Experimental study on wind force coefficient of a truss arch tower with multiple skewbacks

Abstract

A truss arch tower is a large-span arch structure with multiple skewbacks. This tower is made of a large number of members with unique form, and contains more than five kinds of geometric features. The wind forces and the corresponding wind effects on the truss arch tower are notably complicated. In this study, wind tunnel tests were conducted to evaluate the wind forces on the steel latticed structure mentioned above using the high-frequency base balance technique. Four segmental models, including one arch foot of main truss, two arch feet of sub-truss, and one arch crown of main truss were tested in nominally smooth flow. The drag forces were measured and compared with several existing codes, including the British, American, and Chinese codes. The incidence angle effects and the interference effects on the drag coefficient were analyzed. The testing results showed that the direction of the wind forces has a marked effect on the whole truss tower. The solidity ratio and layout of the segmental models, including the cross-section and the centerline of the members, have critical effects on the drag forces.

Keywords

drag coefficient interference effect segmental model truss arch tower wind tunnel test

Introduction

Steel truss towers are made of steel latticed members and are being increasingly used in high-rise structures, such as transmission towers. This type of structure is characterized by light weight, high flexibility, and low damping (Fu and Li, 2007; Li et al., 2017), and the wind load of steel latticed structures is one of the main controlling factors. Many structural failures and progressive collapses of the power transmission towers have been induced by strong wind (Asgarian et al., 2016; Holmes, 2008; Moon et al., 2009). Therefore, new types of truss towers with high stability and high wind resistance should be designed and constructed. A truss arch tower has a large span and multiple skewbacks, which takes advantages of its high structural stability characteristics. The wind forces on a truss arch tower structure are different and more complex than those on a regular steel truss tower. Thus, special studies of the parameter values and calculation methods for these wind loads are warranted to determine the wind loads in structural wind-resistance design.

The wind loads on steel truss towers can be evaluated by two methods: (1) wind tunnel test approach with global or local downscaled models of generic shapes and layouts and (2) computational fluid dynamics (CFD) approach. Studies have been conducted by CFD analysis combined with wind tunnel tests in order to calculate the wind forces acting on steel transmission towers more accurately. Yang et al. (2016) studied the wind loads acting on an angled steel triangular transmission tower by simplifying the tower geometry for their wind tunnel tests and CFD simulations. Deng et al. (2016) investigated the response of a transmission tower subjected to skewed incident winds. Calotescu and Solari (2016) studied the along wind load effects on latticed towers. Xie et al. (2017) conducted a study on wind-induced vibration of transmission tower systems. To decrease the computational time and cost of the simulations, Allegrini et al. (2018) predicted the drag force of a latticed transmission tower based on a computationally efficient porous media CFD model. However, determining the wind loads on a transmission tower with CFD remains infeasible with the currently available computational power.

The resultant force acts in the direction of the wind for the latticed structures and does not consider the calculation of the orthogonal side force in most codes. Being developed and verified on the basis of numerous tests (Bayar, 1986; Georgiou and Vickery, 1980; Whitbread, 1980), this method is highly effective for regular lattices subjected to crossflow. For the latticed structures with irregular or complex geometry at varied wind incidence angles, this method is difficult to apply. However, a modification factor of the wind force is considered with the solidity ratio method, which takes into account the shielding effect of the upstream lattice on the downstream lattice and the diffusion in its wake (National Building Code of Canada (NBCC), 2015). Wind tunnel tests have been most widely used to estimate the wind-induced structural dynamic response of normal structures, such as long-span bridges (Zhang and Ge, 2017; Zhang et al., 2019a, 2019b), building structures (MOHURD, 2012; Zhang and Li, 2017), and high-rise steel latticed structures (Carril et al., 2003; Prud’homme et al., 2018). These tests are the base of the present design codes. For steel latticed structures, there are two main methods (Prud’homme et al., 2014): (1) a global method in which the wind forces are evaluated directly on a whole truss or part of a truss and (2) a local method in which the wind forces are evaluated on each member separately. The first method has been adopted by most codes. This method is based on the drag coefficients determined as a function of the solidity ratio, which may introduce the correction factors of the wind incident angle and the aspect ratio of the truss (BSI, 2005). In the second method, the wind force on a member outside of any wake can be evaluated directly with the force coefficient of the section alone. The wind mean forces on a member need to be calculated using a velocity value that differs from the value of the unperturbed wind or force coefficients that considers the shielding effect. However, there is no local method available to determine the wind force on trusses made of angle members.

