Impact-Resistant Design Method for Circular Hollow Sandwich Steel Tube-Confinement Concrete Based on Dynamic Amplification Factor

Literature Overview

The paper by Wang Shuaifeng, Wang Rui, Zhao Hui, and Guo Zhihui (2022), published in Explosion and Shock Waves, presents a comprehensive impact-resistant design methodology for circular concrete-filled double-skin steel tubular (CFDST) members. Based on prior experimental research, 200 CFDST column finite element models were established using ABAQUS software to investigate the impact mechanisms under combined axial force and impact loading. The study examines the effects of nominal steel ratio, hollow ratio, section diameter, and material strength on impact performance across an axial compression ratio range of 0 to 0.7. The research was supported by the National Natural Science Foundation of China (52108162), the Shanxi Provincial Natural Science Research Project (20210302123119), and the HIT Key Laboratory Open Fund (HITCE201906).

CFDST Structural System Description

The CFDST member features a unique hollow sandwich configuration consisting of:

Outer steel tube: Provides external impact resistance and lateral confinement to the outer concrete layer.
Inner steel tube: Provides internal confinement and serves as a secondary impact resistance layer.
Outer concrete layer: Fills the annular space between the outer and inner steel tubes, providing mass and energy absorption.
Inner concrete core: Fills the inner steel tube, providing additional mass and load-bearing capacity.
Hollow cavity: The central void that reduces weight while maintaining structural efficiency.

Design Parameter	Range Studied	Primary Influence
Axial compression ratio (n)	0.0-0.7	Governs pre-stress state and impact response
Nominal steel ratio (ρs)	5%-15%	Directly affects impact force and deflection
Hollow ratio (α)	0.2-0.5	Minor effect on impact performance
Outer diameter (D)	200-400 mm	Influences section stiffness and mass
Outer steel strength (fy)	235-460 MPa	Affects impact force plateau value
Concrete strength (fc)	30-60 MPa	Minor effect on impact performance

Impact Mechanism Analysis

Dynamic Response Under Combined Loading

The CFDST member under combined axial force and lateral impact loading exhibits a complex dynamic response characterized by:

Initial impact phase: The impactor strikes the member, generating a contact force that propagates as a stress wave through the outer steel tube. The outer steel tube deforms locally, creating a dent or local buckling pattern.
Global bending phase: As the impact force continues to act, the member develops global bending deformation. The mid-span deflection increases, and plastic hinges begin to form at the impact point and at the supports.
Force plateau phase: After the initial peak impact force, the force stabilizes at a plateau value that represents the combined resistance of the member's flexural capacity and the dynamic amplification effect.
Rebound phase: The impactor rebounds as the member's elastic and plastic deformation energy is partially recovered, and the impact event concludes.

Parametric Study Results

The parametric analysis of 200 finite element models revealed the following influence patterns:

Nominal steel ratio: A significant positive correlation with both the mid-span deflection peak and the impact force plateau value. Higher steel ratios increase the member's flexural stiffness and energy absorption capacity.
Outer diameter: Larger diameters increase the section moment of inertia, reducing deflection while increasing the impact force plateau due to greater mass.
Outer steel strength: Higher strength steel increases the impact force plateau value by delaying yielding and plastic deformation.
Impact velocity: Higher velocities increase both the peak impact force and the mid-span deflection, with a nonlinear relationship governed by the dynamic amplification factor.
Impact mass: Greater impactor mass increases the duration of the impact event, leading to larger deflections but lower peak forces.
Hollow ratio: Surprisingly, the hollow ratio has a relatively minor effect on impact performance, suggesting that the hollow cavity does not significantly compromise the member's impact resistance within the studied range.
Concrete strength: Similarly, concrete strength has a minor effect on the impact response, indicating that the steel tubes dominate the impact behavior.

Dynamic Amplification Factor and Equivalent SDOF Method

Dynamic Amplification Factor (DAF)

The dynamic amplification factor is defined as the ratio of the dynamic response (force or deflection) to the corresponding static response under the same loading amplitude. For the CFDST member, the DAF depends on:

The impact velocity relative to the member's natural frequency.
The axial compression ratio, which modifies the member's effective stiffness.
The mass ratio between the impactor and the member.

The study proposes a DAF expression that accounts for the nonlinear behavior of the CFDST member during impact, including the transition from elastic to plastic response.

