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Calculating the weight of visitors to the Eiffel Tower

Negatable quantity or not? Should we take into account the weight of visitors to the Eiffel Tower in calculating the forces to which it is subjected? This question was raised by the engineers who made these calculations, here they are, with their conclusions.

The calculation is done taking the most pessimistic assumptions possible. First of all, we must know the surface on which visitors can stay. On the first floor, there are 3,878 m2 available, the second more than 1,058m2 and finally the third floor is only 272m2, a total of 5208m2. It can be estimated that there can be at most 2 people per m2, which brings us to 10,416 people. The average weight of a person being 70 Kg, the weight added to the structure is 10 416 x 70, or 729 tons, which must be compared to 9 700 tons of the tower itself (it was his weight in construction, nowadays it is a little lighter). The work coefficients due to the expenses therefore only increase by 7.4%.

What is the coefficient of work due to the charges? This is one of two forces that affect the structure of the Eiffel Tower. Those due to the charges correspond to the action of the mass of the tower on itself, the risk that it has to collapse if its weight is too heavy. This load is of course increased by the weight added to the structure itself, like that of elevators, restaurants, and for the calculation that is incumbent upon us, that of visitors. The other work is due to the wind, which is 100Kg per square meter at ground level and triple at the top of the tower.

On a very windy day, the maximum working coefficient is 10.11 kg, of which 8.04 kg for the effect of the loads and 2.07 kg for the effect of the wind. The mass of the 10,000 visitors thus increases this coefficient of 7.4% for the load only, one therefore has an increase of 7.4% x 8.04 = 0.074 x 8.04 = 0.59 Kg. The coefficient of work from 10.11 to 10.70 kg. However, under the effect of the wind admitted in the calculation, the same section of the structure works at the same point at a coefficient of 11.9 kg, which is higher than the previous one. There is therefore no need to involve these surcharges in the calculation of resistance of materials. This influence exists only on sections below the first floor, because above it is almost zero. Clearly, the overload due to visitors is negligible, even considering a very large number of people, all distributed as much as possible on the 3 platforms of the tower on a windy day, which represents the most unlikely situation that can happen.

See also:

All the calculations

History of the Eiffel tower

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