Plastic Limit In-Plane Bending Moment of Tees with Shoulder Thinning Defects

Literature Overview and Context

This 2007 paper published in Chemical Equipment and Piping (Chemical Equipment and Piping, Vol. 44, No. 5, pp. 47–51) by Jia Huiling, Wang Chang, Sun Liang, and Du Pengfei from Inner Mongolia University of Science and Technology, the State General Administration of Quality Supervision, Inspection and Quarantine Special Equipment Inspection and Research Center, and Baotou Transportation Management Bureau presents a systematic study of the plastic limit in-plane bending moment of welded tees containing shoulder thinning defects. The work was supported by the National "15th Five-Year Plan" Science and Technology Key Project (Grant No. 2001BA803B03-05).

Shoulder thinning defects in tees are a manufacturing concern that arises during the forming process of welded tees. When a tee is fabricated by drilling a branch opening in a run pipe and welding a branch pipe to the opening, the material removal process can leave a localized thinning zone at the shoulder — the transition region between the branch opening and the run pipe wall. This thinning reduces the local wall thickness and creates a stress concentration that can significantly reduce the structural capacity of the tee under bending loads.

Core Technical Approach

Defect Characterization and Geometry

Shoulder thinning defects are characterized by several geometric parameters that influence the structural response:

• Thinning depth: the maximum reduction in wall thickness at the shoulder
• Thinning width: the circumferential extent of the thinning zone
• Thinning location: the angular position relative to the branch opening
• Thinning profile: the shape of the thinning zone (circular, elliptical, or irregular)

These parameters must be accurately characterized through NDT and measurement to enable meaningful structural assessment. In practice, shoulder thinning may be detected through ultrasonic thickness measurement, and the defect profile can be reconstructed using phased array ultrasonic testing (PAUT) techniques.

Elastic-Plastic Finite Element Analysis

The authors employed ANSYS finite element analysis software to perform elastic-plastic FEA of welded tees with shoulder thinning defects. The analysis considered the following key aspects:

• Material model: Bilinear or multilinear kinematic hardening model representing the elastic-plastic behavior of the tee material, with appropriate yield strength and strain hardening parameters.
• Boundary conditions: In-plane bending moment applied to the run pipe ends, with appropriate constraint conditions to simulate the tee's connection to the piping system.
• Mesh refinement: Fine mesh at the defect location to accurately capture the stress and strain gradients, with progressive mesh coarsening away from the defect.
• Convergence criteria: Load-controlled incremental analysis with appropriate convergence criteria to ensure accurate determination of the plastic limit load.

Identification of Key Influencing Factors

Through parametric FEA studies, the authors identified the primary factors influencing the plastic limit in-plane bending moment of tees with shoulder thinning defects:

The thinning depth emerged as the most critical parameter, with the plastic limit bending moment decreasing significantly as the thinning depth increased. This finding is consistent with the general principle that local wall thinning reduces the section modulus and therefore the bending capacity of the component.

Engineering Estimation Formula Development

Based on the comprehensive FEA database covering a wide range of tee geometries and defect configurations, the authors fitted engineering estimation formulas for the plastic limit in-plane bending moment. The formula takes a dimensionless form that allows application across different tee sizes and material grades:

M_limit / (σ_y × D² × t) = f(D₁/D₂, t₁/t₂, δ/t, w/t)

where M_limit is the plastic limit in-plane bending moment, σ_y is the yield strength, D is the run pipe outer diameter, t is the run pipe wall thickness, D₁ is the branch diameter, t₁ is the branch wall thickness, δ is the thinning depth, and w is the thinning width.

The formula was validated against independent FEA solutions and demonstrated high accuracy, with deviations typically within a few percent of the FEA results.

Engineering Practice Integration

Fitness-for-Service Assessment Application

The estimation formula developed in this paper can be applied in fitness-for-service assessments of in-service tees where shoulder thinning has been detected through inspection. The assessment workflow is as follows:

1. Defect detection and characterization: Use UT or PAUT to detect and characterize the shoulder thinning defect, determining depth, width, and profile.
2. Geometry measurement: Measure the tee dimensions and obtain material properties from certificates or testing.
3. Formula application: Calculate the plastic limit in-plane bending moment using the estimation formula.
4. Load assessment: Determine the maximum in-plane bending moment from piping stress analysis.
5. Safety margin evaluation: Compare the limit moment with the maximum operating moment, applying appropriate safety factors.
6. Decision: Accept, repair (by welding overlay), or replace based on the assessment.

Connection to Manufacturing Quality

Shoulder thinning defects in tees are primarily a manufacturing quality issue. The thinning occurs during the drilling or cutting operation that creates the branch opening in the run pipe. Factors contributing to excessive thinning include:

• Inadequate tooling or worn cutting tools
• Improper drilling technique or excessive feed rate
• Material softening due to heat input during drilling
• Inadequate quality control during the forming process

From a welding quality control perspective, the presence of shoulder thinning indicates a systemic manufacturing deficiency that should be addressed at the source. The FFS assessment capability provided by this paper allows for continued service of affected components but should not be used to justify poor manufacturing practices.

Comparison with Incomplete Penetration Assessment

The methodology presented in this paper is closely related to the work on incomplete penetration defects (Topic 2 in this batch). Both studies employ the same fundamental approach: extensive FEA analysis, parameter identification, and formula fitting. The key difference is the loading condition — internal pressure for incomplete penetration versus in-plane bending moment for shoulder thinning. In practice, tees may be subjected to combined loading (internal pressure plus bending moment), and a combined assessment approach would be necessary for comprehensive FFS evaluation.

Key Questions and Reflections

Several aspects of this study warrant further consideration. First, the study focuses on in-plane bending moment, but tees in service may also be subjected to out-of-plane bending, torsion, and combined loading conditions. Extension of the methodology to these loading cases would enhance its practical applicability. Second, the study does not address the interaction between shoulder thinning and other defects that may coexist, such as incomplete penetration at the weld or surface cracks. Third, the long-term fatigue behavior of tees with shoulder thinning defects under cyclic loading is not addressed, which is relevant for piping systems subject to thermal cycling or mechanical vibration.

I also note that the estimation formula, while accurate for the validated parameter range, should be applied with caution outside that range. Engineers should verify that the specific tee geometry and defect configuration fall within the FEA database range before applying the formula. For cases outside the validated range, direct FEA analysis is recommended.

Study Insights and Outlook

This paper provides a valuable tool for the fitness-for-service assessment of tees with shoulder thinning defects. The systematic approach — combining parametric FEA, factor identification, and formula fitting — establishes a rigorous methodology that can be extended to other defect types and loading conditions.

The practical value of this work is particularly significant for aging piping systems where inspection has revealed shoulder thinning at tee locations. The ability to quantitatively assess the remaining structural capacity allows for informed decisions about continued service, repair, or replacement, supporting risk-based asset management strategies.

Looking forward, I anticipate that future work will extend this methodology to include combined loading conditions, multi-defect interactions, and fatigue life assessment. The integration of these estimation formulas into digital asset management platforms would enable real-time remaining strength monitoring, supporting predictive maintenance strategies for critical piping systems.