Nonlinear Analysis and Design of a Guyed Mast: Comparison of Two Design Proposals

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1 Advanced Materials Research Online: ISSN: , Vols , pp doi: / Trans Tech Publications, Switzerland Nonlinear Analysis and Design of a Guyed Mast: Comparison of Two Design Proposals Weili Bao a, Yong Zhang b School of Civil Engineering, Beijing Jiaotong University, Beijing,100044, China a @bjtu.edu.cn, b zyz3000@126.com Keywords: Guyed Mast; Nonlinear Analysis; Initial Tension; Wind Vibration Coefficient; Economic Comparison. Abstract. The guyed mast structure consists of a vertical shaft supported along its height by several layers of inclined pre-tensioned guys. The central shaft is generally made of lattice steel structure, and the guys are spaced at equal angles around the mast to ensure the vertical shaft s stability. By taking a 102 m meteorological guyed tower in Hainan as an example, this paper made two design proposals using steel pipe and round steel material for the shaft respectively. According to the requirements of the project, this paper then did non-linear static analysis and buckling analysis of the structure by finite element software SAP2000, and compared the results of the two proposals so as to find the optimal one. The results show that steel pipe material is more economical when used for the mast shaft and more reasonable for bearing forces. The choice of the number and the initial tension of guys, as well as the wind vibration coefficient, which have a great effect on a guyed mast, are also discussed in this paper. Introduction Guyed masts are special structures widely used for wireless broadcasting, communication industries, as well as meteorological towers. Usually, a guyed mast consists of a vertical continuous mast laterally supported at several levels along its height by sets of inclined pre-tensioned guys spaced at equal angles around the mast [2]. The central mast is usually pined or fixed at the base. Guyed masts are always tall and slender, wind load is the major load for these structures. Besides, as wind load is dynamic, and a guyed mast is dynamically sensitive, it is essential to take into account the wind effects caused by wind-induced vibration. Because of geometrical non-linear behavior of the structural system and the random nature of the loads, the structural analysis of a guyed mast is complex. The choice of initial tension and the non-linear behavior of the guys can greatly affect the deflections as well as dynamic behavior of the whole structure. The wind load on the structure depends on the wind climate and the wind resistance of the structure. In order to reduce the wind resistance, the central mast is usually designed into latticed structure which can be classified into three types: round steel mast, steel pipe mast and angle steel mast, based on the section type of members used. The wind resistance of flat-sided profiles, for instance angular profiles, is larger than that of circular profiles. So mast made of angular profiles demands more bracings and more members than that made of circular profiles, and less economical than the other two types. This study is mainly focused on comparing two proposals for a guyed mast: one using steel pipe type and the other using round steel type. The masts of circular profiles using either round steel or steel pipe enjoy an advantage of little wind drag coefficient, so the wind load on them is relatively low. Recently, in the case of masts about 100m high, round steel type has often been adopted in structural design in China, for the material can be derived easily in many districts here. However, it is hard to ensure the quality of production when rolling large diameter round steel. As a result, the structure will be unsafe. In comparison with round steel with identical area of cross-section, steel pipe s radius of inertia is much larger than round steel s, All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-12/05/16,00:59:17)

2 Advanced Materials Research Vols and increases as its thickness decreases. Thus it will save more steel and be more economical than steel pipe in the structural design. Taking a 102 m meteorological guyed tower as an example, this paper compared two design proposals using steel pipe mast and round steel mast respectively. The selected meteorological guyed tower is located in the city of Sanya, Hainan in China. According to the functional requirements, the central mast uses lattice structure with triangular cross-section, supported by several layers of cable. Wind in Sanya is strong, and the wind pressure is 0.85 KN/m 2 which is in accordance with Chinese load code [5]. There is no ice and snow load, and also no need to consider the earthquake though. Structural Design Two design proposals are described below: the first one using steel pipe for the shaft and the other one using round steel. The choice of initial tension of the guys and the number of layers adopted are also discussed, because they exert a great impact on the whole structure. Configuration of mast shaft. In order to facilitate the installation and repair of equipment, the cross-section of the shaft is equilateral triangle, edge width B = 1000 mm. Considering the requirements of the economical use of materials, simple manufacture and installation, and easy transportation, the shaft section length is taken as L = 7.5 m. Above are the same for the two design proposals, the difference between them is the configuration of web members as shown in Fig. 1 and Fig. 2. In the latter proposal more web members are arranged so as to reduce the slenderness ratio of the chord members, as the radius of inertia of round steel material is smaller than steel pipe with the identical area. In addition, secondary horizontal bars are added as a ladder in one side of the shaft. Fig. 1 Configuration of shaft section in proposal 1 Fig. 2 Configuration of shaft section in proposal 2 Design of guys. The mast shaft is elastically supported by non-linear guys. As a result, the strength, stiffness and stability of the whole structure depend on the initial tension and the layout of the guys. The design of guys is the same in the two proposals. Since the meteorological guyed tower is constructed in the wild, there is enough space for the cables to be arranged. As the cross-section of the shaft is triangular, the cables are tensioned in three directions, e.g., at angles in the plan. The inclination angle of the cables is 45 0, and every layer of cable is parallel to each other. Here, we will discuss and compare the effect on the whole structure made by different layers of cable and different initial tension in the cables. Design of cable layers. The distance between the attachment points of cables is smaller when the mast is propped by more layers of cable, thus the slenderness ratio of the shaft is lower and the integral stability of the whole structure better, provided that the cross-section of the shaft remains the same. However, the wind load on the cables will be larger and the project will cost higher when using more layers of cable. It is found that it is relatively reasonable and economical when the slenderness ratio of the shaft is equal to 80. Hence, we assume that the layer number of cable is 2, 3, 4, 5 respectively, and then calculate the slenderness ratio λ as follows: λ = l / i. (1) i = min (i x, i y ), i x,y = (I x,y / 3A) 1/2. (2)

