1 Introduction

The high-mast lighting towers are normally used to provide the light for the airport, sports complex, highway interchange and some industrial yards. The base connection geometry, man access hole and mast arm geometry are the important features of the high-mast lighting towers for their structural performances (Fig. 1).

Fig. 1
A photograph depicts high mast lighting tower and its features. The labels are 1. Lighting system, 2. Steel pole. A close view of an image mentions the base connection and man access hole.

Features of high-mast lighting towers

The wind forces acting on the high-mast lighting towers depend on the basic wind speed of the particular location, terrain type, altitude and dynamic and cross-wind effects. In Sri Lanka, less amount of wind occurs due to thunderstorm and large amount wind occurs due to monsoons. The wind-induced fatigue occurs as a result of the along-wind and cross-wind response of the structures [1]. Along-wind response is mainly due to buffeting by atmospheric turbulence and cross-wind response is mainly due to vortex shedding action on the tower. These two wind actions have the potential to produce the vibration that cause the fatigue failure.

Vortex shedding wind action is a complex physical phenomenon, especially when it degenerates into lock-in condition. Due to this phenomenon, structures may undergo a high numbers of load cycles that leads to damage accumulation and may determine the structural failure without exceeding the ultimate loads [2]. When the wind blows across the high-mast steel arm, vortices are shed alternatively from one side and then to the other. Large amplitude vibrations in the plane normal to the wind may develop when the vortex shedding is in resonance with one of the natural frequencies of the vibration, so that, vortex shedding-induced forces on the structures are perpendicular to along-wind direction as shown in Fig. 2.

Fig. 2
A diagram illustrates the Von karman’s vortices. It includes the following labels such as wind direction, alternating vortices, oscillation in transverse direction.

Von Karman’s vortices [2]

Geometry of the high-mast steel arm and the base connection, especially thicknesses of the mast arm wall and base plate, are important parameters, because these are highly influencing on the fatigue performance of the high-mast lighting tower system under the along- and cross-wind action. Addition to thicknesses of the mast arm wall and base plate, diameter of the base plate, free-standing pole length, number of anchor bolts, welding thickness, diameter and slope of the mast arm wall and mesh refinement also contribute in the fatigue performance of the structure [3]. Also, vortex shedding excitation-induced forces on the high-mast lighting tower system are mainly depends on the natural frequency, mean wind velocity, Reynolds number, Scruton number and effective correlation length factor of the system. These parameters are mainly interconnected with geometry of the high-mast steel arm. Effective correlation length and mode shapes for the first two modes are shown in Fig. 3.

Fig. 3
Two image depicts the shapes of first two modes and its correlating length.

Location of correlation length and mode shapes for first two modes

Fatigue assessment of the high-mast steel arm is performed by estimating the hotspot stress due to along- and cross-wind action using finite element analysis, along-wind and vortex shedding-induced forces and its impact to be applied statically. Generally, shell and solid elements are used for the mast arm wall and base plate, respectively, with finer mesh arrangement to obtain the high accuracy results. In the code-based fatigue assessment, S (direct stress range)–N (number of cycles) curve is used for the estimation of load cycles with consideration of detail category for each structural part of high-mast steel arm as shown in Fig. 4 [4].

Fig. 4
A graph illustrates the stress range for each categories along with the number of cycles. Three lines are mentioned: 1. Detail category, 2. Constant amplitude fatigue limit, 3. Cut-off limit.

S–N curves with different detail category [4]

In the S–N curves, reference value of fatigue strength is obtained at 2 million load cycles as provision given in the EN1993-1-9-2005. Palmgren–Miner theory of cumulative damage method is commonly used to estimate the total fatigue damage. For the selected detail category, the resistance of fatigue is estimated by means of accumulation of individual damage caused by individual stress block of each stress set. The number of stress sets depends on the number of analyzed frequency modes and the number of critical positions in which the vortex excitation occurs. So, in order to avoid the fatigue failures on the high-mast steel arm due to cyclic wind loads, total damage accumulation during the design life should be less than one. Under different amplitude conditions, all stress ranges should be less than the constant amplitude fatigue limit to avoid the fatigue failures on the structures. Size effect due to thickness also should be taken into account. Stress concentration factor (SCF) also is an important parameter in the fatigue performance of the high-mast steel arm. SCF is the ratio of the hot spot stress and the nominal stress.

2 Influence of Geometry in the Fatigue Performance of the System

Geometry of the high-mast steel arm and the base connection are highly influencing on the fatigue performance of the high-mast lighting tower system. There are many geometric variables are influencing on the fatigue performance of the system, which are;

  • Base plate thickness

  • Mast arm wall thickness

  • Number of anchor rods (number of holes in the base plate)

  • Base plate size and welding thickness

  • Slope and size of the mast arm wall.

From the literatures, it was found that the thicknesses of the base plate and the mast arm wall are highly influencing on the fatigue performance of the system [5]. Figure 5 summarized the variation of stress concentration factor (SCF) with base plate thicknesses from three different research studies.

Fig. 5
A graph determines the variation of stress concentration factor along with the thickness of base plate. It includes three research studies: 1. Mark T Koineigs, 2. Margaret K Warpinski, 3. Andrew Stam.

