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H.A. Mang, F. Trappel:
"Physically Linear Buckling Analysis of Reinforced Concrete Cooling Towers - Design Necessity or Academic Exercise?";
in: "Proceedings of the 2nd International Symposium on Natural-Draught Cooling Towers", Springer, Berlin-Heidelberg-New York-Tokyo, 1984, 279 - 297.

The theoretical part of hte paper contains the fundamentals of physically and geometrically nonlinear analysis of thin shells by the finite element method including determination of instability points on the load-displacement path. The numerical investigation consists of a comparison of crack and ultimate load of two different reinforced conrete cooling towers, subjected to dead load and quasistatic wind load, with buckling loads resulting from three different modes of physically linar buckling analysis. With regards to the first cooling tower, three different idealizations of the crown of the shell are taken into account. It is shown that for both shells the ultimate load is considerably smaller than the smallest of the buckling loads obtained from the three modes of physically linear buckling analysis. It is concluded that the latter, although important in its own right as an academic exercise, is not a design necessity. Moreover, it is demonstrated that the crack load, representing a lower bound to the ultimate load, can be estimated through linear extrapolation from linear elastic strength analysis. both shells the ultimate load is