Stress is average force per unit area which results strain of material. The unit of stress is N/mm2 (MPa). Strain is any forced dimension change of a material and strain is a dimensionless quantity. Stress and strain formulas for a bar under axial loading are given in the following table.

Parameter/Condition Symbol Formula
Tensile Stress σ σT = P/A
Normal Stress in any Oblique Section σθ σθ = (P/A)*cos2θ
Shear Stress in any Oblique Section τθ τθ = (P/2A)*sin2θ
Longitudinal Strain ε ε = σ/E
Longitudinal Deflection δ δ = (Pl)/(AE)
Lateral Strain ε' ε' = -νε
Lateral Deflection δ' δ' = ε'd

Stress and Strain Calculator has been developed to calculate tensile stress (or compressive stress), normal/shear stress on any oblique section of the bar, longitudinal/lateral strain, longitudinal/lateral deflection and total strain energy according to stress and strain formulas given above.

If a straight bar, of any cross section, of homogeneous material, is axially loaded , the bar elongates under tension and shortens under compression. On any right section to the load, there is a uniform tensile (or compressive) stress. On any oblique section, there is a uniform tensile (or compressive) normal stress and a uniform shear stress.

Basic assumptions for the Stress and Strain Calculator are:

- The loads are applied at the center of ends,

- Uniform stress distribution is occured at any section of the bar,

- The bar is constrained against buckling,

 - The stress does not exceed the proportional limit.


Tensile Stress in a Bar
Parameter Symbol Value Unit
Applied Load
Cross-sectional Area
(before loading)
Length (before loading) l
Lateral Dimension d
Elastic Modulus E
Poisson's Ratio ν ---
Angle θ deg

Parameter Symbol Value Unit
Tensile Stress σ ---
Normal Stress in any Oblique Plane σθ ---
Shear Stress in any Oblique Plane τθ ---
Longitudinal Strain ε --- ---
Lateral Strain ε' ---
Longitudinal Deflection δ --- ---
Lateral Deflection δ' ---
Total Strain Enegy U ---

Note: Use dot "." as decimal separator.
Note: Negative stresses are compression stresses.



Link Usage
Material Properties Thermal expansion coefficient and elastic modulus values of steels, aluminum alloys, cast irons, coppers and titaniums.