From Cam Design and Manufacturing Handbook


The general state of stress and strain is three-dimensional but there exist particular geometric configurations that can be treated differently.

Plane Stress

The two-dimensional, or biaxial, stress state is also called plane stress. Plane stress requires that one principal stress be zero. This condition is common in some applications. For example, a thin plate or shell may also have a state of plane stress away from its boundaries or points of attachment. These cases can be treated with the simpler approach of equations 12.7.

Plane Strain

There are principal strains associated with the principal stresses. If one of the principal strains (say ? 3) is zero, and if the remaining strains are independent of the dimension along its principal axis, n 3, it is called plane strain. This condition occurs in particular geometries. For example, if a long, solid, prismatic bar is loaded only in the transverse direction, regions within the bar that are distant from any end constraints will see essentially zero strain in the direction along the axis of the bar and be in plane strain. (However, the stress is not zero in the zero-strain direction.) A long, hydraulic dam can be considered to have a plane strain condition in regions well removed from its ends or base at which it is attached to surrounding structures.

Example 12-1: Determining 3-D Principal Stresses Using Analytical Methods.


A triaxial stress element as shown in Figure 12-7 (p. 346) has

Products & Services
Accelerometers are instruments for measuring, displaying, and analyzing acceleration and vibration.
Strain Gauges
Strain gauges are measuring elements that convert force, pressure, tension, etc., into an electrical signal.
Deflectometers and Extensometers
Deflectometers and extensometers are used to indicate the deformation of material while it is subjected to stress.
Waveplates and Retardation Plates
Waveplates and retardation plates are optical elements with two principal axes, one slow and one fast, which resolve an incident polarized beam into two mutually perpendicular polarized beams. The emerging beam recombines to form
Linear Polarizers
Linear polarizers transmit light waves along one axis and absorb them along the other. The transmitting and absorbing axes of linear polarization are oriented at 90 degrees to each other.

Topics of Interest

12.10 APPLIED VERSUS PRINCIPAL STRESSES We now want to summarize the differences between the stresses applied to an element and the principal stresses that may occur on other planes as a result of...

6.2 Contact of Rigid-Perfectly-Plastic Solids When the plastic deformation is severe so that the plastic strains are large compared with the elastic strains, the elastic deformation may be neglected.

4.1 Basic Equations In the analysis of fiber-reinforced composite materials, the assumption of plane stress is usually used for each layer (lamina). This is mainly because fiber-reinforced materials...

Tired of fatigue failures? Analyses that consider several loads produce more accurate results. An automotive steering knuckle is one component that frequently carries loads from several directions,...

Joseph E. Shigley Professor Emeritus The University of Michigan Ann Arbor, Michigan 36.1 DEFINITIONS AND NOTATION The general two-dimensional stress element in Fig. 36.1a shows two normal stresses ?...