Skeleton Curve Determination for Internal Diaphragm Joints of Square Steel Tube Concrete Columns

Literature Overview

This paper by Nie Jianguo (Tsinghua University) and Qin Kai presents a systematic investigation of the moment-story drift deformation skeleton curve for internal diaphragm plate joints of square steel tube concrete (CFST) columns. Published in the China Civil Engineering Journal (2008, Vol. 41, No. 4), the study develops a three-linear (three-slope) model for characterizing the nonlinear behavior of these critical connection details. Supported by the National Natural Science Foundation (Grant 50438020) and the Changjiang Scholars and Innovative Research Teams Program (IRT00736), the research addresses a fundamental need in seismic design: accurate characterization of joint behavior for performance-based analysis.

Core Technical Content and Model Development

The study is based on low-cycle repeated loading tests of square CFST column internal diaphragm plate joints. The primary contribution is the development of a three-slope model for the moment-story drift skeleton curve, which decomposes the total joint deformation into three components:

1. Beam deformation (梁变形): Elastic and inelastic deformation of the connected beam
2. Column deformation (柱变形): Elastic and inelastic deformation of the CFST column
3. Joint deformation (节点变形): Local deformation at the joint region, calculated using a modified component method

This decomposition approach recognizes that the observed joint behavior is a superposition of multiple deformation mechanisms, each with distinct stiffness and strength characteristics. The modified component method accounts for the interaction between these components and the progressive damage accumulation during cyclic loading.

Three-Linear Model Parameters and Characterization

The model parameters are determined from experimental data through curve fitting procedures. The elastic stage shows good agreement between the model and test results, while the elastic-plastic stage exhibits some deviation but remains useful for engineering reference.

Technical Analysis of Joint Behavior

The internal diaphragm plate joint is a widely used connection detail for CFST columns because it provides:

• Direct load transfer between beam and column through the diaphragm plate
• Simple fabrication and assembly
• Good ductility when properly detailed
• Compatibility with square and rectangular CFST columns

The key deformation mechanisms include:

Elastic phase:

• Beam flexural deformation dominates
• Column axial and flexural deformation is minimal
• Joint panel zone deformation is negligible
• Overall behavior is linear and reversible

Elastic-plastic transition:

• Diaphragm plate yielding initiates
• Beam plastic hinge begins to form
• Joint panel zone enters nonlinear range
• Stiffness degradation accelerates

Post-yield phase:

• Full beam plastic hinge established
• Diaphragm plate fully yielded
• Local buckling of steel tube walls near joint
• Concrete core crushing in compression zone
• Strength stabilization or gradual degradation

Steel Pipe Manufacturing and Welding Quality Requirements

The internal diaphragm plate joint imposes specific requirements on steel pipe manufacturing and welding:

Steel tube requirements:

• Square hollow section with precise dimensional tolerances (±0.5% on width and height)
• Uniform wall thickness (±10% of specified minimum)
• Consistent corner radius (typically 1.5t to 2.0t, where t is wall thickness)
• Flat end faces for proper diaphragm plate welding (squareness within 0.5 mm/m)
• Surface quality meeting minimum SA 2.5 standard

Diaphragm plate welding:

• Full-penetration groove welds connecting diaphragm plate to column tube wall
• Weld qualification through procedure qualification testing (PQR) and welder qualification testing (WQT)
• Weld quality verification through RT or UT (typically 100% coverage for primary welds)
• HAZ hardness control within ±1 HRC of base metal (to prevent brittle fracture)
• Residual stress management through post-weld stress relief or controlled welding sequence

Beam-to-diaphragm welding:

• Fillet or groove welds depending on connection design
• Weld throat dimensions verified through UT or MT
• Fit-up tolerances controlled to ensure proper weld geometry
• Weld sequence optimized to minimize distortion

Quality control inspection matrix:

Model Validation and Engineering Application

The theoretical model was validated against multiple experimental test results. The elastic stage predictions show good agreement with test data, confirming the accuracy of the component decomposition approach for linear behavior. In the elastic-plastic stage, some deviations exist due to the complex interaction effects and progressive damage mechanisms that are difficult to capture with simplified models.

For engineering applications, the three-slope model provides:

• A practical tool for nonlinear analysis of CFST frames
• Input parameters for performance-based seismic design
• A basis for connection design optimization
• Guidance for determining appropriate ductility demands on joint components

The model's limitations in the elastic-plastic range suggest that for critical applications, component-level finite element analysis may be necessary to capture the detailed behavior. However, for routine design and preliminary assessments, the three-slope model provides adequate accuracy with significantly reduced computational effort.

Study Insights and Practical Implications

This research by a leading researcher in steel-concrete composite structures provides a systematic framework for understanding and predicting the nonlinear behavior of internal diaphragm plate joints. The component decomposition approach is particularly valuable because it identifies the individual deformation mechanisms and their relative contributions, enabling targeted design improvements.

For steel pipe manufacturers and welding engineers, the key implications are:

1. Connection quality is critical: The joint behavior is dominated by the diaphragm plate welds and the steel tube wall quality near the joint region. Manufacturing tolerances and welding quality directly affect the structural performance.
2. Residual stress management: Welding residual stresses in the steel tube wall near the joint can reduce the effective buckling resistance and influence the cyclic behavior. Controlled welding sequences and, where necessary, post-weld stress relief treatments should be implemented.
3. Material compatibility: The steel grades for the tube, diaphragm plate, and beam must be compatible in terms of yield strength and ductility to ensure a favorable failure sequence. The diaphragm plate should be designed to yield before the steel tube wall buckles.
4. Geometric accuracy: The squareness and flatness of the tube end faces directly affect the weld quality and consequently the joint behavior. Deviations from geometric specifications can lead to incomplete weld penetration or stress concentrations.

The three-slope model represents a significant advancement in the analytical characterization of CFST joints, bridging the gap between detailed component-level analysis and practical engineering application. Its implementation in structural analysis software can enable more accurate performance-based seismic design of CFST structures, ultimately leading to more economical and reliable building systems. The research methodology and findings provide a template for similar investigations of other joint types and structural configurations in the steel-concrete composite field.