Statics Of A Brunelleschilike Dome

Let us define a Brunelleschi-like dome as an octagonal dome, formed by ribbed cylindrical webs, intersecting along circles, inclined 67,5" with respect to the cylinder axis. The surface of this dome is represented by equation (32).

Let us consider the statics of this dome. Timoshenko (1959) and Heyman (1977) consider the statics of cylindrical shells according to the membrane theory.

According to Filippo's specifications, Chapter 1, this assumption could be hazardous for a practical application: this is only one way of understanding the main static aspects of this dome. In the FEM analysis the correct thickness has been used.

With reference to Figure 9 and to the well known symbols of shell structures, the equilibrium equations are the following:

Figure 9. Equilibrium of a cylinder surface with the lines of curvature. q is the vertical force for unit area.

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