In wind tunnel testing, the high-frequency base balance (HFBB) testing technique is commonly used in the load measurements (Chen and Kareem, 2005; Xie and Garber, 2014). This popularity is observed not only because of the low cost, technical simplicity, compact size, and easy operation of this technique but also because of the simple demand for information about the geometric shape of the structures. In the HFBB testing technique, three overturning forces and three torsional moments induced by wind in three directions can be measured, and the shape coefficient can be obtained by considering the flow field effect and Reynolds number effect for the truss towers. Simiu and Scanlan (1996) determined the relationship between drag coefficients and Reynolds numbers of square-section circular-latticed tower structures when the length-to-width ratio is infinite. Georgakis et al. (2009) measured the drag coefficients of four different triangular-latticed mast configurations in a wind tunnel and reported that compared with various design standards, the drag coefficient is generally underestimated when its tested in nominally smooth flow tests, while it is overestimated under turbulent flow. Mara and Galsworthy (2011) completed a series of wind tunnel tests on a typical three-dimensional lattice frame and compared the experimental results to those measured for a corresponding prototype under similar flow conditions for different wind incidence angles. The conclusions of these researchers indicated that the model-scale section tests successfully evaluated the drag coefficient of a triangular-section lattice frame. Reynolds number mismatches between the model-scale section tests and the prototype tests had a small influence on both the individual member drag forces and the overall group effect. Prud’homme et al. (2014) evaluated the aerodynamic loads on simplified latticed structures by taking into account the force on each individual member and the effect of Reynolds number, edge shape, and thickness ratio in smooth and turbulent flows. The results showed that Reynolds numbers between 14,000 and 38,100 have a negligible effect on drag coefficients, and turbulence generally reduces the drag coefficients. Li et al. (2017) experimentally investigated the effects of the vertical and inclined leg members on the aerodynamic forces of circular steel tubular lattice structures and the interference mechanism between the leg and diagonal members. The aforementioned studies indicate that the HFBB technique has sufficient accuracy to measure the wind loads for the wind-resistant design of high-rise latticed structures.

The regulations on the wind loads of tower-type structures with single-leg supports are outlined in various design codes (BSI, 1986, 2013; CEPPEI, 2012; MOHURD, 2012; SEI, 2010). For example, the calculation methods for the shape coefficients of different body types, including latticed truss structures, tower structures, round-section components, and single-pole structures, are available in the Chinese structural design standard (MOHURD, 2012). However, regulations and research on the wind force coefficients of multi-leg supported structures are rare.

This study experimentally investigated the aerodynamic loads of a truss arch tower using the HFBB technique under nominally smooth flow and elucidated the underlying mechanism of wind loads by considering the effect of the multiple skewbacks. The drag coefficients of four segmental models of the truss arch tower were tested under different wind incidence angles. The interference effect between nearby skewbacks was revealed and described with an interference factor.

Wind tunnel tests

Test conditions

The wind tunnel tests using the HFBB technique were conducted in the CSU-2 wind tunnel of Central South University, Changsha, China. The width and height of the cross-section were 12. and 3.5 m, respectively. The wind speed ranged from 0 to 20 m/s. All experiments were carried out in nominally smooth flow with a turbulence intensity lower than 0.8%. The nonuniformity of the wind velocity in the test region is less than 2%. The fluctuating wind forces were measured under a wind speed of 12 m/s with a carefully calibrated six-component HFBB.

Truss arch tower geometry

The truss arch tower is a three-axis symmetrical latticed structure with a span of 200.8 m that is supported by six legs, as shown in Figure 1. This tower is composed of one main truss and four sub-trusses. The inside chord of the main truss is a semi-arc with a diameter of 100.4 m. Four arch-shaped sub-trusses enhance the main truss on both sides of both legs. The configuration and the corresponding global coordinate system of the structure are illustrated in Figure 1. The truss tower is composed of 3462 truss members with different geometric characteristics. All of them are made of round steel pipes. Table 1 summarizes the geometrical characteristics of the prototype.

Figure 1.

