STRESS AND STRAIN FORMULAS WITH CALCULATOR
Stress is average force per unit area which results strain of material. The unit of stress is N/mm^{2} (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 
σ_{T} = P/A 
Normal Stress in any Oblique Section 
σ_{θ} 
σ_{θ} = (P/A)*cos^{2}θ 
Shear Stress in any Oblique Section 
τ_{θ} 
τ_{θ} = (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.
Calculator:
OUTPUT PARAMETERS 
Parameter 
Symbol 
Value 
Unit 
Tensile Stress 
σ 



Normal Stress in any Oblique Plane 
σ_{θ} 


Shear Stress in any Oblique Plane 
τ_{θ} 


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.
Supplements:
Link 
Usage 
Material Properties

Thermal expansion coefficient
and elastic modulus values of steels, aluminum alloys, cast irons, coppers and titaniums. 
Reference: