Thermal Stress Calculator
Calculate thermal stress due to temperature changes in materials and structures
Calculate Thermal Stress
Material's elastic modulus
Linear thermal expansion coefficient
Starting temperature
Final temperature
Thermal Stress Results
Formula: σt = E × α × ΔT
Stress Type: Tensile (expansion)
Analysis & Recommendations
Example Calculation
Copper Bar Heating Example
Material: Copper bar
Young's Modulus (E): 110 GPa
Thermal Expansion Coefficient (α): 17 × 10⁻⁶ K⁻¹
Initial Temperature: 20°C
Final Temperature: 50°C
Temperature Change (ΔT): 30 K
Calculation
σt = E × α × ΔT
σt = 110 × 10⁹ Pa × 17 × 10⁻⁶ K⁻¹ × 30 K
σt = 110 × 17 × 30 Pa
σt = 56.1 MPa
Common Material Properties
| Material | E (GPa) | α (µm/m/K) |
|---|---|---|
| Aluminum | 68 | 23.1 |
| Brass | 106 | 19.0 |
| Copper | 110 | 17.0 |
| Gold | 77.2 | 14.0 |
| Silver | 72 | 18.0 |
| Gunmetal | 103 | 19.8 |
| Nickel | 170 | 13.0 |
| Lead | 13 | 29.0 |
| Titanium | 116 | 8.6 |
| Tungsten | 405 | 4.5 |
| Concrete | 27 | 10.0 |
| Carbon Steel | 200 | 11.7 |
| Stainless Steel | 193 | 17.3 |
| Cast Iron | 100 | 10.8 |
| Bronze | 103 | 18.0 |
Thermal Stress Tips
Positive ΔT causes tensile stress (expansion)
Negative ΔT causes compressive stress (contraction)
Consider expansion joints in design
Monitor cyclic thermal loading
Use low expansion materials for stability
Understanding Thermal Stress
What is Thermal Stress?
Thermal stress occurs when a material is subjected to temperature changes that cause expansion or contraction. When this thermal deformation is constrained, internal stresses develop within the material. These stresses can lead to structural failure if not properly considered in design.
Common Examples
- •Railway track buckling in hot weather
- •Concrete pavement cracking
- •Power line sagging in summer
- •Engine component deformation
Formula Explanation
σt = E × α × ΔT
- σt: Thermal stress (Pa)
- E: Young's modulus (Pa)
- α: Coefficient of thermal expansion (K⁻¹)
- ΔT: Temperature change (K)
Key Factors
- Material Properties: E and α values vary significantly
- Temperature Range: Larger ΔT creates higher stress
- Constraint: Stress only occurs if expansion is restricted
Engineering Applications
🏗️ Structural Engineering
- • Bridge expansion joints
- • Building thermal movements
- • Pipeline design
- • Concrete structures
🔧 Mechanical Engineering
- • Engine components
- • Heat exchangers
- • Turbine blades
- • Pressure vessels
⚡ Electronics
- • Semiconductor devices
- • PCB assemblies
- • Thermal management
- • Package reliability