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Product design CHAPTER 11.2 Fig. 11.2.9 Round bar subject to torsion stress, the straight-line ab becomes the helix ad, and a radial line in the cross section, ob, moves to the position ad. The angle bad remains constant while the angle bod in- creases with the length of the bar. Each cross section of the bar tends to shear off the one adjacent to it, and in any cross section the shearing stress at any point is normal to a radial line drawn through the point. Within the shearing proportional limit, a radial line of the cross section remains straight after the twisting force has been applied, and the unit shearing stress at any point is pro- portional to its distance from the axis. The twisting moment, T, is equal to the product of the their distances from the axis. Thus in a rectangular bar there is no shearing stress at the comers of the sections, and the stress at the middle of the wide side is greater than at the middle of the narrow side. In an elliptical bar the shearing stress is greater along the flat side than at the round side. It has been found by tests as well as by mathematical analysis that the torsional resistance of a section, made up of a number of rectangular parts, is approximately equal to the sum of the resistances of the separate parts. It is on this basis that nearly all the formulas for noncircular sections have been developed. For example, the torsional resistance of an I-beam is approximately equal to the sum of the torsional resistances of the web and the out- standing flanges. In an I-beam in torsion the maximum shearing stress will occur at the middle of the side of the web, except where the flanges are thicker than the web, and then the maximum stress will be at the midpoint of the width of the flange. Reentrant angles, as those in l-beams and channels, are always a source of weakness in members subjected to torsion. The ultimate/failure strength in torsion, the outer fibers of a section are the first to shear, and the rupture extends towards the axis as the twisting is continued.