Guy Mast Analysis

Computers & Strucrwes Vol. 49, No. 5. pp. 797405. 1993 (T, 1994 Elsevier Science Ltd

Printed in Gnat Britain. 0045.7949/93 $6.00 + 0.00

MODELING, LOADING, AND PRELIMINARY DESIGN CONSIDERATIONS FOR TALL GUYED TOWERS

C. GANTES,~‘]~ R. KHOURY,$ J. J. CONNORS and C. POUANGAREDII

tP.0. Box 31830, 100 35 Athens, Greece

$Engineering Information Technology, 545 Concord Avenue, Cambridge, MA, U.S.A.

$Xonstructed Facilities Division, Massachusetts Institute of Technology, Cambridge, MA, U.S.A.

19 Nikokleous Street, Ayia Zoni, Limassol, Cyprus

(Received 17 September 1992)

Abstract--The inherent nonlinearity in the structural behavior of guyed towers leads to difficulties in their structural analysis, and prevents the formulation of a general-purpose design methodology. As a result, simplifying analysis assumptions regarding the loading and the modeling of structural behavior have to be made, and approximate design methods are used, that are often unjustified, and can lead to disastrous failures.

In this paper, the authors fhst summarize the results of an investigation they carried out on the collapse of a 1900 ft tall guyed tower under ice and wind loads. Based on this investigation, they then proceed to present some structural analysis recommendations relating to loading and modeling concerns. Special emphasis is placed on the importance of ice loading, and on the level of accuracy required in modeling the nonlinear response behavior. Finally, the conclusions drawn from this study are used to formulate preliminary design guidelines. This facilitates a systematic approach for the design of tall guyed towers.

1. INTRODUCIION

During recent years there has been an increasing tendency in the structural engineering community for savings in material that result in lightweight, slender structures. Guyed towers supporting telecommunica- tion antennas belong to this general class of structures. They consist of a slender, tall mast laterally supported at several levels along its height by sets of inclined pretensioned guys spaced at equal angles around the mast.

The actual structural behavior of guyed towers is extremely complicated. The guys exhibit, in general, a nonlinear behavior, especially at low values of pretension. Increasing the pretension of the guys lessens the nonlinearity and improves the lateral stiffness, however, it also leads to larger compressive loads, and therefore, to a higher buckling probability for the mast itself. The behavior of the mast is also nonlinear due to its slenderness, and to the large displacements it experiences under substantial wind loading. Moreover, decisions that have to be taken in the design phase regarding loads are also not straightforward. Guyed towers have traditionally been designed for wind loading. However, wind forces are of a dynamic nature, and consideration of equivalent static loads is not always adequate. In addition to wind load, there is also ice load. This load stresses

IlFormerly with the Civil Engineering Department, Massachusetts Institute of Technology, Cambridge, MA, U.S.A.

the members of the tower in a completely different manner than wind, and can therefore be potentially critical. Simultaneous ice and wind loads can fre- quently occur, and have been found to be responsible for several catastrophic failures of guyed towers in the past. And with the inability of analysts or designers to model accurately this complicated behavior, the attention of investigators has been focused on identi- fying reasonable simplifications in the required loading and the structural modeling for guyed towers.

A number of researchers have investigated the structural behavior of cables. A fairly complete de- scription of cable behavior under several types of load can be found in [l, 21. A commonly used tech- nique to take into account the nonlinearity due to sag is that of the equivalent cable modulus [3]. Design expressions for the response of cables under concentrated and uniform loads are given in [4]. Interesting contributions have also been made by designers of cable-stayed bridges [S, 61 who face similar difficulties in modeling cable behavior. The advent of digital computers and the finite element method has led to the formulation of a series of numerical methods for cable treatment [7-91. Some very recent work pub- lished in [lo] gives what could be considered to be state-of-the-art for cable modeling today, comparing more accurate numerical to approximate analytical solutions.

Other investigators have dealt more specifically with behavior and design issues of guyed towers. In [ll] analytical expressions for the simpler problem of ‘short’ towers with a single set of guys are given.

797

798 C. GANTFS et al.

Finite element methods for the analysis of guyed towers are described in [ 12-151. The Electronic Indus- tries Association [ 161, and the German DIN 413 1 [ 171 provide guidelines for minimum design requirements, while optimum sizing recommendations are pub- lished in [18]. A number of papers [19,20] deal with the effect of wind loading on towers, while [21,22] stress the potential danger induced by ice formation.

