Static Analysis and Testing of Guyed Masts

STATIC ANALYSIS AND TESTING OF GUYED MASTS Donatas Jatulis1, Zenonas Kamaitis2, Algirdas Juozapaitis3 Dept of Bridges and Special Structures, Vilnius Gediminas Technical University, Sauletekio al. 11 LT-10223 Vilnius-40, Lithuania E-mail:[email protected]; [email protected], [email protected];

Abstract. The static behaviour of guyed mast with combined guys was investigated. In this study the main emphasis is focused on the influence of the factor of initial equilibrium of guy cables, which takes into account the position of guys attachment points with mast shaft as well as loading conditions. Two different analyses were employed using finite element modelling and experimental model testing. The static numerical analysis of a one-level guyed mast has been undertaken. For the purpose of verification of the FE model, two steel scale models with different factors of initial equilibrium of guy cables are fabricated and tested in bending with the aid of special designed device. Findings with regard to mast displacements and bending moments are presented. Keywords: guyed mast, combined guys, geometrical and physical parameters, behaviour modelling, model testing

1. Introduction Usually, a guyed mast consist 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. The masts are usually pined or fixed at the base. The other components of guyed masts are the foundations, accessories of the structure, and the equipment. The present trend in guyed mast construction is toward higher, more complex configurations with more peculiar stiffness requirements. The guyed masts are tall and flexible structures loaded by wind pressure, ice and temperature changes. The wind is predominant action causing sometimes serious problems for guyed masts as dynamically sensitive structures. The failures under wind action of some guyed masts and towers have highlighted the need for more precise response evaluation and criteria for design. The geometrical behaviour of the guyed mast is non-linear due to its slenderness and compliant guysupported system significantly complicating analysis of the structural system. The loads from wind, ice and temperature changes cannot be exactly defined. The structural behaviour of guyed masts has been studied by many researchers and methods of static or dynamic analysis have been proposed in many countries [1, 2, 3, 4, 5, 6]. Methods of static analysis are given in the various National Codes [i.e., 7, 8, 9, 10]. Implementation of new types of guyed masts or structural modification of

existing ones as well as the methods of analysis is of vital importance. The laboratory or full scale testing of light guyed masts can help to better understand the structural behaviour and to provide bases for determining or revision of loading and design criteria of mast structures. As the authors know, testing of full-scale tall guyed masts is not feasible at present due to complexity of experiment. Useful information is obtained from instrumentation of full scale guyed masts in natural conditions [11]. The actual behaviour of structures is most easily studied in laboratories. Hence the structural model plays an important role in fundamental research and also in applied design studies. It seems that the testing of scale laboratory models provides additional valuable information in this area [11, 12, 13, 14]. New type of guyed mast is proposed by the authors of present paper [15]. In the present investigation of the mast behaviour under static loading two different analyses were employed using FE modelling and experimental scale model testing. The displacements of the mast shaft were found to be a function of the geometrical parameters of the guy cables. The testing of guyed mast model was carried out to study the influence of geometrical and physical parameters of guy cables on the displacements and bending moments in the mast shaft. Displacements and bending moments of the mast obtained from the testing were compared with the values obtained from FE simulation.

2. Structural type

Fig 1. Attachment of combined guys to the mast shaft: a – solid mast shaft; b – latticed shaft with the guys attached to the legs of a mast in vertical plan; c − latticed shaft with the guys attached to the legs of a mast in vertical and horizontal plan: 1 − central mast; 2 − main guy; 3 − additional secondary guy

The guyed mast structure consists of vertical mastcolumn, main and secondary guys (Fig 1). The central mast can be constructed using solid, circular or open steel lattice typically square or triangular cross-section. The mast is normally guyed in three or four directions, e.g., at 1200 or 900 angles in the plan. The main guys are propped by two additional secondary guys to increase number of intermediate elastic supports and to reduce the effective buckling lengths of the mast. The standard cables are used for main and secondary guys. The number of secondary guys depends of crosssection shape of the mast column. It is intended to use for a main guy two secondary guy cables situated in vertical

plane (in the case of solid mast) (Fig 1,a) and two or four secondary guys, if a mast is latticed (Fig 1, b and c). It seems that the steel lattice is the most acceptable form of structure for this type of combined guys. The secondary guys are attached to the main guy by a special connectors assuring invariable length of the secondary guys. The later are attached to the vertical mast by the same connectors as in the case of standard guyed masts. Termination of the guy cables at the lower end includes a length variation mechanism to allow tensions to be adjusted from time to time.