3 22 Advances in Structures Where, λ is the slenderness ratio of the shaft, l is the average distance between the anchoring nodes of adjacent cable layers, i stands for the radius of inertia of shaft s cross-section, i x, i y are radius of inertia about axis x and axis y respectively, I x,y stands for the moment of inertia about axis x and axis y, A is the area of each chord member of the shaft. Through comparing the calculation results, it is found that it is most reasonable when arranging 3-layer cable, as the slenderness ratio λ = Thus 3-layer cable is adopted in the design proposals. In addition, in order to make the chord members of the shaft use equal cross-section along the whole height, the cables are arranged with different distances, gradually increasing distance from bottom to top: 27m, 30m, 32.5m respectively. The overall layout of the meteorological guyed tower is shown in Fig. 3. Fig. 3 The overall layout of the guyed tower Design of cable s initial tension. When the initial stress of the cable is relatively large, the guyed mast will be stable as the integral stiffness of the structure is good, and the displacement of the nodes where the cables are attached to the shaft will be small. However, the axial force of the shaft will be increased, leading to the higher consumption of steel for the shaft. On the contrary, if the initial stress of the cable is too small, the guyed mast will be prone to vibration and instability because the integral stiffness of the tower is bad. According to Chinese code for design of high-rising structures (GB ) [4], the initial tension of the cable can be chosen in the range of 100 ~ 250 N/mm 2. Here, we applied different pre-stress in the cables (each layer with the identical pre-stress), 150 N/mm 2, 200 N/mm 2, 250 N/mm 2 respectively, and then carried out modal analysis of the structure. The natural vibration period and mode shape can be obtained from the analysis results. It can be observed that higher cables initial tension leads to shorter fundamental natural period of the guyed mast (as shown in Table 1), which improves the stability of the whole structure. Additionally, the wind vibration coefficient of guyed mast structure is closely related to the fundamental natural period of the structure, the shorter the fundamental natural period, the smaller the wind vibration coefficient is. It will also take full advantage of the guys when the initial tension is larger, so each layer of guys is imposed an initial tension of 250 N/mm 2. Table 1 The fundamental natural period of guyed mast with different initial tension Initial tension of cables [N/mm 2 ] Fundamental natural period [s] Structural modeling and analysis FE modeling. In order to carry out non-linear static analysis and buckling analysis of the guyed tower, FE model of the structure was established by finite element software SAP2000. The mast shaft was modeled by frame element, the chord members by rigid frame element and the web members by pinned frame element. The guys were modeled by ten-unit cable element. The central shaft and the guys were pinned at the base. The guys were hinged at the shaft.

