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An experimental investigation into failure mechanism of a full-scale 40 m high steel telecommunication tower
Accepted Manuscript An experimental investigation into failure mechanism of a full-scale 40 meters high steel telecommunication tower Jacek Szafran PII: DOI: Reference:
S1350-6307(15)00148-X http://dx.doi.org/10.1016/j.engfailanal.2015.04.017 EFA 2565
To appear in:
Engineering Failure Analysis
Received Date: Revised Date: Accepted Date:
6 February 2015 22 April 2015 23 April 2015
Please cite this article as: Szafran, J., An experimental investigation into failure mechanism of a full-scale 40 meters high steel telecommunication tower, Engineering Failure Analysis (2015), doi: http://dx.doi.org/10.1016/ j.engfailanal.2015.04.017
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An experimental investigation into failure mechanism of a full-scale 40 meters high steel telecommunication tower Jacek Szafran Department of Structural Mechanics, Chair of Reliability of Structures, Faculty of Civil Engineering, Architecture and Environmental Engineering, Lodz University of Technology, Al. Politechniki 6, 90-924 Łódź, Poland email: [email protected], tel. 48-42-631-35-64
Abstract: The main objective of this paper is to present and discuss failure mechanism, failure mode, as well as plastic deformation of a lattice telecommunication tower obtained during a full-scale pushover test. The manuscript consists of a detailed description of the tested structure and the experimental site. Displacements of particular nodes of the tower are presented as a function of the external load. The main conclusion is that the rigidity of joints between particular elements, which depends on thickness and diameter of connecting flanges and number and quality of bolts, determines the failure mode of the compressed tower legs. In the article, values of axial forces under compression, taken directly from the conducted test, were compared with the standard buckling resistance. On the basis of this comparison, discussion about the effective slenderness factor has been generated, and the proper determination of this coefficient has been proposed. Keywords: failure mechanism, buckling, plastic deformation, structural failures, breaking load, code of practice, deflection
1. Introduction Experiments on full-scale engineering structures, although difficult to perform because of, both technical and financial reasons, can produce results that are impossible to obtain in a different way. Structure response searching in the context of, e.g. stresses, strains, displacements, and last but not least, failure mechanism and failure mode, may help enrich the knowledge about structures like lattice towers. Steel lattice towers are extensively utilized in telecommunication industry as supporting structures providing services such as telephoning, wireless internet or television. The more pressing the mobile networking needs of today’s customers are, the more requirements are being imposed on telecommunication devices which, in turn, causes repetitive replacements, upgrades, and modernizations. Antennas and radio units which get attached to telecommunication towers have different shapes, dimensions and weight. They are installed at various heights which considerably alters forces distribution of a supporting structure as well as carrying capacity of tower elements. Taking into consideration constant change of operating conditions, there is recurring need of determining bearing capacity of such structures. Due to the advancements in telecommunication engineering, including a growing number of new technological solutions, the scientists and civil engineers also contribute to the effort of meeting the new demands with numerous scientific publications devoted to problems in the field of telecommunication structures.. As an example of current state of knowledge of high, slender engineering structures and, in particular, of their dynamic behavior and fatigue, the works of Repetto and Solari [1, 2] may be mentioned. One of the most practical and comprehensive scientific manuscripts dealing with communication structures is one written by Smith [3].The author thoroughly elaborates on utilization of structures of that type, taking into account a variety of design aspects: meteorological parameters, strength, fatigue, and etc., where the conclusions coming from structural failures of masts and towers caused by external loads are particularly important. One type of load that determines cross-section size of particular elements of steel lattice towers is obviously wind load. The effect that the wind has on various engineering structures is a subject of many research articles. The comparison of results taken directly from wind tunnel tests and those predicted by Eurocode [4] for a slender tower structure can be found in [5]. Various problems in design, and analysis of telecommunication structures in particular, were published in [6] by Travanca et al. From the standpoint of engineering practice, a significant problem was tackled: the comparison of standards’ records and definitions from various codes of practice, which change over time, with their impact on subsequent estimation of
