The growing demand for aerodynamically advantageous forms, for smooth surfaces, and last but not least for a better ratio of useful cross section to total cross section of fuselages lead to an increasing application of monocoque structures in aircraft construction. Unlike ordinary beams the behaviour of such thin walled structures under loads and their ultimate failure is influenced a great deal by instability phenomena. In the present paper these problems are dealt with in some detail for the case of pure bending.

It is known from both theoretical and experimental investigations that St. Venant's assumption on the constancy of the shape of the cross section of girders in pure bending does not hold true in case of thin-walled sections. The greater flexibility than calculated according to ordinary bending theory of initially curved tubes, as experimentally found by Professor Bantlin, was perfectly explained by Professor von Kármán in 1911 on the assumption of a flattening of the section.

In 1927 Brazier with the aid of the variational method determined exactly that the shape of an originally circular thin-walled bent cylinder corresponding to the least potential energy is quasi elliptical and that the cross section of the cylinder, therefore, must flatten, even if the centre line of the cylinder was originally straight. In consequence of the flattening St. Venant's linear law for the curvature loses its validity and the curvature increases more rapidly than the bending moment. For a certain value of the curvature the bending moment is a maximum, and after this value was reached the curvature increases even if the applied moment remains unchanged or decreases, fulfilling thereby the criterion of instability. This instability occurs when the rate of flattening, i.e., the maximum radial displacement of any point of the circumference of the tube divided by the original radius of the tube, will equal 2/9.

In case of normal monocoque aeroplane fuselages relatively strong rings are spaced at distances equal to diameter of the fuselage, failure of the structure always occurs by instability of the most stressed stringer. The buckling stress, however, is mostly very low, especially, when the number of stringers is great and consequently the cross section of one stringer is small. The value of the stress at failure may be raised by spacing the rings nearer and reducing thereby the free length and, consequently, the slenderness ratio of the stringers. In this case the rings should be constructed of lighter sections in order to balance the increment of weight of the whole structure due to the greater number of rings.

By decreasing gradually the interval between rings a critical distance is reached when the most stressed stringer does not buckle between adjacent rings, but forces one or more supporting rings to deform simultaneously. This form of instability will in the following be termed local buckling of the monocoque structure.

With the aim to get a rough check on the theoretical results obtained in the body of the present paper concerning shape and magnitude of distortions and magnitude of stresses corresponding to the stable and instable forms of deformations of a cylindrical monocoque structure in bending, an experimental girder has been constructed and tested.

In the present paper two forms of instability of monocoque structures in pure bending have been discussed in extenso, viz., the flattening and the local buckling. For ease of calculation it is assumed that the structure is cylindrical, of circular cross section and consisting of a great number of evenly spaced uniform longitudinal stiffeners, denoted stringers and of several evenly spaced uniform transverse stiffeners, called rings. The applicability of the results obtained to practical fuselages of non-circular cross section and the effect of different neglections have been dealt with in §§15 and 20.

I.—Preliminary to the discussion of the above problems, the results obtained by different authors concerning both the load carrying capacity of panels after buckling and the failure of stringers have been collected in Part I.