3. Initial equilibrium of guy cable

F2

b)

c)

hb

a)

u2

u2

F1

ha

O

u1

Fig 2. Possible kinematical displacements of combined guys

u1

Let us consider a system of rigid bars loaded by two forces F1 and F2 (Fig 2, a). In the case that no motion of the system is allowed, the condition of equilibrium for the bars requires

ha F2 = hb F1

.

(1)

If this condition of equilibrium is not satisfied, the kinematical displacements will occur (Figs 2, a and 2, b). Note that displacements u1 and u2 of nodes are in opposite directions. If we now replace rigid bars by flexible cables, the additional displacements will occur due to elastic elongation and kinematical displacements of the cables. Hence, for behaviour analysis of guyed mast with combined guys the factor of initial equilibrium of guy cables is introduced:

K eq =

F1 ha F2 h b

.

(2)

4. FE modelling

2.

F1 = F2 = 12kN

;.

2 u1, (1) u2, (1)

1,5

u1, (2) u2, (2) u1, (3)

1

u2, (3)

b) hi+1

a)

h F1 = 0,1 ÷ 2 ; a = 1 ; hi = 30m ; F2 hb

ha = 0,1 ÷ 2 ; hi = 18 ÷ 46m . hb The non-dimensional lateral displacements ui/hi were defined at each point where the secondary guys are connected to the mast. Displacements are summarized in Fig 4. It can be observed that an increase in the parameter Keq leads to slightly increase in displacements of anchoring node 1 and to decrease in displacements of node 2. This increase in displacements is relatively more important for node 2 than that for node 1. For values of Keq = 1, the displacements of nodes are approximately equal to each other. 3.

Keq

In order to determine the influence of parameter Kef on the behaviour of guyed mast, the numerical analysis using commercial program Robot Millennium was performed. The mast shaft was modelled as beam-column element and guys are modelled as two-node cable element. The geometric non-linear static analyses have been performed using Newton-Raphson iterative technique.

assumed hinged at two edges at the level of guy supports. The cross-sections of main and secondary cables are identical with EAcab=12 MN. Bending stiffness of the mast EIm = 73,4 MNm2. It is also assumed that hi−1 = hi = hi+1 = 30 m. The sum of two concentrated forces F1 + F2 = 24 kN. Horizontal projection of secondary guys lx = 7,5 m;. Three scenarios were analyzed: h 1. F1 = F2 = 12kN ;. a = 0,1 ÷ 2 ; hi = 30m ; hb

0,5 F2

2

2

hb

0 hi

-10

20

30

40

A

1

1

hi-1

F1

Fig 4. Relative displacements of nodes 1 and 2 versus parameter Kef

5. Model testing

Lu

L

10

(u/hi)x1000

ha

A

0

lx

Fig 3. Intermediate segment of the guyed mast, including the combined guy: a − geometrical parameters; b – scheme of loading

Consider the vertical segment of the guyed mast between two consecutive groups of cables supported laterally by a single guy and loaded with two concentrated forces F1 and F2 at the anchoring nodes of each secondary guy (Fig 3, b). The mast segment is

To testify the numerical analysis presented above, a physical steel scale-modelled a 3 m high guyed mast is fabricated and tested in the Structural Laboratory of the University (Fig 5). The scale model is two-level guyed mast. The mast shaft is a steel box profile □25 × 1,5 mm with a constant bending stiffness EIm = 2500 Nm2. The cables are made of brass wires with a diameter of 2 mm and EAcab = 193 kN. The equivalent Young’s module is E cab = 135 GPa . One cable end with two branches is attached to the mast, and the second one to an anchored mechanism, allowing control of tension in the cable. Two positions of bottom guy cable are considered (3.1 and 3.1’, see Fig 5).

