Piping Stress Analysis Skill

Purpose

The Piping Stress Analysis skill provides capabilities for analyzing piping system stresses per ASME B31 codes, ensuring code compliance and equipment protection through proper flexibility analysis.

Capabilities

• Piping flexibility analysis
• Thermal expansion stress calculation
• Support and restraint design
• Nozzle load verification
• Flange leakage assessment
• Code compliance verification (B31.1, B31.3)
• CAESAR II integration
• Piping isometric review

Usage Guidelines

ASME B31 Code Overview

Code Selection

Code	Application
B31.1	Power piping
B31.3	Process piping
B31.4	Liquid transportation
B31.5	Refrigeration piping
B31.8	Gas transmission
B31.9	Building services

Stress Categories

B31.3 Stress equations:

Sustained stress:
S_L = (P*D)/(4*t) + (0.75*i*M_A)/Z <= S_h

Expansion stress:
S_E = sqrt(S_b^2 + 4*S_t^2) <= S_A

Occasional stress:
S_L + S_occ <= k*S_h

Where:
P = pressure
D = outside diameter
t = wall thickness
i = stress intensification factor (SIF)
M_A = sustained moment
Z = section modulus
S_h = hot allowable stress
S_A = allowable stress range
k = occasional load factor

Thermal Expansion Analysis

Thermal Movement

Linear expansion:
delta_L = alpha * L * (T2 - T1)

Where:
alpha = coefficient of thermal expansion
L = pipe length
T2 - T1 = temperature change

Typical alpha values (in/in/F):
Carbon steel: 6.5 x 10^-6
Stainless steel: 9.5 x 10^-6
Copper: 9.3 x 10^-6

Flexibility Analysis

Key principles:
1. Piping expands when heated
2. Expansion induces stress if restrained
3. Flexibility (bends, loops) reduces stress
4. Over-constrained systems have high stress
5. Under-constrained systems have excessive movement

Stress Intensification Factors

Common SIF Values

Component	i-factor (approx)
Straight pipe	1.0
Long radius elbow	0.9/h^(2/3)
Short radius elbow	0.75/h^(2/3)
Miter bend (1 cut)	1.52/h^(5/6)
Welding tee	0.9/h^(2/3)
Reinforced fabricated tee	Variable
Branch connection	Variable

Flexibility characteristic:
h = t*R/(r^2)

Where:
t = wall thickness
R = bend radius
r = mean radius of pipe

Support Design

Support Types

Type	Restrains	Allows
Rest (shoe)	Vertical down	Horizontal, vertical up
Guide	Lateral	Axial, vertical
Anchor	All directions	None
Rod hanger	Vertical	Horizontal
Spring hanger	Vertical (variable)	Horizontal
Constant hanger	Vertical (constant)	Horizontal

Support Spacing

Suggested maximum spans (B31.1):

| Pipe Size | Water (ft) | Steam/Gas (ft) |
|-----------|------------|----------------|
| 1" | 7 | 9 |
| 2" | 10 | 13 |
| 4" | 14 | 17 |
| 6" | 17 | 21 |
| 8" | 19 | 24 |
| 12" | 23 | 30 |

Nozzle Loads

Equipment Protection

Nozzle load limits:
- Equipment vendor provides allowables
- Common standards: API 610, API 617, NEMA SM23
- Consider sustained and thermal loads separately
- Combined loads may use interaction formula

Typical check:
sqrt((F_x^2 + F_y^2 + F_z^2)/(F_allow^2) +
     (M_x^2 + M_y^2 + M_z^2)/(M_allow^2)) <= 1.0

Load Combinations

Operating case:
W + P + T + D

Hydrotest case:
W + H + D

Where:
W = Weight
P = Pressure
T = Thermal
D = Displacement
H = Hydrotest pressure

Flange Leakage

Assessment Methods

ASME B16.5 flange rating:
- Check P-T rating at operating conditions
- Include pressure equivalent from moments

Equivalent pressure method:
P_eq = P + (16*M)/(pi*G^3)

Where:
M = bending moment at flange
G = flange gasket diameter

NC(T)MF method:
Uses ASME VIII Appendix 2 calculations
More accurate for high moment cases

Modeling Guidelines

Model Building

Key elements:
1. Include all pipe runs
2. Model equipment properly (rigid/flexible)
3. Define support locations accurately
4. Include all branch connections
5. Apply correct operating conditions
6. Model spring hangers if used

Operating Cases

Case	Temperature	Pressure	Weight	Use
Sustained	Ambient	Design	Full	Code check
Operating	Operating	Operating	Full	Equipment loads
Thermal	Operating-Ambient	None	None	Expansion stress
Hydrotest	Ambient	Test	Full + Water	Support design

Process Integration

• Related to structural analysis for piping systems

Input Schema

{
  "piping_system": {
    "line_number": "string",
    "code": "B31.1|B31.3",
    "material": "string",
    "size": "string (NPS)",
    "schedule": "string"
  },
  "operating_conditions": {
    "design_pressure": "number (psig)",
    "design_temperature": "number (F)",
    "operating_pressure": "number (psig)",
    "operating_temperature": "number (F)"
  },
  "geometry": {
    "isometric": "file reference",
    "length": "number (ft)",
    "elevation_change": "number (ft)"
  },
  "equipment_connections": [
    {
      "equipment": "string",
      "nozzle": "string",
      "allowable_loads": "object"
    }
  ]
}

Output Schema

{
  "stress_results": {
    "code_compliance": "pass|fail",
    "sustained_stress": {
      "max_value": "number (psi)",
      "allowable": "number (psi)",
      "location": "string",
      "ratio": "number"
    },
    "expansion_stress": {
      "max_value": "number (psi)",
      "allowable": "number (psi)",
      "location": "string",
      "ratio": "number"
    }
  },
  "nozzle_loads": [
    {
      "equipment": "string",
      "forces": "array [Fx, Fy, Fz]",
      "moments": "array [Mx, My, Mz]",
      "compliance": "pass|fail"
    }
  ],
  "support_schedule": [
    {
      "location": "string",
      "type": "string",
      "load": "number (lb)"
    }
  ],
  "thermal_movements": {
    "max_displacement": "number (in)",
    "location": "string"
  },
  "recommendations": "array"
}

Best Practices

1. Start with proper piping layout for flexibility
2. Verify equipment nozzle allowables early
3. Include all weight loads (insulation, contents)
4. Model actual support conditions
5. Check flange ratings at all operating conditions
6. Document all assumptions and simplifications

Integration Points

• Connects with Pressure Vessel Design for equipment interface
• Feeds into Support design for structural requirements
• Supports FAI Inspection for as-built verification
• Integrates with Design Review for approval