The Analysis of Masts and Towers

The Analysis of Masts and Towers Mogens G. Nielsen, MSc CEng, Chief Consultant, Secretary of IASS Working Group no. 4 Masts and Towers, Rambøll Denmark, Bredevej 2, DK-2830 Virum, Denmark Received February, 7, 2008; Revised version February, 6, 2009; Acceptation March, 25, 2009 ABSTRACT: For many years both guyed masts and self-supporting towers have been used for supporting antennas for mobile and other communications. The choice between masts and towers has often been determined by the tradition. However masts have its clear advantages in the open country, whereas the towers are more likely to be chosen in the urban areas. Masts and towers are often used for broadcasting of radio and television or antennas for cellular phones. The masts and towers consequently are situated on the top of hills and mountains, where the climate often is extreme with respect to wind load and in some cases due to atmospheric icing. Since the wind is turbulent and the masts and towers are flexible and sensitive to dynamic load, the dynamic response becomes important in the analysis of towers and guyed masts. However there are some differences in the analysis of masts and towers. The wind resistance for lattice sections is dependent on the type of members, the solidity of the sections and for tubular members also dependant on the Reynolds number. Furthermore, latest research within the IASS Working Group for Masts and Towers has shown that the wind resistance of tubular sections is dependent on the turbulence of the wind. The masts act strongly in non-linear fashion since the guy ropes are varying from slackened to a taut string. Over the years different methods have been used for analysing guyed masts making the methods more and more realistic: starting by a gust factor method, over the IASS patch wind method to the Eurocode patch wind method, which gives results close to the results from a stochastic analysis and the time domain analysis. The towers do not act as non-linear as the masts. However, the towers are also sensitive to the dynamics of the wind and a dynamic factor should be applied depending on the turbulence of the wind, the height of the structure etc. Keywords: Masts, Towers, Wind, Ice, Buckling, Guy rupture

1. INTRODUCTION Within the last few decades the need for tall structures has accelerated with the requirements for effective communication especially with the advent of radio, radar and television. Recently the exponential growth in the use of cellular phones has led to a new era for self-supporting towers and guyed masts. In addition to the complexity in the structural system itself, the predominant loads of self-supporting towers and guyed masts are natural loads due to wind •Corresponding

and ice and these also affects the structural behaviour. The wind load is a dynamic load and the slender structures are sensitive to the dynamic part in the wind. Ice on a mast will by its weight change the dynamic behaviour, as well as it may increase the wind drag of a lattice mast dramatically. The overall layout of telecommunication masts is governed by the requirements to the transmission and receiving conditions. Added hereto the access and working conditions for installation and service are

author. E-mail Address: [email protected]

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2. BASIS OF THE DESIGN The operator normally specifies their basic requirements to the structures, as for instance [13] & [18]: • • • • •

the placing of antennas and cables the stiffness of the structure the access system for service and working and the cable management system the codes and standards to be used for the project the standard heights of the structures

Overall Drag Coefficients for Masts 5,0 4,5 4,0

Drag Coefficient

important issues for the design. The first requirement often leads to relatively tall structures or in mountainous areas a smaller structure on the top of hills or mountains. Both solutions lead to various problems with regard to analysis, design and construction.

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Figure 1. Drag Coefficients Dependent on the Solidity Ratio, Type of Cross Section and Profile.

The Eurocode for Towers and Masts [3] and the American TIA/EIA-222-G [1] are two codes that include the specific considerations regarding guyed masts and self-supporting towers. The predomi-nating design parameter for the structures is the wind load on the structure itself and on the antennas and feeders. The wind load on the structure depends on the wind climate and the wind resistance of the structure, antennas etc. If a large number of structures are going to be built it could be an advantage to divide the structures into different groups:

Fig 1 illustrates the drag coefficient dependent on the solidity ratio, type of cross section and profile. The values are based upon data from wind tunnel tests and are given in EC 3: Part 3-1 1997 [3]. For circular profiles the drag coefficient is dependent on the Reynolds number (proportional to the wind speed and the diameter) since the wind generates some turbulence around the cylinder which decreases the wind drag for larger circular profiles [10]. Some codes like the old American TIA/EIA-222-F [2] does not take this reduction of the wind load for circular profiles into account.

