2023-07-27 11:05:53
The first name of what we know today as the Eiffel Tower was the Tour de 300 mètres, and it is included in the project that the engineers Koechlin and Nougier presented to Gustave Eiffel, builder of the monument. That name already anticipated the will to carry out an outstanding construction, a technological challenge that would establish a height record. The striking thing is that right now, in the middle of summer, the Eiffel Tower, like every year, grows.
After an aesthetic retouching by the architect Sauvestre, the Eiffel Tower was raised at the universal exhibition of 1889 to commemorate the centenary of the French Revolution.
Eiffel chose puddled iron for his construction, a material he was familiar with and had used in previous works to good effect. It is a steel material with high mechanical capacity, which would allow the erection of a large and very light tower, safe against horizontal wind actions and with a limited own weight.
The Eiffel Tower should be a privileged place of observation and a support for radio broadcasting. Its current weight, about 7,300 tons, is close to the weight of the air of the parallelepiped that contains it (about 6,300 tons), which gives an idea of its lightness.
The tower is a gigantic triangulated lattice structure, like the Garabit viaduct (from the Eiffel office) or the bridge over the Forth, also from the same period.
All of them experience growth when the temperature of the material increases. And unlike bridges, which behave more complexly, the Eiffel Tower experiences primarily vertical growth and decline due to changes in temperature. This phenomenon is known as thermal expansion.
What is the dilation due to?
We know that most solids increase when the temperature increases and decrease when the temperature decreases. This is because the increase in temperature causes a greater agitation in the atoms, which leads to an increase in the average separation distance between them. Depending on the nature of the bond, different families of solids experience greater or lesser growth, which we characterize with great care. Thus, ceramics and glasses, with stronger bonds, expand less than metal ones and these, in turn, less than polymers.
So how can we estimate the magnitude of motion in a solid? When the elements are of a linear type –as occurs in public and architectural works where it is easy to find beams, supports or bars– the movement is proportional to three parameters: the length of the bar, the increase or decrease in its temperature and the coefficient of linear expansion of the material used.
the thickness of a hair
Many ceramic materials usually have expansion coefficients ranging between 0.5×10⁻⁶ and 1.5×10⁻⁶ (℃)⁻¹, while metals would be between 5×10⁻⁶ and 30×10⁻⁶ (℃)⁻¹, and polymers between 50×10⁻⁶ and 300×10⁻⁶ (℃)⁻¹. This strange number would indicate the growth experienced by a bar of unit length when the temperature rises one degree Celsius.
Thus, the most expandable materials are polymers, which expand about ten times more than metals, and these ten times more than ceramics.
When we say that the puddled iron that makes up the Eiffel Tower, or the steels, have a coefficient close to 12×10⁻⁶ (℃)⁻¹, it means that an iron bar one meter long experiences a growth of 12×10⁻⁶ meters when increase the temperature one degree. That is, barely a dozen microns, a length less than the thickness of a hair.
So does the heat produce any perceptible effect on public works? Yes, if we take into account that there are two other parameters to consider: the length of the element and the range of temperatures that we consider to be between.
The length can be very long. The Eiffel Tower is 300 m high, the Garabit viaduct 565 m long, and the bridge over the Forth no less than 2.5 km. And surely we know of larger linear development works, not to mention the very rails of the railway line that many bridges support.
The temperature range must also be analyzed, and it should be done historically, even if in the future the minimum and maximum temperatures recorded may be exceeded. In Paris it has been recorded for more than two centuries, with winter minimums below -20 ⁰C and summer maximums of about 40 ⁰C. In addition, we should take into account the effect of radiation, and we are well aware that metallic materials can be found at higher temperatures under the sun, which can exceed 60 ⁰C or 70 ⁰C.
A slight curvature, as if the Tower turned away from the sun
Now, let’s do the exercise. We consider a range of 100 ⁰C to make our estimates. Can we thus estimate the growth of a simple metal bar 100 meters long when the temperature fluctuates around 100 ⁰C?
The calculation is simple. If a one meter bar grows 0.000012 meters as the temperature rises one degree, a 100 meter bar grows 0.12 meters as the temperature rises 100 degrees. And a 300 meter would do it three times more: 0.36 meters. That is, 36 cm. This is indeed an appreciable length.
It is evident that the behavior of a simple bar and a tower made of more than 18,000 pieces of iron riveted and oriented in all directions is not the same. In addition, the sun always falls on one of its sides, so that one of its faces grows more than the others, which limits its deformation, producing a slight curvature in the tower, as if it were moving away from the sun.
Various authors estimate that the Eiffel Tower grows, in fact, between 12 and 15 centimeters if its size is compared on cold winter days with the hottest summer days. And that means that, in addition to being a communications tower, Parisians have a gigantic thermometer in this monument.
This article was originally published on ‘The Conversation’.
ABOUT THE AUTHOR
Federico de Isidro Gordejuela
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