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Seminário do INCT/NAP/GFCx : "Mathematical Models for the Shape of the Eiffel Tower: Historical Perspective and New Results"

3ª. FEIRA – 11/11/2014

Seminário do INCT/NAP/GFCx

Ed. Principal do IFUSP, Auditório Sul, às 16:15h.


Mathematical Models for the Shape of the Eiffel Tower:

Historical Perspective and New Results


P. D. Weidman

Department of Mechanical Engineering

University of Colorado, Boulder CO



Equations modeling the shape of the Eiffel Tower are investigated. One model,

based on equilibrium of moments, gives the wrong tower curvature. A second

model, based on constancy of vertical axial stress, does provide a fair ap-

proximation to the tower’s skyline profile of twenty-nine contiguous panels.

However, neither model can be traced back to Eiffel’s writings. Reported here

is a new model embodying Eiffel’s concern for wind loads on the tower, as

documented in his communication to the French Civil Engineering Society on

March 30, 1885. The result is a nonlinear, integro-differential equation which

may be solved to yield an exponential profile. An analysis of actual panel

coordinates reveals a profile closely approximated by two piecewise continuous

exponentials with different growth rates. This is explained by specific safety

factors for wind loading that Eiffel & Company incorporated in the design and

construction of the free-standing tower.