Combined stresses

In the direct design procedure the assumption is made that no abrupt changes occur in cross-section, discontinuities in the surface, or holes through the member. This is not the case in most structural parts. The stresses produced at these discontinuities are different in magnitude from those calculated by various design methods. The effect of the localized increase in stress, such as that caused by a notch, fillet, hole, or similar stress raiser, depends mainly on the type of loading, the geometry of the product, and the material. As a result, it is necessary to consider a stress-concentration factor. In general it will have to be determined by the methods of experimental stress analysis or the theory of elasticity, and by a simple theory without taking into account the variations in stress conditions caused by geometrical discontinuities such as holes, grooves, and fillets. For ductile materials it is not customary to apply stress-concentration factors to members under static loading. For brittle materials, however, stress concentration is serious and should be considered.

There are conditions of loading a product that is subjected to a combination of tensile, compressive, and/or shear stresses. For example, a shaft that is simultaneously bent and twisted is subjected to combined stresses, namely, longitudinal tension and compression, and torsional shear. For the purposes of analysis it is convenient to reduce such systems of combined stresses to a basic system of stress coordinates known as principal stresses. These stresses act on axes that differ in general from the axes along which the applied stresses are acting and represent the maximum and minimum values of the normal stresses for the particular point considered. There are different theories that relate to these stresses. They include Mohr's Circle, Rankine's, Saint Venant, Guest, Hencky-Von Mises, and Strain-Energy.

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