Wind Load Factors Research Articles

Investigation of wind loads on angle steel columns in lattice structures via force measurement method on members

As the demand for precise prediction of fatigue and collapse continues to grow, it is imperative to conduct research on wind load calculation methods for lattice structures using members as the fundamental unit. This study focuses on the tower body of an angle steel lattice structure with a rectangular cross-section. The aerodynamic characteristics of entire segments, column members in lattice structures, and a single angle steel were investigated, along with the aerodynamic interference effects on members within lattice structures. The research findings indicate that drag coefficients cannot universally substitute the SRSS coefficients of column members or a single angle steel across all wind directions. Therefore, considering that the drag coefficient of the column member or single angle steel surpasses 98% of their SRSS coefficients at a wind direction of 45°, a particular skewed wind load factor was defined, and its fitting formula was proposed. Additionally, a calculation method for wind loads on columns within lattice structures was developed, introducing the concepts of SRSS angle and aerodynamic interference factors on members. The comparison among the experimental data, fitting formula, and proposed calculation method, were conducted. To facilitate the practical application, the simplified formulas for both AIF and SRSS were recommended.

Experimental study on critical wind velocity of a 33-meter-span flexible photovoltaic support structure and its mitigation

Flexible photovoltaic (PV) modules support structures are extremely prone to wind-induced vibrations due to its low frequency and small mass. Wind-induced response and critical wind velocity of a 33-m-span flexible PV modules support structure was investigated by using wind tunnel tests based on elastic test model, and the effectiveness of three types of stability cables on enhancing the critical wind velocity of the flexible PV modules support structures was carefully examined. First, an elastic test model of the flexible PV modules support structure was designed and manufactured. Second, a series of wind tunnel tests based on the elastic test model were carried out to obtain the wind-induced responses of the 33-m-span PV modules support structure. Third, three types of stability cables (T1, T2 and T3) were installed on the test model, and a series of wind tunnel tests were carried out to examine the effectiveness of the three types of mitigation countermeasures. Finally, the wind load factor was discussed by using the displacement time histories measured from the wind tunnel tests. The results show that 180° and 0° are the two most unfavorable wind directions, and the critical wind velocity is only about 18.5 m/s for the deformation threshold of 1/100 span. The critical wind velocities for stability cables T1, T2 and T3 (1/100 of the span) are respectively 24.6, 29.3 and 36.7 m/s, which are significantly higher than the value without stability cable (18.5 m/s). The wind load factor at the windward side under wind directions of 0° and 180° are respectively 1.56 and 1.30 for the test case with stability cable T3.

Experimental Study of Wind Loads on Tubular Crossarms of Transmission Towers

The actions exerted by yawed wind on the crossarm substantially differ from those on the tower body due to the presence of the angle between the crossarm’s cross-section and the incoming flow, and this phenomenon deserves a better understanding. Focusing on the tubular crossarms with round-section members, this paper aims to determine insights into wind actions, as affected by various factors, such as the tower type, the mean width to mean height ratio, the solidity ratio, and the wind incidence angle, and thereby derive the wind loads for design. Accordingly, a succession of wind tunnel tests was conducted by using quadrilateral and triangular crossarm models with various solidity ratios and mean width to mean height ratios. The method of direct force measurement (DFM) is employed for the high frequency force balance (HFFB) test to attain the transverse and longitudinal forces on the crossarm simultaneously. It was found that the wind load coefficients increase with increases of the mean width to mean height ratio and decreases of the solidity ratio. Moreover, in the case of the incoming flow perpendicular to the crossarm face, it is concluded that compared to the quadrilateral crossarm, the triangular crossarm possesses a relatively smaller drag coefficient, provided a moderate mean width to mean height ratio of 1.19. Furthermore, an analysis of the experimental results shows that the skewed wind load factor specified in the relevant codes would overestimate the effects of the wind incidence angle and the variations in mean width to mean height ratio, which is evident in the tests but not considered in the codes. It is worth noting that the experimental results show that the crosswind force is pronounced, which is usually ignored in the skewed wind load factor-based approach. Comparatively, using wind load distribution factors seems to be more rational. Thus, the corresponding estimating equations are proposed for the wind load-distribution factors of the crossarms, which agree well with the experimental results. The developed equations would greatly facilitate the determination of wind loads on tubular crossarms.

