The horizontal wind pressure is highest at the top of the Eiffel Tower, and
decreases near the ground. The geometry of the Tower reflects an opposing trend,
where its width (and wind bearing area) is smallest at the top and increases near the
ground. If we assume that the high pressure on the small bearing area (top of
Tower) produces the same force as a lower pressure on the large area (near the
ground), the wind pressure on the Tower can be approximated in two dimensions as
a continuous line of equal horizontal point loads (figure 4). In our analysis, we will
neglect the wind pressure on the Tower above the Top Platform (figure 1).
Reactions
A free body diagram is used to graphically represent equilibrium on a
structure, where the applied loads (wind and self weight in our case) are
counterbalanced by equal and opposite forces called reactions. The Eiffel Tower is
designed to transmit its own self weight and horizontal wind pressures to the ground
through its internal framework. Reactions from the ground on the structure prevent
the Tower from sinking into the soil or from tipping over.
Analysis
In this study, we will only concern ourselves with the behavior of the Tower as
a cantilever under the influence of wind (figure 4). As the wind blows, internal forces
develop to resist the tendency of the Tower to tip over on its side. These resisting
internal forces can be characterized as a moment. On the following page, general
equations are presented to calculate the moment and forces in the Tower from wind
(figure 5). Also, an example is provided for the moment calculation at the Second
Platform (figure 6).