Stress concentration due to four-point fixing at front end of monocoque fuselage, theoretical analysis

Abstract

This report is a sequel to previous work by Williams, Starkey and Taylor (R. & M. 2098) and by Williams and Fine (R. & M. 2099) and treats the problem of the stress distribution in a stringer-reinforced cylindrical shell (representing a modern monocoque fuselage) under transverse loads when the reactions at the supported end are provided by four fixing points. It is assumed that these reactions are transmitted to the shell through four heavylongitudinal members, or longerons, and the purpose of the report is to discuss the manner in which the load in these members is passed on via the skin to the adjacent stringers. Two cases are considered. In the first the longerons are assumed to be of constant cross- section and to extend from end at end of the shell. In the second the longerons are tapered from the root outwards in such a way as to maintain a constant stress. Appendices I and III of the report treat the problems with some rigour and the solutions obtained are made the bases of quick approximate methods that can be applied with facilfty to any practical case. The results obtained by the approximate methods agree very satisfactorily with those derived by the far longer basic method. From working out typical cases it is inferred that for the end-to-end constant-section longerons the disturbance due to the four-point fixing does not extend a greater distance from the root fixing than ½ to ¾ of the average root diameter, this distance being greater the greater the value of the ratio of total stringer area to total skin area in the cross-section. It is found that the constant-stress longeron tapers very quickly and appears to offer a good practical basis for design. The most important stress concentration in both cases is the shear stress in the skin immediately adjacent to the longerons at their root ends, and reinforcement of the skin thickness in this region is probably essential in all practical cases, especially for the constant stress longeron. The extent of this stress concentration is indicated by certain contour diagrams of stress distribution included in this report.