🎓 Lesson 20
D5
Thermal Stress Estimation in Pressure Vessels & Piping
Thermal stress in pipes and pressure vessels is the internal force that builds up when metal expands or shrinks due to temperature changes and can’t move freely.
🎯 Learning Objectives
- ✓ Calculate thermal stress magnitude in a restrained pipe segment using linear elasticity and thermal expansion principles
- ✓ Analyze combined stress states (thermal + pressure + bending) in ASME B31.1/B31.3-compliant piping systems
- ✓ Design anchor and expansion loop configurations to limit thermal displacement and peak stress below code-allowed values
- ✓ Explain how material selection (e.g., stainless vs. carbon steel) affects thermal stress severity in high-temperature service
📖 Why This Matters
In mining and mineral processing plants, steam lines, hot leach solution piping, and autoclave feed systems routinely operate between 120°C–350°C. Uncontrolled thermal stress causes flange leaks, weld fatigue cracking, support failure, and catastrophic rupture—especially at anchor points or changes in direction. A single failed 250°C sulfuric acid line in a copper SX-EW plant caused $2.1M downtime and triggered a Tier-2 process safety incident. Understanding and managing thermal stress isn’t theoretical—it’s foundational to mechanical integrity and ALARP compliance.
📘 Core Principles
Thermal stress originates from constrained thermal strain: when a material attempts to expand (α·ΔT) but is physically restricted (e.g., fixed anchors, adjacent equipment, or geometry), reaction forces develop. In uniaxial restraint, σ_thermal = E·α·ΔT; however, real piping is multiaxial and dynamically loaded. Stress intensification factors (SIFs), flexibility analysis (using guided cantilever or computerized CAESAR II methods), and creep effects (above 0.4T_melt) must be considered. ASME B31.1 (Power Piping) and B31.3 (Process Piping) define allowable sustained and expansion stresses separately—and require cumulative evaluation of all load cases (e.g., operating + thermal + occasional).
📐 Uniaxial Thermal Stress (Basic Case)
Used for preliminary assessment of fully restrained straight pipe segments—e.g., short spools between rigid supports or flanges. Not applicable to flexible systems but essential for bounding estimates and identifying high-risk locations.
Linear Thermal Stress (Fully Restrained)
σₜ = E · α · ΔTAxial stress developed in a completely restrained homogeneous bar or pipe segment subjected to uniform temperature change.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| σₜ | Thermal stress | Pa (or MPa) | Induced axial normal stress due to thermal constraint |
| E | Young's modulus | Pa | Modulus of elasticity at average operating temperature |
| α | Coefficient of linear expansion | /°C | Material property quantifying strain per degree temperature change |
| ΔT | Temperature change | °C | Difference between operating and reference (installation) temperature |
Typical Ranges:
Carbon steel piping (20–250°C): 11.0 – 12.5 × 10⁻⁶ /°C
304 Stainless steel (20–300°C): 16.0 – 17.5 × 10⁻⁶ /°C
💡 Worked Example
Problem: A 6-inch NPS Schedule 40 carbon steel pipe (ASTM A106 Gr. B) is anchored at both ends. Operating temperature rises from 25°C (installation) to 220°C during startup. Calculate axial thermal stress.
1.
Step 1: Identify parameters — α = 12.0 × 10⁻⁶ /°C (carbon steel avg.), ΔT = 220 − 25 = 195°C, E = 182 GPa at 200°C (ASME B31.3 Table C-1)
2.
Step 2: Apply σ = E·α·ΔT = (182 × 10⁹ Pa) × (12.0 × 10⁻⁶ /°C) × 195°C
3.
Step 3: Compute: σ = 182e9 × 12e-6 × 195 = 425.9 MPa
Answer:
The calculated thermal stress is 426 MPa, which exceeds the ASME B31.3 allowable stress for A106 Gr. B at 220°C (137 MPa). This confirms full restraint is unsafe—flexibility (loops, bends, or anchors with sliding pads) is mandatory.
🏗️ Real-World Application
At Newcrest’s Telfer Gold Mine (Western Australia), a 300 mm diameter HP leach line (200°C, 3.2 MPa) suffered repeated weld cracks at a rigid elbow near a crusher foundation. CAESAR II modeling revealed peak thermal+pressure stress of 218 MPa (>1.2× allowable). Redesign replaced the fixed anchor with a guided sliding support and added a 4-m radius expansion bend—reducing peak stress to 112 MPa and eliminating failures over 5+ years of operation. Post-implementation thermographic scans confirmed predicted displacement (8.7 mm axial, ±0.3 mm) matched field measurements.
📋 Case Connection
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