Hysteretic Constitutive Model of Semi-Rigid Connections Between Square Steel Tube Concrete Columns and Steel Beams

Overview of the Study

The paper by Ge Jiping, Zong Zhouhong, and Yang Qiangyue (2005), published in Journal of Earthquake Engineering and Engineering Vibration, presents a rigorous investigation into the nonlinear hysteretic behavior of two types of semi-rigid connections used between square steel tube concrete (STC) columns and steel beams. These connection types are laced plate connections and through-bolt end-plate connections. The research combines experimental testing, finite element model calibration, and parametric analysis to establish simplified analytical formulas for moment-rotation hysteretic models. This work is particularly relevant to engineers designing seismic-resistant steel and composite structures, where semi-rigid connection behavior governs the overall structural response under cyclic loading.

Core Technical Content and Key Findings

The study identifies the primary geometric parameters that govern the rotational stiffness and energy dissipation capacity of each connection type. For laced plate connections, the thickness of the lacing plate is the dominant factor influencing rotational performance. For through-bolt end-plate connections, the end-plate thickness and bolt diameter are the critical parameters. These findings are summarized in the following table.

The parametric finite element analysis reveals that increasing lacing plate thickness from 8 mm to 16 mm can increase the initial rotational stiffness by approximately 40-60 percent, while for through-bolt end-plate connections, increasing bolt diameter from M20 to M30 can raise the yield moment by 35-50 percent. The regression analysis produces simplified formulas that engineers can directly apply in preliminary design calculations without resorting to full nonlinear finite element simulations for every configuration.

Engineering Practice Implications

From a practical standpoint, the hysteretic constitutive models derived in this paper provide a bridge between detailed component-level behavior and system-level structural analysis. In seismic design, the moment-rotation relationship of a semi-rigid connection directly affects the distribution of internal forces, the drift demands, and the ductility requirements of the frame. Engineers should note that the simplified formulas are calibrated for specific connection geometries and material grades, and extrapolation beyond the tested parameter ranges requires caution.

The use of square steel tube concrete columns offers significant advantages in terms of fire resistance, stiffness, and constructability compared to hollow steel tube columns or reinforced concrete columns. However, the connection detail becomes a critical design bottleneck because the thin-walled nature of steel tubes and the composite action between steel and concrete create complex stress distributions at the joint. The laced plate connection is simpler to fabricate but may exhibit lower rotational ductility, while the through-bolt end-plate connection provides higher stiffness but demands more precise fabrication and alignment tolerances.

Study Insights and Reflections

One of the most valuable contributions of this work is the systematic identification of the dominant design parameters for each connection type. In my experience reviewing connection designs for composite structures, it is common to see engineers over-design all parameters uniformly rather than focusing on the critical variables. This paper provides the analytical justification for a more targeted design approach. Furthermore, the hysteretic model formulation accounts for stiffness degradation and strength deterioration under cyclic loading, which is essential for performance-based seismic design. Engineers should integrate these models into their nonlinear time-history analysis workflows to obtain more realistic predictions of structural performance under earthquake loading.