3__Wind Analysis of Microwave Towers

INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 1, No 3, 2010

© Copyright 2010 All rights reserved Integrated Publishing Association

RESEARCH ARTICLE ISSN 09764259

574

Wind Analysis of Microwave Antenna Towers Siddesha.H

Lecturer, Department of Civil Engineering, S.I.T., Tumkur, Karnataka, India. [email protected]

ABSTRACT

Open latticed steel towers are used widely in a variety of civil engineering applications. The angle sections are commonly used in microwave antenna towers. This paper presents, the analysis of microwave antenna tower with Static and Gust Factor Method (GFM). The comparison is made between the tower with angle and square hollow section. The displacement at the top of the tower is considered as the main parameter. The analysis is also done for different configuration by removing one member as present in the regular tower at lower panels.

Keywords: GFM, panels, configuration, displacement

1. Introduction

While Communication Satellites are used for sending and receiving information signals, very tall towers are required for transmission of signals through antennae. Tall towers are being used by different agencies such as television and radio departments, telecommunication industry, defense, railways and police for their communication network. The microwave towers, which are space structures in steel, carry mainly communication antennae. These towers are mostly square in plan, made of standard steel angles and connected together by means of bolts and nuts. Triangular towers attract lesser wind loads compared with square towers. However they are used only for smaller heights of tower due to difficulties in joint detailing and fabrication using angle sections (Gomathinayagam,S,June 2000).

Ultimately, the general availability of a wide range of square, rectangular, and round structural tubing increased. The use of tubular joints greatly improved the aesthetic qualities of the truss, and the higher load carrying capacity of the structural capacity of the structural tube members provided a wide range of applications for a triangular cross section truss. Tubular sections are used for truss members, the range of different standard shapes and sizes produced is much less than wide flange shapes and availability of some standard shapes is still limited.

In order to reduce the unsupported length and thus increase their buckling strength, the main legs and the bracing members are laterally supported at intervals in between their end nodes, using secondary bracings or redundants. These secondary bracings increase the buckling strength of the main compression members (N.Prasad Rao, September 2001), K and X bracing with secondary bracings were commonly using in microwave towers.

Optimization is the art of obtaining best results under given conditions. An optimization problem consists of a function, which is to be optimized, and with or without constraints. The constraints are the conditions to be satisfied during optimization. Optimal design methods assist engineers to evolve the best possible designs in terms of cost, weight, reliability or a combination of these parameters. As for as tower and tower like structures are concerned




575

limiting the displacement and stresses to allowable limits optimizes the weight using different sections. Many methods have been developed and are in use for design optimization of structural systems. Structural optimization using mathematical programming was very expensive in the early stages of its development and hence applications to problems were limited in scope. Recent advances in computer hardware have encouraged researches to give a new thrust to structural optimization.

The structures like towers and masts are sensitive to dynamic wind load. The need to design a lattice tower considering resonant dynamic response to wind loads arises when their natural frequencies are low enough to be excited by the turbulence in the natural wind (J.D. Holmes,1994). These types of structures, which are vulnerable to wind induced oscillations are required to be examined for dynamic effects of wind. Further, the structural loads produced by wind gusts depend of the size, natural frequency and damping of the structure in addition to the inherent wind turbulence. One of the approaches used for evaluating the dynamic response of lattice towers is the GFM (Abraham, AugustSeptember 2005).

Dynamic effects of wind for design of lattice towers are considered in GFM. In this approach, the equivalent wind loading is equal to the mean wind force multiplied by a Gust Factor. This load is applied as an equivalent static loading on structures. This factor is a function of wind, terrain and structural characteristics. The Gust present in strong winds are caused by mechanical disturbance to the flow resulting from the roughness of the ground surface (T.A. Wyatt, October 1984).

Stewarts and Lloyds first introduced the hollow structural sections in 1952, they have become increasingly popular as structural elements, mainly due to their structural advantage like high torsional capacity, structural efficiency and aesthetic qualities (A.N. Nayak, November 1997). Less work has been reported in the literatures with regards to square hollow sections used in tower structures.

Many of the towers were failed for wind loads with leg and brace members in angle sections. A few examples are: the failure of 101m tall microwave tower, during Nov.1989, at kavali, Andhra Pradesh, and the collapse of 101m microwave tower during Nov.1996 at Ravalepalm, Andhra Pradesh, due to cyclonic wind forces. In June 1998 eight microwave towers of height 80100m collapsed during cyclone, which ravaged Kutch region of Gujrat. These failures revealed the importance of investigating the static and dynamic effects of wind of tall tower structures with angle sections. It is necessary to replace the angle section in microwave tower with different sections and configuration.