Configuration of the truss arch tower (unit: mm): 1-chord member; 2-vertical web member; 3-diagonal web member.

Table 1.

Sectional characteristics of the main members.

Member No.	Size (mm)		Area, A_p (cm²)	Inertial moment, I (cm⁴)	Gyration radius, i (cm)	Elastic modulus, E (MPa)	Specific gravity, ρ (kg/m³)
Member No.	Outer diameter, D_p	Thickness, t	Area, A_p (cm²)	Inertial moment, I (cm⁴)	Gyration radius, i (cm)	Elastic modulus, E (MPa)	Specific gravity, ρ (kg/m³)
1	325	10	98.96	1.2287E + 04	11.143	2.1 × 10⁵	7850
2	299	8	73.14	7.7474E + 03	10.292	2.1 × 10⁵	7850
1	245	7	52.34	3.7091E + 03	8.418	2.1 × 10⁵	7850
3	194	6	35.44	1.5672E + 03	6.650	2.1 × 10⁵	7850
1, 3	168	6	30.54	1.0031E + 03	5.731	2.1 × 10⁵	7850

Four typical segments of the truss arch tower, including one arch foot of the main truss (AFMT), two arch feet of the sub-truss (AFST), and one arch crown of the main truss (ACMT), as shown in Figure 1, were selected for wind tunnel tests. The scaled ratio is set as 1/20. The heights $H$ of segmental models AFMT, AFST, and ACMT are 0.79, 0.78, and 0.602 m, respectively. The AFMT and AFST sections are 0.3 m × 0.3 m, and the ACMT section is 0.2 m × 0.2 m. The calculation formula of the Reynolds number is $R_{e} = VD / ν$ , where $V$ is the mean wind speed (12 m/s), $D$ is the outside diameter of the tubular member, and $ν$ is the kinematic viscosity of air $(ν = 1.45 \times 10^{- 5} m^{2} / s)$ . The outer diameters and Reynolds numbers $R_{e}$ of the aforementioned cylinder members are listed in Table 2. The Reynolds number $R_{e}$ , which is 6.9 × 10³–1.34 × 10⁴, is in the subcritical range. The Reynolds number effect on the average drag coefficients and flow field of the cylinder is small (Liu et al., 2016).

Table 2.

External diameters and Reynolds numbers of the cylinder members.

Item	Member No.	Outer diameter D (10⁻³ m)	R _e
Model AFMT	1	16.25	1.34 × 10⁴
	2	14.95	1.23 × 10⁴
	3	9.70	7.97 × 10³
Model AFST	1	16.25	1.34 × 10⁴
	2	14.95	1.23 × 10⁴
	3	8.40	6.90 × 10³
Model ACMT	1	12.25	1.01 × 10⁴
	2	14.95	1.23 × 10⁴
	3	9.70	7.97 × 10³

AFMT: arch foot of main truss; AFST: arch foot of sub-truss; ACMT: arch crown of main truss.

Test cases

The wind incidence angle β for the segmental models is defined as shown in Figure 2. The interval of the wind incidence angle is 15°. The general views for the location and local coordinate system of segmental models are illustrated in Figure 3. The segmental models were fixed vertically on the HFBB using the base-plate, which was approximately 120 mm away from the bottom wall of the CSU-2 wind tunnel, as shown in Figure 4. The transverse bracing was set as the end plate. Considering the complex geometry, arched sectional axis, small diameter (8.4–16.25 mm), and small subcritical Reynolds number effect of the cylinder members for the segmental models, the end effect was not to be considered in this study. The HFBB coordinate systems were consistent with the local coordinate systems of the segmental models.

Figure 2.

Definition of the wind incidence angle.

Figure 3.

Locations and local coordinate systems of segmental models.

Figure 4.

Photos of the segmental models in the wind tunnel: (a) AFMT in Case 1; (b) AFST in Case 2; (c) ACMT in Case 3; and (d) three segmental models in Case 4.

