At any height on the Tower, the moment of the weight of the higher part
of the Tower, up to
the top, is equal to the moment of the strongest wind on this same part.
Writing the differential equation of this equilibrium allows us to find
the "harmonious equation"
that describes the shape of the Tower.
Let f(x) be the half-width of the Tower at A. The moment of
the weight of the Tower relative to point A is equal to P(x)·f(x).
Let us consider a slice of the Eiffel Tower located at a distance t
from the top of the Tower, its thickness being equal to dt.
Viewed from the top, this slice looks like a square whose
width is 2·f(t).
The forces applying on this slice are:
These 2 moments relative to point A sould be equal:
Let a be
. The function
, which gives the width of the Eiffel Tower as a function
of the distance from top, is a solution of the following equation:
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