# 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) (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))

### Generalized Hooke's Law Calculator:

 KNOWN PARAMETERS Stress Strain PARAMETERS Parameter Value Unit Elastic modulus (E) GPa psi*10^6 Poisson's ratio (v) --- Modulus of rigidity (G) --- --- STRESS Parameter Value Unit Normal stress (σx) MPa psi 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.

### Reference:

• Beer.F.P. , Johnston.E.R. (1992). Mechanics of Materials , 2nd edition. McGraw-Hill