The center distance 36.9 m of the AFMT and AFST sections was smaller than the tower height 100.4 m. At different wind incidence angles, the degree of occlusion between the three arch feet for the truss arch tower was different; therefore, the interference effect of nearby trusses was considered. To investigate the characteristics of the drag coefficient, the interference effect and the skewed wind loads of the latticed truss tower, four test cases were designed. All test cases are listed in Table 3 and shown in Figure 4. Cases 1 to 3 investigated the local drag coefficient of segmental models of AFMT, 1^#AFST, and ACMT at different wind incident angles, respectively. The interference effect of nearby segmental models of the skewbacks was ignored. Case 4 investigated the local drag coefficients of segmental models of AFMT and 1^#AFST by considering the interference effects of nearby segmental models of the skewbacks. In Case 3, the segmental model of ACMT was horizontally arranged to change the wind attack angle easily, and the wind attack angle varied from –12° to +12° with an interval of 1°.

Table 3.

Illustrations of the wind tunnel test cases.

Case No.	Model arrangement	Model mounted with HFBB	β (°)
1	Single AFMT	AFMT	−180°~+ 180°
2	Single 1^#AFST	1^#AFST	−180°~+ 180°
3	Single ACMT	ACMT	−12°~+ 12°
4	AFMT + 1^#AFST + 2^#AFST	AFMT + 1^#AFST	−180°~+ 180°

HFBB: high-frequency base balance; AFMT: arch foot of main truss; AFST: arch foot of sub-truss; ACMT: arch crown of main truss.

Experimental results and discussion

Data process

The measured data were processed and expressed using dimensionless parameters, as shown in equation (1)

F_{i} = \frac{1}{2} ρ V^{2} C_{i} ϕ_{i} BH

(1)

where $i = X', Y' and Z'$ are the three main directions in the local coordinate system; $F_{i}$ and $C_{i}$ are the overall aerodynamic forces and force coefficient of a segmental model corresponding to the ith direction, respectively; $ρ$ is the air density; $V = 12 m / s$ is the mean wind speed; $ϕ_{i}$ is the solidity ratio of the total projected area in the windward face perpendicular to the ith direction; $B$ is the nominal cross-sectional dimension, as defined in Figure 5; and $H$ is the height of the segmental model. In subsequent discussions, the experimental results are presented in terms of dimensionless parameters $C_{i} ϕ_{i} = {P_{C ϕ}}_{i}$ , similar to the effective projected area used in bridge structures (ANSI, 2006). This method reduces the solidity ratio effect when discussing the yaw angle effect. Figure 5 shows the definition of body axis coordinates and wind axis coordinates.

Figure 5.

Definition of aerodynamic forces in body axis and wind axis coordinates.

The measured dimensionless drag and lift parameters of the segmental models in the body axis coordinates, ${P_{C ϕ}}_{X'}$ and ${P_{C ϕ}}_{Y'}$ , transform into those in wind axis coordinates, $C_{D β} ϕ_{β}$ and $C_{L β} ϕ_{β}$ , through the following equations

C_{D β} ϕ_{β} = {P_{C ϕ}}_{X'} \cos β + {P_{C ϕ}}_{Y'} \sin β

(2)

C_{L β} ϕ_{β} = {P_{C ϕ}}_{Y'} \cos β - {P_{C ϕ}}_{X'} \sin β

(3)

where $ϕ_{β}$ is the solidity ratio of the windward face under a wind incidence angle β. The corresponding local drag coefficient $C_{D β}$ and lift coefficient $C_{L β}$ are expressed as

C_{D β} = \frac{{P_{C ϕ}}_{X'} \cos β + {P_{C ϕ}}_{Y'} \sin β}{ϕ_{β}}

(4)

C_{L β} = \frac{{P_{C ϕ}}_{Y'} \cos β - {P_{C ϕ}}_{X'} \sin β}{ϕ_{β}}

(5)