Experimental study of static wind force on typical substation post disconnect switchgear three-post structure under different wind angles

As a wind load-sensitive structure, the wind characteristics of typical post-disconnect switchgear in substations are of great significance to the design of the wind resistance of the structure. To study the static wind characteristics of the three-post structure of post-disconnect switchgear, this paper conducts high-frequency force balance (HFFB) wind tunnel tests on the three-post model of post-disconnect switchgear and obtains information on the variation law of the static wind force coefficient of the model with the wind angle and the most unfavorable wind angle. The results show that the model drag coefficient, combined force coefficient, and skewed wind load factor are M-shaped and symmetric at about 90° under different wind angles, and the most unfavorable wind angles are 60° and 120°; the lift coefficient and torsional moment coefficient are antisymmetric about 0°, and the overall values are small. In general, the model is mainly subjected to along-wind static wind force, and the static wind force distribution is influenced by the skewed wind and changes uniformly. The model mainly produces a bending effect under the action of static wind force, and the torsion effect is not obvious.

Fitting generalized Pareto distribution based on the expected order statistics and its application for ice accretion hazard mapping

The extreme value analysis of the ice accretion thickness can be carried out based on the peaks-over-threshold (POT) approach to take advantage of the available rare samples in assessing the ice accretion thickness hazard. For the POT approach, the generalized Pareto distribution (GPD) with location, scale, and shape parameters has been frequently employed, although the estimators of parameters of GPD by using existing fitting methods could be associated with significant bias or variability. In the present study, we propose a new nonlinear least-squares fitting method by considering the expected order statistics. We compare its performance with some existing methods through simulation analysis, showing that the proposed method outperforms some well-known existing methods for a range of values of the shape parameter.We then apply the POT approach with GPD as well as the block maximum approach with Gumbel distribution to estimate T-year return period value of the annual maximum ice accretion thickness, xT, for Canadian sites. The analysis results indicate that xT is sensitive to whether the POT or the annual maximum approach with Gumbel distribution is employed. For the considered cases, the use of GPD fitted to POT values is preferred. Also, based on the wind-on-ice analysis results, it is suggested a companion wind load factor of about 0.5 to 0.55 could be adopted.

Evaluation of wind loads on square transmission towers with angle members under skewed winds

In the current wind loading codes for transmission towers, the wind loads under skewed winds are characterized by the global drag coefficient, skewed wind load factor, and wind load distribution factor. The recommended global drag coefficients in the codes borrowed from the lattice frames and trusses show discrepancy with the wind tunnel test. The skewed wind load factor reflecting the amplification of wind loads at skewed directions is demonstrated to vary with the tower geometry, which is not factored in the codes. In addition, the wind load distribution factor in the codes is determined by assuming that the wind load direction is the same as the wind direction, whose rationality needs to be examined. In this paper, a series of wind tunnel tests on the body, cross-arm and head sections of the widely used square angle-steel transmission towers are performed under multi-directional winds. Based on wind tunnel tests, the three coefficients and factors in the codes are extensively examined, and new formulas for them are calibrated. The results of this study could provide more accurate estimate of wind loads on the transmission towers.

Renewable Electricity Generation in Small Island Developing States: The Effect of Importing Ammonia

Recently, we demonstrated for Curaçao that renewable electricity generation from wind combined with energy storage in the form of ammonia is competitive with imported fossil fuels, such as LNG, oil, and coal. In the current work, we have expanded the model by considering imported green ammonia as an alternative to local electricity generation and storage. Local production of ammonia as an energy storage medium was compared with imported ammonia to make up the electricity produced from onshore wind, for Curaçao and Fiji’s largest island Viti Levu. Curaçao and Viti Levu have been selected as two interesting extremes with favorable and non-favorable wind conditions, respectively. Assuming a market price of 500 USD/t NH3, it is found that importing ammonia is the most feasible solution for both islands, with a levelized cost of electricity (LCOE) of 0.11 USD/kWh for Curaçao and 0.37 USD/kWh for Viti Levu. This compares to 0.12 USD/kWh for Curaçao; however, for Viti Levu, this value increases to 1.10 USD/kWh for a completely islanded system based on onshore wind and imported ammonia. These islands represent two extreme cases in terms of wind load factor and load consistency, as Curaçao has a high and consistent wind load factor when compared to Viti Levu. Thus, the conclusions obtained for these locations are expected to be applicable for other small island developing states.

