Pressure Vessel

Shell and Head Design

Cylindrical Shell (Division 1)

Internal pressure:
t = (P * R) / (S * E - 0.6 * P)

External pressure:
t = iterative based on L/D_o and D_o/t

Where:
t = required thickness
P = design pressure
R = inside radius
S = allowable stress
E = joint efficiency

Head Types

2:1 Elliptical Head

t = (P * D) / (2 * S * E - 0.2 * P)

Where:
D = inside diameter
S = allowable stress
E = joint efficiency

Nozzle Reinforcement

Area Replacement Method

Required reinforcement area:
A = d * t_r * F

Where:
d = finished nozzle diameter
t_r = required shell thickness
F = correction factor for plane

Available area from:
- Excess shell thickness (A1)
- Excess nozzle thickness (A2)
- Reinforcing pad (A3)
- Weld area (A4, A5)

Criterion: A1 + A2 + A3 + A4 + A5 >= A

Reinforcement Limits

Horizontal limit: d or R + t_n + t
Vertical limit (shell): d or R + t_n + t
Vertical limit (nozzle): 2.5 * t_n or 2.5 * t + t_e

Flange Design

Flange Types

Flange Rating

ASME B16.5 pressure-temperature ratings:
- Class 150, 300, 600, 900, 1500, 2500

Select class where:
P_design <= P_rating at T_design

MDMT Determination

Impact Test Exemption

Impact test required if:
T_design < MDMT

MDMT determination:
1. Base MDMT from UCS-66 curves
2. Adjust for actual stress ratio
3. Consider coincident ratio
4. Apply Table UCS-66.1 reduction

Stress ratio reduction:
MDMT_adjusted = MDMT - temperature credit

Impact Test Requirements

If impact testing required:
- Test temperature <= MDMT - 30 F (typical)
- Minimum energy: 15 ft-lb (full size Charpy)
- Average of 3 specimens
- Single specimen minimum: 10 ft-lb

Hydrostatic Test

Test Pressure

Division 1:
P_test = 1.3 * MAWP * (S_test / S_design)

Division 2:
P_test = 1.43 * MAWP * (S_test / S_design)

Where:
MAWP = Maximum Allowable Working Pressure
S_test = allowable stress at test temperature
S_design = allowable stress at design temperature

Test Procedure

1. Fill vessel completely with water
2. Remove all air pockets
3. Apply test pressure slowly
4. Hold for minimum 10 minutes
5. Reduce to MAWP for inspection
6. Inspect all welds and connections
7. Document results

Stress Classification (Division 2)

Stress Categories

Stress Combinations

Primary stress:
Pm <= S
PL <= 1.5S
PL + Pb <= 1.5S

Primary + Secondary:
PL + Pb + Q <= 3S

Fatigue:
Use peak stress F in fatigue curves

Code Compliance Documentation

U-1 Data Report

Required information:
- Manufacturer identification
- Vessel description and design data
- Material specifications
- Joint efficiencies
- Inspection data
- Test data
- Stamping information

Process Integration

• Related to structural analysis processes for pressure equipment

Input Schema

{
  "vessel_type": "pressure|vacuum|combined",
  "design_conditions": {
    "pressure": "number (psig or barg)",
    "temperature": "number (F or C)",
    "MDMT": "number (F or C)"
  },
  "geometry": {
    "diameter": "number",
    "length": "number",
    "head_type": "elliptical|hemispherical|torispherical|flat"
  },
  "material": {
    "shell": "string (SA-XXX)",
    "heads": "string",
    "nozzles": "string"
  },
  "code_edition": "string",
  "division": "1|2"
}

Output Schema

{
  "design_summary": {
    "MAWP": "number",
    "required_thicknesses": {
      "shell": "number",
      "heads": "number"
    },
    "selected_thicknesses": "object"
  },
  "nozzle_schedule": [
    {
      "size": "string",
      "purpose": "string",
      "reinforcement": "object"
    }
  ],
  "MDMT_evaluation": {
    "MDMT": "number",
    "impact_test_required": "boolean"
  },
  "hydrostatic_test": {
    "test_pressure": "number",
    "test_procedure": "string"
  },
  "code_compliance": {
    "paragraph_references": "array",
    "calculation_summary": "object"
  },
  "drawings_required": "array"
}

Best Practices

1. Always use current code edition
2. Verify material availability and certification
3. Consider corrosion allowance
4. Check MDMT early in design
5. Coordinate with authorized inspector
6. Document all design decisions

Integration Points

• Connects with Material Selection for appropriate materials
• Feeds into FEA Structural for Division 2 analysis
• Supports Welding Qualification for weld procedures
• Integrates with FAI Inspection for verification