carrying capacity of the structures with emphasis being placed on existing object evaluation. This problem seems to be particularly significant for telecommunication towers due to changing nature of their load conditions (technological requirements). Additionally, the subject of tower strengthening and upgrading, where maintaining an object in a fair condition over years is concerned, is extremely valid. It is not uncommon that these objects are utilized for several dozen years. Hence the constant need for modernization, renovation, or upgrading to fulfill the above requirements [7]. The replacement of structure’s elements with ones of larger cross-sections, manufacturing additional truss elements or adding weight to the foundations are very common, exemplary attempts of upgrading telecommunication support structures. Reliability modeling is the next aspect of research and development in this branch of engineering. The requirements concerning the reliability are included in [8]. They impose a structural design process which ensures compliance with top quality standards. Computational probabilistic analysis and reliability assessment of steel telecommunication towers subjected to material and environmental uncertainty can be found in author’s previous works [9-12] and book of Kamiński [13]. One of more interesting and challenging problems is either analytical or numerical determination of carrying capacity of steel tower elements made of cold-rolled or hot-rolled L-sections. In particular, it involves the determination of support conditions influence, load applying manner, failure mechanism, and failure modes which results in carrying capacity estimation. Many scientific publications tackle the problem of structural elements behavior and their plastic deformation in particular [14]. An analysis of such elements often used in steel structures may involve full 3D behavior; consideration of axial, bending and shearing actions; various slenderness ratios; loading and displacement eccentricities. The comparison of numerical calculations with a full-scale destructive test may be found in the work of Lee and McClure [15]. The manuscript elaborates on highly relevant aspects of structures composed of hot-rolled single angle shapes with eccentric connections and, most importantly, allows for comparison of the obtained numerical results with full-scale, destructive test data. The authors of [15] should be also noted for pointing out that, in the context of mechanical security where the assessment of modes of failures and the confinement of failure are key, it becomes important to predict the actual strength and failure mechanism of such towers with a reasonable accuracy for failure scenarios in both static and dynamic regimes. Some consideration about non-local and local buckling and their influence on overall stability of truss and arched structures can be found in [16, 17]. The use of FEM
analyses with the experimental study findings considerably extends the knowledge of buckling phenomenon for structures’ elements. 2. Experimental, full-scale test 2.1. Experimental study objective One of the main objectives of the experiment was to reveal failure mechanism and failure mode of the 40 meters high, steel, lattice telecommunication tower under breaking load. The experiment has been conducted in such a manner that the external load was exerted on the tower and the maximum compression forces in its legs were created. It was achieved by applying the load in the least favorable direction for a tower of a triangular cross-section causing the maximum value of the compression stresses at one of the legs. Particular attention was paid to the observation of the tower legs behavior. One of the goals of the performed test was the determination of their buckling resistance. Another purpose was to determine the nature of destruction of diagonal bracings comprising hot-rolled angle sections. For these purposes, a tower of a complex structure and specific bearing elements was chosen. 2.2 Tower description The tower is a 40 meter lattice structure with a triangular cross-section. It is divided into seven sections. The sections may be classified into two types, with convergent and parallel legs. The bottom part of the tower (up to 34th meter) forms a pyramid frustum of convergence of 5%. The centerline dimension is 4.90 m at its base and 1.50 m at the top. The upper part of the tower is a parallelepiped of a height equal to 6.0 m with the cross-section of an equilateral triangle of side length equal to 1.50 m. Geometric division of sections and their heights, the layout of elements in two bottom sections as well as the structure of the tower under average exploitation are shown in Fig. 1. The general construction manner of particular sections shall be presented as the following: the legs were made with round solid bars, the diagonal bracing members with hot-rolled single angles, both symmetric and non-symmetric. The profiles of particular tower elements are presented in Tab. 1 below:
Section S-1 S-2 S-3 S-4 S-5 S-6 S-7
Legs Ø 65 Ø 65 Ø 65 Ø 80 Ø 80 Ø 90 Ø 90
Diagonal bracings ∟60x60x6 ∟60x60x6 ∟60x60x6 ∟60x60x8 ∟90x60x8 ∟90x60x8 ∟90x60x8
Tab. 1. Selected tower element profiles, units are mm Intersections of the diagonal bracings (of type X) are made with a spacer and a single bolt. The joints of the diagonal bracing and legs were realized with gusset plates and bolts (two for a node). The legs at the connections of individual sections of the structure were made using round plates (connecting flanges) welded at their ends and an adequate number of bolts as presented in Fig. 2. Data concerning individual joints, thickness and size of the flanges, and the number and type of bolts in individual sections were presented in Tab. 2. Section
S-1 S-2 S-3 S-4 S-5 S-6 S-7
Diameter of lower/upper connecting flange 180/180 180/180 200/180 220/200 230/220 260/230 270/260
Thickness of lower/upper connecting flange 25/25 25/25 30/25 30/30 30/30 35/30 35/35
Bolts in lower/upper connecting flange
Number of bolts in joint
M16x75(8.8)/M16x75(8.8) M16x75(8.8)/M16x75(8.8) M16x85(8.8)/M16x75(8.8) M20x85(8.8)/M16x85(8.8) M20x85(8.8)/M20x85(8.8) M24x100(8.8)/M20x85(8.8) M24x100(8.8)/M24x100(8.8)
6 6 6 6 6 6 6
