HOOKE'S LAW FOR GENERAL STRESS - STRAIN CALCULATION

Hooke's law stress-strain calculation tool was developed to calculate stress-strain relations for 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.

The formulas used for the calculations are given in the "List of Equations" section.



Calculator:

PARAMETERS
Parameter Symbol Value Unit
Elastic modulus E
Poisson's ratio v ---
Known parameters           
Modulus of rigidity G --- ---
STRESS
Parameter Symbol Value Unit
Normal stress σx
Normal stress σy
Normal stress σz
Shear stress τxy
Shear stress τyz
Shear stress τzx
STRAIN
Symbol Parameter 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.

Hooke's Law: 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)

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.

List of Equations:

Parameter Symbol 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))

Reference: