Construction of the Eiffel Tower

As once said by Eiffel, the Eiffel tower was built in order to withstand the high winds that were present in France:

“What phenomenon did I have to give primary concern in designing the Tower? It was wind resistance. Well, I hold that the curvature of the monument’s four outer edges, which is as the mathematical calculations have dictated it should be, will give a great impression of strength and beauty.”

As demonstrated by the illustration below, the forces of wind produce a torque that around the bottom left of the Eiffel Tower are countered by its weight.

The force of the wind (dF) produces a torque around the bottom left corner of the tower which is countered by the force of the Tower’s weight (dW) [1]

From a mathematical standpoint, the equation for the tower is [1] :

 where  is the half-width of the Tower at height ,  is the half-width of the Tower at the ground and  is the maximum wind pressure the Tower can withstand at a height .

(This is a root of the quadratic equation describing a parabola resting against the right side of the Tower, so the curve of the Tower’s right side is described by the negative arm of the parabola.)

The fastest winds recorded at the Tower reached a speed of 214 km/h in 1999 and would have produced pressures of just 2.28 kN/m^2.

In conclusion, the Eiffel tower was constructed in a manner to be sure that the wind did not affect it. After all, it was the tallest tower in the world for a long time (~42 years). [2]

The Eiffel tower, notes Weidman, “is a structural form molded by the wind.” This was Eiffel’s point more than a century ago, when he wrote about the four stout legs supporting the legendary tower: “Before they meet at such an impressive height, the uprights appear to spring out of the ground, moulded in a way by the action of the wind itself.”

Hope this helps!

Sources:

[1]: Elegant Shape Of Eiffel Tower Solved Mathematically By University Of Colorado Professor
[2]:http://plus.maths.org/content/sh…