Although a considerable amount of research has been done on the behavior of guyed towers, the problem of finding a commonly accepted methodology for their design remains unsolved. Currently used design approaches can lead to unsafe or unstable towers, as indicated by investigations of several failures that occurred in the recent past.

In this paper, the authors first summarize the conclusions drawn from their investigation of a tower collapse under combined ice and wind loading. Then, they try to use these conclusions to formulate some general recommendations pertaining to the analysis and design of guyed towers. Considerations related to the types of load that have to be accounted for and how they should be modeled are presented. This is followed by a discussion of several modeling techniques for the mast and cables, and the level of accuracy achieved by each one of them. And finally, some guidelines for the preliminary design of guyed towers are given.

2. CONCLUSIONS DRAWN FROM GUYED TOWER COLLAPSE

The mast of the tower, shown in Fig. 1, was a space truss in the shape of a triangular prism with strong columns at the three corners, horizontal members at regular intervals of 5 ft, and diagonal X-bracing. It was 1900 ft tall, 9 ft per side, and supported a TV antenna. It was supported laterally by three planes of guys equally spaced at 120” intervals.

The tower collapsed under heavy ice and light wind loads. The wind direction and the location of the

TOWER

DIRECTION

Fig. 2. Post-collapse situation

debris after the collapse are illustrated in Fig. 2. According to the meteorological data, the wind vel- ocity was around 15 mph, and the ice was distributed triangularly along the height of the tower with a maximum thickness of loin at the top.

An investigation of the response of the tower under these two loads indicated that it had been sufficiently designed for lateral wind loads much stronger than those that occurred at time of collapse. However, the vertical load bearing capacity was inadequate. No allowance for ice load was considered in the initial design since there was no such code requirement.

Ice had a triple effect on the behavior of the tower. It not only created a substantial axial load in the mast, but also increased the projected exposure area for the wind and the sag of the guys, thus reducing their lateral stiffness. The effect of ice on the structural response is indicated by the deflected shapes of the mast shown in Fig. 3. The cantilever type behavior that is observed for wind loads only changes as ice is applied. Similar deflection patterns were observed by Williamson [22].

Axial stresses in the legs of the tower under combined ice and wind loads revealed that local buckling

wind and ice : uniform distribution

I wind and Ice : triangular distribution

Fig. I. Perspective view of the collapsed tower. Fig. 3. Influence of ice distribution on deflected shape.

Modeling considerations of tall guyed towers 799

initiated in a vertical member on the leeward side between the sixth and seventh guy levels. Once this member buckled, the guys at the seventh and eighth level, highly tensioned due to the combined loading, pulled the upper tower section down causing the lower five guy levels to behave out-of-phase with one another. A push-pull mechanism instantly developed between these remaining five clusters of guys causing the collapse of the entire tower in a ‘domino-effect’ manner.

Location of the debris relative to the tower base and to the direction of wind at time of collapse strongly corroborated this failure mechanism. A large pile of broken members along with chunky ice for- mations near the base of the tower in the up-wind direction was the final post-collapse scene. Due to the extreme pulling and pushing of the guy cables, several of them had their concrete foundations upheaved.

In conclusion, the tower collapsed although no evidence of obvious design or construction errors was found. The cause for collapse was the lack of accurate loading information, and, more specifically, the lack of consideration for possible ice formation. While investigating this failure the authors made several observations regarding analysis and design practice for tall guyed towers. Besides emphasizing the main lesson drawn from this collapse, which refers to the importance of ice loading, in the next sections of this paper it will be attempted to provide a review of the state-of-the-art in tall guyed tower design, and recommendations for its improvement.

3. MODELING CONSIDERATIONS

This section will address the issue of modeling of the mast and cables of guyed towers. Towers like the one investigated in the previous section will be exam- ined, since they constitute a fairly common and quite representative class of guyed towers. A typical mast is a space truss with the shape of a triangular pyramid. The three corner columns are connected at regular intervals by horizontal beams and diagonal bracing. The tower is laterally supported by a series of three guys spaced around the mast at angles of 120” and distributed along the height of the mast.

