency of the structure built so far to allow for better calibration of the model for the seismic analysis.
Furthermore, as construction of the building has advanced over the years, all of the structural elements have been defined more precisely and, therefore, it has been possible to update the model of the building. The model has been recalculated with the new data in order to ensure, among other things, that it can stand up to seismic activity. So, with the beginning of works on the central lanterns in 2014, the general structural model of the Temple was updated with the geometry, mass and stiffness of all the existing structural elements, as well as the structure in the tower project. Furthermore, to make it even safer, a specific study was carried out to determine how an earthquake would affect the towers.
Taking all of this into account, we can draw the conclusion that seismic activity has been properly taken into account in the calculations of the Temple structure, in line with current standards for our region.