Stress notation

Vector and Tensors

Vector quantities are those, which requires only one magnitude and only one direction for its complete definition. Whereas tensors quantities require more than one directions for their definition. Stresses are tensor quantities. For its complete definition, it requires two directions:
  • The direction of the plane on which they act.
  • The direction along which they act.

The direction of the plane

The direction of the plane is defined by the direction of its outward normal. A plane is considered as positive if the direction of its outward normal is along the positive direction of the coordinate axis. Otherwise, it is considered as a negative plane. In the figure shown below, the outward normal to the plane ABCD is along the positive x – axis. Hence, ABCD is a positive plane. Whereas the outward normal to the plane EFGH is along the negative x axis. Hence, EFGH is a negative plane. Similarly, CDHG is a positive plane (since its outward normal is long the positive y – axis) and ABFE is a negative plane (since its outward normal is along the negative y – axis)

Stress notation


Sign convention

The stresses are tensor quantities that require two directions for its complete specification.
  1. The direction of the plane on which they act.
  2. The direction along which they act.
The sign of the stress component depends on the signs of these two directions. If both the directions are same (i.e., both positive or both negative) then the stress component is considered as positive stress. On the other hand, if the directions are different (i.e., if one is positive and another is negative) then the stress component is considered as a negative stress. A positive normal stress produces tension and a negative normal stress produces compression in the body.

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