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4. ICE LOAD

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heights of the structures self-supporting towers and guyed masts different categories of sites depending of the wind climate wind resistances from antennas

3. WIND LOAD Apart from the wind load on the antennas, cables and other ancillaries, the lattice structure itself contributes significantly to the wind loading on the tower. The wind resistance of the flat-sided profiles such as angular profiles is larger than for the circular profiles. Consequently is the demand for the strength and the stiffness of the sections of the tower and the foundation dependent on the type of members. The wind resistance of the lattice towers is dependent on various parameters: e.g. type of cross section, solidity ratio and type of members. The wind resistance is larger for square cross sections than for triangular cross sections. The drag coefficient for lattice bracing is decreasing for increasing solidity ratio in situations where the solidity ratio is moderate. Finally the wind resistance for flat-sided profiles is often up to 50 % larger that the circular profiles [14]. 98

In some regions heavy ice load occurs on the structure and the dimensioning load can be the weight of the ice or the combination of ice load and wind load. The weight per meter of ice on a profile is dependent on the free surface area and since all the surfaces on angular profiles are exposed to ice load; the amount of ice on an angular profile is more than for a tubular profile, see Fig 2. The special considerations concerning ice load is further described in [9].

5. BUCKLING CAPACITY The design of the members in the bracing of lattice towers is normally controlled by their buckling capacity. Important parameters for the buckling capacity are radius of inertia, buckling length, eccentricity and the buckling curve. When comparing a circular tube to a single angular profile with identical width and area of cross sections, the radius of inertia of a circular tube will typically be 10% larger than the radius of inertia about the strong axis of the angular profile and 70 % larger compared to the radius about the weak axis. This results in a International Journal of Space Structures Vol. 24 No. 2 2009

Mogens G. Nielsen

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rolled circular profiles compared to the angular profiles for a typical slenderness of 60-120. The American standards [1] & [2] do not separate the buckling curves. Consequently it is more difficult for the towers with circular tubes to compete with the towers of angular profiles when the American standard is followed. In order to meet the requirements laid down in the codes, the design of towers of angular profiles demands more bracings and more members than for towers of circular profiles. This makes the towers of angular profiles more complicated to erect. The major advantage of towers with angular sections is the simplicity in detailing at joints as compared to tubular sections.

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6. ANALYSIS OF MASTS AND TOWERS Wmax

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Figure 2. Ice Accretion Model for Rime on Circular and Angular Profiles.

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Figure 3. Buckling Curves According to EC 3:Part 1-1 1992. A Significant Lower Buckling Capacity of the Single Angle Profile for the Same Distance Between the Bracings.

significant lower buckling capacity of the single angle profile for the same distance between the bracings (See Fig 3). Furthermore, the diagonals for the sections with single angular profiles are often eccentrically loaded, which results in even lower buckling capacity. The buckling curve according to EC 3: Part 1-1 1992 gives less critical stresses for angular profiles than the buckling curve used for hot rolled or even cold formed circular profiles. This result in an approx. 20% higher buckling capacity for the hot International Journal of Space Structures Vol. 24 No. 2 2009

