Zhuojin Pipe Fitting Co., LtdSimplified Nonlinear Analysis Method for Steel Tube Concrete Lattice Structures with Shear Deformation and Related Buckling Effects
Literature Overview
This paper by Sun Chao and Chen Baochun from Fuzhou University, published in Highway and Transportation Research in 2009 (Vol. 26, No. 8, pp. 51-56), addresses a critical engineering challenge in the structural analysis of steel tube concrete (SRC) lattice or hollow structures. The study was funded by the National Natural Science Foundation of China (Grant No. 50578042). The authors propose a simplified dual-nonlinear analysis approach that considers both shear deformation effects and related buckling phenomena simultaneously, which is essential for the accurate assessment of ultimate bearing capacity of SRC lattice columns.
Core Technical Approach
The fundamental innovation lies in the derivation of an equivalent continuous beam stiffness matrix from the discrete lattice structure, incorporating shear deformation through a Timoshenko beam formulation. The method replaces the conventional member-by-member finite element model with a single equivalent beam element, dramatically reducing computational cost while maintaining accuracy.
Key Analytical Framework
The stiffness matrix is constructed using the ratio of shear stiffness to flexural stiffness to account for the shear deformation effect on bending stiffness. The effective axial compressive stiffness is employed for both chord members and web members, which implicitly captures the influence of initial member curvature on overall structural stability. This is a dual-nonlinear treatment because it simultaneously accounts for:
- Geometric nonlinearity through the effective stiffness approach (P-Δ and P-δ effects)
- Material nonlinearity through the constitutive relationship of the steel tube and concrete composite
Program Implementation and Verification
A FORTRAN-based program was developed to implement the simplified algorithm. The verification examples demonstrate excellent agreement between the simplified method and conventional truss-model finite element analysis, confirming the validity of the equivalent beam approach.
Technical Parameter Analysis
| Parameter | Symbol | Influence on Ultimate Capacity |
|---|---|---|
| Overall slenderness ratio | λ | Higher λ reduces shear deformation influence |
| Member slenderness ratio | λ₁ | When λ₁ >> λ, local member buckling dominates |
| Chord-to-web area ratio | A_chord/A_web | Higher ratio increases shear deformation influence |
| Effective axial stiffness | EA_eff | Captures initial curvature effects |
| Shear-flexure stiffness ratio | k_s/k_b | Governs shear deformation contribution |
Related Buckling Behavior Classification
The paper establishes a clear classification of failure modes based on the relationship between member slenderness (λ₁) and overall slenderness (λ):
- Local buckling dominance: When λ₁ >> λ, individual chord members buckle locally before the overall structure fails.
- Overall buckling dominance: When λ₁ << λ, the structure fails through global lateral displacement.
- Related buckling (most critical): When λ₁ ≈ λ, the interaction between local and global instability is maximized, producing the most severe reduction in ultimate capacity.
This finding has direct engineering implications: designers must ensure that λ₁ and λ are not equal to avoid the most unfavorable buckling interaction.
Engineering Practice Implications
From a steel pipe manufacturing and structural engineering perspective, this study has several practical implications:
- Pipe selection for lattice columns: When selecting steel tubes for chord members of SRC lattice columns, engineers should target a member slenderness ratio that is either significantly smaller or significantly larger than the overall slenderness ratio to avoid the related buckling critical condition.
- Quality control emphasis: The initial member curvature (captured through effective stiffness) is a manufacturing quality parameter. In pipe fabrication, straightness tolerances per standards such as ASTM A53 or GB/T 8163 directly influence the effective stiffness and therefore the predicted ultimate capacity.
- Computational efficiency: For preliminary design and rapid assessment of multiple design alternatives, the simplified method offers a practical tool that reduces unit count substantially while maintaining acceptable accuracy.
Study Insights and Reflections
The dual-nonlinear approach presented here is particularly valuable because it bridges the gap between simplified hand calculations and full nonlinear finite element analysis. In my experience with steel structure design, the related buckling phenomenon is often underappreciated in practice because conventional design codes treat local and global stability separately. The finding that shear deformation influence increases with the chord-to-web area ratio is somewhat counterintuitive and warrants careful attention in the design of heavily loaded lattice columns where large chord sections are used.
The method's applicability extends beyond SRC lattice columns to any hollow or trussed structural system where the interaction between member-level and system-level stability is significant, including certain types of offshore jacket platforms and transmission tower structures.