Tab. 2. Data concerning leg joints of individual tower sections, units are mm The tower was equipped with a climbing - cable ladder. The ladder is attached at every section to the tower legs with two angle braces and bolts (Fig. 3). In order to determine the mechanical properties of the structural steel tensile testing of the 14 specimens (5 for L-sections and 9 for full round bars), according to standard [19], were performed. Mechanical properties obtained during the laboratory tests are listed in Tab. 3. Mechanical properties Young modulus Lower yield strength Upper yield strength Tensile strength
Tab. 3. Mechanical properties of structural steel
Values L-sections 205,0GPa 323,6 MPa 333,8 MPa 447,0 MPa
Legs round bars 203,3 GPa 284,7 MPa 290,0 MPa 467,4 MPa
2.3 Full-scale experiment Full-scale experiments are the type of scientific and engineering effort which allows for understanding of authentic behavior of a structure under ultimate load. As mentioned in [15], experimental tests are frequently used as a validation procedure in the development process of numerical models. Taking engineering structures into account, the complexity level, scale, and nonlinearities of any kind are considerably large making it impossible to give analytical solutions in most structural problems. Thus, in engineering practice, approximated numerical formulae and elements of lower complexity levels are being used. As one can see, it may be concluded that conducting full-scale tests, although particularly difficult, laborious, and most of all, costly, cannot be overstated enough. There is apparent need for testing with those features provided. Taking the above into consideration, as well as analyzing the tower structure described in 2.2, the tested tower undeniably complies with all the requirements above. The experiment was carried out in November, 2014. As it is known to the author of this manuscript, no prior experiments have been conducted for this type of telecommunication towers. There are about 2000 such structures in Poland, which was the reason for choosing this particular type of the tower. In order to conduct the test, the structure was provided with a diaphragm to which external load was applied. It was designed, constructed and welded to the legs of the tower especially for the experiment. Its steel elements, their dimensions, and attachment manner were designed to apply the pulling force to the whole cross-section of the tower rather than a single joint connecting the bracings and legs. Such application of load results in the most unfavorable load distribution for a tower structure of a triangular cross-section. The technical solution of the diaphragm is depicted in Fig. 4. The element during assembly and testing is presented in Fig. 5. The experiment consisted of slow line pulling action with one end of the line attached to the diaphragm described above and the other to a towing truck. The load was being increased in steps. It was caused by the intermediate necessity of geodetic measurements at individual tower nodes. A load cell measuring the force in the line was located right at the diaphragm. The testing site is presented in Fig. 6 (scheme) and Fig. 7 (photo taken during the experiment). The tower along with specially laid foundation constituted its main part. The structure was attached to a steel frame equipped with special anchors enabling fixing into the foundation. Everything got loaded with pavement slabs of dimensions 3.0 x 1.5 x 0.15 meters which summed up to the total weight of about 108 tons. The
mass of the foundation and the geometrical dimensions were determined beforehand on the basis of tower stability calculations as well as on an analysis of over a dozen towers of the same type and height. As the comparative analyses indicated, the total mass of the foundation of existing towers with height equal to 40 meters amounted to, with ground above, 60-100 tons. The foundation of the tower prepared for the test is depicted in Fig. 8. 3. Failure mechanism of the tower Yielding of one of the compressed towers legs at section S-5 is presented in the movies which can be accessed
online
at
https://www.youtube.com/watch?v=qtLBw_RumVA&feature=youtu.be
and
https://www.youtube.com/watch?v=abDk-VRVTmc&feature=youtu.be. During the test, the changing values of the external force were controlled and recorded. The data of the measurements of the external load were gathered every 1.7 s. The measuring device was synchronized with special computer software which correlated the data from the load cell and electric resistance strain gauges placed on the elements of the structure. The leg plastic deformation occurred when the force recorded in the line reached about 108.7 kN. It is worth noting that the loss of stability occurred in the leg of section S-5 where the diameter of the round bar was equal to 80 mm. In the recorded movie mentioned above, the failure mechanism and plastic large deformations of particular elements of the tower can be observed. The buckling of the leg occurred along the plane parallel to the wall opposite to that bar which indicates that, in accordance with the assumptions of the experiment, the force applied to the transverse cross-section of the structure remained alongside the bisector of the angle between the walls of the tower. In the movie - the displacement of individual nodes and tower deflection may be observed best if compared with the initial position of the structure. 3.1 Tower nodes displacements Geodetic measurements of the displacements of structure nodes are highlighted in Fig. 9 and Fig. 10. It should be emphasized that the measurements were taken for two different locations of the total station theodolite. Arithmetic average of measurement values (planes X and Z of nodes A, B, and C) are shown in Tab. 4.
