Simplified Numerical Method for Ultimate Bearing Capacity of Square CFST Eccentric Compression Columns

Literature Overview

This paper by Li Sipeng, Wang Jing, Jiang Xiaodong, and Huang Yuying, published in the Journal of Huazhong University of Science and Technology (1997, Vol. 25, No. 4, pp. 93-94), presents a simplified numerical method for calculating the ultimate bearing capacity of square concrete-filled steel tube (CFST) columns under eccentric compression. The authors simplify the numerical solution method found in earlier literature by prescribing the shape of the column deflection curve, thereby reducing computational complexity while maintaining acceptable accuracy. This approach was developed at the intersection of Zhengzhou University of Technology and the Department of Mechanics at Huazhong University of Science and Technology. The work is significant because eccentric compression is a common loading condition in practical CFST column design, and an efficient analytical method is essential for routine engineering applications.

Core Technical Analysis

Theoretical Framework for Eccentric Compression

Square CFST columns under eccentric compression experience a combination of axial force and bending moment. The eccentricity of the axial load induces bending, which creates a non-uniform stress distribution across the column cross-section. The steel tube, being thin-walled relative to the column depth, is susceptible to local buckling under compressive stresses, while the concrete core provides confinement and contributes to the compressive resistance. The interaction between the steel tube and the concrete core is governed by the lateral pressure exerted by the concrete on the steel tube, which in turn provides confining pressure to the concrete.

The governing equilibrium equation for a CFST column under eccentric compression can be expressed as:

P·e = M(x)

where P is the axial load, e is the eccentricity, and M(x) is the bending moment at section x, which depends on the deflection of the column and the P-Δ second-order effect.

The deflection curve of the column is governed by the moment-curvature relationship, which is highly nonlinear due to the material nonlinearity of both steel and concrete and the geometric nonlinearity of the large deflections. A rigorous numerical solution requires iterative procedures that solve the equilibrium equation at each load increment, which is computationally intensive.

Simplification Strategy

The key simplification proposed by Li and colleagues is to prescribe the shape of the deflection curve rather than solving for it iteratively. The most common assumption is a sinusoidal deflection curve:

w(x) = w_max · sin(πx / L)

where w_max is the maximum deflection at midspan and L is the column length. This assumption is valid for simply supported columns and provides a reasonable approximation for the deflection shape of columns with other boundary conditions when modified with appropriate effective length factors.

By prescribing the deflection shape, the curvature at any section can be expressed directly in terms of w_max:

κ(x) = (π² / L²) · w_max · sin(πx / L)

This eliminates the need for iterative solution of the differential equation and allows the bending moment to be computed directly from the moment-curvature relationship. The ultimate bearing capacity is then determined by finding the load level at which the moment-curvature capacity of the critical section is exhausted.

Influence of Key Parameters on Bearing Capacity

Through extensive calculations using the simplified method, the authors analyze the influence of several key parameters on the ultimate bearing capacity of square CFST eccentric compression columns:

• Eccentricity ratio (e/h): As the eccentricity ratio increases, the bearing capacity decreases due to the increased bending demand. The relationship is nonlinear, with a more rapid decrease at higher eccentricities where the section approaches a pure bending failure mode.
• Steel tube wall thickness ratio (t/D): Increasing the wall thickness improves the bearing capacity by providing greater steel contribution and enhanced confinement to the concrete core. The improvement is most pronounced at moderate wall thickness ratios, beyond which the marginal benefit diminishes as the concrete confinement effect saturates.
• Concrete strength (f_c): Higher concrete strength increases the compressive capacity of the core and the confinement pressure on the steel tube. However, the benefit of higher concrete strength is moderated by the reduced ductility of the concrete, which may lead to a more brittle failure mode at ultimate load.
• Steel yield strength (f_y): Higher steel yield strength increases the tensile capacity of the steel tube on the tension side of the section, which is particularly important at higher eccentricities. The benefit is more pronounced for slender columns where the steel contribution to the total capacity is relatively larger.
• Column slenderness ratio (L/D): Slenderness is a critical parameter that governs the magnitude of second-order effects. As the slenderness ratio increases, the P-Δ effect becomes more significant, and the bearing capacity decreases more rapidly with increasing eccentricity. The simplified method captures this behavior through the prescribed deflection curve and the associated curvature.

Engineering Practice and Design Implications

The simplified numerical method presented by Li and colleagues offers a practical tool for engineers who need to evaluate the bearing capacity of square CFST eccentric compression columns without resorting to computationally intensive full numerical analysis. The method is particularly useful in the following scenarios:

• Parametric studies: When evaluating the effect of design parameters on bearing capacity, the simplified method allows rapid computation of capacity curves for various combinations of eccentricity, section dimensions, and material properties.
• Retrofit assessment: When assessing the load capacity of existing CFST columns under modified loading conditions, the simplified method provides a quick estimate that can be used for preliminary decision-making.
• Design optimization: When optimizing the section dimensions of a CFST column for a given loading condition, the simplified method enables efficient exploration of the design space.

However, engineers should be aware of the limitations of the simplified method. The prescribed sinusoidal deflection curve assumes a specific failure mode that may not be the actual failure mode for all column configurations. For columns with high slenderness ratios or unusual boundary conditions, the simplified method may underestimate or overestimate the bearing capacity. The method is most reliable for columns with slenderness ratios in the range of 5 to 30 and for square sections with wall thickness ratios between 1 percent and 5 percent.

The contribution of Li Sipeng and colleagues lies in demonstrating that a significant simplification of the numerical procedure is possible without a substantial loss of accuracy, provided that the deflection curve assumption is appropriate for the column being analyzed. This work represents an important step in making advanced CFST column analysis accessible to practicing engineers who may not have access to sophisticated finite element software.