Page 41 - Shigley's Mechanical Engineering Design

bud29281_ch01_002-030.qxd 11/11/2009 5:35 pm Page 16 pinnacle s-171:Desktop Folder:Temp Work:Don't Delete (Jobs):MHDQ196/Budynas:

16 Mechanical Engineering Design
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 par-
ticular 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, S y is a yield strength, S u an ultimate
strength, S sy a shear yield strength, and S e an endurance strength.
In accordance with accepted engineering practice, we shall employ the Greek let-
ters σ(sigma) and τ(tau) to designate normal and shear stresses, respectively. Again,
various subscripts will indicate some special characteristic. For example, σ 1 is a princi-
pal normal stress, σ y a normal stress component in the y direction, and σ r a normal 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. A review of stress analy-
sis for basic load states and geometry is given in Chap. 3.

1–10 Uncertainty
Uncertainties in machinery design abound. Examples of uncertainties concerning stress
and strength include
• Composition of material and the effect of variation on properties.
• Variations in properties from place to place within a bar of stock.
• Effect of processing locally, or nearby, on properties.
• Effect of nearby assemblies such as weldments and shrink fits on stress conditions.
• Effect of thermomechanical treatment on properties.
• Intensity and distribution of loading.
• Validity of mathematical models used to represent reality.
• Intensity of stress concentrations.
• Influence of time on strength and geometry.
• Effect of corrosion.
• Effect of wear.
• Uncertainty as to the length of any list of uncertainties.
Engineers must accommodate uncertainty. Uncertainty always accompanies change.
Material properties, load variability, fabrication fidelity, and validity of mathematical
models are among concerns to designers.
There are mathematical methods to address uncertainties. The primary techniques
are the deterministic and stochastic methods. The deterministic method establishes a
design factor based on the absolute uncertainties of a loss-of-function parameter and a