Pipe Stress Analysis & Flexibility

1. Overview & Load Cases

Pipe stress analysis ensures piping systems can safely accommodate internal pressure, dead weight, thermal expansion, and external loads while keeping equipment nozzle loads within manufacturer's allowable limits. Modern analysis uses software such as Caesar II, but understanding the underlying principles is essential for proper modeling and result interpretation.

Primary Analysis Objectives

• Code compliance: Verify stresses are within ASME B31.3, B31.1, or B31.8 allowables
• Equipment protection: Ensure nozzle loads don't exceed pump, compressor, or vessel limits
• Support design: Size supports, springs, and guides for actual loads
• Flexibility: Provide adequate flexibility for thermal expansion without overstress

Standard Load Cases

The following load cases are typically required for a complete stress analysis:

Case	Description	Purpose
1	Operating: Max normal temp + emergency pressure	Equipment loads, stresses, movements
2	Operating: Emergency temp + emergency pressure	Upset condition stresses
3	Sustained: Emergency pressure (ambient temp)	Weight + pressure stress check
4	Expansion: Case 1 − Case 3	Thermal expansion stress range
5	Expansion: Case 2 − Case 3	Emergency thermal stress range

Relief Valve Reaction Forces

When relief valves are present in the system, an additional occasional load case should be generated:

• Load combination: W + P1 + F1 (Occasional)
• F1: Relief valve reaction force calculated per API 520/521
• Stress check: Sustained + Occasional ≤ 1.33 S_h

See the Relief Valve Sizing Fundamentals for reaction force calculation methods.

Conditions to Evaluate

2. Allowable Stress Criteria

ASME B31.3 defines three primary stress categories, each with different allowable limits. Understanding these categories is fundamental to proper stress analysis.

Stress Categories & Limits

Stress Type	Formula	Allowable Limit
Sustained (weight + pressure)	SL = PD/4t + MA/Z	≤ Sh
Displacement (thermal expansion)	SE = √(Sb² + 4St²)	≤ SA = 1.25Sc + 0.25Sh
Sustained + Occasional	SL + Socc	≤ 1.33 Sh

Where:

• S_h = Allowable stress at hot (operating) temperature
• S_c = Allowable stress at cold (ambient) temperature
• M_A = Resultant moment from sustained loads (in-lb)
• Z = Section modulus (in³)
• S_b = Resultant bending stress from expansion
• S_t = Torsional stress from expansion

Weld Joint Strength Reduction Factor

For sustained loads, the allowable stress S_h must be multiplied by the Weld Joint Strength Reduction Factor "W" at circumferential welds:

Temperature	W Factor
≤ 950°F (510°C)	1.00
1000°F (538°C)	0.91 (interpolated)
1100°F (593°C)	0.73 (interpolated)
1200°F (649°C)	0.64 (interpolated)
1500°F (816°C)	0.50

Note: Interpolate linearly for intermediate temperatures. This factor accounts for reduced creep strength at welds in elevated temperature service.

Weight Stress Guidelines

While codes don't explicitly limit weight-induced stress, industry practice limits sustained bending stress from weight to ¼ of the allowable:

3. Pipe Support Design

Proper pipe support design ensures the piping system maintains its intended geometry, limits stresses within allowable values, and accommodates thermal movements without imposing excessive loads on equipment.

Basic Design Criteria

Criterion	Limit	Application
Deflection (onsite piping)	½ inch	Plant piping, process units
Deflection (offsite piping)	1 inch	Pipe racks, long runs
Weight stress	≤ Sh / 4	General guideline
Pipe shoe minimum length	18 inches	Standard practice

Maximum Guide Spacing – Horizontal Piping

Guides prevent lateral movement while allowing axial thermal expansion. Maximum spacing depends on pipe size:

Pipe Size	Max Span (ft)	Notes
2" and smaller (insulated)	20	Shorter due to insulation weight
2" and smaller (uninsulated)	40	Bare pipe only
3" – 8"	60	Most common range
10" – 16"	80	Intermediate sizes
18" – 20"	100	Large bore
24" and larger	120	Major transmission lines

Spring Support Selection

Spring supports accommodate vertical thermal movements while maintaining controlled support loads:

• Variable springs: Load varies with displacement; use when movement < 3 inches and load variation < 25%
• Constant springs: Maintain constant load regardless of displacement; use for larger movements or critical equipment
• Minimum movement: If spring movement cold-to-hot < ⅛", list as ⅛" on data sheet and manually calculate equivalent hot load

