Wind Vibration Response Analysis of Four-Circuit Steel Pipe-Angle Steel Combined Transmission Tower

Literature Overview

This paper by Ju Yanzhong and Zhang Xiaolei from Northeast Electric Power University, published in the Journal of Basic Science and Engineering (Vol. 22, No. 5, 2014), presents a comprehensive wind vibration response analysis of a four-circuit steel pipe and angle steel combined lattice tower used in high-voltage transmission line engineering. The study employs finite element modeling combined with stochastic wind field simulation to evaluate the dynamic response characteristics of this hybrid structural system under wind loading. Two distinct wind field models are compared: one combining the Davenport wind speed spectrum with the Shiotani coherence function, and another combining the Kaimal wind speed spectrum with the Davenport coherence function. The analysis focuses on the along-wind dynamic response at a 90° wind direction angle over a 600-second simulation period with 10 samples for each wind field model.

Core Technical Points

Wind Field Modeling Approach

The selection of appropriate wind speed spectrum and coherence function models is fundamental to the accuracy of wind-induced response predictions for tall, flexible structures such as transmission towers. The Davenport spectrum, characterized by its exponential decay with frequency, has been widely used for wind engineering applications but may underestimate the contribution of high-frequency components. The Kaimal spectrum, derived from empirical measurements, provides a more realistic representation of turbulent wind characteristics across the frequency range. The coherence function describes the spatial correlation of wind fluctuations between different points on the structure, and the choice between Shiotani and Davenport formulations significantly affects the dynamic response prediction, particularly for wide-structure or multi-member systems.

The 90° wind direction angle represents a cross-wind orientation where the tower faces the wind perpendicular to the main axis of the structure. This orientation is critical because it maximizes the exposed frontal area of the tower members and produces the most severe wind loading conditions for a lattice tower with a rectangular or diamond cross-section.

Dynamic Response Statistical Analysis

The paper's key finding concerns the comparison between different statistical processing methods for dynamic response data. Three statistical approaches were employed: (1) mean of sample means, (2) root mean square (RMS) of sample values, and (3) mean plus or minus three times the root variance of sample values. The results demonstrate that the RMS method yields results close to the mean of means method, while the extreme value methods (maximum of samples, and mean ± 3σ) produce significantly higher response values.

These amplification factors have direct implications for structural design. If only mean-value analysis is performed, the actual extreme response may be underestimated by 30–70% for displacements and 14–29% for member axial forces, depending on the wind field model used. This represents a significant safety concern, particularly for structures where member buckling or fatigue damage is governed by peak axial forces.

Structural Behavior of Combined Towers

The four-circuit steel pipe and angle steel combined tower represents a hybrid structural system where steel pipe members (typically used for the main columns and critical bracing) provide superior buckling resistance and fatigue performance, while angle steel members (used for secondary bracing and non-critical connections) offer economic advantages. The interaction between these two member types creates complex load paths and dynamic coupling effects that must be properly captured in the finite element model. The steel pipe members, being more rigid in bending, attract a disproportionate share of the wind-induced bending moment, while the angle steel members primarily carry axial forces from the bracing action.

Process and Standards Analysis

The analysis methodology follows the general framework established by GB 50009 (Code for Wind Load Effects on Buildings and Structures) and GB 50660 (Code for Design of High Voltage Transmission Line Engineering), which recommend dynamic analysis for tall transmission towers where the first natural period exceeds a certain threshold. For four-circuit towers, which typically have heights exceeding 100 meters and first natural periods in the range of 1.0–2.5 seconds, dynamic analysis is essential to capture the resonant amplification effects that static analysis would miss.

The finite element model should include geometric nonlinearity to account for P-Δ effects, member-level wind loading with appropriate drag coefficients per GB 50660, and soil-structure interaction effects at the tower base. The damping ratio assumption is particularly important, as transmission towers typically exhibit low damping (1–2%) due to the absence of significant energy dissipation mechanisms, making them more susceptible to wind-induced resonant response.

Key Questions and Reflections

The paper raises several important questions for engineering practice. First, the significant discrepancy between Wind Field 1 and Wind Field 2 results suggests that the choice of wind field model is not merely an academic exercise but has direct consequences for design safety. Engineers must carefully select the wind field model based on the specific site conditions, terrain category, and structural characteristics of the tower. The Shiotani coherence function, with its faster decay of coherence with separation distance, produces higher dynamic amplification because it allows more independent fluctuation between different tower members, leading to larger overall structural response.

Second, the recommendation to perform multiple dynamic response analyses and obtain statistical results rather than relying on a single time history is well-founded. Wind turbulence is inherently stochastic, and a single simulation may not capture the extreme conditions that govern design. The paper's approach of using 10 samples per wind field model is a reasonable minimum, though modern computational capabilities would support even larger sample sizes for more robust statistical conclusions.

Third, the practical implication for tower design is that the design axial forces in critical members should be based on extreme value statistics rather than mean values. This may require increasing the cross-sectional area of main members or providing additional bracing to accommodate the higher peak forces identified through proper dynamic analysis.

Study Insights and Implications

This paper provides valuable methodological guidance for the wind engineering analysis of complex transmission towers. The key takeaway is that proper dynamic analysis, with appropriate wind field modeling and statistical processing of results, is essential for ensuring the safety and reliability of tall transmission towers. The significant amplification factors identified (up to 70% for displacements and 29% for axial forces) underscore the inadequacy of simplified static analysis methods for modern high-voltage transmission structures. Engineers should adopt the multi-sample stochastic analysis approach recommended in this paper as a standard practice for the design of four-circuit and multi-circuit transmission towers, particularly in high-wind regions. The findings also have implications for the inspection and maintenance of existing towers, as structures designed using simplified methods may be more vulnerable to wind-induced damage than previously assumed.