MAXIMUM NORMAL STRESSES:
PRINCIPAL STRESSES
The combination of the applied normal and shear stresses that produces the maximum normal stress is called the maximum principal stress, σ1. The magnitude of σ1 can be computed from the following equation:
Eq. 4-1. Maximum Principal Stress
The combination of the applied stresses that produces the minimum normal stress is called the minimum principal stress, σ2. Its magnitude can be computed from
Eq. 4-2. Minimum Principal Stress
Particularly in experimental stress analysis, it is important to know the orientation of the principal stresses. The angle of inclination of the planes on which the principal stresses act, called the principal planes, can be found from
Eq. 4-3. Angle for Principal Stress Element
The angle ϕσ is measured from the positive x-axis of the original stress element to the maximum principal stress, σ1. Then, the minimum principal stress, σ2, is on the plane 90° from σ1.
When the stress element is oriented as discussed so that the principal stresses are acting on it, the shear stress is zero. The resulting stress element is shown in Figure 4-4.
FIGURE 4-4
Principal stress element