Force in line [kN] 0 20 30 40 52 60 65 70 75 80 85 90 95 100 105
Point A X 0
Point B
Point C
Z
X
Z 0 3 7 6 6 8
X 0
Z 0
34 58 82 115 134
0 0 0 0 7 6
0 56 97 138 193 226
72 128 180 250 298
4 3 7 9 9
148 166 183 204 229 268
6 3 4 2 3 5
251 282 311 349 391 455
10 12 12 11 12 8
330 370 410 464 518 608
13 20 19 19 21 16
324 449
-10 -26
549 750
34 48
735 1012
49 83
588
-30
975
71
1320
101
Tab. 4. Displacements of monitored structure nodes, all measurements are given in mm Due to the elastic characteristic of the line, the force recorded in the line decreased each time the pulling effort by the towing truck paused. Therefore, the results obtained are approximated with an accuracy of around 1.0 kN. One significant observation concerns the displacement along Z axis of node A which was at the top of the leg that lost its stability. The buckling effect itself started when the force in the line was reaching around 90kN. A change of displacement direction was the sign that the buckling eventually started leading to the stability loss of the bar. Since then, the displacements of all the measuring points increased dramatically. During the process of line pulling, the back edge of the foundation started to rise. Taking into account the mass and the geometry, such a behavior revealed a truly global effort of the tower. The vertical displacement of the back edge of the foundation is presented in Tab. 5 below.
External load [kN] 0 40 73 80 85 90 95 100 105 110
Vertical displacement of the foundation [mm] 0 0 10 10 10 40 60 120 170 190
Tab. 5. Vertical displacement of foundation with corresponding force in line Deformed state of the tower after the experiment is shown in Fig. 11, the front view (left) and the base view (right). The difference in the impact of bending on the upper part of the structure (above S-5) and the rest of the tower, and the state of the leg after the stability loss may be observed. Fig.12 depicts how the displacement of the leg bar occurred – the main plastic deformations can be found in the compressed leg of section S-5. Most importantly, the rotation of the cross-sections of the legs does not occur at joints. It also happens not only in the buckled leg of section S-5, but also at the legs of neighboring sections, S-4 and S-6, which is particularly visible in Fig. 13. The stiffness and thickness of the connecting flanges, the number of bolts, and the attachment manner of neighboring diagonal bracing elements determine the character of the stability loss. The plastic hinges of the legs under ultimate load occurred below the node connecting sections S-6 and S-5, as well as above the node connecting sections S-4 and S-5, which is precisely shown in Fig. 14. In Fig. 15, the deformed state of the leg is shown from the view inside of the tower. Measured deformations of individual leg cross-sections in section S-5 are presented in Fig. 16. It may be noticed that the largest plastic deformations occurred on plane XZ. The plastic hinges were located at ¼ and ¾ of the span of the section wherein larger deformations were observed for a cross-section located above, at ¾ of the span. The fact worth noting is that, for the lower cross-section, the maximum displacements of 70 mm occurred on the plane YZ. It should be mentioned that the measured values were recorded after the disassembly of all tower elements took place. Therefore, the deformations are shown on the plot from the start of the leg, which results from the fact that the disassembly of bolts in connecting flanges of particular tower legs caused rotation of these elements and loss of elastic deformations.
