Axial Stress, which is also called compressive or tensile stress, is a measure of the axial force acting on a beam.
It is a quantitatively measuring the internal forces acting within in the beam.
The equation used to describe the normal stress is in the bar pictured below is:
Here σ represents stress, P represents the internal force at cross sectional area A. Stress is represented in either psi/ksi: pounds per square inch, kips (kilo-pounds) per square inch, or in SI by Pa: Pascals, which are equivalent to Newtons per meter squared. For a further breakdown of the equation into its visual pieces see the image below.
Compressive stress means the member is in compression (being smashed) vs. tensile stress which means the beam is in tension (being pulled apart). The sign convention is to call compression positive and tensile stress negative.
To see more information on axial stress and solved problems see this online mechanics book, Chapter 1
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