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The bifurcation strength of open cylindrical shells with torsionally very stiff edge stiffeners of rectangular cross section subject to uniform axial load is determined analytically using Donnell's simplified equations. A deflection function with arbitrary undetermined coefficients satisfying the end conditions is assumed. The stress resultants are derived in terms of these coefficients. These stress resultants and the deflections of the shell are made to satisfy the assumed boundary conditions along the longitudinal edges. The resulting determinant of the equations is set equal to zero in order to obtain the critical buckling stress. The limited results obtained in this paper indicates an interesting phenomena that the critical buckling stress of a shell with a shallow edge stiffener is well above the critical buckling stress of a shell with free edges, whereas the buckling of a shell with moderate depth edge stiffeners in a narrow region is only slightly above the critical buckling stress of a shell with free edges.

Simplified formulas are developed not only for reducing computing time but also for improving accuracy; closed-form solutions are obtained for certain series forms that converge very slowly; reciprocal relationships between moments at one point and load at other points are carefully examined; method of integrating moment curves is given and example of application of orthotropic plate theory to bridge design is shown.

The buckling of cylindrical shells with free longitudinal edges subjected to uniform axial compression is examined. The solutions are based on the simplified elastic equations of the small deflection theory known as the Donnell's equations. Results obtained were presented in a number of charts. It was found that in the practical range of thin shell structures, the critical buckling stress of a cylindrical shell may be 1/10, 1/100, or 1/1000 of the buckling value of a corresponding cylindrical tube with the same radius, R , thickness, t , and length L , as the ratio of t/R decreases and the ratio of L/R increases. Although the small deflection theory may give buckling stresses higher than the actual buckling values, it will serve the purpose of establishing the upper bounds of the buckling loads. The study of shells with free longitudinal edges and subjected to uniform axial compression may be regarded as an initial step for studying shell roofs with edge beams and subjected to longitudinal membrane stresses varying from compression to tension.