Effect of wind incidence angles

The aerodynamic force parameters ${P_{C ϕ}}_{X'}$ and ${P_{C ϕ}}_{Y'}$ in the local coordinate system of three separate models mentioned in Case 1, Case 2, and Case 3 are calculated according to equation (1). Figures 6 and 7 show the calculated ${P_{C ϕ}}_{X'}$ and ${P_{C ϕ}}_{Y'}$ of Case 1, Case 2, and Case 3 under different incidence angles. The results show that the ${P_{C ϕ}}_{X'}$ parameters of the AFMT and AFST models are antisymmetric when the wind incidence angle varies from –180° to 180°, and the ${P_{C ϕ}}_{Y'}$ of the AFMT and AFST models are almost symmetric. As ${P_{C ϕ}}_{X'}$ and ${P_{C ϕ}}_{Y'}$ are symmetric and antisymmetric in the incidence range of –90° and 90°, for the convenience of the subsequent analysis, only those in the range of 0°–90° are discussed in the following text. The ${P_{C ϕ}}_{X'}$ and ${P_{C ϕ}}_{Y'}$ parameters of both models reach their maximum values at incidence angles of 75° and 15°, respectively. Both ${P_{C ϕ}}_{X'}$ and ${P_{C ϕ}}_{Y'}$ of the ACMT model reach their maximum at an incidence angle of 12°, and the maximum values are largely consistent. This finding is observed because the section characteristics along the X′-axis are the same as those along the Y′-axis, and the difference among the geometric characteristics of the four lateral planes is small.

Figure 6.

Aerodynamic force parameters ${P_{C ϕ}}_{X'}$ of separate segmental models: (a) Case 1 and Case 2; (b) Case 3.

Figure 7.

Aerodynamic force parameters ${P_{C ϕ}}_{Y'}$ of separate segmental models: (a) Case 1 and Case 2; (b) Case 3.

The drag parameter $C_{D β} ϕ_{β}$ and lift parameter $C_{L β} ϕ_{β}$ in the local coordinate systems of the three separate models are calculated according to equations (2) and (3). The $C_{D β} ϕ_{β}$ curves of Case 1, Case 2, and Case 3 are plotted in Figure 8, and Figure 9 shows the $C_{L β} ϕ_{β}$ curves. It can be seen that $C_{L β} ϕ_{β}$ is very small, exhibiting a maximum absolute value of 0.067. The calculated $C_{D β} ϕ_{β}$ of AFMT and AFST is in the range of 0.48–0.61 and that of ACMT is in the range of 0.61–0.73. This finding means that $C_{D β} ϕ_{β}$ is more important than $C_{L β} ϕ_{β}$ for arch crown structures. The $C_{D β} ϕ_{β}$ of AFMT in Case 1 reaches its maximum at a wind incidence angle of 15°, and the $C_{D β} ϕ_{β}$ of AFST in Case 2 reaches its maximum at a wind incidence angle of 75°, which is smaller than that of AFMT. This finding means that the wind loading on the square-section latticed segmental models with round-section member shapes at wind incidence angles of 15° or 75° merits further study.

Figure 8.

Drag parameters $C_{D β} ϕ_{β}$ of separate segmental models: (a) Radar graph for Case 1 and Case 2; (b) Case 3.

Figure 9.

Lift parameters $C_{L β} ϕ_{β}$ of separate segmental models: (a) Radar graph for Case 1 and Case 2; (b) Case 3.

The drag coefficients $C_{D β}$ of the three separate models are calculated according to equation (4). For square-section latticed truss structures with round-section member shapes, the force coefficients are determined by multiplying the value by the correction factors (Chen and Kareem, 2005). The correction factor is based on the ASCE standard. Tables 4 and 5 summarize the drag coefficients $C_{D β}$ and the solidity ratios $ϕ_{β}$ for the aforementioned cases. Figure 10 shows the results of experimental values $C_{D β}$ , under non-correction and correction conditions, and a comparison with different design codes. The results show that the experimental values $C_{D β}$ without correction are generally larger than the code values for separate segmental models. When the correction factors were introduced, the experimental values are generally smaller than those predicted by codes and closest to the Chinese code. This result shows that $C_{D β}$ values obtained from the codes above are on the safe side, except for the individual incidence angles in the range of 0°–15°, which are calculated using the Chinese code. In Figure 10(a) and (b), the maximum experimental value $C_{D β}$ for Case 1 appears at a wind incidence angle of 30° and that for Case 2 appears at a wind incidence angle of 60°. For Case 3, the maximum experimental value $C_{D β}$ appears at a wind incidence angle of 12°. However, it is important to note that the varying trend of $C_{D β}$ obtained from the codes is symmetric to a certain $C_{D β}$ at a wind incidence angle of 45° but that of the experimental values is asymmetric for the square-section latticed truss segmental models. This finding may be due to the sectional axis of the segmental models being arched and the model height in different parts of the section being asymmetric to the wind incidence angle of 45°.

Table 4.

