This report covers Parts I and II of the data resulting from an investigation of structural members subjected to combined axial and transverse loads. It contains the theoretical portion of the development of the United States Army Air Service formulas and includes tables of functions which greatly facilitate the use of these formulas. Studies are now being made as to the agreement of the deflections computed by the use of these formulas with the deflections actually obtained by tests made on experimental struts and trusses, it being considered that a satisfactory check on the dependability of the formulas can be obtained in this way. When these studies, which have now been carried far enough to indicate that the formulas are reliable, are completed, Section II of this report will be issued. The reason for publishing this report in two sections is to furnish the airplane industry immediately with a more complete set of data on the development and use of the precise formulas than is now available. This section is self-contained in that it includes all information necessary to the intelligent use of the precise formulas in the design of airplane structures. The purpose of this investigation, the results of which are given in this report, was to obtain a satisfactory method of computing the stresses in such members of an airplane structure as are subjected to combined axial and transverse loads. The investigation was initiated for the purpose of making a comparative study of a number of approximate methods for the design of members, under combined loads to ascertain their relative degrees of conservatism and ease of application. Several approximate methods were studied and applied to a specific problem for purposes of comparison. A full discussion of the methods and results obtained will be found in Part I of this report.