Stability Analysis of Large-Span Square Steel Tube Spatial Truss Structures

Literature Overview

The paper by Jiang Cangru, Zhang Dongqiang, and Yuan Jian (Spatial Structures, 2009, Vol. 15, No. 4, pp. 56–59) presents a comprehensive stability analysis of a square steel tube spatial truss from a sports arena, subjected to simultaneous vertical and horizontal loads. The study employs three levels of analysis—linear buckling, geometric nonlinear stability, and elastoplastic nonlinear stability—to obtain the critical load–displacement relationship curve. The work demonstrates that simultaneously considering both geometric and material nonlinearities provides the most accurate prediction of actual load-bearing capacity, and that the truss structure possesses a reasonable safety reserve.

Analytical Methodology and Progressive Nonlinearity

The progressive analytical approach adopted in this study is methodologically sound and reflects best practices in structural stability assessment. The following table compares the three analytical levels and their applicability.

Analysis Level	Nonlinearity Considered	Computational Cost	Accuracy	Applicable Range
Linear buckling	None (eigenvalue analysis)	Low	Low—overestimates capacity	Preliminary screening only
Geometric nonlinear	P-Δ, P-δ effects	Moderate	Moderate—captures large displacement	Elastic range, λ < 100
Elastoplastic nonlinear	Geometric + material	High	High—captures full behavior	Full-range design analysis

The finding that the truss possesses a safety reserve when analyzed with full nonlinear considerations is encouraging but should be interpreted with caution. In practice, the safety reserve is highly sensitive to the initial imperfections present in the fabricated truss. According to EN 1993-1-5 and GB 50017, the equivalent initial imperfection amplitude for truss members is typically taken as 0.2% to 0.4% of the member length. For a 10-meter-long square tube chord member, this corresponds to an initial deviation of 20–40 mm, which can reduce the buckling load by 15–30% compared to the theoretically perfect member.

Square Tube Selection and Manufacturing Considerations

The choice of square steel tube for large-span trusses involves several critical manufacturing and material considerations. The following table outlines the key parameters and their influence on truss stability.

Parameter	Typical Specification	Influence on Stability
Tube dimensions	100×100×6 mm to 200×200×10 mm	Larger section increases I and reduces λ
Steel grade	Q345 or Q355 per GB/T 1591	Higher σ_y increases elastic buckling load
Wall thickness tolerance	±10% per GB/T 6728	Thinner walls reduce local buckling resistance
Straightness	≤ 1.5 mm/m	Reduces initial imperfection effects
Corner radius	R = 1.5t to 2.5t	Affects effective section properties
Weld type	ERW, HFW, or MIG	Determines HAZ quality and defect risk

From a welding quality perspective, the chord members and diagonal members of large-span trusses are typically connected by bolted or welded joints. For welded connections, the quality of the tube end preparation is critical. The tube ends should be cut perpendicular to the axis with a deviation of no more than 1 mm per 100 mm of diameter, and the bevel angle should be precisely controlled to 30° ± 2° for full-penetration groove welds. Inadequate end preparation leads to incomplete fusion at the weld root, which is a common cause of fatigue failure in truss joints under cyclic wind and seismic loading.

Local Buckling and Member Stability

A critical aspect of square tube truss stability that warrants emphasis is the interaction between global buckling and local buckling of the tube walls. For square tubes with width-to-thickness ratios (b/t) exceeding 30, local buckling of the flat walls can initiate before global member buckling, reducing the effective cross-sectional properties and thus the overall truss stability. According to GB 50017 and EN 1993-1-1, the limiting b/t ratio for plastic design of square hollow sections is 40ε, where ε = √(235/f_y). For Q345 steel (f_y = 345 MPa), this gives a limit of approximately 28.4, meaning that tubes with b/t > 28.4 require reduced design strength due to local buckling.

b/t Ratio	Local Buckling Classification	Design Strength Reduction	Recommended t for 100 mm Tube
< 20	Plastic (Class 1)	None	≥ 5 mm
20–28	Elastic-plastic (Class 2)	None	3.5–5 mm
28–40	Elastic (Class 3)	Moderate reduction	2.5–3.5 mm
> 40	Slender (Class 4)	Significant reduction	< 2.5 mm

The elastoplastic nonlinear analysis in this study implicitly accounts for local buckling through the material nonlinearity, but the accuracy of this representation depends on the stress–strain model used. For square tubes with high b/t ratios, a more refined model that explicitly captures local buckling behavior—such as a shell element formulation—would be more appropriate than the simplified beam element approach. This is an important consideration for engineers evaluating the safety reserve claimed in the paper.

Study Insights and Reflections

This paper provides a valuable demonstration of the importance of progressive nonlinear analysis in the stability assessment of large-span steel truss structures. The finding that the truss possesses a safety reserve is encouraging, but as I have emphasized, this reserve is highly dependent on manufacturing quality, particularly the control of initial imperfections and weld defects.

In my experience with truss manufacturing, the most common cause of stability-related failures is not the theoretical buckling capacity but rather the accumulation of local defects—weld cracks, tube ovality, and connection misalignment—that collectively reduce the actual load-bearing capacity below the analytical prediction. I strongly recommend that engineers performing stability analyses of large-span trusses incorporate measured initial imperfection profiles from the fabrication stage, rather than relying on assumed equivalent imperfection amplitudes. This practice, while requiring additional survey effort, provides a more reliable basis for safety assessment and is particularly important for structures with long service lives and high consequence of failure.