Drag coefficients and solidity ratio for Case 1 and Case 2.

$β$ (°)	Case 1			Case 2
	$ϕ_{β}$	$C_{D β}$		$ϕ_{β}$	$C_{D β}$
	$ϕ_{β}$	Non correction	Correction	$ϕ_{β}$	Non correction	Correction
0	0.266	2.091	1.401	0.257	1.992	1.335
15	0.290	2.067	1.385	0.281	1.981	1.327
30	0.276	2.134	1.430	0.268	2.081	1.394
45	0.272	1.965	1.317	0.263	2.114	1.416
60	0.276	1.921	1.287	0.268	2.191	1.468
75	0.290	1.796	1.203	0.281	2.085	1.397
90	0.266	1.745	1.169	0.257	1.999	1.339

Table 5.

Drag coefficients and solidity ratio for Case 3.

$β$ (°)	$ϕ_{β}$	$C_{D β}$		$β$ (°)	$ϕ_{β}$	$C_{D β}$
$β$ (°)	$ϕ_{β}$	Non correction	Correction	$β$ (°)	$ϕ_{β}$	Non correction	Correction
0	0.336	1.880	1.308	7	0.379	1.828	1.323
1	0.394	1.618	1.188	8	0.376	1.859	1.343
2	0.391	1.634	1.197	9	0.374	1.887	1.360
3	0.389	1.690	1.235	10	0.372	1.915	1.378
4	0.386	1.731	1.261	11	0.370	1.948	1.399
5	0.383	1.750	1.272	12	0.369	1.980	1.420
6	0.381	1.795	1.302

Figure 10.

Drag coefficients of separate segmental models: (a) Case 1; (b) Case 2; and (c) Case 3.

The varying trends of $C_{D β} ϕ_{β}$ and $C_{D β}$ and the incidence angles of maximum $C_{D β} ϕ_{β}$ and $C_{D β}$ are different. With the same solidity ratio at different wind incidence angles for the same case or for different segmental models, the drag coefficients are different. These results indicate that not only the solidity ratio $ϕ_{β}$ but also the layout of the segmental models, such as the cross-section and the centerline of the members, might exert critical effects on the drag forces. This study emphasizes the necessity of considering the effects of wind incidence angle and configuration, solidity ratio, and geometric shape of the latticed structure on the drag coefficients in the current wind codes and standards.

Interference effect

The aerodynamic force coefficients of separate segmental models have been discussed in the above text. In an actual situation, the AFMT and AFST are close and on the same side of the global X-axis. The interference effects on the drag coefficients $C_{D β}$ are considered in this section. The angle between the axis of the center points of the AFMT and AFST sections and the global Y-axis is 28.5°.

Figure 11 shows the comparison of the drag coefficients of the AFMT and 1^#AFST for Case 1, Case 2, and Case 4 in the incidence angle range of 0°–90°. For both AFMT and 1^#AFST in Case 4, $C_{D β}$ decreases compared with those of separate segmental models. For Case 4 at $β = 0^{°}$ , the segmental models of AFMT and 2^#AFST are on the windward side, and the segmental model of 1^#AFST is on the leeward side, which is sheltered by that of 2^#AFST. This phenomenon causes inflow deceleration on the 1^#AFST, thereby greatly decreasing the drag forces. Similarly, at $β = 30^{°}$ , the $C_{D β}$ of AFMT notably decreases due to the aerodynamic interference between the segmental models, especially the shelter from 2^#AFST.

Figure 11.

Comparison of the drag coefficients for Case 1, Case 2, and Case 4.

To conveniently describe the interaction of nearby skewbacks, the interference factor $f_{am}$ is applied. This factor is defined as

f_{am} = 1 - \frac{C_{Dm}}{C_{Ds}}

(6)

where $C_{Dm}$ is the drag coefficient considering the interference of nearby skewbacks, and $C_{Ds}$ is the drag coefficient regardless of the interference. The interference factor, obtained from equation (6), is presented in Table 6.

Table 6.

Interference factor $f_{am}$ at different wind incidence angles.

Segmental models	Wind incidence angle $β$ (°)
Segmental models	0	15	30	45	60	75	90
AFMT	0.198	0.152	0.364	0.190	0.066	0.044	0.075
1^#AFST	0.131	0.030	0.021	0.059	0.070	0.092	0.078

AFMT: arch foot of main truss; AFST: arch foot of sub-truss.