Spring Hanger Guidelines

Parameter	Guideline
Hanger type (overhead)	Type C preferred unless interference or top-mount required
Spring range	Mid-range (PTP-2/C-268) preferred over short-range (PTP-1)
Rod exposure	Minimum 6" of exposed threaded rod for adjustment
Installed height	Average of min/max catalog heights + load flange, round to nearest ¼"
Galvanizing limit	Do not use galvanized clamps above 400°F

Support Load Review Thresholds

The following guide loads require additional review:

Support Type	Review If Exceeds
Single web pipe shoe (guide load)	300 lbs
Double web pipe shoe (guide load)	1,000 lbs (1.0 kip)
High horizontal load on guides	2,000 lbs (2.0 kips)

Anchor Design for Friction

In configurations with long horizontal runs and multiple expansion loops:

First Support Near Rotating Equipment

The first pipe support adjacent to pump or compressor nozzles should be:

• Spring support: To accommodate thermal movement and minimize nozzle loads, OR
• Adjustable rigid support: Base ell with steel baseplate for steel-on-steel sliding
• Requirement: If using hard support (not spring), provide adjustable base ell at minimum

4. Flange Bending Stress Limits

Flanged connections are potential leak points and require special attention to bending moments. While not a code requirement, the following limits serve as screening criteria—stresses exceeding these values warrant further investigation.

Bending Stress Screening Limits

Based on standard weight pipe, stresses at flanged connections exceeding the following values should be investigated further:

Nominal Pipe Size	Max Bending Stress (psi)	Notes
3" and smaller	5,000	Small bore more sensitive to misalignment
4" – 10"	4,000	Most common process piping
12" – 18"	3,000	Large flanges with more gasket area
20" – 24"	2,000	Very large connections
30" – 36"	1,500	Major headers and manifolds

Factors Affecting Flange Leakage

• Bending moment: Creates uneven gasket loading, potential leak path
• Axial force: Adds to (tension) or relieves (compression) bolt load
• Thermal cycling: Repeated heating/cooling can relax gasket and bolts
• Gasket type: Spiral wound more forgiving than sheet gaskets
• Bolt material: B7 bolts lose strength above 450°F; consider B16 for high temp

For more on connection stresses, see Bending Stress Fundamentals.

5. Equipment Nozzle Loads

Calculated nozzle loads on equipment shall not exceed manufacturer's allowable loads. Equipment covered by industry standards has specific load requirements.

Equipment Nozzle Load Standards

Equipment Type	Governing Standard	Load Reference
Centrifugal Pumps	API 610	Table 5 (or Appendix F for relaxed limits)
Steam Turbines	NEMA SM23	Values specified in standard
Centrifugal Compressors	API 617	Annex 2E
Reciprocating Compressors	API 618	Manufacturer datasheet
Air Cooled Heat Exchangers	API 661	2× values in standard (specify in requisition)
Shell & Tube Exchangers	TEMA	Per vendor datasheet or requisition
Pressure Vessels/Drums	WRC-107/537	Shell/nozzle stress analysis

API 610 Pump Nozzle Loads

For pumps manufactured per API 610:

• Primary limit: Table 5 values (based on nozzle size and pump type)
• Relaxed limits: Appendix F may be used if Table 5 cannot be met, after review with Lead Stress Engineer
• Load combination: √(F_x² + F_y² + F_z²) ≤ F_R and √(M_x² + M_y² + M_z²) ≤ M_R

API 661 Air Cooler Nozzle Loads

Vessel Nozzle Load Verification

For pressure vessels, towers, reactors, and drums:

• New equipment: Issue required allowable loads in vendor requisition
• Existing equipment: Check loads via WRC-107/537 or NozzlePro analysis
• Acceptance criteria: Nozzle and shell not overstressed per ASME Section VIII

For pump piping analysis details, see Pump Sizing Fundamentals.

6. Friction & Sliding

Friction at pipe supports affects thermal expansion behavior and creates loads on guides and anchors. Proper friction modeling is essential for accurate stress analysis.

Coefficient of Friction Values

Surface Combination	Coefficient (μ)
Steel on Steel	0.50
Stainless Steel (2B finish) on Teflon	0.15
Teflon on Teflon	0.15
Graphite on Graphite	0.15
Steel on Lubricated Slide Plates	0.15

Friction Analysis Guidelines

• Nozzle load reporting: Friction loads shall NOT be used to reduce calculated nozzle loads on rotating equipment
• Pump/compressor piping: Exclude friction effects at adjacent supports when comparing to allowable loads
• Anchor/guide design: Friction loads SHALL be included in structural design
• First support near equipment: If not a spring, require steel baseplate for steel-on-steel sliding

When to Model Friction

Review friction effects in the following situations:

Documentation: Notations can be made on the calculation title page in instances where friction was reviewed but not archived as part of the final calculation.

