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

Literature Overview

This paper published in the Journal of Basic Science and Engineering Applications in 2014 (Volume 22, Issue 5, pages 964-975) presents a wind vibration response analysis of a four-circuit steel pipe and angle steel combined lattice tower for high-voltage transmission lines. The authors, Ju Yanzhong and Zhang Xiaolei from Northeast Electric Power University, address the dynamic behavior of a complex hybrid structural system under stochastic wind loading conditions. The work is particularly relevant to transmission line engineers who must design towers that can withstand extreme wind events while maintaining economic efficiency.

The four-circuit configuration represents a significant structural challenge because it combines the aerodynamic complexity of multiple conductor bundles with the dynamic interaction between steel pipe and angle steel members. Unlike conventional all-angle-steel or all-tube towers, this hybrid design leverages the superior bending stiffness of steel tubes for primary load-bearing members while utilizing the economic efficiency of angle steel for secondary bracing and panel members.

Core Technical Approach and Methodology

Wind Field Simulation

The authors employ two distinct wind field models to simulate the stochastic wind loading, recognizing that different spectral models can yield significantly different dynamic response predictions:

The Davenport spectrum is widely used for boundary layer wind modeling and provides a good approximation of the mean wind speed profile with height. The Kaimal spectrum, derived from extensive field measurements, captures additional high-frequency content that may be significant for structural response at higher modes. The Shiotani coherence function and Davenport coherence function represent different assumptions about the spatial correlation of wind velocity across the tower cross-section.

Dynamic Analysis Methodology

The analysis employs a Monte Carlo simulation approach with 10 samples per wind field condition, each simulating a 600-second duration wind event at a 90-degree wind direction angle. This approach captures the statistical variability of wind loading and provides more realistic response estimates than deterministic equivalent static wind loading methods.

The finite element model of the tower represents the steel pipe members as beam elements with appropriate cross-sectional properties and the angle steel members with their actual cross-sectional geometry. The joint behavior is modeled with rigid connections, which is a simplification that may underpredict local flexibility at bolted or welded connections.

Key Results

The statistical analysis reveals important insights about the adequacy of different response estimation methods:

The most striking finding is that the mean of sample maxima can be 58-70% larger than the mean of means for displacement responses under Wind Field 1 conditions. This magnitude of difference has direct implications for design load estimation and safety factor calibration. The axial force response shows a more moderate amplification, suggesting that the displacement response is more sensitive to the stochastic nature of wind loading.

Technical Interpretation and Engineering Implications

Spectral Model Sensitivity

The comparison between Wind Field 1 and Wind Field 2 reveals that the choice of spectral model significantly affects the predicted dynamic response. Wind Field 1 (Davenport spectrum with Shiotani coherence) produces larger response amplifications than Wind Field 2 (Kaimal spectrum with Davenport coherence). This finding underscores the importance of selecting appropriate wind field models that represent the actual wind climate at the tower location.

The difference between the two wind fields likely stems from the coherence function assumption. The Shiotani coherence function exhibits lower coherence at higher separation distances, which effectively increases the turbulence intensity experienced by the structure. For a four-circuit tower with significant width, the spatial correlation of wind loading across the tower face is a critical parameter that directly influences the dynamic amplification.

Structural Response Characteristics

The four-circuit configuration creates a complex aerodynamic loading pattern. The multiple conductor bundles generate distinct vortex shedding patterns that interact with each other and with the tower structure. The steel pipe members, with their smooth cylindrical surface, exhibit different aerodynamic characteristics compared to the angle steel members, which have a more complex cross-sectional geometry that promotes earlier flow separation.

The dynamic response analysis reveals that the tower's first few modes dominate the response, as expected for a tall slender structure. However, the four-circuit configuration introduces additional modes related to the asymmetric loading of the conductor bundles, which can couple with the tower's structural modes to produce unexpected response peaks.

Design Code Implications

The results suggest that conventional design approaches based on equivalent static wind loads or single-sample dynamic analysis may be non-conservative for this type of structure. The 58-70% amplification in displacement response indicates that the design displacement demand could be substantially underestimated if only mean values are considered. This has implications for:

• Conductor sag and clearance calculations under wind loading
• Tower member stress verification under dynamic loading
• Foundation design considering dynamic overturning moments
• Fatigue assessment of critical connections

Study Insights and Recommendations

From a practical engineering perspective, this study provides several valuable recommendations:

1. Multiple-sample dynamic analysis should be standard practice: The significant variability between samples demonstrates that single-sample analysis is insufficient for critical transmission towers. At minimum, 10 samples should be analyzed to capture the statistical characteristics of the response.
2. Spectral model selection requires site-specific justification: The large difference between the two wind field models indicates that the choice of spectral parameters is not trivial. Site-specific wind measurement data should be used to calibrate the spectral model whenever possible.
3. Hybrid tower design requires careful dynamic analysis: The combination of steel pipe and angle steel members creates a structurally heterogeneous system that may exhibit complex dynamic behavior. The dynamic analysis should account for the different stiffness characteristics of the two member types.
4. Response estimation methodology should be explicitly defined: The difference between "mean of means" and "mean of sample maxima" highlights the importance of clearly defining the response metric used for design. Design codes should specify which statistical measure is appropriate for serviceability and ultimate limit state checks.

Summary

This literature provides valuable insights into the dynamic wind response of four-circuit steel pipe-angle steel combined transmission towers. The key finding is that stochastic wind loading can produce response amplifications of 58-70% in displacement compared to deterministic mean-value approaches, with significant sensitivity to the choice of spectral model. For practicing engineers, the study underscores the importance of employing rigorous dynamic analysis methods with appropriate statistical treatment when designing complex transmission towers. The hybrid structural configuration, while offering economic and performance advantages, introduces additional complexity that must be properly addressed in the design phase to ensure long-term structural reliability under extreme wind events.