Maximum Fiber Stress Research Articles

The Stresses Developed in Sections Subjected to Bending Moment

It is a well known fact that the (simple) Engineers’ Theory of Bending is based on the assumption of the Law of Proportionality, that is to say that the stress-strain characteristic of the material concerned is a straight line, and it accordingly follows that stress values determined by the formulæ: , for the stress at any station on the section, and M/Z for the maximum fibre stress can be correct only when the M/Z value lies within the limit of proportionality of the material.

Stresses in Helical Compression Springs—Present Status of the Problem

Abstract Since Dr. Röver, in 1913, first formulated the modern theory of the stress distribution in a helical spring, including the effect of bar curvature, pitch angle, direct-shear stress, etc., a number of investigators have treated the problem. Wahl, Göhner, Adams, Vogt, Perkins, and Keysor have all presented interesting analyses. Most of these vary somewhat in the detailed method of treatment, but they all arrive at substantially the same result, in terms of the maximum fiber stress in the section. Wahl, in a notable series of experiments, demonstrated that these maximum stresses postulated by the theory are actually present in the spring. Thus it would appear that we have a satisfactory working theory. But practical spring men feel that there must be something wrong; the theory, when applied to certain standard spring designs with very satisfactory service records, predict stresses which seem far too high to be compatible with good endurance in service. This feeling is supported by the results of a few endurance tests, which indicate rather clearly that the maximum stresses predicted by the theory, though undoubtedly present, do not correctly index the actual endurance. In the author’s opinion, all the evidence points to the conclusion that the problem of design stresses in helical springs is not one for the mathematician, but must be worked out in the laboratories, by actual experiment.

A Theory of Flexure for Beams With Nonparallel Extreme Fibers

Abstract A theory of flexure for beams with nonparallel extreme fibers is presented. The theory is shown to reduce to the ordinary theory of flexure as the angle between the extreme fibers approaches zero. Maximum fiber stresses computed by the theory and by the ordinary theory for a plate girder with nonparallel flanges show that for angles between the flanges up to twenty degrees the ordinary theory can never be in error more than about five per cent, but for larger angles the error in general increases rapidly with the angle. Finally an example is given of the application of the theory as an approximation to a beam with curved extreme fibers. In this case the theory was confirmed by the results of tests.

Phosphor-Bronze Helical Springs From the Standpoint of Precision Instruments

Abstract This paper gives the results of tests made on phosphor-bronze helical springs investigated at the Bureau of Standards to obtain knowledge useful in the design of springs for precision instruments. The characteristics of the spring material, the method of construction of the springs, the apparatus in which the springs were tested and the procedure followed are set forth by the author. The results relate to stiffness, maximum fiber stress, hysteresis, after-effect, drift, and buckling.

The Transverse Strength of Beams as a Direct Function of the Tensile and Crushing Stresses of Material

The theory of the transverse strength of beams of any shape is based on the assumption that the intensity of fiber resistances is directly proportional to the respective distances of the fibers from an axis called neutral, and that the sum of all the fiber stresses above the axis is equal to the sum of those below. Hence the neutral axis must pass through the center of gravity of the beam section, and, as a consequence, the maximum fiber stress in beams of unsymmetrical section is at those extreme fibers which are most distant from the neutral axis. A further consequence of this theory is that no matter what may be the material and section of the beam, its transverse strength in regard to the neutral axis is the same, whether the extreme fibers parallel to this axis are subjected to the one or to the opposite kind of forces.