Moment-Rotation Relationship Model of Rectangular SC Column-Steel Beam Repairable Joint with S-Shaped Damper

Literature Overview

This study develops a moment-rotation relationship model for a repairable joint connecting rectangular steel tube concrete (SC) columns to steel beams, incorporating an S-shaped damper element. The research addresses the critical challenge of post-earthquake structural repairability, a growing concern in earthquake-prone regions where rapid restoration of structural functionality is essential. The S-shaped damper, functioning as a replaceable energy-dissipating component, allows the joint to sustain seismic damage while maintaining structural integrity, enabling subsequent repair without complete joint replacement.

Joint Configuration and Damper Mechanism

The proposed joint configuration integrates the following components:

Rectangular SC column: Typically 300×300 mm to 500×500 mm cross-section with steel tube wall thickness of 6–12 mm
Steel beam connection: H-section beam connected via end plate or bolted flange connection
S-shaped damper: Fabricated from high-strength steel (Q355 or Q420) with specific geometric parameters
Replaceable connection bolts: High-strength bolts (Grade 10.9 or 12.9) serving as the sacrificial component

The S-shaped damper operates through cyclic bending of its characteristic S-geometry, generating hysteresis energy dissipation through plastic deformation of the damper material. The geometric parameters of the S-shape, including the amplitude, wavelength, and cross-sectional dimensions, are designed to achieve target energy dissipation capacity while maintaining replaceability.

Moment-Rotation Model Development

The moment-rotation (M-θ) relationship model captures the nonlinear behavior of the joint through the following stages:

Stage	Rotation Range (mrad)	Behavior Description
Elastic	0–15	Linear stiffness, no permanent deformation
Elastic-plastic transition	15–30	Progressive yielding of damper and bolt connections
Plastic hardening	30–60	Damper fully yielded, moment plateau with hardening
Post-peak degradation	60–100+	Bolt elongation, damper fracture, stiffness degradation

The model incorporates the following key parameters:

Initial elastic stiffness (K₀): Governed by connection bolt preload and joint geometry
Yield moment (M_y): Corresponds to damper first yield and bolt slip
Peak moment (M_u): Maximum moment capacity before degradation
Post-peak stiffness degradation rate: Function of rotation amplitude and loading cycles

The S-shaped damper's contribution to the joint moment capacity is modeled through its bending stiffness and plastic moment capacity, which depends on the damper's cross-sectional geometry and material yield strength. The replaceable bolt connection contributes through bearing resistance and slip resistance, with the bolt preload playing a critical role in maintaining joint integrity during early loading stages.

Welding and Fabrication Requirements

The fabrication of the S-shaped damper requires precise control of the following welding and forming parameters:

Base plate welding: Full-penetration groove welds connecting the damper to the column and beam connection plates
Damper forming: Cold bending of high-strength steel plates to achieve the S-geometry with controlled strain
Surface treatment: Shot blasting and coating for corrosion protection
Bolt hole machining: Precision drilling to ensure proper bolt fit and alignment

The welding of the S-shaped damper to the connection plates must be performed with particular attention to the HAZ microstructure, as the damper's energy dissipation capacity depends on maintaining the base material's ductility. The recommended welding procedure uses low-hydrogen electrodes with controlled heat input below 2.5 kJ/mm to minimize HAZ softening. Post-weld inspection using MT and UT is mandatory to verify weld integrity, with acceptance criteria per ISO 5817 Level B.

Repairability and Performance Assessment

The repairability concept embedded in this joint design represents a paradigm shift in seismic design philosophy. After a major earthquake, damaged S-shaped dampers and elongated bolts can be replaced with new components, restoring the joint to its original capacity without major structural intervention. The repair process typically involves:

Assessment of joint damage extent through visual inspection and non-destructive testing
Removal of damaged dampers and elongated bolts
Installation of new dampers and bolts with specified preload
Verification of joint performance through load testing

The research demonstrates that the joint can sustain multiple seismic events with progressive damage accumulation, maintaining residual strength above 70% of initial capacity after significant deformation. This performance level ensures life safety while enabling rapid post-earthquake structural restoration.

Study Insights and Practical Implications

The development of repairable joints with S-shaped dampers represents a significant advancement in performance-based seismic design. The moment-rotation model provides a reliable basis for structural analysis and design, enabling engineers to predict joint behavior under various seismic scenarios. The practical implementation of this joint type requires standardized fabrication procedures, quality control protocols, and clear maintenance guidelines to ensure long-term reliability.

The research also opens avenues for further innovation, including the integration of smart sensors within the damper for real-time damage monitoring and the development of automated replacement procedures to accelerate post-earthquake restoration. These advancements will contribute to the creation of more resilient and sustainable structural systems in earthquake-prone regions.