One observation, captured also in the attached movie, is that tower legs, not bracing elements are crucial in determination of reliability of a structure as understood in the serial reliability system. It is worth underlining that the deformation of the diagonal bracings of section S-5 occurred at the time of the yielding of the compressed leg. The effects of that deformation can be observed in Fig. 17 and Fig. 18.The main cause of the deformation of L-section diagonal bracings is the vertical displacement of gusset plates located at the center of the section. At the moment of adoption of a large deformation state, deflection of those plates occurs, which causes bending of bracing elements. That way a very complex load state is created. Apart from an eccentric (due to attachment manner) compression and relative tension, a moment which bends bracing elements is created by the buckling behavior of the leg. Deformed gusset plates at joints of L-sections of section S-5 are presented in Fig. 19 and Fig. 20. The confirmation of the thesis concerning diagonal bracing bending can be witnessed in Fig. 21. A crack in material occurred near one bolt hole. It was also caused by the element attachment manner which involved two bolts. 3.2 Standard buckling resistance versus experimental compression in the tower legs According to standard [18], buckling resistance of a compression member in a lattice tower should be determined as: N b,Rd
Af y , M1
(1)
where is the reduction factor for the relevant buckling mode, A is the cross section of the tower element, f y is the yield strength, and M 1 is the partial safety factor.
The most important issue in calculations of the buckling resistance of the tower elements is the proper determination of . For constant axial compression in members of a constant cross section the reduction factor should be calculated as follows:
1 2 2 eff
(2)
,
where
2 0,5 1 eff 0,2 eff .
(3)
In formula (3) is the imperfection factor equal to 0.49 for full round rods and eff is the effective slenderness ratio defined by:
eff k
, 1
(4)
where k is the effective slenderness factor, is the slenderness for the relevant buckling mode defined in [18], and 1 93.9 235 f y . In order to complete the presentation of the standard calculation procedure, the buckling resistance of the tower legs in section S-7 and S-6 is introduced below. All the parameters, both geometrical and mechanical, are collected In Tab. 6. Standard definition of the geometrical division of legs is presented in Fig. 22. Length of the leg members:
L 600 cm
Distance between the diagonal bracing members and both ends of the legs:
L1 300 cm
Diameter of the leg member:
d 9 cm
Cross sectional area:
A 63.6 cm 2
Moment of inertia
J 321.9 cm 4
Radius of gyration:
i 2.25 cm
Grade of steel
S 235 E 210 GPa
Standardized value of the Young’s modulus: Standardized value of the yield strength (reduced because of the thickness of the element): Partial safety factor:
f y 215 MPa
M1 1
Tab. 6. Geometrical and mechanical parameters of the tower legs in sections S-6, S-7 Considering the slenderness of leg members for the analyzed tower that are braced symmetrically, the following formula should be implemented:
L1 300 133.3. i 2.25
(5)
Effective slenderness factor k for the leg members of the analyzed tower is equal to 1.0 according to the definition given in standard [18].Taking that value into account, the effective slenderness ratio is equal to:
eff 1.0
133.3 93.9 235 215
1.36.
(6)
Using all the previously determined values, the buckling resistance of the analyzed leg members can be defined as:
N b,Rd
0.36 63.6 104 215 103 492.3 kN . 1
(7)
The maximal compression forces obtained during the experiment for the value of the external load equal to 108.7 kN are collected in Tab. 7; in fact, this is the breaking load for this particular structure. Measuring point located on tower legs at: middle of section S-7 top of section S-7 bottom of section S-6 middle of section S-6 top of section S-6
Experimental compression forces [kN] 521.3 461.0 756.5 654.3 410.2
Tab. 7. Experimental compression forces in the tower legs in sections S-7, S-6 There is quite significant scatter of the results. In the opinion of the author, the reference values of the axial forces shown in Tab. 7 are for centers of individual sections, which are 521.3 kN for section S-7 and 654.3 kN for S-6. Taking into account that the legs in both sections, S-7 and S-6, have the same diameter and the same system of diagonal bracing (resulting in the same L1 parameters), it can be concluded that the greater value can be treated as buckling resistance of such elements. It should be underlined that the loss of the stability of the tower leg took place in section S-5, not in S-7 or S-6, where the axial compression forces were measured. Therefore it can be assumed that “real” buckling resistance is greater than 654.3 kN for these particular leg members. In order to compare the results of the axial compression forces, taken directly from the experiment with the standard buckling resistance, the values of N b,Rd as a function of
effective slenderness factor k are
presented in Tab. 7. Effective slenderness factor k
Standard buckling resistance N b,Rd [kN]
0.95 0.90 0.85 0.80 0.75 0.70
527.9 569.0 623.2 661.9 713.5 768.2