Several methods are used in practice for modeling both the mast and the cables. They vary in the level of accuracy they can provide, as well as in the cost associated with their use. The selection by the designer of one model versus another should be based on the available resources and on the particular design stage, i.e. preliminary versus final design. The most common alternatives for modeling the mast and guys and their corresponding virtues and handicaps are presented here.

3.1. Modeling of the mast

The simplest way to model the mast is by using an equivalent beam. Referring to Fig. 4, the cross-

A

d a I d 1

t

aed%

2 I A d

A

Fig. 4. Schematic mast section.

sectional properties of the equivalent beam can be obtained as follows:

and

A, = 3A (1)

These expressions neglect the contributions of both the horizontal and diagonal members of the mast to the axial and bending stiffness of the equivalent beam. More exact calculations performed as part of this study indicated that this contribution increases Z, only by approximately 5%, and is therefore indeed negligible.

The number of beam elements required to model the equivalent beam for a finite element analysis should be sufficiently high to accurately represent the variation in column size or A, along the height of the mast. In addition, a number of about ten elements between successive guy attachment levels was shown to be adequate to capture nonlinear effects and buckling of the mast.

Regarding the boundary conditions at the base of the mast, both pinned and fixed supports have been used in the past. The actual behavior is somewhere in between, and can be modeled by using a rotational spring, an element widely available in commercial finite element programs. This issue should not bc of major concern anyway, since the boundary conditions only affect the tower locally, in the neighbor- hood of the base.

A more detailed mast modeling involves idealizing every single member, vertical, horizontal, and diagonal, with a corresponding element. Treating each member as a beam element would be the most accurate approach. However, the more conservative solution of using truss elements has proven to provide sufficient accuracy, and is considerably more econ- omical, since it cuts in half the active degrees of freedom.

A comparison of the results obtained when using the two different mast models indicated the

800 C. GANTES et al.

sufficiency of the equivalent beam model in pre- dicting the global tower behavior for preliminary calculations. This is illustrated in Fig. 5 where the horizontal displacement at the top of the tower is plotted against a scale factor for wind load corresponding to 75 mph. Use of the more exact model however, is necessary for final design, and when we are interested in the response of individual members, or in investigating the influence individual member defects could have on the global structural response. It should be noted that the performance of the equivalent beam model could be improved by taking shear deformations into account.

Another alternative is to use techniques of discrete field analysis as proposed in [23]. Then, a closed form solution can be obtained for the space truss that is accurate and avoids the high computational effort of a member by member analysis. In addition, bar forces can then be obtained through back-substi- tution.

3.2. Modeling of the guys

The modeling of the guys is more complex than that of the mast due to the inherent nonlinearity of cable structures. The behavior of cables is presented in detail in [l, 21, where interested readers can be referred to for more information. Here, only issues of interest for the modeling of guys will be addressed.

There are two phases of behavior in the life of cable structures. The first phase includes the deployment and initial pretensioning of cables and is character- ized by being highly nonlinear. The second phase is the so called in-service phase during which various

Wind Load Normalized

,__ wrt 75mph

Displacement

Fig. 5. Comparison of P-u graphs for the mast models.

+

-a-

Fig. 6. Tower with single cluster of cables.

static and dynamic loads are superposed on the pretensioned configuration. The response in this second phase can be either linear or nonlinear depending on the relative magnitudes of the pretensioning and service loads.

Both straight and curved cable elements have been developed and incorporated in finite element programs [7-lo]. Having access to such a program, the designer can use either element type to model the guys. A study presented in [lo] indicates that five curved elements or ten straight elements per guy provide satisfactory accuracy.

The present study, however, addresses situations where such cable elements are not available. This is often the case, since many widely used finite element codes do not include cable elements, but instead recommend the use of nonlinear truss elements for the modeling of cable structures. Furthermore, re- liable simple models can be very useful during the preliminary design stage, even if cable elements are available.