Influence of Refined Wind Load Parameters and Wind-Loading Mode on Wind-Induced Responses of a Long Cross-Arm Angle-Steel Transmission Tower

This study aims to investigate refined wind load parameters on main rods and the influence of wind-loading mode on wind-induced responses of the angle-steel transmission tower. The wind load parameters discussed in this study include drag coefficients, wind load distribution factors and skewed wind load factors. To achieve the aim, wind tunnel tests were conducted to explore aerodynamic loads for integrated frame, single frame, and main rod models of cross-arm and tower body. The wind load parameters of the different models were investigated. In addition, a series of wind-induced vibration simulation was applied to examine the wind-induced responses of an ultra-high voltage (UHV) transmission tower with a long cross-arm under concentrated and distributed wind loads. The simulated results under the two types of wind loads were compared. The results show that the longitudinal drag coefficients of the main rods are smaller than the values of the integrated frame, and equivalent on average to the values of the single frame. The experimental shielding factor of the cross-arm is larger than those in different standards due to the joint drag effects of leeward, upper, and lower faces of the cross-arm in the wind tunnel test. The experimented shielding factor of the tower body is in line with those referring to the Chinese and AS/NZS standards, and slightly larger than those based on the British and JEC standards. The skewed wind load factors of the main rod models are quite different from other models for cross-arm and tower body. The wind-induced vibration simulation suggests that, the wind-loading mode has limited impact on the displacements, accelerations, and gust factors of the transmission tower, but significantly influences the maximum normal stresses (MNSs) of the rods’ cross-sections. The MNSs caused by the distributed wind loads are obviously greater than those caused by concentrated wind loads, especially for the rods at the two ends of the cross-arm.

Dynamic Windage Yaw Angle and Dynamic Wind Load Factor of a Suspension Insulator String

A simplified calculation method is proposed for determining the peak dynamic windage yaw angle φ ^ of electricity transmission line (TL) tower suspension insulator strings (SISs). According to the rigid-body rule, the geometric stiffness matrix in the calculation of the windage yaw angle φ of SISs is dominated by the average wind loads, while the fluctuating wind loads are the dominant factor in the elastic stiffness. With the average wind state of conductors as the initial calculation condition, the load-response-correlation (LRC) method can be used to determine the fluctuating windage yaw angle φ d and the corresponding equivalent static wind loads (ESWLs). Then, the improved rigid straight rod model, which uses the actual length of conductors rather than the projected length, was used to determine the average windage yaw angle φ ¯ . Through the linear superposition of the horizontal increments of φ ¯ and φ ^ d (the peak value of φ d ), the formulae to calculate the φ ^ of SISs were derived. Additionally, the formulae for the dynamic wind load factor, β c , which is a key factor in designing wind loads for φ , were derived according to the principle of ESWLs, rather than being empirically determined by the Chinese code. Thus, the calculation model regarding the loads and response for the φ of SISs was established, and an actual TL was used to verify the established calculation model. Afterward, the influence of the different engineering design parameters on φ and its β c were analyzed. The parameter analyses show that the wind speed, span, and ground roughness influence the magnitudes of φ ^ and β c , however, the height difference between the two suspension points of the conductors, the nominal height, and the sag-to-span ratio may be neglected in the approximate calculation. Our method offers a new solution to TL design when there are large deformations and small strains.

Investigation on aerodynamic characteristics for steel tubular cross-arms of transmission tower under skew wind

A study of the aerodynamic characteristics of steel tubular butterfly-shaped cross-arms in a transmission tower head under skew wind is presented. A wind tunnel test was conducted under skew wind by using a scaling model, and a numerical simulation was performed with a high-precision three-dimensional tower head model. The drag coefficient, skew wind load factor, and wind load distribution factor of the cross-arms obtained from the experiment and numerical simulation were identified and compared with those acquired from different codes. It is concluded that the indirect force measurement method was found to underestimate aerodynamic forces acting on windward cross-arms. For single cross-arm, the horizontal cross-arm showed stronger shielding effect than the inclined cross-arm. A fitting formula for the skew wind load factor of the cross-arm is proposed, and values obtained from it matched experimental and simulation data well. A comparison between calculated and measured wind load distribution factors showed that although longitudinal load distribution factors calculated with the Chinese standard (2018) were consistent with measured data, calculated transverse load distribution factors did not match measurements well. It is suggested that the effect of the transverse lift wind force should be considered in the calculation of wind load distribution factors.

