Calculation Method for Eccentric Bearing Capacity of Curved Hollow Sandwich Concrete-Filled Steel Tube Curtain Wall

Literature Overview

This study addresses the calculation methodology for eccentric bearing capacity of curved hollow sandwich concrete-filled steel tubes (CFST) used in curtain wall structures. The hollow sandwich design introduces an intermediate air gap or secondary material layer between the outer steel tube and the inner concrete core, creating a composite structural system that differs fundamentally from conventional monolithic CFST members. The curvature of the tube introduces additional geometric nonlinearity, making the eccentric loading behavior significantly more complex than that of straight members. This is particularly relevant for architectural applications where curved façade elements must resist lateral wind loads, seismic actions, and self-weight eccentricities simultaneously.

Core Technical Points

Structural Configuration and Load Path

The hollow sandwich CFST consists of an outer steel shell, an inner concrete core, and a separation layer that may be filled with lightweight material or left as an air cavity. Under eccentric loading, the load path involves three distinct mechanisms: direct axial compression through the concrete core, bending moment resistance through the steel-concrete composite section, and additional curvature-induced membrane stresses in the outer tube. The eccentricity ratio (e/h, where e is the eccentricity distance and h is the section height) governs the transition from compression-dominated to bending-dominated failure modes.

Key Design Parameters

Parameter	Typical Range	Influence on Eccentric Capacity
Eccentricity ratio e/h	0.05–0.35	Primary governing factor for interaction curve shape
Outer steel tube diameter D	150–400 mm	Controls section modulus and moment resistance
Steel tube wall thickness t	4–12 mm	Affects buckling resistance under eccentric compression
Concrete core diameter d	D − 2t − gap	Determines axial load capacity
Gap thickness g	20–80 mm	Influences composite action and stress distribution
Steel grade	Q235–Q460	Governs yield strength and post-yield ductility
Concrete strength fc	C30–C80	Controls compressive capacity and confinement effectiveness

Calculation Methodology

The proposed calculation method typically follows a unified interaction curve approach that accounts for:

The P-M interaction envelope modified by the hollow sandwich geometry
The additional bending moment induced by initial curvature (P-Δ-δ effects)
The reduced composite action due to the separation layer between steel and concrete
Local buckling of the outer steel tube under compressive zones

The interaction curve is constructed by parametric finite element analysis or analytical integration of the cross-sectional stresses under combined axial and bending loads. The curvature introduces a second-order moment amplification factor that depends on the slenderness ratio and the applied eccentricity.

Process and Standards Analysis

Relevant Standards and Codes

The design of curved CFST curtain wall members intersects multiple standards:

Standard	Scope	Key Provision for This Application
GB 51248-2016	CFST structure design	Provides basic P-M interaction formulas for straight CFST
GB 50017-2017	Steel structure design	Governs local buckling checks and stability analysis
JGJ 118-2011	Steel structure curtain wall	Specifies lateral displacement limits for façade systems
EN 1993-1-1	Eurocode 3 Part 1-1	Provides interaction formula for compression members
AISC 360-22	Steel construction specification	Interaction equations for beam-columns

Limitations of Existing Codes

Existing codes primarily address straight CFST members under concentric or eccentric loading. The curved geometry and hollow sandwich configuration introduce several phenomena not covered by standard provisions:

The curvature creates an inherent moment amplification even under pure axial load
The separation layer reduces the composite action factor, requiring modified confinement models
The thin-walled outer tube of curved sections is susceptible to ovalization under eccentric loading
Thermal expansion differences between steel and concrete across the gap can cause additional stresses

Integration with Engineering Practice

Manufacturing Considerations

From a pipe manufacturing perspective, curved hollow sandwich CFST members require specialized fabrication techniques. The outer steel tube must be bent to the specified radius, which introduces residual stresses from the bending process. These residual stresses interact with the applied eccentric loads and can reduce the effective buckling capacity. The bending process for large-diameter thin-walled tubes typically employs cold bending or hot bending methods, each with distinct residual stress distributions.

Bending Method	Applicable Diameter	Residual Stress Level	Cost Factor
Cold bending	< 300 mm	High (up to 0.3σy)	Low
Hot bending	200–600 mm	Moderate (0.1–0.2σy)	Medium
Roll bending	> 400 mm	Low (0.05–0.1σy)	High
Segmental welding	Any	Depends on weld quality	Variable

Welding Quality Requirements

The separation between the outer tube and inner core requires careful consideration of welding connections at member ends. End plates or connection brackets welded to the outer tube must transfer eccentric loads effectively. Common welding defects in this application include:

Undercut at the weld toe reducing fatigue life
Incomplete penetration at fillet welds connecting end plates
Distortion of the curved tube profile during welding due to thermal contraction
Hydrogen-induced cracking in high-strength steels (Q390 and above)

Quality Control Procedures

A comprehensive QC plan for curved hollow sandwich CFST fabrication should include:

Visual inspection (VT) of all welds per ISO 17637
Magnetic particle testing (MT) or dye penetrant testing (PT) for surface defects
Ultrasonic testing (UT) for volumetric defects in thick weld sections
Dimensional inspection of curvature radius and gap uniformity
Hydrostatic testing of the assembled member to verify structural integrity
Mechanical testing of coupon specimens taken from the same heat as the parent steel

Key Questions and Reflections

The hollow sandwich concept raises fundamental questions about the optimal gap thickness. Too small a gap provides minimal insulation or secondary material benefit but risks composite action that may lead to differential thermal stress. Too large a gap reduces the effective section modulus and increases the slenderness of the outer tube. The optimal design likely requires a parametric study balancing thermal performance, structural capacity, and manufacturing feasibility.

Another critical question concerns the long-term behavior under cyclic loading. Curtain wall structures experience repeated wind loading, and the hollow sandwich configuration may exhibit progressive damage accumulation at the gap interfaces. Fatigue assessment of these members requires careful consideration of stress concentration at geometric discontinuities.

Study Insights and Implications

This research contributes significantly to the design methodology for curved CFST façade systems by providing a rational calculation framework that accounts for the unique geometric and material characteristics of hollow sandwich members. The proposed method enables engineers to move beyond empirical approaches and design curved CFST curtain walls with quantifiable safety margins.

For steel pipe manufacturers, this work highlights the importance of controlling bending residual stresses and ensuring dimensional accuracy in curved tube fabrication. The eccentric loading scenario demands higher quality in the compressive zone of the outer tube, where local buckling initiates failure. Future work should integrate digital manufacturing techniques to optimize the bending process and reduce residual stress through controlled cooling or post-bending stress relief.