F = -kx
The original formulation of Hooke's Law for helical springs and elastic elements. Force is proportional to displacement, with the negative sign indicating restoring force direction.
| Material | Value | Unit |
|---|---|---|
| Steel Spring (Light) | 100-500 | N/m |
| Steel Spring (Medium) | 500-2,000 | N/m |
| Steel Spring (Heavy) | 2,000-10,000 | N/m |
| Rubber Band | 10-50 | N/m |
| Suspension Coil | 15,000-50,000 | N/m |
σ = Eε
Uniaxial stress-strain relationship for rods, bars, and structural members. Young's modulus (E) represents material stiffness in the elastic region before yielding.
| Material | Value | Unit |
|---|---|---|
| Steel (Structural) | 200 | GPa |
| Aluminum (6061) | 68.9 | GPa |
| Copper (Pure) | 110-130 | GPa |
| Titanium (Grade 5) | 113.8 | GPa |
| Concrete | 25-30 | GPa |
τ = Gγ
Shear deformation relationship for torsional loading, bolted joints, and shear panels. Shear modulus (G) is typically 40% of Young's modulus for isotropic materials.
| Material | Value | Unit |
|---|---|---|
| Steel (Structural) | 79.3 | GPa |
| Aluminum (6061) | 26 | GPa |
| Copper (Pure) | 44-48 | GPa |
| Brass | 35-40 | GPa |
| Rubber | 0.0003-0.003 | GPa |
σ ≤ σ_y (elastic)
Boundaries of linear elastic behavior. Proportional limit marks end of perfect linearity; yield strength defines onset of permanent (plastic) deformation.
| Material | Value | Unit |
|---|---|---|
| Steel A36 | 250 | MPa (σ_y) |
| Aluminum 6061-T6 | 276 | MPa (σ_y) |
| Copper (Annealed) | 70 | MPa (σ_y) |
| Titanium Grade 5 | 830 | MPa (σ_y) |
| Concrete (C30) | 30 | MPa (σ_c) |