Calibration of the design wind load and snow load considering the historical climate statistics and climate change effects

In the present study, an updating of the probabilistic models used for calibrating the wind load, snow load and companion load factors for the National Building Code of Canada (NBCC) are presented. The update of probabilistic models for the extreme wind speed and ground snow depth is based on historical climatological data over Canadian sites. For the updating of the statistics of the extreme wind speed, the effect of mixed wind climate (i.e., thunderstorm winds and non-thunderstorm winds) is considered. Reliability analysis is carried out based on this update by considering different load combinations. The results indicate that, for an improved reliability consistency, the use of a high return period to specify the environmental loads and with a unit load factor is preferable to the use of 50 year return period and a load factor greater than one for structural design code making, if the coefficient of variation of the extreme climatological elements is spatially varying. Most importantly, based on these findings and the results from the climate change modelling results, sets of load scaling factors accounting for climate change effects are calibrated for different regions in Canada. Both the use of the target reliability index for a 50-year design working life as well as of the target minimum required annual reliability index within each of the 50-year design working life are considered for the reliability-based calibration. Specific recommendations on the load and companion load factors are suggested for a future edition of NBCC.

Experimental and numerical study on the aerodynamic characteristics of steel tubular transmission tower bodies under skew winds

A study of the aerodynamic characteristics of circular steel tubular lattice tower bodies in an ultrahigh-voltage direct-current transmission tower under skew winds is presented. The objective of the study, which was based on experimental and numerical methods, was to investigate the aerodynamic coefficients of tower bodies under both yaw and tilt angles. Scaled rigid models of tower bodies with a scale ratio of 1:30 were tested, and the influence of the wind velocity and turbulence intensity on the aerodynamic coefficient was examined. Furthermore, a modified formula for the skewed wind load factor is proposed and compared with different standards. The aerodynamic coefficients of tower bodies with different solidity ratios and tilt angles were obtained via numerical simulation. Additionally, a recommended calculation formula of tilted wind load factor is proposed. The results show that the drag coefficients calculated by standards for different yaw angles were significantly underestimated and that the wind direction corresponding to the predicted maximum drag coefficient was inconsistent with observed wind direction. The formulas proposed in this study accurately describe the characteristics of wind load factor under different yaw and tilt angles. In particular, the influence of the tilt angle on the drag coefficient cannot be ignored.

Investigation on Combined Wind Load Factors of Lattice Transmission Tower Body under the Action of Skewed Wind

In the current standards, wind loads on lattice transmission tower (LTT) bodies only account for the action of horizontal winds, which may not be suitable for an LTT under the action of extreme winds. The wind load coefficients of LTT bodies subjected the skewed wind with both horizontal and vertical components were measured via several well-designed wind tunnel tests. The test results and standard calculations of the skewed wind load factors (SWLF) at a wind attack angle of 0° were compared and analyzed. A new parameter—combined wind load factor (CWLF) was introduced, and a suggested formula is proposed for it. The results showed that the standard-recommended formula was unable to accurately reflect the characteristics of SWLF, and its calculated results were significantly smaller than the test results, indicating that the actual wind loads were underestimated. The CWLF could correctly describe how wind load factors changed with the yaw angles or the attack angles. The CWLF effectively improved the calculation accuracy of the SWLF, and the absolute error between the calculations and test results under the critical yaw and attack angles was less than 7%.