The simplest model is the one where each set of three guys connected to the mast at a given level is substituted by a spring. Consider the simple case of a mast supported laterally by a single set of three cables with initial prestressing tension T, (Fig. 6). The approach introduced in [ 1, pp. 135-l 391, based on the concepts of force equilibrium, deformation compati- bility, and linear elastic material behavior, was followed. Then, the horizontal component of the resultant of the tension forces in the three guys due to a horizontal displacement u and a vertical displace-


ment w in the directions shown in the figure, is given

by

F,=3T, ; 0

+;@A,-T,) ; 0

2

x (;){I -$)(;)}. (4)

This result is based on the assumptions that w is of order u2, and that terms of order u3 or higher are negligible. For the opposite horizontal displacement direction we have

F,=3T, : 0

+$A,-T,) ; ’ z 00

x { 1 +;(;)(g}. (5)

The vertical component of the resultant is the same for both horizontal displacement directions

(6)

For small displacements the terms of order (u/c)~ can be neglected. In addition, it is assumed that T, < EA,.

Then, we obtain the same horizontal force component regardless of displacement direction

The vertical component is

Fw=3Tp b . 0 C

Taking advantage of the isotropic nature of the results for small displacements we can generalize expressions (7) and (8) for the case of a cluster of N guys arranged symmetrically around the mast

and for the vertical component

F,= NT, b 0

. C

These results can be modified using Dishinger’s formula to take into account the nonlinearity due to

sag [31

(EA& = EAg ,+y2E&’ ( >

(11)

P P

where mg is the dead weight of the cable per unit

length. This approximate approach is well known and

provides satisfactory results, especially for high initial

pretensioning and small additional in-service displacements [lo]. Note that in reality the tension along a guy is not constant due to sag and dead weight effects. Use of an average initial guy tension T,, is recommended. Then, the expressions for the horizontal component of tension becomes

F, = N U

0

_

c (12)

Hence, the cluster of guys can be modeled by a linear spring in the direction of wind, and a vertical concentrated load. Ths stiffness of the spring is

k,, = N

The vertical load is given by eqn (10). This model is adequate for initial approximations

and for low in-service loads in comparison to the pretensioning forces. For a more refined analysis, and given the lack of cable elements, the guys can be modeled as a linkage of nonlinear truss elements. To avoid having an unstable stiffness matrix due to zero stiffness of all degrees of freedom associated with displacement perpendicular to the cable, the initial pretensioning strains have to be introduced. A method that has been used in the past consists of modeling the cable as a straight series of truss elements with the initial pretensioning, and then applying the dead weight of the cable incrementally to obtain the deformed configuration at the beginning of the in-service phase. This model however, over- estimates the lateral stiffness provided by the guys, because the stresses due to dead weight are added to those due to mechanical pretensioning, which is not an accurate simulation of the real pretensioning process.

Alternatively, one can use this model of a straight truss linkage with the initial pretensioning, but use a reduced axial stiffness EA, according to Dishinger’s formula (11). This accommodates for softening of the cables due to their dead weight. Then, the service loads are applied directly on the configuration with straight cables. This approach gives satisfactory results for cases of high initial pretensioning.

A more general approach is to calculate analyti- cally the sagged cable shape, and to start the finite element analysis from that deformed configuration. The sagged geometry can be modeled with a series of straight truss elements (Fig. 7). Either a continuous


a

Fig. 7. Inclined cable under lumped dead load

or lumped representation of the dead load can be used for the analytical calculations. Discretization of each cable into 12 straight two-node truss elements and lumping of the dead load on the correpsonding nodes has shown sufficient accuracy in our calculations. The caluclation of the deformed shape is based on the known initial tension. A more general formulation concerning cables under multiple concentrated loads given in [l 1, pp. 25-341, can be used here. This approach consists of calculating the mo- ments at all points of application of concentrated loads, and setting them equal to zero. Then we obtain the following element sag

d=a p i(J-4

’ 0 H 2J2 ’

where P is the total weight of the cable, H is the horizontal component of the known initial tension T, a is the horizontal projection of the cable, and J is the number of elements. This formula assumes discretization in elements of equal horizontal projection. Then, the tension in each element can be obtained since the geometry is known and the horizontal component H remains constant along the cable. Since the slope at the base is changed due to sag, some iterations are required to match H and T. The starting configuration for the finite element analysis of the in-service phase consists of using this deformed shape, and applying the calculated initial tension in all elements and the lumped dead weight on all nodes. This system is self-equilibrating except for the influence of the discretization error.