The predominant load on self-supporting towers and guyed masts is the wind load. In some areas also the atmospheric icing on the structure may have important influence on the design. Especially when icing is combined with wind this may be decisive for the design in some countries [9]. The wind is a dynamic load and slender structures like self-supporting towers and guyed masts are sensitive to dynamic load as, they are flexible and they have low structural damping characteristics. It is therefore essential that self-supporting towers and guyed masts are analysed for the dynamic response of the structure to the wind. In the case of self-supporting towers, whose natural frequencies usually are well separated, the response of the structure to wind gusts is governed by the fundamental mode of vibration. This enables simplified analysis procedures to be adopted using appropriate gust response factors. Nevertheless, care needs always to be exercised in the design, especially for heavily eiffelated tower configura-tions [16]. Guyed masts are essentially of a more complex nature for several reasons. Some of them are due to the static system of a mast shaft as a column subjected to bending moments and elastically supported by guys with non-linear stiffness. The guyed mast is also dependent of the loading directly on the guys themselves, for instance wind and ice. Some of them are as mentioned due to the nature of the loads, namely natural loads as wind and ice, where an accurate estimation of the design values and combinations often is difficult. Most important is perhaps that the wind load acts dynamically and guyed masts are sensitive to dynamic loads. If the static system of a guyed mast is complex it is nothing compared with the complexity of the dynamic 99

The Analysis of Masts and Towers

0.766 Hz

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Figure 4. Modes of a Lattice Tower Compared to a Guyed Mast.

system. In guyed masts the fundamental mode of vibration alone does not govern the design, as the modes are not well separated and many modes may contribute to the response of the structure to turbulent wind [8] & [11]. It is not only the modes of the shaft that are interesting but in some instances the modes of the guys are important too. The frequencies of the structure are dependent on the loading on the mast due to wind, and ice if appropriate, and also dependent on the direction of the wind on the structure. Also, if nonsymmetrically deposit of ice on the mast shaft and the individual guys shall be taken into consideration, the dynamic analysis of the guyed masts will be almost impossible. Fig 4 illustrates some of the modes of a guyed mast compared to a tower. There are few computer programs available for a full dynamic stochastic analysis of guyed masts. Even with the latest generation of fast high capacity computers a fully dynamic analysis of guyed masts may run for several hours. Therefore considerable efforts has been expended in trying to produce simplifications for the design rules for codes and standards, and recently a relatively reliable simplified procedure has been developed and adopted in new codes, latest in the list is the Eurocode 3: Part 3.1 Towers and Masts [3]. For a number of different existing guyed masts the procedure based on simplified static patch wind models has been compared with a full dynamic analysis - and reasonable agreement has been found. The principle of applying the patches is described in the Eurocode 3 Part 3-1 model. Fig 5 shows the comparison of the extreme forces in the leg members of a 160 m guyed mast. Besides the new patch model as adopted in the Eurocode for Towers and Masts [3], the former IASS Patch Wind Model has also been compared with the result of a full dynamic analysis. Fig 6 shows the extreme forces developed in the diagonals for the three analytical models. It may be seen that the Eurocode Model is quite close to the full 100

— EC3 part 3.0

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Axial forces in leg members Comparison analysis Overall extreme values Figure 5. The Comparison of the Extreme Forces in the Leg Members of a 160 m Guyed Mast.

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Axial forces in diagonals Comparison analysis Overall extreme values Figure 6. Extreme Forces Developed in the Diagonals for the Three Analytical Models.

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Mogens G. Nielsen

dynamic response analysis and that the IASS Model is clearly on the safe side. Analysis in the time domain has shown similar results as the results from the stochastic method and the Eurocode patch [4].

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7. GUY RUPTURE

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Guy rupture is an additional design criterion for design of guyed masts, which is seldom considered by designers. However guy rupture relative often leads to collapses of guyed masts. The most significant incident was the fall of the tallest guyed mast in the World [12]. Guy rupture is a critical event, which can lead to collapse of the guyed mast. Consequently it should be included in the design analysis for guyed masts in high reliability class. This is already recommend-ded in the Eurocode for towers and masts [3] and the TIA-222-G [1]. The guyed masts must be able to withstand guy rupture in still air conditions and at a reduced wind pressure in the absence of the ruptured guy.

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Also the development of new materials, particularly those with high structural strength and good electrical resistivity - may have a significant effect on mast and tower design in the future.