Variational Mode Decomposition Based Time-Varying Force Identification of Stay Cables

Stay cables are important structural members of cable-stayed bridges, which play a significant role in the health monitoring and assessment of cable-stayed bridges. The in-service cable force, which varies from the effects of vehicle load, wind load and other environmental factors, may cause fatigue damage in stay cables. Traditional force identification methods can only calculate the time-average cable force instead of the instantaneous force. A novel method has been proposed in this paper for identifying time-varying cable tension based on the variational mode decomposition (VMD) method. This recent method decomposes signals and adaptively estimates instantaneous frequency combined with the Hilbert–Huang transform method. In the proposed study, the time-varying modal frequencies were identified from stay cable acceleration data, and then the time-varying cable tension was identified by the relationship between cable tension and identified fundamental frequency. Scaled and full-scale models of stay cables were implemented successively to illustrate the validity of the proposed method. The results showed that the variational mode decomposition (VMD) method has a good effect on identifying the time-varying cable forces, even the sudden changes in cable force. According to the cable force identification results, the maximum error was 8.4%, which meets the actual application of time-varying cable force measurements. An on-site test was also implemented to monitor the cable force during a construction period, and the results showed that the proposed method can provide accurate real-time results for evaluation and decision-making.

Mean wind loads on equilateral triangular lattice tower under skewed wind loading

Compared with lattice towers with square or rectangle cross sections, triangular lattice towers have the advantage of smaller foundation footprint. Triangular lattice towers have been widely used in transmission towers and communication towers, yet only a few studies have been conducted on their wind loads. Therefore, a series of wind tunnel tests on a triangular lattice tower were conducted using direct force measurements in this study. Effective drag coefficients and effective skewed wind load factors normalized with the “true” windward projected areas were proposed and obtained from the test results. Piecewise functions were suggested to calculate the effective skewed wind load factors and skewed wind load factors. It is found that the skewed wind load factors show an approximate “W” profile which the British standard formula does not fit. The effective skewed wind load factors show a strong regularity and are only related to yaw angles and solidity ratios. The analytical effective skewed wind load factors have a good agreement with fitting results with a maximum error of 3.1%. The recommended formula for skewed wind load factors is concise and can effectively illustrate the changing tendency of drag coefficient curves.

Wind Tunnel Investigations of Aeroelastic Electricity Transmission Tower under Synoptic and Typhoon Winds

Wind tunnel tests of an aeroelastic tower model at a length scale of 1∶40 were conducted to investigate the dynamic responses of an electricity transmission tower under synoptic and typhoon winds. The aeroelastic tower model was successively subjected to boundary layer and typhoon wind forcing in a single wind tunnel. The purpose of this study is to assess differences of the dynamic structural responses under two types of wind forcing and understand the underlying mechanism of transmission tower failures due to strong typhoons. The results indicated that the acceleration responses of the aeroelastic tower model were composed of resonant and background parts, while dominated by the resonant counterpart, and the dynamic responses of the transmission tower could be increased by up to 30% in the along-wind and crosswind directions under typhoon wind forcing. The wind load factors determined from the experimental results under typhoon winds were generally larger than those obtained from Chinese codes and standards. Suggestions on the wind-resistant design of an overhead transmission tower in typhoon-prone areas were proposed. The dynamic wind loads should be substituted by the most conservative values among different Chinese standards in estimating the equivalent static wind loadings of overhead towers under typhoon wind forcing.

Reliability evaluation of reinforced concrete columns designed by Eurocode for wind-dominated combination considering random loads eccentricity

With the capacity models in the 2004 edition of the European Committee for Standardization’s Standard Design of Concrete Structures, a more realistic limit state function is obtained for reinforced concrete columns with random loads eccentricity. Using this function, the applicability of the code-based design factors is discussed. Taking the wind-dominated combination as an example, the probabilistic distribution of loads eccentricity and the statistics of column resistance are analyzed for representative cases. The analysis indicates that the possible loads eccentricity is scattered over a large range, and the probabilistic model of column resistance varies from case to case, which is largely different from the resistance model assumed in previous reliability calibration. With Monte Carlo simulation, the column reliability and the contributions of both tension failure and compression failure to the total failure probability are calculated and obtained for different cases. The results show that the fixed loads eccentricity criterion underestimates differences in the reliability of columns for different loads eccentricity cases and overestimates the column reliability in some tension failure cases. Furthermore, it is found that the tension failure mode contributes most to the total failure probability for not only some columns designed to fail in tension failure but also for some columns designed to fail in compression failure. To attain a robust design, a group of optimum wind load factors varying with cases is recommended. The new calibration results prove that the recommended wind local factors can achieve a better goal.