2. Modeling and analysis of tower

The modeling and analysis of tower is done by using ANSYS software. For the present analysis, the members of the tower are modeled by using BEAM 188 element. Several authors have done the experimental (P.Harikrishna, 2003, and K.Hiramatsu, 1988) and analytical investigations by using various finite element softwares (J.G.S. da Silva, 2005, M.J. Glanville, 1995 and P.J. Murtagh, 2004).




576

2.1 Material properties

The most widely used commercial structural material low carbon steel (C 14) with Density 7870 kg/m 3 , Tensile strength (yield) 415 Mpa, Modulus of Elasticity200 Gpa, has been selected for the study. The chemical composition of the section used in the present analysis has been shown in Table 1.

Table 1: Chemical Composition

Composition C Fe Mn P S

% 0.120.18 99.1399.58 0.30.6 <=0.04 <=0.05

2.2 Tower Configuration and Sections

In this study, a 40mheight tower of square in plan is considered which is having a base width of 4m and reduces to 1.91m at the top. The analysis has been done for the following sections in regular tower configuration for the entire tower as shown in Figure 1. The sections adopted for this configuration are as below,

§ A tower with Leg and bracing members as Angle Sections (LA & BA)

§ A tower with Leg members as Square Hollow and bracing members as Angle Sections (LS & BA)

§ A tower with Leg and bracing members as Square Hollow Sections (LS & BS).

The total weight of the tower is kept nearly constant for all these sections. The wind load has been calculated using static method and GFM. The calculated values have been applied on the tower.

The analysis is also done for different configuration with different sections at bottom first, second and both the panels. The remaining bracings in panels (that is from 3 rd to 14 th ) are kept constant in terms of configuration and sections as in regular tower (that is case i). The sections adopted for leg members are similar as explained above (that is case i to iii), but for bracing members the sectional dimensions were changed. In the present work X, X and Horizontal and X and M bracing have been used. The configuration of which have been shown in Figure 2 to Figure 4.

In this study, the loads calculated from regular tower with angle sections is applied on all configuration and sections under static and GFM, in order to analyse the performance of the tower.




577

Figure 1: Views of Regular Microwave Tower, a. 3D, b. Front

Figure 2: Configurations of the microwave tower at lower First Panel, a. X, b. X and Horizontal bracing, c. X and M bracing

Figure 3: Configurations of the microwave tower at lower Second Panel, a. X, b. X and Horizontal bracing, c. X and M bracing

Figure 4: Configurations of the microwave tower at lower two Panels, a. X, b. X and Horizontal bracing, c. X and M bracing




578

2.3 Boundary conditions and Loading

All the tower configurations used in this study are assumed as rigidly connected at the base and all degrees of freedom at the bottom nodes are restrained. Figure 5 (a) shows the Panels considered for the calculation of wind loads. Figure 5 (b) shows the variation of wind loads at different panels. In GFM, damping ratios of 0.02 (Structural) as per the IS: 875 (part 3)1987 and 0.04 (Structural and Aerodynamic) were considered (Abraham, Augustseptember 2005). The aerodynamic damping force arises when the relative motion between the tower and the wind is considered (J.D. Holmes,1996).

For the calculation of wind loads by static method the following parameters were considered as per IS: 875 (part 3)1987.Wind speed 55m/s, Risk coefficient (k1)1.08, Terrain, height and structure size factor (k2) category 2 and class B (assumed), Topography factor (k3)1 (assumed). For the calculations of wind loads by GFM following parameters were considered as per IS: 875 (part 3)1987. Wind speed 55m/s, Risk coefficient (k1)1.08, Terrain and height factor ( 2 k )category 2 (assumed), Topography factor (k3) 1(assumed).

The antenna loads have been calculated as reported in the early literature (Gomathinayagam,S,June 2000 and Sujatha Unnikrishnan.2002) A 3mdiameter paraboloid type antenna without radome is considered in the present analysis. It is assumed that the antenna is mounted at a height of 40meter (that is top of the tower) on one of the leg member facing normal to the direction of wind. The wind incidence angle for the antenna is assumed as zero degrees. The gust factor is taken as unity. The wind force along the direction of the wind is obtained as 25044.06 N. This antenna load is used in both the Methods and is applied for all other configurations.

a

0

5000

10000

15000

20000

25000

30000

1 3 5 7 9 11 13

Pane ls

Load

s (N)

Static Method

GFM f or 2% damping

GFM f or 4% damping

b

Figure 5:Wind load calculation, a. Panels of regular microwave tower, b. Variation of loads

at different Panels




579

3 Results and Discussions

3.1 Modal analysis of tower

In the present study, the modal analysis of the tower is carried out by Subspace iteration method. The modal analysis helps in computation of natural frequencies and the corresponding mode shapes of the structure, which essentially depends on distribution of stiffness and mass within the structure. The natural frequencies obtained through modal analysis are shown in Table 2. First three mode shapes of the tower are shown in Figure 6. The first modal frequency of the tower is taken for wind load calculation from GFM.

