Effective Breadth Problems by an Eigenfunction Approach

Abstract

The problem of effective breadth of a stiffened panel with two different edge or support conditions, namely (i) stres -free ed es and (ii) displacement restrained edges, has been solved for the first time, in this paper, by the e.• enfunctoon approach o the end problem of semi-infinite strips. It is shown that these two edge condollens lead to complex eogenvalue problems and thus the plane-stress problem of the plating cannot be solved by the classical methods which have been hitherto successfully used to obtain the estimates of effective breadths for the two other possible mixed edge conditions, namely, (i) vanishing direct stress and tangential displacement and (ii) vanishing normal displacement and shear stress. It is brought out that this end eigenlunetion formulation, using a generalized orthogonality of Papkovich, provides a general analytical framewerk for the stress field problems of stiffened panels in bending. Numerical results are presented for the first problem nly. The two classical problems have been revisited from this viewpoint, and certain well-known effectove breadth results have been rederived and compared. An alternative form of the generalized orthogonality relation, which offers a certain analytical advantage, has been used and the exostence of such a form is proved for all four edge conditions.