Variation of SCF with thickness of the base plate

SCF is decreased with increasing of the base plate thickness of the mast arm structure. It can be concluded that the base plate thickness of the high-mast lighting tower system is an important parameter, and special concerns should be given at the time of the fatigue design of high-mast lighting tower systems. Further, increasing the base plate thickness provides significant improvement to the fatigue life of the tower by reducing the maximum stress at the base plate to tube wall connection as shown Fig. 6. So, base plate flexibility has a considerable influence on the stress behavior in the tube wall adjacent to the unstiffened connection of the high-mast lighting tower system.

Fig. 6
A graph illustrates the variation of hotspot stress along with the base plate thickness. Two values of tube wall thickness are mentioned as 4.688 millimeters and 12.50 millimeters.

Variation of hot spot stress with thickness of base plate

Also, from literature [5], it was found that the variation of the hot spot stress is highly influencing on the tube wall thickness of the mast arm wall of the structure. So, increasing the tube wall thickness provides significant improvement to the fatigue life of the tower by reducing the maximum hotspot stress at the mast arm wall adjacent to the base connection.

Addition to these two parameters, number of anchor bolts, welding thickness, base plate geometry, mast arm geometry and free-standing length of the pole also influencing the fatigue performance of the mast arm structures. Based on these results, it can be concluded that the thicknesses of the base plate and the mast arm wall are highly influencing on the fatigue performance of the high-mast lighting tower structure under unstiffened base connection. In the design stage, the proposed base plate thickness and the mast arm wall thickness for a particular high-mast lighting tower structure should satisfy all these fatigue design requirements to avoid the damages on the mast arm wall and the base connection.

3 Vortex Shedding-Induced Forces

The vortices create across-wind deflections due to an increase in static pressure on one side of the structure and decrease on the other, such that an across-wind forces acts on the structure. Alternating vortices produces alternating forces. The vortices have a primary frequency of Ns, according to the Strouhal relation which is given in Eq. (1) below.

$$ S = \, N_{\text{s}} D/U $$
(1)

where S is the Strouhal number, D is the diameter of the mast and U is the wind velocity. Also, Strouhal number is dimensionless and depends on the cross section of the particular structure and Reynolds number of the air flow [6]. Vortex shedding tends to be organized at sub-critical and trans-critical Reynolds numbers. In the critical range, vortex shedding tends to be irregular unless the structural motion is sufficiently large to organize the fluctuating flow around the body. This phenomenon referred to as “locking in” which becomes important for the lightly damped members [2].

The accurate prediction of maximum displacement and induced load on the structures due to vortex shedding is very difficult due to the many variables involved. The important variables are mean velocity profile, turbulence characteristics of approach flow, Reynolds number, Scruton number, mode shape, natural frequency, damping and mass distribution. Based on the Ruscheweyh modification, vortex shedding-induced forces can be applied over a height range less than the total height of the structure [7]. This particular length is known as “effective correlation length.” The assumed vortex shedding-induced forces on the high-mast lighting tower system (Fw) can be calculated using Eq. (2), which is given in EN 1991-1-4:2005.

$$ F_{\text{w}} (S) = m(s).(2\pi n_{i,y} )2\Phi_{i,y} (s)y_{{\text{F}},\max } $$
(2)

where m(s) is the vibrating mass of the structure per unit length (kg/m), Φi,y is the mode shape of the structures normalized to 1, ymax is the maximum displacement over time of the point with φi,y (s) equal to 1 and ni,y is the natural frequency of the system. In order to further study the influence of the thicknesses of the mast arm wall and the base plate on fatigue behavior, study was continued with FE models [8]. The geometric details used in the study are given in Table 1.

Table 1 Geometry of the high-mast lighting tower

Here except the thicknesses, all the other parameters were kept as constants. The FE model was developed using shell elements in SAP2000. Basic wind velocity of 22 m/s from zone 3 of the wind zonation map of Sri Lanka used [9]. From the modal analysis, the natural frequency was obtained, and first, two natural frequencies at a particular direction and the critical locations are presented in Table 2 and Fig. 7, respectively.

Table 2 Natural frequency with mast arm wall thicknesses
Fig. 7
An image depicts the critical locations of first and second mode shapes. The critical point of first mode shape is noted as 25.0 meters. The critical points of second mode shape are noted as 25.0 meters and 14.25 meters.

First and second mode shape with critical location

Sinusoidal or harmonic excitation model is generally used for the calculation of vortex shedding-induced forces on the high-mast towers perpendicular to the wind direction. In this study, vortex shedding-induced forces on the high-mast tower were estimated based on EN1991-1-4:2005. As shown in Fig. 8, critical wind velocity ratio is increased with the increasing of the mast arm wall thicknesses, because the critical wind velocity of the mast arm wall is proportional to the natural frequency of the system.

