Precast Square Steel Tube Confined Concrete Pier Restoring Force Model

Study Scope and Modeling Framework

This paper develops a restoring force model for precast square steel tube confined concrete bridge piers using finite element simulation. The research is relevant to steel pipe and tube engineering because it combines hollow structural members, concrete filling, embedded connections, and cyclic lateral loading. The study extracts backbone curve characteristics such as elastic stiffness, peak lateral load, peak displacement, and descending stiffness, and then proposes calculation formulas for these parameters.

The finite element analysis uses ABAQUS and considers several expansion parameters, including axial compression ratio, slenderness ratio, confinement coefficient, square steel tube yield strength, concrete strength, embedded steel tube depth, and ratios related to nested steel tube diameter and thickness. The resulting formulas agree well with finite element results, with average ratios near unity and acceptable standard deviations.

The parameter table shows that the model is not merely a theoretical curve fit, but a bridge between structural behavior and fabrication dimensions that can be controlled during manufacturing and assembly.

Interpretation of Restoring Force Parameters

The elastic stiffness is largely governed by the composite action between the steel tube and concrete. If the steel tube wall is thin, the confinement is weak, and the peak load may be reached earlier with less stable post peak behavior. If the tube is too thick without adequate concrete quality, the member may become overly stiff and lose economic efficiency. The study therefore highlights the need to balance material strength, section proportions, and deformation capacity.

The descending stiffness is particularly important for seismic performance. A pier with a gradual descending branch can dissipate energy without sudden collapse, while a steep drop indicates brittle failure or loss of confinement. In precast systems, this descending branch is sensitive to connection integrity, because joint rotation and anchorage slip can accelerate stiffness degradation.

The formulas for peak load and peak displacement provide practical design shortcuts, but they should be used with caution when local buckling, weld defects, or construction tolerances are present. The finite element model assumes idealized material behavior and geometry, while a fabricated pier may contain weld seams, grout voids, or misaligned embedded plates. These variables can shift the backbone curve even when the nominal parameters are unchanged.

Fabrication and Assembly Implications

For steel pipe and fitting engineers, the key point is that the confinement effect depends on the actual geometry and material condition of the square steel tube, not only on nominal dimensions. Wall thickness tolerance, corner radius, weld seam quality, and residual stress from forming all influence the effective confinement. A tube with excessive out of roundness may allow local concrete separation or premature local buckling, reducing the predicted ductility.

The embedded depth and nested tube dimensions are assembly variables that require tight control. If the embedded steel member is not positioned accurately, the moment transfer may be uneven, causing premature cracking or bearing failure at the connection. In precast construction, the quality of the steel tube interface, grout filling, and base plate welds should be inspected as carefully as the tube itself.

The study also suggests that steel tube yield strength and concrete strength should be selected as a matched system. High strength concrete can increase load capacity, but if the steel tube is too weak, the confinement may fail before concrete crushing. Conversely, high yield strength steel with ordinary concrete may be economically attractive, but the designer must check ductility and crack control. This paper is valuable because it converts numerical results into formulas that can guide preliminary design while reminding engineers that fabrication quality ultimately controls the behavior.