Finite Element Strength Analysis of Unequal Tee Fittings

Literature Overview

The paper by Ren Keren, Pu Rongchun, Shen Dachun, Hui Xiangche, and Chen Degang, published in Petroleum Machinery in 2007 (Vol. 35, No. 7, pp. 21-24), presents a finite element analysis (FEA) of 90-degree cast steel unequal tee fittings under working and test pressure conditions. Conducted by Baoji Petroleum Machinery Co., Ltd., this study addresses the recurring problem of cracking in high-pressure tees and validates design modifications against ASME code requirements.

Core Technical Analysis

Problem Background

Tee fittings in high-pressure manifold systems frequently experience cracking (bursting) during service. The unequal tee, where the branch pipe diameter differs from the body pipe diameter, presents additional stress concentration challenges compared to equal tees. The study specifically addresses 90-degree cast steel tees used in petroleum industry applications.

Analysis Methodology

The FEA was conducted using ANSYS software following ASME code stress analysis methodology:

Stress Classification and Combination

Following ASME Section VIII or B31.3 methodology, the analysis classified stresses into:

Primary stress components:

• Membrane stress (Pm): Average stress across the section
• Bending stress (Pb): Linear variation across the section
• Combined primary stress (P = Pm + Pb)

Secondary stress components:

• Thermal stress (Q): Due to temperature differentials
• Misfit stress (Q): Due to geometric discontinuities

Peak stress components:

• Stress concentration effects at geometric discontinuities
• Local stress peaks at the branch root

Key Findings

Initial design analysis:

• High stress concentration confirmed at the branch root
• Peak stress exceeded allowable limits under certain conditions
• Stress category classification identified critical regions

Modified design analysis:

• Structural improvements implemented based on initial findings
• Re-analysis demonstrated compliance with ASME requirements
• Both working pressure and hydrostatic test pressure conditions satisfied code limits

Design Modification Principles

The modifications likely involved:

• Increased fillet radii at the branch root to reduce stress concentration
• Thickened wall sections at high-stress regions
• Modified internal geometry to smooth stress flow
• Possibly increased overall fitting dimensions at critical locations

ASME Code Compliance Verification

The final analysis verified compliance with ASME code requirements:

Engineering Practice Integration

FEA in Fitting Design and Certification

This study exemplifies the application of FEA as a design validation tool for pressure-containing fittings. In practice, FEA serves multiple purposes:

1. Design optimization: Identifying high-stress regions before manufacturing
2. Code compliance: Demonstrating fitness for service under applicable codes
3. Failure investigation: Understanding cracking mechanisms to prevent recurrence
4. Weight optimization: Reducing material usage while maintaining safety margins

Stress Concentration Management

The branch root of unequal tees is a critical stress concentration location due to:

• Geometric discontinuity between body and branch
• Triaxial stress state at the intersection
• Potential for stress relaxation through plastic deformation
• Interaction with residual stresses from casting or forming

Mitigation strategies include:

• Maximizing fillet radii (typically minimum 0.5D per ASME B16.9)
• Local wall thickness reinforcement
• Shot peening or burnishing of the root area
• Careful control of casting quality to minimize internal defects

Quality Control Integration

For production of unequal tees, a comprehensive quality control program should include:

FMEA Application

Applying FMEA to the unequal tee cracking problem:

Study Insights and Reflections

This paper demonstrates the practical application of FEA in resolving real production problems. The approach of analyzing the initial design, identifying deficiencies, implementing modifications, and re-verifying compliance represents a systematic engineering methodology that is directly transferable to other fitting design challenges.

The focus on ASME code compliance is particularly important for international applications, as many petroleum and chemical industry specifications reference ASME standards for fitting design and qualification. The study's demonstration of code compliance provides a template for similar analyses on other fitting types.

A limitation of the study is the focus on static pressure loading only. In actual service, tees may experience:

• Cyclic pressure loading (fatigue concerns)
• Thermal cycling (thermal stress fatigue)
• Mechanical vibration
• Combined loading conditions

These dynamic loading scenarios would require additional analysis beyond the static FEA presented.

The study also does not address the specific metallurgical aspects of cast steel tees, such as:

• Casting quality and porosity distribution
• Heat treatment effects on mechanical properties
• Microstructural variations between thick and thin sections
• Hydrogen-induced cracking susceptibility in high-strength castings

These factors can significantly influence the actual failure behavior compared to idealized FEA predictions.

Summary

This research effectively demonstrates the application of finite element analysis in identifying and resolving stress-related failure issues in cast steel unequal tee fittings. The systematic approach of initial analysis, design modification, and code compliance verification provides a clear methodology for ensuring fitting structural integrity. The findings directly address the practical problem of tee cracking in high-pressure manifold systems, offering validated design solutions that meet ASME code requirements. For engineers involved in fitting design, certification, or failure investigation, this work exemplifies the essential role of computational analysis in modern pressure equipment engineering.