Stress and Strain

Stress (σ) = Force / Area (Pa or N/m²). Strain (ε) = Change in length / Original length (dimensionless).

Young's Modulus

E = σ/ε (in the elastic region). A higher E means a stiffer material.

• Steel: E ≈ 200 GPa
• Aluminum: E ≈ 69 GPa
• Rubber: E ≈ 0.01–0.1 GPa

Types of Stress

• Tensile: Pulling apart
• Compressive: Pushing together
• Shear: Sliding along a plane

Elastic vs. Plastic Deformation

Below a material's yield point, stress and strain are proportional (Hooke's Law) and the material springs back to its original shape when the load is removed — elastic deformation. Beyond the yield point, deformation becomes permanent (plastic) even after the load is removed, which is the difference between a paperclip bending back (elastic) and staying bent (plastic).

Factor of Safety

Engineers never design a structure to operate right up to a material's yield stress — a safety factor (commonly 1.5–4× depending on application and consequence of failure) is built in to account for material variability, unexpected loads, and fatigue over the structure's lifetime.