Table 2: Natural frequencies using Modal Analysis

Mode Frequency (Hz)

1 0.723542

2 0.723817

3 1.82300

Figure 6: Mode shapes, a. First, b. Second, c. Third




580

3.2 Displacement at the top of Microwave Antenna tower for regular configuration with different sections.

In the present analysis, the displacement of microwave antenna tower at the top 40m level has been considered as the main parameter. A regular tower with different sections and regular configuration has been studied under static and GFM.

Figure 7 show the variation of displacement at the top of the regular tower for different sections. Wind forces calculated by static method and GFM were evaluated earlier. In GFM, the Gust Factor (G) has to be multiplied with the design wind pressure. So, the design wind forces in GFM (for 2% and 4% damping) get increased as compared to the static method. However, for 4% damping (structural and aerodynamic), G values get reduced as compared to 2% (structural) damping. Hence, Figure 7 (b) illustrates, the displacement at the top of the tower gets reduced for 4% damping in GFM.

0.27

0.275

0.28

0.285

0.29

LA & BA LS & BA LS & BS

Sections

Displacem

ents (m

)

a

0.29

0.3

0.31

0.32

0.33

0.34

0.35

0.36


Sections

Displac

ements (m

) 2% Damping

4% Damping b

Figure 7: Variation of Displacement at top with different crosssections in regular tower, a. Static method, b. GFM

The square hollow sections used in tower shows a maximum reduction of displacement in comparison with angle sections. This is due to, the moment of inertia of square hollow section is larger than angle section. Figure 7 illustrates the regular tower with LS & BS shows maximum reduction of displacement in comparison with LS & BA and LA & BA. However, there is no much reduction of displacement between the tower with LS & BS and LS & BA.

3.3 Displacement at the top of Microwave Antenna tower for different configuration with different sections at different panels under Static and GFM.

Wind forces calculated by static method and GFM were evaluated earlier. In GFM, the Gust Factor (G) has to be multiplied with the design wind pressure. So, the design wind force in GFM (for 2% and 4% damping) gets increased as compared to the static method. However, for 4% damping (structural and aerodynamic), G values get reduced as compared to 2%




581

(structural) damping. Hence the displacement at the top of the tower will reduced for 4% damping. Figure 8 and Figure 9 show the variation of displacement for different configuration and sections by both these methods.

As we know, by adding members or changing configuration in the panels stiffness of the tower increases and thereby displacement of the tower gets reduces. From Figure 8 and Figure 9, X and M bracing will shows the maximum reduction of displacement as compared to X and X and Horizontal bracing in both the methods.

The bending moment increases with increase in distance from the point of application of the force. Since antenna load is applied at the top point of the tower, the lower first panel with X and M bracing shows maximum reduction of displacement as compared to lower second and lower two panels.

The square hollow sections used in tower shows a maximum reduction of displacement in comparison with angle sections. This is due to, the moment of inertia of square hollow section is larger than angle section. From Figure 8 and Figure 9, the tower with LS & BS shows maximum reduction of displacement in comparison with LS & BA and LA & BA. The top line in Figure 8 shows the regular tower with angle section, which is taken for the comparison. However, there is no much reduction of displacement between the tower with L S & BS and LS & BA.