Investigation on wind loads on angle-steel cross-arms of lattice transmission towers via direct force measurement

Cross-arms are key structural components of transmission towers usually located horizontally on the upper part and therefore bear large wind loads that contribute a lot to the base bending moment. In wind tunnel tests of wind loads on cross-arms, indirect force measurement (IFM) method is usually applied, which obtains the wind loads on the cross-arms by subtracting the forces measured on tower-body models with and without the cross-arms. This method over-simplifies the interference of the flow field between the cross-arm and the tower-body and therefore cannot provide an accurate evaluation on the exact wind forces on the cross-arm. A novel wind tunnel test method – direct force measurement (DFM) method, which directly measures the wind loads on a cross-arm attached to a tower model, is proposed in this article. DFM method and IFM method are both employed to investigate wind loads on cross-arms of a lattice transmission tower. Drag coefficients and cross-wind force coefficients of cross-arms are then identified. Wind tunnel test results and standard-calculated values of skewed wind load factors are compared. Calculation methods of wind load distribution factors from various standards are derived and wind tunnel test results and standard calculations are compared. It is concluded that drag coefficients of cross-arms obtained with the DFM method is very close to the standard-calculated values and are larger than those obtained with IFM method. A fitting formula for the skewed wind load factors is proposed which well fits the test data. Comparison between wind load distribution methods illustrates that ASCE (2010) standard-calculated values match well with all wind tunnel test results which show significant differences from other standards. It is indicated from wind tunnel test results that the calculation formula for skewed wind factor proposed in this article is simple but effective.

Wind Pressure Statistics and Target Reliability Index for Wind Load-governed Limit State of Reliability-based Bridge Design Codes

This paper presents a general procedure for evaluating a proper target reliability index and corresponding wind load factor for a wind load-governed limit state in reliability-based design codes. The Monte-Carlo simulation is conducted to reveal relationships between statistical parameters of wind velocity and pressure. The normalized wind pressure is defined and used in the simulations. The analytical form of the wind load factor is presented in terms of the statistical parameters of wind velocity and the target reliability index. The return period of a nominal wind velocity is expressed for the target reliability index and the wind load factor. An approach determining the target reliability index based on the return period of wind velocity at the limit state is proposed. The return period of wind velocity at the limit state is set to that of the design earthquake in a design code. The proposed approach is applied to calculate the target reliability index for the Korean Highway Bridge Design Code-Cable supported Bridge. The target reliability index is found as 2.25, and the corresponding wind load factor ranges from 1.60 to 1.82 depending on the Coefficient of Variation (COV) of wind velocity. Detailed discussions on the return period of wind velocity, target reliability index and wind load factor are made. A simplified expression of the wind load factor corresponding to the target reliability of 2.25 is proposed. The basic wind velocities for five regions in the Korean Highway Bridge Design Code (Limit State Design) are estimated through the proposed procedure.

Wind loads on transmission tower bodies under skew winds with both yaw and tilt angles

Transmission tower networks play an important role in the infrastructure system of many countries around the world. Many studies have been directed towards the evaluation of aerodynamic coefficients of the vertical tower body sections of transmission towers. Most of these studies obtain drag coefficients of tower sections from wind tunnel tests with yawed wind. However, strong winds like hurricane, downburst, tornado etc., which are the leading causes of transmission tower failures, often attack the towers with both yaw and tilt angles. Transmission towers constructed on the top or slope of mountains may also suffer the action of skew winds with both yaw and tilt angles. This paper addresses wind loads of transmission towers under winds with both yaw and tilt angles. By performing wind tunnel tests with multi-balance synchronous force measurement, the wind loads acting on a lattice tubular steel transmission tower under skew winds were measured, and the drag coefficients under 19 yaw angles and 13 tilt angles were obtained. Besides providing a more accurate modified formula for the skewed wind load factor, concepts of tilted and combined wind load factors are proposed with recommended formulas. By comparing the experimental and standard-calculated values of skewed wind load factor under a tilt angle of 0°, it is found that the standards underestimate the skewed wind load factor by at least about 10%, whereas the error of the proposed formula is less than 4% under the design key angles. In this study, the values of tilted wind factor under a yaw angle of 0° and combined wind load factor are recommended as 0.3 and 0.2, respectively. When the recommended values are used in calculation, the deviations between calculated drag coefficients and wind tunnel test results are less than 5%.