Table 1 compares the tangent stiffness of the eight cable clusters of the collapsed tower calculated with

Level

I 2 3 4 5 6 7 8

Table 1

Truss model Spring model

1215.1 1215.5 575.9 579.1 399.4 411.7 252.1 263.3 180.4 193.3 158.2 175.0 178.9 203.3 101.2 117.5

this approach, to the corresponding linear spring stiffnesses.

The accuracy of the spring model for small displacement analyses is evident. Its effectiveness is decreased at higher altitudes where the sag is relatively large. Figure 8 illustrates the range of validity of the equivalent spring model. The horizontal displacement at the top of the tower is plotted against the scaling factor of wind load corresponding to a wind speed of 75 mph. In both cases an equivalent beam was used to model the mast. As expected, the stiffening of the guys at increased deformation is modeled effectively by the truss linkages but not by the springs. The performance of the equivalent spring model can be improved if iterations are carried out during which the calculated spring reactions are used to update the values of spring constants in order to account for the nonlinearity of the response [23].

In conclusion, the simple equivalent spring model is an acceptable solution for preliminary design pur- poses, especially for large initial cable pretensioning and small in-service loads. For more detailed analysis and final design, the modeling of the guys in their sagged position as linkages of pretensioned straight truss elements provides an acceptable solution when cable elements are not available.

4. LOADING CONSIDERATIONS

As rather flexible structures, guyed towers exhibit dynamic response under turbulent wind load. The connecting guy cables also behave dynamically, and are very susceptible to galloping, especially when their pretensioning is low. Galloping is an unstable

Wind Load Normalized wrl75mph

i

P ,

Truss model , ’ I

I

, ,m ’ Spring model

/

Fig. 8. Comparison of P-u graphs for truss and spring model.


condition triggered by self-excited vibrations that result in a single degree of freedom motion [21].

As long as the designer can avoid unstable behavior of both the tower and the cables, the dynamic nature of the wind load can be accounted for by applying a gust factor on the equivalent static loads. All available preliminary design approaches, including the methodology proposed in this paper, are based on the behavior of towers under equivalent static loads using height and gust factors.

The combination of the wind loads with the accumulated ice loads complicates the response further. As discussed earlier, accumulated ice formation on the tower and the cables has a multiple effect. The dead load increases considerably. The projected area of the members increases, and therefore, the wind loads become larger. The sag in the cables also increases and, as a result, their lateral stiffness de- creases. In addition, the distribution of ice along the height of the tower is not uniform. Usually, there is more ice at the top than at the bottom. This worsens the effect of the combined ice and wind action on the tower. This effect is illustrated by both our studies (Fig. 3), and those of Williamson [22].

The most recent guidelines for the design of guyed towers are the ones given by the ANSI/EIA-222-D code [16], and our studies have been carried out in accordance with them. The design wind load on the tower and the guys is determined using the expressions provided by this code. The expressions for the drag and lift forces on the guys involve the angle between the wind direction and the cable direction. Three angles of attack for the wind relative to the vertical plane of a series of guys have been taken into consideration. These angles are O”, 60”, and 90”, with respect to one of the three symmetry axes of the triangular mast basis.

The load combinations used are

D + W,

D +0.75W,+Z,

where D is the dead load, W, is the wind load on the structure without ice, Wi is the wind load on the structure with ice, and I is the ice load.

Again, the effective area taken into account for wind loads on the structure without ice, is smaller than the one used to calculate wind loads on the structure with ice. As a genera1 rule, the projected area of the members is increased by 6A = 2tL, where t is the accumulated ice thickness and L is the length of the member. Based on weather reports, it is also reasonable to assume a linearly varying ice thickness from a low value at the bottom of the tower to a maximum value at the top.

It should be noted, however, that the assumption of triangular ice distribution along the height of the tower, although an improvement in comparison to uniform distribution, is not a satisfactory represen-

tation of reality. The critical ice formation will be of ‘in cloud icing, and the deposits on guy wires will be influenced not only by altitude, but also by wind direction relative to guy cable direction. Significantly different cable tensions at each of the three guys at a level can be expected because of irregular ice deposits. The overall tower safety will ultimately be ensured only if these unsymmetric loading cases are taken into consideration. Further research on statistical aspects of these irregular deposits is necessary before recommendations for their consideration on design practice can be formulated. Until then application of higher factors of safety is recommended.

