Finite Element Analysis of Stress in Unstiffened Equal-Diameter Welded Tee Under Internal Pressure

Literature Overview

The paper by Liu Fenghuai, Wang Taimao, and Mu Lin, published in Journal of Shandong Jiaotong University (2015, Vol. 23, No. 2, pp. 78-81), presents a finite element analysis of stress in an unstiffened equal-diameter welded tee used in a 150 t/h biomass fuel boiler. The authors used ANSYS finite element software to analyze the stress distribution under internal pressure loading and investigated the effect of different weld reinforcement heights on the stress state. This work addresses a practical engineering challenge in boiler manufacturing: determining the optimal weld reinforcement height to ensure the safety and integrity of welded tees without external reinforcement.

Background and Engineering Context

In boiler and pressure vessel applications, tees are frequently used to create branch connections in the main piping system. When the tee is fabricated by welding a branch pipe to the main run pipe, the resulting junction creates a geometric discontinuity that produces stress concentration. For small-diameter branch connections, external reinforcement (such as a reinforcing ring or saddle) may not be practical or economical, and the tee must rely on the inherent strength of the weld and the adjacent pipe material.

The unstiffened equal-diameter welded tee analyzed in this paper has the branch pipe diameter equal to the run pipe diameter, which is a particularly challenging configuration because the geometric discontinuity is maximal. The application context is a 150 t/h biomass fuel boiler, which operates under moderate pressure and temperature conditions typical of industrial steam generation.

Finite Element Analysis Methodology and Results

The authors used ANSYS to create a three-dimensional solid model of the unstiffened equal-diameter welded tee and applied internal pressure as the loading condition. The analysis focused on the stress distribution at and around the branch-to-run intersection, with particular attention to the weld reinforcement height as a variable parameter.

The key finding is that the weld reinforcement height significantly affects the stress distribution at the junction. Insufficient reinforcement height leads to high stress concentration at the weld toe, which can initiate fatigue cracks under cyclic loading. Excessive reinforcement height, while reducing stress concentration, may introduce residual stresses from the welding process and create geometric discontinuities that are difficult to inspect.

Weld Reinforcement Height Optimization

The concept of weld reinforcement height optimization is critical for the design and fabrication of unstiffened welded tees. The reinforcement height refers to the additional weld metal deposited above the nominal pipe surface at the branch-to-run intersection. This reinforcement serves two functions: it provides additional material at the stress concentration zone and it smooths the geometric transition between the branch and run pipes.

The optimal reinforcement height is determined by the balance between:

• Stress concentration reduction (favors larger reinforcement)
• Welding residual stress management (favors smaller reinforcement)
• Inspection accessibility (favors smaller reinforcement)
• Fabrication cost and time (favors smaller reinforcement)

The finite element analysis provides the quantitative basis for this optimization. By varying the reinforcement height in the FEA model, the engineer can identify the height that minimizes the peak stress while keeping the stress gradient at an acceptable level.

Engineering Practice Implications

For boiler manufacturers, this study provides a methodology for optimizing the fabrication of unstiffened welded tees. The key practical recommendations include:

1. Always perform FEA analysis for unstiffened tee designs before fabrication to identify stress concentration zones and determine optimal weld reinforcement parameters.
2. The weld reinforcement height should be determined through systematic parametric analysis rather than empirical rules of thumb.
3. The stress distribution should be evaluated not only at the design pressure but also at the maximum expected operating pressure including transient conditions.
4. Fatigue assessment should be performed for the identified high-stress zones, particularly at the weld toe where fatigue cracks typically initiate.

A limitation of the study is that it focuses on internal pressure loading only. In actual boiler service, the tee is also subjected to thermal cycling, mechanical loads from pipe weight and support reactions, and potentially cyclic pressure variations. A comprehensive design should consider all these load cases, and the FEA model should be extended to include thermal-mechanical coupled analysis.

Study Insights and Outlook

This paper demonstrates the practical value of FEA in the design and optimization of pressure vessel components. The focus on weld reinforcement height as a design variable is particularly relevant to fabrication engineers who must make practical decisions about weld procedures and quality requirements. The study could be extended to include thermal stress analysis, fatigue life prediction, and comparison with reinforced tee configurations. The methodology of parametric FEA for weld design optimization is a powerful tool that should be adopted more widely in pressure vessel and piping engineering.