chapter  21
8 Pages

## V

Complete proof of these relations may be found in [2] and [4] for the case with no axial load and in [5] and [6] for other cases. The first definition of S applies to a shell with internal pressure and external stiffeners. The second one applies for external pressure and internal stiffeners. As previously explained, absolute values of efficiencies are independant from pressure’s direction. Unfortunately, two definitions for S arise from some unsymetry of the yield polygon (Tresca) for the web of the stiffener. Of course the presented interaction is always related to a failure with a plastic mechanism excluding elastic or elastoplastic instability. For a stiffener with rectangular cross section, one has simply to let p i = 0. Efficiencies have to be calculated from choosen plastic profiles for shell and flange of the stiffener. Calculations of p& are depending from the selected value of axial strength modifying the yield polygon of the shell. Calculations of p i are much more simple and may be found in [8] or [2], p i being an one parameter function depending only from af. In a first approximation, a f may be taken equal to 1 for current stiffeners. Preceeding relations show obviously the dependance of the limit pressure versus the shell geometry and the strength param eter S for the stiffener. Definitions of S permit a very good physical interpretation of the geometrical param eters of the stiffener. With pi = 1 and ri — rs < < rSf S may be writed under approximate forms, showing the influence of the area of the stiffener.:

S=^ 2 h { a(rs~n) + 2lt!} S = - (6)2 L t I ' * 7s For internal pressure some small reduction in the efficiency of the aera of the stiffened flange is

seen. Generalization of definition of S may be obtained for a I stiffener (external and internal flange) and a sandwich shell [2], [7].