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 GPa psi*10^6 Poisson's ratio v --- Known parameters Stress            Strain Modulus of rigidity G --- --- STRESS Parameter Symbol Value Unit Normal stress σx MPa psi 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

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 (σx/E-vσy/E-vσz/E) Normal strain εy (σy/E-vσz/E-vσx/E) Normal strain εz (σz/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))