Stress Calculator
Calculate stress, strain, and Young's modulus for materials under load
Calculate Stress and Strain
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Stress Calculation (σ = F/A)
Calculation Results
Applied Formulas
Example Calculation
Steel Rod Under Tension
Given:
• Force: 30 kN (30,000 N)
• Cross-sectional area: 1 cm² (1×10⁻⁴ m²)
• Initial length: 2 m
• Extension: 3 mm
Solution
Stress: σ = F/A = 30,000 N / (1×10⁻⁴ m²) = 300 MPa
Strain: ε = ΔL/L = 0.003 m / 2 m = 0.0015
Young's Modulus: E = σ/ε = 300 MPa / 0.0015 = 200 GPa
This matches typical values for steel!
Common Materials
Types of Stress
Tensile Stress
Material is being pulled apart
Positive stress values
Compressive Stress
Material is being pushed together
Negative stress values
Shear Stress
Force parallel to surface
τ = F/A (different calculation)
Key Formulas
Stress
σ = F / A
Force per unit area
Strain
ε = ΔL / L₁
Relative deformation
Young's Modulus
E = σ / ε
Material stiffness
Hooke's Law
σ = E × ε
Linear elastic behavior
Understanding Stress and Strain
What is Stress?
Stress is the intensity of internal forces within a material. It represents how much force is applied per unit area and determines whether a material will deform, yield, or break under load.
Types of Stress
- •Normal Stress: Perpendicular to the surface (tensile or compressive)
- •Shear Stress: Parallel to the surface
- •Bending Stress: Combination of tensile and compressive
- •Torsional Stress: Due to twisting moments
What is Strain?
Strain is the measure of deformation of a material. It's the ratio of the change in dimension to the original dimension, representing how much a material stretches or compresses.
Young's Modulus (E)
Young's modulus describes the stiffness of a material. A higher modulus means the material is stiffer and resists deformation more effectively.
Engineering Insight: The stress-strain relationship is fundamental to structural design, helping engineers ensure safety and predict material behavior under load.
Applications
Structural Engineering
- • Building design
- • Bridge analysis
- • Foundation sizing
- • Safety factor calculations
Materials Testing
- • Tensile testing
- • Quality control
- • Material characterization
- • Failure analysis
Mechanical Design
- • Component sizing
- • Load calculations
- • Material selection
- • Performance prediction
Understanding the Stress-Strain Curve
Linear Elastic Region
In this region, stress and strain are directly proportional (Hooke's Law). The material returns to its original shape when the load is removed.
σ = E × ε (constant slope)
Beyond Elastic Limit
After the yield point, permanent deformation occurs. The material may strain harden before reaching ultimate strength and failure.
Plastic deformation begins