2010

by an uniaxial stress test, then the real stress system is related by combining
the six stress components to a single equivalent stress.
Maximum and Minimum Principal Stresses
According to elasticity theory, an infinitesimal volume of material at an
arbitrary point on or inside the solid body can be rotated such that only normal
stresses remain and all shear stresses are zero. When the normal vector of a
surface and the stress vector acting on that surface are collinear, the direction
of the normal vector is called principal stress direction. The magnitude of the
stress vector on the surface is called the principal stress value.
Deformation
Deformation is the amount of stretching that an object undergoes due to the
loading. Use the deformation results to determine where and how much a
part will bend, and how much force is required to make it bend a particular
distance.
Safety Factor
All objects have a stress limit depending on the material used, which are
presented as material yield or ultimate strengths. If steel has a yield limit of
40,000 psi, any stresses above this limit result in some form of permanent
deformation. If a design is not supposed to deform permanently by going
beyond yield (most cases), then the maximum allowable stress in this case is
40,000 psi.
A factor of safety can be calculated as the ratio of the maximum allowable
stress to the equivalent stress (von-Mises), when using Yield Strength, and
must be over 1 for the design to be acceptable. (Less than 1 means there is
some permanent deformation.) When using Ultimate Strength, Maximum
Principal stress is used to determine safety factor ratios.
Factor of safety results immediately points out areas of potential yield, where
equivalent stress results always show red in the highest area of stress, regardless
of how high or low the value. Since a factor of safety of 1 means the material
is essentially at yield, most designers strive for a safety factor of between 2 to
4 based on the highest expected load scenario. Unless the maximum expected
load is frequently repeated, the fact that some areas of the design go into yield
does not always mean the part will fail. Repeated high load may result in a
10 | Chapter 1 Get Started With Stress Analysis