Equivalent Single-Degree-of-Freedom (SDOF) Method

The equivalent SDOF method simplifies the complex CFDST member into a single-mass oscillator with equivalent stiffness and mass properties. The method involves:

Determining the equivalent mass by distributing the member mass based on the mode shape.
Calculating the equivalent stiffness from the static bending stiffness of the member.
Applying the DAF to convert the static impact force into a dynamic impact force.
Computing the dynamic mid-span deflection using the SDOF oscillator response.

The simplified calculation method was validated against the finite element results and demonstrated good predictive accuracy for both the impact force plateau value and the mid-span deflection response.

Engineering Practice Implications

Design Methodology Summary

Design Step	Method	Key Input Parameters
Step 1: Static analysis	Elastic/plastic bending analysis	Section geometry, material properties, axial force
Step 2: DAF determination	Empirical/analytical formula	Impact velocity, impactor mass, member natural frequency
Step 3: Dynamic force calculation	Static force × DAF	Step 1 and Step 2 results
Step 4: Dynamic deflection	SDOF oscillator response	Equivalent mass, equivalent stiffness, dynamic force
Step 5: Capacity verification	Compare demand vs. capacity	Dynamic force/deflection vs. member strength/ductility

Practical Design Recommendations

Nominal steel ratio selection: A nominal steel ratio of 10-15% provides an optimal balance between impact resistance, material efficiency, and constructability. Ratios below 8% may result in insufficient impact force resistance, while ratios above 15% offer diminishing returns.
Hollow ratio optimization: The minor effect of hollow ratio on impact performance suggests that the hollow ratio can be selected primarily based on weight optimization criteria rather than impact resistance considerations. Hollow ratios of 0.3-0.4 provide a good balance between weight reduction and structural performance.
Outer steel strength selection: High-strength steel grades (Q355 or higher) are recommended for the outer steel tube, as they provide significant improvements in impact force plateau value without substantially increasing the member weight.
Concrete strength: Standard concrete grades (C30-C40) are sufficient for the CFDST member's impact performance. Higher concrete strengths do not provide proportional improvements in impact resistance and may introduce brittleness concerns.

Welding and Fabrication Considerations for CFDST Members

The CFDST member fabrication involves several critical welding operations:

Outer tube longitudinal weld: For HFW or ERW welded outer tubes, the weld quality directly affects the impact resistance at the weld location. Any weld defects could serve as crack initiation sites under impact loading.
Inner tube longitudinal weld: Similar requirements apply to the inner tube weld, though the inner tube is less directly exposed to impact loading.
Ring welds at tube ends: The end ring welds connecting the outer and inner tubes must be full-penetration welds with rigorous NDT inspection (RT or UT) to ensure complete fusion.
Concrete filling quality: Complete and uniform concrete filling is essential for the CFDST member to achieve its designed impact performance. Incomplete filling creates voids that compromise the confinement effectiveness and reduce the member's mass participation in the impact event.

Study Insights and Reflections

This research provides a practical and validated design methodology for the impact-resistant design of CFDST members, which are increasingly used in critical infrastructure applications including ultra-high voltage transmission towers, offshore platforms, and military protective structures. The finding that the hollow ratio and concrete strength have relatively minor effects on impact performance is particularly valuable for engineers, as it simplifies the design optimization process by identifying the parameters that truly matter.

The dynamic amplification factor and equivalent SDOF method offers a computationally efficient alternative to full nonlinear finite element analysis for preliminary design and code compliance verification. However, engineers should recognize that this simplified method is validated within the specific parameter ranges studied and should be used with appropriate caution for designs outside these ranges.

From a steel pipe manufacturing perspective, the CFDST member represents a demanding application that requires high-quality steel tubes with excellent dimensional accuracy, surface quality, and weld integrity. The impact loading scenario imposes severe demands on the material's ductility and fracture toughness, particularly at the weld locations. Future research should investigate the effect of weld metal properties, heat-affected zone microstructure, and residual stress distributions on the impact performance of CFDST members, as these factors are not explicitly addressed in the current study but are critical for practical fabrication and quality control.

The proposed design methodology represents a significant advancement in the impact engineering of composite steel-concrete structures and provides a foundation for future code development and standardization efforts in this emerging field.