5. PRELIMINARY DESIGN GUIDELINES

Due to the complicated behavior of guyed towers, their design is today still a trial-and-error procedure. Our conclusion, both from an extensive literature survey, and from discussions with experienced designers, is that the selection of initial trial sizes for member cross-sections and level of pretensioning is largely based on past experience. To our knowledge, no systematic procedure exists in the literature that actually comes up with recommendations for initial dimensioning. In this section a simple but systematic methodology for this initial selection is proposed. The procedure is based on the observations made in the preceding sections.

Several simplifying assumptions have been adopted in order to obtain analytical expressions for the response. The main assumption is that the mast will remain approximately straight in the deformed position and will just rotate about its base by an angle 4. This assumption is based on the so-called ‘straightness constraint’[6], according to which the deformations at all guy attachment points must be less than 6 in from a line joining the tower base to its top. The physical meaning of this constraint is to reduce individual member deformations and overall buckling probability.

The deformed configuration of the model used for preliminary design is shown in Fig. 9. The equivalent spring model is used for the guys and the equivalent beam model for the mast. The tower is subjected to

3 (Y)

1 Fig. 9. Model used for preliminary design.


vertical loads q,,(y) including, in general, dead load of the mast, ice on the mast, and concentrated loads from the cables due to their own dead weight, ice, and wind, and horizontal loads y,(y) resulting from wind on the mast and the guys.

5.1. Preliminary design of the guys

The design strategy for the preliminary design of the guys is based on the following criteria:

The working stresses in all cables should be very close to their allowable stress so that full advantage of the material used is taken. All guy clusters should provide equal lateral resistance to the tower. This leads to a relatively uniform distribution of forces along the height of the mast.

Hence, the proposed preliminary design methodology is based on a clear philosophy regarding the desired behavior, consisting of satisfaction of the straightness constraint, stressing of the guys at all levels to their full capacity. and uniform lateral resistance.

The critical wind direction for the guy design is the one shown in Fig. 6. The calculation of the required pretensioning is based on the first criterion. The tension T, in the ith guy is given by

+ O(u2), (15)

where T,, is the initial pretension, &,, is calculated from Dishinger’s formula, A, is the cross-section area of the guy, and a,, h,, L’,, u, refer to the notation of Fig. 6. For the working stresses we have

where y is the density of the material of the cable. Assuming that the geometry of the guys is known, cr, is equal to the allowable stress call, and 4 is specified as the maximum allowable rotation &,,, we can solve the above equation numerically for o,,,. The method of successive iterations can be used for the numerical solution starting with the trial value

CP, = 0.40,,, . as recommended in [ 181. Hence, the initial trial values for the pretensioning stresses can be calculated. It is interesting to observe that these values depend only on geometry and material properties. and not on the intensity of applied external loads. Variations in this intensity is accommodated by appropriate scaling of cross-sections as explained below.

The calculation of the cross-sections of the guys is based on the second criterion. In order to have equal lateral resistance by all springs, it is required that

F,,=F,-k,u,=k,u,-k,h,tan&=k,b,tan$. (17)

Hence

k, = k, ; . I

(18)

Moment equilibrium about the base gives

M,,, is known for 4 = &,,. In addition, F,, = F,, Vi. Then.

Applying this relation for the nth guy, we get

k,b, tan r$ = 2 -k, = Kx,

b, tan 4 Cb, (21)

The other k,s can then be obtained from (18). For the cross-sections A,,. eqn (13) gives

c,k, (22)

Hence, the initial trial sizes for the required cross- sectional areas of the guys can also be calculated.

5.2. Preliminary design oj’ the mast

The design of the mast is quite straightforward. Knowing the guy reactions, equilibrium considerations at any desired mast level can provide the axial force F and the bending moment M for the corresponding cross-section. Keeping eqn (2) in mind, and choosing d, we can obtain the required section area A of the columns

It should be stressed here again that the procedure proposed in this section can serve only as a methodology for the preliminary initial sizing of the basic components of a guyed tower. Using these results as a starting point the designer should proceed and carry out a more refined analysis taking nonlinear and dynamic effects into account.

