Stress Calculator
What is Stress in Physics?
In everyday language, "stress" is what you feel before an exam. In physics and engineering, Stress ($\sigma$) measures the internal forces that particles of a continuous material exert on each other.
Think of a concrete pillar holding up a bridge. The cars on the bridge push down. The pillar pushes back up. The intensity of this internal struggle is "Stress."
The Formula (Sigma)
Stress describes the concentration of force over a specific area. The formula is mathematically identical to Pressure.
- $\sigma$ (Sigma): Stress (Pascals or psi).
- F (Force): The load being applied (Newtons or lbf).
- A (Area): The cross-sectional area carrying the load (m² or in²).
Why does Area matter? Imagine someone stepping on your foot. If they wear sneakers (Large Area), it hurts a little. If they wear stiletto heels (Tiny Area), it exerts massive Stress and pierces your skin. Same Force, different Area.
Stress vs. Pressure
Students often ask: "This looks exactly like the Pressure formula. What is the difference?"
• Stress is usually internal (how the molecules of a solid bar pull or push against each other).
Common Units: MPa vs. PSI
Because engineering standards differ globally, you will encounter two main systems.
1. Metric (SI)
The base unit is the Pascal (Pa), which is 1 Newton per square meter. However, a Pascal is tiny (like the weight of a sheet of paper). Engineers almost always use:
- Megapascals (MPa): 1,000,000 Pascals (N/mm²). Used for steel and concrete strength.
- Gigapascals (GPa): 1,000 MPa. Used for Modulus of Elasticity.
2. Imperial (US)
The base unit is PSI (Pounds per Square Inch). For high-strength materials, engineers use ksi (kilo-pounds per square inch), where 1 ksi = 1,000 psi.
Real World Material Strengths
Every material has a "Yield Strength" (where it bends permanently) and an "Ultimate Tensile Strength" (where it snaps). Here are common values:
| Material | Yield Strength (MPa) | Yield Strength (PSI) |
|---|---|---|
| Rubber | 15 | ~2,200 |
| Aluminum | 95 | ~14,000 |
| Structural Steel | 250 | ~36,000 |
| Titanium Alloy | 830 | ~120,000 |
| Carbon Fiber | 1,600+ | ~230,000+ |
Types of Stress
Our calculator primarily solves for Normal Stress (perpendicular to the surface), but there are other types:
- Tensile Stress: Pulling apart (like stretching a rubber band). Values are usually positive.
- Compressive Stress: Pushing together (like a stone pillar). Values are usually negative.
- Shear Stress ($\tau$): Sliding forces (like scissors cutting paper). This acts parallel to the surface.