7. Insulation Properties

Insulation adds weight to the piping system and must be included in stress analysis for accurate deadweight calculations and support sizing.

Insulation Density Values

Insulation Type	Density (lb/ft³)	Typical Application
Calcium Silicate	15	High temperature (up to 1200°F)
Perlite	13	Cryogenic and high temperature
Mineral Wool	9	Moderate temperature (up to 1000°F)
Foam Glass	9	Cold service, moisture resistant
Fiber Glass	5	Low-moderate temperature
Polyurethane	2.4	Cold service (cryogenic)

Insulation Weight Calculation

Note: Also add weight of jacketing (aluminum, stainless steel) if applicable—typically 0.5 to 2 lb/ft depending on thickness and material.

8. Occasional Loads (Wind & Seismic)

Occasional loads are transient or short-duration loads that are additive to sustained loads. The primary occasional loads in pipe stress analysis are wind, seismic, and relief valve reactions.

Wind Load Criteria (Gulf Coast Typical)

Parameter	Value
Governing Standard	ASCE 7-05 (or later)
Risk Category	III
Basic Wind Speed	120 MPH (3-second gust)
Importance Factor (I)	1.15
Exposure Category	C
Gust Effect Factor	0.85
Topographic Factor (Kzt)	1.0
Directionality Factor (Kd)	0.95
Shape Factor (cylindrical pipe)	0.8

Seismic Loads

Seismic analysis is not typically applicable on the Gulf Coast. No separate seismic cases are run unless the site dictates otherwise (California, Alaska, etc.).

For projects requiring seismic analysis:

• Apply horizontal and vertical accelerations per site-specific seismic hazard analysis
• Use equivalent static method for most piping systems
• Dynamic (response spectrum) analysis may be required for safety-related piping
• Reference ASCE 7 Chapter 13 and ASME B31E for seismic design

Combined Stress Check

9. Pump Piping Considerations

Pump piping requires careful analysis because pump nozzles are sensitive to external loads. The following conditions should be evaluated to ensure reliable operation.

Operating Cases to Analyze

Case	Description	Purpose
All pumps operating	Full flow through all parallel pumps	Maximum thermal expansion
Spare pump isolated	Pump on standby, no flow	Ambient temp from pump to header
Spare with min flow bypass	Minimum flow recirculation active	Fluid temp in bypass piping

Installation Condition Checks

Evaluate the "as installed" condition for the following scenarios:

1. Cold, empty, springs locked:
   • Ambient temperature, no contents
   • Spring stops in place, piping bolted up
   • Check: Nozzle loads within allowable
2. Cold, empty, nozzle free:
   • Same as above but pump nozzle disconnected
   • Check: Pump nozzle movements (for alignment)
3. Cold, empty, springs active:
   • Springs at installed setting (stops removed)
   • Check: Nozzle loads within allowable

Top Suction/Discharge Piping

For pumps with top suction or top discharge connections:

Exception: Consider including content weight of an annular ring of liquid in the following circumstances:

• Multiple size difference between main pipe size and nozzle size (reducer at nozzle)
• Significant vertical run of larger pipe size above the reducer

Temperature Assumptions for Spared Pumps

Configuration	Temperature	Section
No minimum flow bypass	Ambient	Pump to branch connection
With minimum flow bypass	Fluid temperature	All piping with flow

For pump hydraulic calculations, see Pump Sizing Fundamentals.

Related Topics

References

• ASME B31.3-2022 – Process Piping
• ASME B31.1-2022 – Power Piping
• ASME B31.8-2022 – Gas Transmission and Distribution Piping Systems
• API 610 – Centrifugal Pumps for Petroleum, Petrochemical and Natural Gas Industries
• API 617 – Axial and Centrifugal Compressors and Expander-compressors
• API 661 – Air-Cooled Heat Exchangers for General Refinery Service
• NEMA SM23 – Steam Turbines for Mechanical Drive Service
• WRC Bulletin 107 – Local Stresses in Spherical and Cylindrical Shells
• WRC Bulletin 537 – Precision Equations and Enhanced Diagrams for Local Stresses in Cylindrical Shells
• ASCE 7 – Minimum Design Loads and Associated Criteria for Buildings and Other Structures