When the approaching wind flows through the three segmental models for Case 4, the free shear layer shed from the upstream segmental models reattaches on the downstream segmental model immersed in the wake region of the upstream segmental model, thereby developing a quasi-stationary wake between them. As a consequence, the drag coefficient of the downstream segmental model is reduced differently at different wind incidence angles, which is smaller than that of the separate segmental model. Meanwhile, there also exist obvious discrepancies of $C_{D β}$ variation at the same incidence angle for two different segmental models. Especially at $β = 30^{°}$ , the decrease in $C_{D β}$ of AFMT is the largest with a value of 0.364, and that of 1^#AFST is the smallest with a value of 0.021.

In summary, the experimental investigation of the interference mechanism of the three segmental models implies that the presence of nearby skewbacks in the truss tower would decrease the drag coefficients of separate sections of the arch foot to varying degrees with the wind incidence angle. For this circular-steel-made truss tower, the $C_{D β}$ of AFMT is the most sensitive to the interference of nearby skewbacks at $β = 30^{°}$ , and that of AFST is at $β = 0^{°}$ .

Conclusion

In this study, the aerodynamic forces of a truss arch tower were experimentally investigated through wind tunnel testing. The drag coefficient of three typical scaled segmental models was measured using the HFBB technique under nominally smooth flow. The effects of incidence angle and interference from nearby skewbacks were discussed. The major findings are summarized as follows:

The drag coefficients of the segmental models for the truss arch tower are generally smaller than the values outlined in the BS 8100 code and ASCE code and are close to the Chinese code. The drag coefficients obtained from the codes are on the safe side, except for the individual incidence angles in the range of 0°–15°, which are calculated by using the Chinese code.

A comparison between the values of $C_{D β} ϕ_{β}$ and $C_{D β}$ reveals that the solidity ratio and layout of the segmental models, such as the cross-section and the centerline of the members, might exert crucial effects on the drag forces and the corresponding variation trend of the drag forces with the wind incidence angles. It is proposed that the effects of wind incidence angle and configuration, solidity ratio, and geometric shape of the latticed structure on the drag coefficients should be further considered in codes.

The drag coefficient of the downstream segmental model is smaller than that of the separate segmental model because of the interference effect. For this particular truss arch tower, the drag coefficient of AFMT is most sensitive to the interference of nearby skewbacks under a wind incidence angle of 30°.

Footnotes

Acknowledgements

The authors acknowledge the contributions of M.A. Xiongjie Liu and Dr. Xiaoyan Zhao studying at Central South University in performing the experimental phases of the study.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research presented in this paper was supported by the National Natural Science Foundation of China under project no. 51508574, project no. U1534206 and the National Key R&D Program of China under project no. 2017YFB1201204; their support is gratefully acknowledged.

ORCID iD

Lingyao Li

References

Allegrini

Maesschalck

Alessi

, et al. (2018) Porous and geometry-resolved CFD modelling of a lattice transmission tower validated by drag force and flow field measurements. Engineering Structures 168: 462–472.

ANSI (2006) Structural Standard for Antenna Supporting Structures and Antennas. Arlington, VA: Telecommunications Industry Association.

Asgarian

Dadras

Eslamlou SE

Zaghi

, et al. (2016) Progressive collapse analysis of power transmission towers. Journal of Constructional Steel Research 123: 31–40.

Bayar

(1986) Drag coefficients of latticed towers. Journal of Structural Engineering 112(2): 417–430.

BSI (1986) Lattice Tower and Masts—Part 1: Code of Practice for Loading. London: British Standards Institution.

BSI (2005) Eurocode 1: Actions on Structures—Part 1—: General Actions—Wind Actions. London: British Standards Institution.

BSI (2013) Overhead Electrical Lines Exceeding AC 1 kV —Part 1: General Requirement—Common Specifications. London: British Standards Institution.

Calotescu

Solari

(2016) Alongwind load effects on free-standing lattice towers. Journal of Wind Engineering and Industrial Aerodynamics 155: 182–196.

Carril

Isyumov

Brasil

RMLRF

(2003) Experimental study of the wind forces on rectangular latticed communication towers with antennas. Journal of Wind Engineering and Industrial Aerodynamics 91: 1007–1022.