Fig. 8
A graph illustrates the variation of critical wind velocity ratio along with the mast-arm wall thickness. The lines in trend from bottom to top are named, 1. First mode, 2. Second mode at top, 3. Second mode at middle. They are slightly constant

Variation of critical wind velocity ratio with mast arm wall thicknesses

Addition to the critical wind velocity ratio, the lateral force coefficient (Clat), effective correlation length (Lj), mode shape factor (K), effective correlation length factor (Kw) and the maximum displacement (YF,max) were estimated based on the procedures described in the EN1991-1-4:2005 and given in Eq. (3);

$$ Y_{{\text{F,}}\max } /b = ({1}/S_{{\text{t}}^{2} } ).\left( {{1}/Sc} \right).K.K_{\text{w}} .c_{{\text{lat}}} $$
(3)

It is observed that the maximum displacement of the high-mast steel arm is decreased with the increasing of the mast arm wall thickness as shown in Fig. 9. The equivalent mass per unit length is increased with the increasing of the mast arm wall thickness. So, the maximum displacement is decreased due to the increasing of Scruton number of the high-mast tower system (Fig. 10).

Fig. 9
A line graph illustrates the variation of maximum displacement along with the mast-arm wall thickness. The lines in trend from bottom to top are named, 1. first mode, 2. Second mode at top, 3. second mode at middle. They form a downward curve

Variation of maximum displacement with wall thicknesses of the mast arm wall

Fig. 10
A line graph illustrates the variation of vortex shedding-induced forces along with the mast-arm wall thickness. The lines in trend from bottom to top are named 1. First mode which remains constant, 2. Second mode at top and 3. second mode at middle form an upward curve.

Variation of vortex shedding-induced forces with mast arm wall thicknesses

Also, vortex shedding-induced forces on the high-mast steel arm are increased with the increasing of the mast arm wall thickness. Because, the natural frequency and the vibrating mass are increased with the increasing of the mast arm wall thickness, but maximum displacement is decreased with the increasing of the mast arm wall thickness, so resultantly, vortex shedding-induced forces are increased with the increasing of the mast arm wall thickness.

Vortex shedding-induced forces at the first mode are relatively low compared to the second mode due to less frequency and frontal width or diameter of the mast arm. However, it contributes in the estimation of the cumulative total fatigue damage (D) of the high-mast tower.

4 Fatigue Assessment

FEA analysis is performed for the selected geometry of the high-mast lighting tower system with various thicknesses of the mast arm wall and the base plate to obtain the hot spot stress and SCF considering the estimated vortex shedding wind action. High-mast lighting towers can oscillate at various frequencies and additionally vortex shedding excitation can occur at different heights of the mast arm for a particular frequency mode. In order to satisfy the fatigue design criteria, total cumulative damage (D) should be less than 1. Assessment of fatigue behavior is carried out using Palmgren–Miner theory of cumulative damage method. Total damage can be estimated using Eq. (4), [10].

$$ D = \Sigma \{ n_i (\Delta \sigma )/N_i (\Delta \sigma )\} $$
(4)

where niσ) is the number of cycles of stress load for a specified stress range for which Niσ) is the cycles of load which is expected before the structure suffers damage [11]. Number of cycles for the particular stress is obtained using S–N curves with consideration of suitable detail category for each structural element. Generally, detail category 140 is used for the mast arm wall and detail category 80 is used for the connection as shown in Fig. 11 [12]. Number of load cycles caused by vortex excitation can be calculated using mean and critical wind velocity profile and natural frequency of cross-wind mode as given in EN1991-1-4:2005 (E10).

Fig. 11
A graph depicts the stress range for the detail category of 80 and 140 along with the number of cycles in fatigue resistance.

S–N curves for the detail category of 140 and 80

5 Conclusion

In order to study the fatigue performance of the high-mast lighting tower with different thicknesses of the base plate and mast arm wall, it is required to compute the along- and cross-wind-induced forces along the free-standing length of the structures. The following conclusions that can be drawn from this investigation are as follows;

  • Natural frequency of the high-mast lighting tower is increased with increasing of mast arm wall thicknesses, because the period of the structural system is depending on the mass of the mast arm structures.

  • Critical height for the first and second mode was identified at 25 m and 14.25 m height, respectively, with assumption of critical location occurs at antinode points.

  • The critical wind velocity ratio is increased with increasing of mast arm wall thicknesses, because critical wind velocity of the mast arm wall is proportional to the natural frequency of the system.

  • Maximum displacement of the high-mast steel arm is decreased with increasing of mast arm wall thicknesses, because equivalent mass per unit length is increased with increasing of mast arm wall thicknesses. So, maximum displacement is decreased due to increasing of Scruton number of the high-mast lighting tower system.

  • Natural frequency and vibrating mass are increased with increasing of mast arm wall thicknesses, but maximum displacement is decreased with increasing of mast arm wall thicknesses, so resultantly, vortex shedding-induced forces are increased with increasing of mast arm wall thicknesses.

  • Vortex shedding-induced forces at first mode is relatively low compare to second mode of the high-mast lighting tower system.

  • Thicknesses of the base plate and mast arm wall are highly influencing on the fatigue performance of the high-mast lighting tower structures under unstiffened base connection.

In order to obtain the high accuracy on the vortex shedding action, wind tunnel test or CFD simulation should be performed. Further study on the damage behavior of the high-mast steel arm should be performed.