10. REFERENCES [1]

8. MAST FAILURES Guyed masts are more likely to collapse than other structures as for example towers due to the non-linear behaviour of the guy ropes. An overview over all collapses is difficult to get. However J. Laiho has created a database of the known collapses of mast and towers [5]. According to this the most common cause of failure of guyed masts is ice load (70 %), but collapses due to guy rupture also appear quite often (8 %). At least 14 collapses have been registrated by Laiho and among these was the tallest mast in the world the 646 m mast in Poland. Guy rupture can be caused by a number of events e.g. cut of guys (Aeroplanes, falling objects etc.), broken insulators (Lightning), vandalism, erection failures, deterioration of the guys (fatigue, corro-sions) etc.

9. THE FUTURE Even though today we have a wide knowledge of the various factors affecting the analysis, design and behaviour of masts, there are still areas which are not fully understood and which need further development and research. As examples of such areas the following phenomena may be mentioned: •

improved assessment of the drag force of lattice sections with circular profiles exposed to turbulent wind;

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assessment of atmospheric ice loading and especially the combination of wind and ice; galloping of guys, the true theoretical background, the computer modelling, the way to predict galloping and how to prevent/dampen when it occurs, etc.; non-linear dynamic response analysis of a guyed mast; aero elastic instability of various mast sections/antenna configurations; assessment of various parameters for full dynamic response and fatigue analyses including, for instance, full-scale measure-ments; convergence on an acceptable procedure to predict vortex excitation on masts suppor-ting cylindrical sections.

[2]

[3] [4] [5] [6] [7]

[8]

[9]

[10] [11]

[12] [13]

[14]

ANSI/TIA-222-G 2006. Structural standards for Steel Antenna Towers and Antenna Supporting Structures, Telecommunications Industry Association (TIA), USA. TIA/EIA-222-F 1996. Structural standards for Steel Antenna Towers and Antenna Supporting Structures, Telecommunications Industry Association (TIA), USA. EC3 Part 3-1 (1997) “Eurocode 3: Design of Steel Structures, Part 3.1: Towers and Masts”, ENV 1993-3-1 Bakmar, C.B. (2004) “Wind Load on Guyed Masts”, Master Thesis, DTU Laiho, J, (1997) “Some known mast failure”, IASS WG4, Chicago Heslop, P, (2007) “Functional Requirements for Telecoms Masts and Towers”, SEWC, Bangalore Leuchsenring, P., Støttrup-Andersen, U. (1997), “Aesthetic Approach to Mast and Tower Design”, IASS Symposium, Singapore Nielsen, M.G. (1995), “Comparison of Maximum Dynamic Response for Guyed Masts using four different Methods of Analysis”, IASS WG4, Winchester Nielsen, M.G. & Nielsen, S.O. 1998, “Telecommunication Structures in Arctic Regions”, POLARTECH, Nuuk Nielsen, M.G. (2001), “Wind Tunnel Tests”, IASS WG4, Oslo Nielsen, M.G., Støttrup-Andersen, U. (2005), “Design of Guyed Masts”, 2nd Latin American Symposium on Tension Structures, Caracas Nielsen, M.G. (2006),”Guyed masts Exposed to Guy Failure”, ASCE Congress, St. Louis Nielsen, M.G., Støttrup-Andersen, U. (2006), “Comparison of the Advantages of Guyed Masts to Selfsupporting Towers”, ASCE Congress, St. Louis. Nielsen, M.G.; Støttrup-Andersen, U. (2006), “Advantages of using tubular profiles for telecommunication structures”, ISTS11, Québec.

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[15] Peil, U. (1997) “Mast Failures - Gales and Guy Rupture”, IASS WG4, Chicago. [16] Smith, B.W., Støttrup-Andersen, U. (1997), ”Towers and Masts: The Past, Present and the Future”, IASS Colloquium, Madrid.

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[17] Støttrup-Andersen, U. (2002), “Analysis and design of masts and towers”, IASS Symposium on Lightweight Structures in Civil Engineering, Warsaw. [18] Støttrup-Andersen, U. (2005), “Mast and towers for the UMTS networks in Sweden”, Eurosteel, Mastricht.

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