What is the modulus of elasticity?
The modulus of elasticity, also called Young’s modulus or E-modulus, is a material constant that indicates how stiff a material is — formally, the ratio of mechanical stress (force per area) to the strain (deformation per unit length) it causes within the elastic range. The higher the E-modulus, the less a material deforms under the same load.
Formula and unit
The E-modulus is defined through Hooke’s law:
E = σ / ε
Where:
– σ (sigma) = stress in N/mm² (megapascal, MPa)
– ε (epsilon) = relative strain (dimensionless, ΔL/L)
– E = modulus of elasticity in N/mm² or GPa
The unit is always pressure (often GPa = 1000 N/mm²).
Values for building materials
| Material | E-modulus (GPa) |
|---|---|
| Steel (S235, S355) | 210 |
| Aluminium | 70 |
| Glass | 70 |
| Concrete C20/25 | 30 |
| Concrete C30/37 | 33 |
| Concrete C50/60 | 37 |
| Timber (parallel to grain, softwood) | 10–14 |
| Timber (perpendicular to grain) | 0.3–0.5 |
| Brick masonry | 5–15 |
| Rubber / elastomer | 0.01–0.1 |
A steel wire is therefore about seven times stiffer than a concrete cross-section of the same size.
Application in calculations
The E-modulus is essential for:
- Deflection calculation — δ = F·L³ / (n·E·I)
- Buckling calculation — critical load depends on E·I
- Vibration and natural frequency — governs dynamic behaviour
- Prestress losses in prestressed concrete
- Composite design — combining materials based on stiffness
Key considerations
- E decreases with temperature — steel loses stiffness in fire
- Concrete creeps — long-term effect is much greater
- Timber is anisotropic — different E along and across the grain
- Initial E vs. tangent E — values differ for non-linear materials
Related terms
- Elasticity
- Elastic deformation
- Compressive strength
- Flexural strength
- Concrete
- Steel
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