10.

CEPPEI (2012) Technical Code for the Design of Tower and Pole Structures of Overhead Transmission Lines. Beijing, China: China Planning Press.

11.

Chen

Kareem

(2005) Validity of wind load distribution based on high frequency force balance measurements. Journal of Structural Engineering 131: 984–987.

12.

Deng

Duan

, et al. (2016) Experimental and numerical study on the responses of a transmission tower to skew incident winds. Journal of Wind Engineering and Industrial Aerodynamics 157: 171–188.

13.

(2007) Wind effects on the world’s longest spatial lattice structure: loading characteristics and numerical prediction. Journal of Constructional Steel Research 63: 1341–1350.

14.

Georgakis

Støttrup-Andersen

Johnsen

, et al. (2009) Drag coefficients of lattice masts from full-scale wind-tunnel tests. In:5th European African Conference on Wind Engineering, Florence, 19–23 July.

15.

Georgiou

Vickery

(1980) Wind loads on building frames. Wind Engineering 1: 421–433.

16.

Holmes

(2008) Recent developments in the specification of wind loads on transmission lines. Journal of Wind & Engineering 5: 8–18.

17.

Yan

, et al. (2017) Wind forces on circular steel tubular lattice structures with inclined leg members. Engineering Structures 153: 253–263.

18.

Liu

Shao

Zheng

, et al. (2016) Experimental study on Reynolds number effect on aerodynamic pressure and forces of cylinder. Journal of Experiments in Fluid Mechanics 30: 7–13. (In Chinese)

19.

Mara

Galsworthy

(2011) Comparison of model-scale and full-scale wind tunnel test results for a typical 3-dimensional lattice frame. In:13th International Conference on Wind Engineering, Amsterdam, 10–15 July.

20.

MOHURD (2012) Load Code for the Design of Building Structures. Beijing, China: China Architecture and Building Press.

21.

Moon

Park

Lee

, et al. (2009) Performance evaluation of a transmission tower by substructure test. Journal of Constructional Steel Research 65: 1–11.

22.

National Building Code of Canada (NBCC) (2015). Available at: https://www.canadianconsultingengineer.com/buildings/canadas-2015-national-building-codes-now-official/1003403002/

23.

Prud’homme

Legeron

Langlois

(2018) Calculation of wind forces on lattice structures made of round bars by a local approach. Engineering Structures 156: 548–555.

24.

Prud’homme

Legeron

Laneville

, et al. (2014) Wind forces on single and shielded angle members in lattice structures. Journal of Wind Engineering and Industrial Aerodynamics 124: 20–28.

25.

SEI (2010) Guidelines for Electrical Transmission Line Structural Loading. Reston, VA: American Society of Civil Engineering

26.

Simiu

Scanlan

(1996) Wind Loads on Structures. Chichester: John Wiley & Sons.

27.

Whitbread

(1980) The influence of shielding on the wind forces experienced by arrays of lattice frames. Wind Engineering 1: 405–420.

28.

Xie

Garber

(2014) HFFB technique and its validation studies. Wind and Structures 18: 375–389.

29.

Xie

Cai

Xue

(2017) Wind-induced vibration of UHV transmission tower line system: wind tunnel test on aero-elastic model. Journal of Wind Engineering and Industrial Aerodynamics 171: 219–229.

30.

Yang

Dang

Niu

, et al. (2016) Wind tunnel tests on wind loads acting on an angled steel triangular transmission tower. Journal of Wind Engineering and Industrial Aerodynamics 156: 93–103.

31.

Zhang

(2017) Wind tunnel test and field measurement study of wind effects on a 600-m-high super-tall building. The Structural Design of Tall and Special Buildings 26(11): e1385.

32.

Zhang

(2017) Wind tunnel investigation on flutter and buffeting of a three-tower suspension bridge. Wind and Structures 24: 367–384.

33.

Zhang

Qian

Wang

, et al. (2019a) Aerostatic instability mode analysis of three-tower suspension bridges via strain energy and dynamic characteristics. Wind and Structures 29: 163–175.

34.

Zhang

Qian

Xie

, et al. (2019b) An iterative approach for time-domain flutter analysis of bridges based on restart technique. Wind and Structures 28: 171–180.