GENERALIZED HOOKE'S LAW FOR STRESS - STRAIN CALCULATION


Generalized Hooke's Law stress-strain calculator is used to calculate stress-strain relations of a homogeneous isotropic material under most general stress/strain conditions. If strains on a structure are measured in elastic range, stresses can be calculated from these results with the usage of Hooke's law strain - stress calculator.

Hooke's Law is the relation in which the stress σ is directly proportional to the strain ε. (σ=E ε). Hooke’s law is also valid for shear stress and strain in the linear elastic range (τ=Gγ)

The generallized Hooke's law formulas used for the calculations are given below.

Parameter Formula
Normal strain (εx)
x/E-vσy/E-vσz/E)
Normal strain (εy) y/E-vσz/E-vσx/E)
Normal strain (εz) z/E-vσx/E-vσy/E)
Shear strain (γxy) τxy/G
Shear strain (γyz) τyz/G
Shear strain (γzx) τzx/G
Modulus of rigidity (G) E/(2(1+v))

Generalized Hooke's Law Calculator:

KNOWN PARAMETERS
PARAMETERS
Parameter Value Unit
Elastic modulus (E)
Poisson's ratio (v) ---
Modulus of rigidity (G) --- ---
STRESS
Parameter Value Unit
Normal stress (σx)
Normal stress (σy)
Normal stress (σz)
Shear stress (τxy)
Shear stress (τyz)
Shear stress (τzx)
STRAIN
Symbol Value Unit
Normal strain (εx) μm/m (μin/in)
Normal strain (εy)
Normal strain (εz)
Shear strain (γxy)
Shear strain (γyz)
Shear strain (γzx)

 



Note: Use dot "." as decimal separator.


Definitions:

Homogeneous Material: Material which has got same material properties at all of its points.

Isotropic Material: Material in which strength, elastic modulus and thermal conductivity properties are independent from the choice of coordinate system.

Modulus of elasticity (Young’s modulus): The rate of change of unit tensile or compressive stress with respect to unit tensile or compressive strain for the condition of uniaxial stress within the proportional limit. Typical values: Aluminum: 69 GPa, Steel: 200GPa.

Modulus of rigidity (modulus of elasticity in shear): The rate of change of unit shear stress with respect to unit shear strain for the condition of pure shear within the proportional limit. Typical values Aluminum 6061-T6: 24 GPa, Structural Steel: 79.3 GPa.

Poisson’s ratio: The ratio of lateral unit strain to longitudinal unit strain under the condition of uniform and uniaxial longitudinal stress within the proportional limit.


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