Deflection of Beams with Special Reference to Shear Deformations. The Influence of the Form of a Wooden Beam on Its Stiffness and Strength.

摘要

This publication is one of a series of three reports prepared by the Forest Products Laboratory of the Department of Agriculture for publication by the National Advisory Committee for Aeronautics. The purpose of these papers is to make known the results of tests to determine the properties of wing beams of standard and proposed sections, as conducted by the Forest Products Laboratory and financed by the Army and the Navy. Many of the mathematical operations employed in airplane design are nothing more than the solution of equations which are either empirical or are based on assumptions which are known to be inaccurate, but which have been adopted because of their simplicity. These inaccuracies of the formulas were not of primary consideration as long as the stresses used for design were obtained by the test of specimens of the same form as those to be used, and great refinement was not necessary. The advent of the airplane and the impetus given to its development by the recent war has created a demand for more definite knowledge of the limitations and proper application of the common theory of flexure. There is probably no other field in which greater refinement in the design of wooden members is required than in that of aircraft construction. The ever-present problem of weight reduction has led to the use of comparatively small load factors and the introduction of such shapes as are not commonly used for other construction purposes. Formulas which give comparable results when applied to wooden beams of rectangular section have been found to be considerably in error when applied to wooden beams of other shapes. The tests were made at Madison, Wis., in cooperation with the University of Wisconsin. An analysis of the results of these tests has furnished information which, when correlated with that from other studies conducted by the Forest Service for the past 18 years, provided a more exact method of computing the stiffness of wood beams and led to the development of formulas for estimating the strength of beams of any cross section, using the properties of small rectangular beams as a guide. For convenience, the report of this investigation has been divided into three parts. The first part deals with the deflection of beams with special reference to shear deformation, which usually has been neglected in computing deflections of wood beams. The second part has to do with stresses in beams subjected to transverse loading only, with a subdivision on nonsymmetrical sections; and the third part, with stresses in beams subjected to both longitudinal thrust and bending stresses.