Stress and Strength

The survival of many products depends on how the designer adjusts the maximum

stresses in a component to be less than the component’s strength at specific locations of interest. The designer must allow the maximum stress to be less than the strength by a sufficient margin so that despite the uncertainties, failure is rare.

In focusing on the stress-strength comparison at a critical (controlling) location, we often look for “strength in the geometry and condition of use.” Strengths are the

magnitudes of stresses at which something of interest occurs, such as the proportional

limit, 0.2 percent-offset yielding, or fracture. In many cases, such events represent the stress level at which loss of function occurs.

Strength is a property of a material or of a mechanical element. The strength of an element depends on the choice, the treatment, and the processing of the material.

Consider, for example, a shipment of springs. We can associate a strength with a specific spring. When this spring is incorporated into a machine, external forces are applied that result in load-induced stresses in the spring, the magnitudes of which depend on its geometry and are independent of the material and its  processing. If the spring is removed from the machine unharmed, the stress due to the external forces will return to zero. But the strength remains as one of the properties of the spring. Remember, then, that strength is an inherent property of a part, a property built into the part because of the use of a particular material and process.

Various metalworking and heat-treating processes, such as forging, rolling, and cold forming, cause variations in the strength from point to point throughout a part. The spring cited above is quite likely to have a strength on the outside of the coils different from its strength on the inside because the spring has been formed by a cold winding process, and the two sides may not have been deformed by the same amount.

Remember, too, therefore, that a strength value given for a part may apply to only a particular point or set of points on the part. In this book we shall use the capital letter S to denote strength, with appropriate subscripts to denote the type of strength. Thus, Ss is a shear strength, Sy a yield strength, and Su an ultimate strength.

In accordance with accepted engineering practice, we shall employ the Greek letters ó (sigma) and ô (tau) to designate normal and shear stresses, respectively. Again, various subscripts will indicate some special  characteristic. For example, ó1 is a principal stress, óy a stress component in the y direction, and ór a stress component in the radial direction.

Stress is a state property at a specific point within a body, which is a function of load, geometry, temperature, and manufacturing processing. In an elementary course in mechanics of materials, stress related to load and geometry is emphasized with some discussion of thermal stresses. However, stresses due to heat treatments, molding, assembly, etc. are also important and are sometimes neglected.

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Mechanical Engineering

McGraw−Hill Primis

ISBN: 0−390−76487−6

Text:

Shigley’s Mechanical Engineering Design,

Eighth Edition

Budynas−Nisbett

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