4 Advanced Materials Research Vols Load simulation. In the case of guyed mast structure, it is important to correctly simulate the initial tension of the cable and the wind load on the shaft and cables in the software. In this study, cooling method was employed to apply pre-stress in the cable. First, calculate the negative temperature needed to apply in the cable according to Eq. 3, and then adjust the negative temperature little by little to achieve the desired pre-tension state. Usually the initial stress of the cable is close to the expected value by adjusting 3 to 5 times. ΔT = N / (εea). (3) Where, ΔT stands for the negative temperature, N is the initial tension, ε is the coefficient of thermal expansion of steel wire rope, which is equal to 1.2 x 10-5, E is the elastic modulus of steel wire rope, equal to 1.2 x N/m 2, A is the area of cable s cross-section. Several load cases are considered in the static analysis of the guyed mast, such as pre-stress case TEMP, dead load case DL, live load case LL and three wind load cases WL1, WL2, WL3. The directions of the wind load cases are shown in Fig. 4, as a result of the shaft with triangular cross-section. WL1 WL2 WL3 Fig. 4 Wind load cases Modal analysis. Apply pre-stress case TEMP, dead load case DL and live load case LL on the structure, and define structural mass source as 1.0DL + 0.5LL, then carry out modal analysis of the structure and observe the results. The natural vibration period and the mode shape of the structure in the two proposals are both reasonable. The fundamental natural period of the guyed mast structure in the first proposal is T=1.4396s > 0.25s, according to GB [4], the effect on the structure by wind-induced vibration should be considered. It also shows that the first 12 modes of vibration is the vibration of cables, and the vibration of the shaft is at 13 mode shape that is used for calculating the wind vibration coefficient of the shaft. The modal analysis results of the other proposal are similar, as is omitted here. Nonlinear static analysis. For the guyed mast structure with pre-stressed guys, it is always essential to consider geometrical nonlinearity. In this study, the nonlinear static analysis has been performed by SAP2000, the options of P-Δ effect and large displacement effect in the software should be opened when analyzing. Besides, the load cases should be considered in sequence, because the stiffness matrix of the structure is not constant for each load case. Thus pre-stress case TEMP is analyzed first, then dead load case DL, followed by other load cases. This is in accordance with the actual process of the guyed mast structure bearing load. After continuous adjustment and analysis, the displacement and the stress distribution of the structure were all appropriate in the two design proposals. The maximum horizontal displacements are mm and 85.2 mm respectively (both less than H/75 = 1360 mm), and the maximum inner-story displacements are 38.5 mm and 30.1 mm respectively (both less than Δh max /50 = 650 mm). The maximum stress ratio of the shaft members is in the range of 0.8 ~ 0.9, and that of the cables is about 0.56, and all the members meet the requirements of strength, stiffness and stability. Eigen buckling analysis. In the eigen buckling analysis, the eigen buckling forces of the structure can be calculated through the realistic elastic buckling theory. According to the code [4], the safety

5 24 Advances in Structures factor of the overall stability of the guyed mast calculated by the critical buckling pressure of the shaft can t be less than 2.0, that is, the buckling factor of eigen buckling analysis should not be less than 2.0. Eigen buckling analysis of the guyed mast structure under three wind load cases were performed, because the wind load is the main factor leading to structural instability. It is found that the buckling factors are all above 2.0 in the two design proposals, which meets the requirements in the code. Economic comparison of two design proposals Weight of steel for main structure. After analysis and design of the guyed tower, the structural components chosen for the proposals are listed in Table 2. Comparing the statistical weights of steel for main structure, it is found that the proposal 1 can save 1826 kg of steel relative to proposal 2, that is, about 16.3%. Proposal 1 Table 2 Structural components for proposal 1 and proposal 2 Chord member Φ146x6 Shaft member Web member Material Φ45x4, Φ50x4 Proposal 2 Φ60,Φ70 Φ25,Φ30 Q235-B steel pipe Q235-B round steel 1st layer 2nd layer Cable 3rd layer Φ28 Φ32 Φ36 Φ28 Φ32 Φ36 Material 6x37+FC-1870 steel wire rope 6x37+FC-1870 steel wire rope Project cost. There are many factors affecting the project cost. For steel structure, the steel price is an important factor, but it is subject to market fluctuation. Here, the project costs of the two design proposals are compared based on the steel price investigated in Beijing. The price of steel pipe is 5000 Yuan RMB/t and the price of round steel is 4500 Yuan RMB/t. It can be found that the proposal 1 using steel pipe material is more economical after a comparative analysis. Besides, the materials used for the foundation are less as the main structure is lighter in proposal 1. All in all, the cost of proposal 1 is much less than proposal 2. Conclusions After carrying out analysis and design of the guyed mast structure, and comparing the results of two design proposals for a guyed tower, the author comes to several conclusions. Under the condition of meeting the force requirements, it will be more economical for a guyed tower with fewer guy layers and larger initial tension of the guys. Besides, the guyed mast using steel pipe for the shaft is more economical compared with the round steel one, and the advantage will be more obvious for the guyed mast with greater height. References [1] Ulrik Støttrup-Andersen: Masts and Towers. Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium (2009), p [2] Donatas Jatulis, Zenonas Kamaitis, Algirdas Juozapaitis: Journal of Civil Engineering and Management,Vol. XIII, No. 3(2007), p [3] Zhaomin Wang, Zhihong Wang, Mingzhong Yan: Mast Structures. Science Press, 2001 (In Chinese). [4] Code for Design of High-rising Structures (GB ) (In Chinese). [5] Load code for the design of building structures (GB ) (In Chinese).

6 Advances in Structures / Nonlinear Analysis and Design of a Guyed Mast: Comparison of Two Design Proposals /