0.265

0.27

0.275

0.28

0.285

0.29

0.295

Regular tow er

X bracing X and Horizontal bracing

X and M bracing

Configuration

Displacem

ents (m

)


a

0.265

0.27

0.275

0.28

0.285

0.29

0.295

Regular tow er


X and M bracing

Configuration

Displacem

ents (m

)


b




582

0.265

0.27

0.275

0.28

0.285

0.29

0.295

Regular tow er


X and M bracing

Configuration

Displacem

ents (m

) LA & BA LS & BA LS & BS

c

Figure 8: Displacement at top of the tower for different sections with different configuration from Static method, a. Lower first panel, b. Lower second panel, c. Lower two panels

0.29

0.3

0.31

0.32

0.33

0.34

0.35

0.36


Configuration

Displacem

etnts (m

)

2% X bracing 2% X and Horizontal bracing 2% X and M bracing 4% X bracing 4% X and Horizontal bracing 4% X and M bracing

a

0.29

0.3

0.31

0.32

0.33

0.34

0.35

0.36


Configuration

Displacem

ents (m

)


b




583

0.29

0.3

0.31

0.32

0.33

0.34

0.35

0.36


Configuration

Displac

emen

ts (m

)


c

Figure 9: Displacement at top of the tower for different sections with different configuration from GFM, a. Lower first panel, b. Lower second panel, c. Lower two panels

4. Conclusions

The analysis of microwave antenna tower with different sections and configurations were done for wind loads. The following conclusions may be drawn from the above analytical results.

• Square hollow sections can be used more effectively in leg members in comparison with the angle sections in regular tower under static and GFM.

• Square hollow Sections used in bracings along with the leg members do not show much reduction of displacement compared to tower with Square Hollow sections used in Leg members under static and GFMs.

• X and M bracing in Square hollow Sections for legs and bracings at the lower first panel shows a maximum reduction of displacement compared to the regular tower with angle sections under static and GFMs.

• X and M bracing in Square hollow Sections for legs and bracings at the lower first panel shows a maximum reduction of displacement in comparison with the tower with Square hollow Sections for legs and bracings in lower second, lower first and second panels with different configurations in both static and GFM.

5. References

1. Gomathinayagam,S., Shanmugasudaram,J., Harikrishna,P., Lakshmanan,N., and Rajasekaran,C. (June 2000). “ Dynamic Response of Lattice Tower with Antenna under Wind Loading.” J. of The Institution of Engineers (India), 81, pp 3743.




584

2. N.Prasad Rao, V. Kalyanaraman, (September 2001), “ Nonlinear behaviour of lattice panel of angle towers”, J. of Constructional Steel Research, 57, pp 1337 1357.

3. J.D. Holmes,(1994), “Alongwind response of lattice towers: part I derivation of expressions for gust response factors”. Engng Struct., 16(4), pp 287292.

4. Abraham, Harikrishna.P, Gomathinayagam.S, and Lakshmanan.N, (August September 2005), “Failure investigation of microwave towers during cyclones A case study.” J. of Struct. Engg., 32,(3), pp 147157.

5. T.A. Wyatt, (October 1984), “An assessment of the sensitivity of lattice towers to fatigue induced by wind guts.” J. of Struct. Engg., 6, pp 262267.

6. A.N. Nayak, Dr.S.K. Bhattacharya, (November 1997), “Behaviour of Joints with Rectangular and Square Hollow Sections.” J. of the institution of Engineers, Civil Engineering Division.78, pp 116122.

7. P.Harikrishna, A.Annadurai, S.Gomathinayagam, N.Laxman,(2003), “Full scale measurements of the structural response of a 50 m guyed mast under wind loading.” Engng Struct. 25,pp 859867.

8. K.Hiramatsu and H.Akagi, (1988), “The response of latticed steel towers due to the action of wind.” J. of Wind Engineering and Industrial Aerodynamics, 30, 716.

9. J.G.S. da Silva, P.C.G. da S. Vellasco, S.A.L. de Andrade, M.I.R. de Oliveira, (2005), “Structural assessment of current steel design models for transmission and telecommunication towers.” J. of Constructional Steel Research, 61,pp 11081134.

10. M.J. Glanville, K.C.S. Kwok, (1995), “Dynamic characteristics and wind induced response of a steel frame tower.” J. of Wind Engineering and Industrial Aerodynamics, 54/55,pp 133149.

11. P.J. Murtagh, B. Basu, B.M. Broderick, (2004), “Simple models for natural frequencies and mode shapes of towers supporting utilities.” Computers and Structures, 82,pp 17451750.

12. IS: 875 (part 3)1987, Indian Code of Practice for Design Loads (other than Earthquake) for Buildings and Structures, Part 3: Wind Loads. Bureau of Indian Standards, New Delhi (1989).

13. J.D. Holmes,(1996), “Alongwind response of lattice towersII. Aerodynamic damping and deflections.” Engng Struct.,18(7),pp 483488.

14. Sujatha Unnikrishnan.(2002), “Dynamic Analysis of Microwave Antenna Tower.” M.Tech thesis, B.V.B. College of Engineering, Hubli.

Documents

3__Wind Analysis of Microwave Towers