Seminário do INCT/NAP/GFCx
3ª. FEIRA 11/11/2014 - 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
Abstract
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 towers skyline profile of twenty-nine contiguous panels.
However, neither model can be traced back to Eiffels writings. Reported here
is a new model embodying Eiffels 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.