Fig 5. Structural model of guyed mast: 1 − central mast; 2 − main guy; 3.1 − secondary bottom guy at Keq = 0,46; 3.1’ − secondary bottom guy at Keq = 0,90; 3.2 − secondary top guy.

model test underwent three cycles of loading and unloading. A total of 24 strain gages were used to measure strains on the surface of the mast at selected positions. Deflections were measured at 6 points of the mast, and the tensions in the guys determined by suitable dynamometers. The test data are summarized in Fig 6.

The mast model was tested in bending with the aid of special designed device. The model with a pined foot was placed centrally and loaded laterally. Loading was produced by weights. To simulate the uniformly distributed wind pressure, the concentrated horizontal forces spaced at short intervals of 25 cm are applied. Each

b

H, m

3

3

2,5

2,5

2

2

1,5

1 2

1

H, m .

a

1,5 1

1

1' 2'

0,5

2 1'

0,5

2' 0

0 -30

0

30

D isp la ce m e n t, m m

60

-0,12 -0,09 -0,06 -0,03

0

0,03 0,06

Bending moment, kNm

Fig 6. Comparison of experimental and predicted deflections (a) and bending moments (b) of the mast shaft: 1 − Kef = 0,46; 2 − Kef = experimental; ------ FE modelling (pre-tension stresses in cables σ0 = 38,5 MPa) 0.90;

Fig 6, a represents deflection curves of the two models along the total height of the mast. They show a fundamental difference of behaviour between the mast with Kef = 0,90 which is approximately linear, and the mast with Kef = 0,46 characterized by the opposite to loading direction deflections until H ≈ 1,0. The maximum lateral displacement of the mast top is approximately 2 times greater for mast with Kef = 0,46. The bending moments induced in the mast are distributed as shown in Fig 6, b. This indicates that the mast with Kef = 0,46 is subject to positive moments along a large length of the mast. The redistribution of moments similar to that in continuous beam is observed in the mast with Kef = 0,90. The general redistribution trend is to shift from positive moment region to negative moment region. The magnitude of positive bending moment decreased while magnitude of bending moment increased, leading to their approximately equal values. Experimental results indicate an average 2 times decrease in maximum moment at the attachment point of the bottom cable. From Fig 6 it is also observed that there is a reasonable match between the curves from the FE analysis and the test respectively. As can be seen from this analysis, designs of guyed mast must take into consideration the configuration of combined guys, i.e. take into account the factor Kef. From Fig 6 it can be seen that the experimental results were in good agreement with the results from the FE analysis. The finite element model can predict the displacements of the guyed mast to an acceptable range of 7,2% to −8,8%, and that of bending moments of 12% to −9,8%. So the results of FE simulation match well with the experimental data. 6. Conclusions The following conclusions may be drawn from the results of this investigation on the masts with combined guys: 1. New type of guyed mast with combined guys was investigated. The main guys are propped by two additional secondary guys to increase number of intermediate elastic supports and to reduce the deflections and bending moments in the mast shaft. It seems that new type of guyed mast can extend the field of application of these masts to the construction of antenna supporting structures. 2. Two different analyses of guyed mast behaviour under static lateral loading were employed using finite element modelling and experimental model testing. The lateral displacements and bending moments in the mast were determined. The results from both methods match well. It was shown that FE analysis can be used for improved assessment of masts with combined guys. 3. Two comparative analyses indicated that proposed factor Kef [see Eq. (2)] is very important for behaviour of

guyed masts under horizontal static loading. The deflections, bending moments and stresses in the guyed mast can be controlled by appropriate choosing of design parameter Kef. References 1.

2.

3.

4.

5.

6.

7. 8. 9. 10. 11.

12.

13.

14.

15.

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