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.

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