About Axial Stress
Axial stress (σ) is the force per unit area acting perpendicular to the cross-section of a member. It's calculated using σ = F/A, where F is the applied force and A is the cross-sectional area.
More Information
What is Stress?
Stress is the internal resistance or reaction of a material to external forces. It is measured as force per unit area and is a critical factor in determining whether a component will deform or fail under given loading conditions.
The total stress at a point often includes multiple components acting in different directions. Understanding these components and their interactions is essential for proper engineering design.
Axial Stress
Force acting perpendicular to a cross-section:
Where:
- F = applied force
- A = cross-sectional area
Shear Stress
Force acting parallel to a cross-section:
Where:
- F = applied force
- A = area of the shear surface
Bending Stress
Stress due to bending moments:
Where:
- M = bending moment
- y = distance from neutral axis
- I = moment of inertia
Torsional Stress
Stress due to twisting moments:
Where:
- T = applied torque
- r = radius from center
- J = polar moment of inertia
Von Mises Stress
Combines stresses for failure prediction:
Where:
- σₓ = normal stress in x-direction
- σᵧ = normal stress in y-direction
- τₓᵧ = shear stress in xy-plane
Failure Theories
Several theories predict material failure:
- Maximum Normal Stress Theory
- Maximum Shear Stress (Tresca)
- Distortion Energy (von Mises)
- Mohr's Theory
- Coulomb-Mohr Theory
Most common criterion:
Where SF = safety factor, σₑ = yield strength, σᵢ = induced stress
Safety Considerations
The safety factor is the ratio of the material's yield strength to the calculated stress. Generally:
- SF < 1: Failure is likely to occur
- SF = 1-1.5: Marginal safety, suitable for well-controlled conditions
- SF = 1.5-2: Typical for well-understood static loads
- SF = 2-3: Used for average conditions with some uncertainties
- SF > 3: Used for uncertain loading conditions or critical applications
Important Notes
- Stress units are typically in Pascal (Pa) or its multiples (MPa, GPa).
- Stress analysis assumes linear-elastic behavior for most calculations.
- Cross-sectional properties significantly influence stress distribution.
- Temperature changes can introduce thermal stresses.
- Stress concentrations occur at geometric discontinuities (holes, fillets, etc.).
- Fatigue failure can occur at stress levels below the material's yield strength when subjected to cyclic loading.