6. SUMMARY AND CONCLUSIONS

The first part of this paper investigates the collapse of a tall guyed tower under ice and wind loads. The observations of previous investigators about the importance of ice loads are verifed. Then, several


approaches for the modeling of the mast and the guys 8. are evaluated. An equivalent beam model appears to be a simple and acceptable solution for the mast, 9. while equivalent springs are satisfactory for modeling of the guys for preliminary analysis. A nonlinear truss representation in the sagged configuration is possible lo. for a more exact finite element analysis when cable elements are not available. Considerations about 11. the calculation of wind and ice loads are also presented. 12.

Finally, a methodology for preliminary design is proposed as a first step towards a more systematic *3. approach for the design of guyed towers. It is believed that this methodology constitutes an improvement to today’s state of the art by introducing a clear design 14.

philosophy as outlined in Sec. 5.1, and by recom- mending specific initial trial values for member cross- 15. sections and guy pretensioning. This approach is intended to improve the current trial and error tower design practice.

16.

H. B. Jayaraman and W. C. Knudson, A curved element for the analysis of cable structures. Comput. Struct. 14, 325-333 (1981). J. W. Leonard and J. H. Nath, Comparison of finite element and lumped parameter methods for oceanic cables. Engng Struct. 3, 153-167 (1981). D. Bruno, F. Maceri and R. S. Olivito, Analysis of the elastic response of stays and stayed systems. IABSE Periodica i, 29-44 (19%). _ _ A. Chaies and W.-S. Chen. Stabilitv of euved towers. J. Struit. Div., ASCE 105,‘163-174-(197$.- N. V. Raman, G. V. Surya Kumar and V. V. Sreedhara Rao, Large displacement analysis of guyed towers. Comput. Struct. 28, 93-104 (1988). F. Rosenthal and R. A. Skop, Guyed towers under arbitrary loads. J. Struct. Div., ASCE 106, 679492 (1980). F. Rosenthal and R. A. Skop, Method for analysis of guyed towers. J. Struct. Div. ASCE 108, 543-558 (1982). B. A. Schrefler, S. Odorizzi and R. D. Wood, A total Lagrangian geometrically nonlinear analysis of combined beam and cable structures. Comput. Struct. 17, 115-127 (1983). Electronic Industries Association, Structural standards for steel antenna towers and antenna supporting structures. American National Standard, ANSI/EIA-222-D- 1986 (1986). DIN 4131, Antennentragwerke aus Stahl (1988). W. H. Greene, Minimum weight sizing of guyed antenna towers. J. Struct. Engng, ASCE 111, 2121-2137 (1985). R. T. Nakamoto and A. N. L. Chiu, Investigation of wind effects on tall guyed tower. J. Struct. Engng, ASCE 111, 232&2332 (1985). J. W. Vellozzi, Tall guyed tower response to wind loading. Proceedings of the 4th International Con- ference on Wind Effects on Buildings and Structures, (Edited by K. J. Eaton) pp. 735-743, Heathrow, London (1975). M. Novak, A. G. Davenport and H. Tanaka, Vibration of towers due to galloping of iced cables. J. Engng Mech. Div. ASCE 104, 457473 (1978). R. A. Williamson, Stability study of guyed towers under ice loads. J. Struct. Div., ASCE 99, 2391-2408 (1973). R. R. A. Issa and R. R. Avent, Microcomputer analysis of guyed towers as lattices. J. Struct. Engng, ASCE 117, 1238-1256 (1991).

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H. M. Irvine, Cable Structures. MIT Press (1981). 17. J. W. Leonard, Tension Structures: Behavior and Analy- 18. sis. McGraw-Hill (1988). A. G. Davenport and G. Steels, Dynamic behavior of massive guy cables. J. Struct. Div., AXE 91, 43-70 19. (1965). A. J. Wilson and R. J. Wheen, Inclined cables under load-design expressions. J. Struct. Div., ASCE 103, 20. 1061-1078 (1977). M.-C. Tang, Analysis of cable-stayed girder bridges. J. Struct. Div., ASCE 97, 1481-1496 (1971). Task Committee on Cable-Suspended Structures of the Committee on Special Structures of the Committee on 21. Metals of the Structural Division of ASCE, Commen- tary on the tentative recommendations for cable-stayed bridge structures. J. Struct. Div. ASCE 103, 941-959 22. (1977). R. L. Huston and J. W. Kamman, Validation of finite 23. segment cable models. Comput. Struct. 15, 653-660 (1982).

Guy Mast Analysis

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