Tab. 7. Standard buckling resistance of the tower leg members in sections S-7 and S-6 as a function of the effective slenderness factor Is worth noting that for the determination of the buckling resistance, mechanical parameters like Young’s modulus or yield strength were taken from the standard assumption for the particular grade of steel: S235 in
this case. There are significant differences between standardized values of these parameters and ones obtained during the laboratory tests (see Tab.3 and Tab.6). Higher values of the mechanical steel properties have, without any doubt, additional and positive influence on the “real” buckling resistance of the tower legs. That’s why, in opinion of the author, comparable value of the standard N b,Rd to experimental axial forces is the one obtained for slenderness factor k equal to 0.85.Taking that assumption into account, one can compare the experimental force during the compression of the tower legs equal to 654.3 kN and standard buckling resistance (obtained for k 0.85) equal to 623.2 kN. Achieving the experimental results allowed for comparison with the analytical ones based on the standard assumptions. 4. Conclusions and perspectives The manuscript presents the results of a full-scale, push-over test of a 40 meters high lattice telecommunication tower. The focus has been placed on the overall behavior of the structure under the ultimate load. One of the purposes of the experiment was to reveal the failure mechanism and failure mode. This goal has been achieved. The buckling of the leg member in section S-5 of the tower has been registered. After observing progress of the displacements increase, plastic deformations and, above all, failure mode of the tower leg member, one can conclude that joints between particular sections of the tower determine the form of the stability loss. Connecting flanges at both ends of the leg remained rigid, whereas cross-sections of the full round rods above and below these nodes underwent the plastic deformation. It confirms that the rigidity of the connections resulting from the flange thickness, number and diameter; and bolts quality is significantly higher than the rigidity of the leg members. A comparative analysis of the axial compression forces in the tower legs and standard buckling resistance have been presented. The results of N b,Rd calculations using standard procedure are significantly lower than the ones obtained experimentally.
It is worth pointing that standard procedure of buckling resistance
determination does not take into account quality of joints of particular tower legs. The value of buckling resistance, what was proven during the experiment, depends not only on the diagonal bracing distance between the elements, cross-sectional area of the legs, and mechanical properties of the material, but on the quality of the joints as well. Consequently, it is postulated that effective slenderness factor k should take the value of about 0.85 in buckling resistance analysis in the context of the standard records.
The results shown in the article demonstrate a significant raise of the back edge of the foundation under ultimate load. It can be concluded that, for this particular case, the buckling of the tower leg occurred before the loss of the stability of the foundation, which have caused overturning of the structure. It is worth underlining that, for other practical realizations (e.g. for lower values of the foundation mass or other geometrical properties), this behavior can be completely different which can cause stability loss of the foundation(s). The results of the conducted experiment will foster development of behavior analyses of similar steel telecommunication towers, which concerns mainly carrying-capacity analyses of already existing structures with a prospect of telecommunication equipment addition. In such cases, nonlinear analysis like the one carried out in work [20] is planned to be conducted. Moreover, knowing the results of an experiment with a full-scale structure, it is further planned to develop a numerical model for predicting structural failure. Behavior of diagonal bracing elements will be the next aspect subjected to computer simulation. In L-section modeling with complex strain state and complex geometric nonlinearities, aspects involving number and disposition of bolts, edge effects and tightening torque will be examined as given in [21]. As observed during the experiment, the elements suffer damage at the point where they are connected to legs, the fact which will also have to be taken into consideration in future perspectives. 5. Acknowledgements The author of this document would like to express his deepest gratitude to T-Mobile Poland S.A. whose financial support made this project possible. He would like to express his gratefulness to Mr. Michał Wójcicki. Acknowledgements should be given to Professors Kazimierz Rykaluk at Wrocław University of Environmental and Life Sciences and Marcin Kamiński at Lodz University of Technology for their support in the research project.
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FIGURE CAPTIONS Fig. 1. View of the tower, static scheme, 3D view for sections S-6 and S-7 Fig. 2. Legs and diagonal bracing joints details Fig. 3. Attachment of the cable-climbing ladder to the tower legs Fig. 4. Diaphragm view (left and right elevations) Fig. 5. Steel diaphragm during the assembly process (left) and the experiment (right) Fig. 6. Experiment test site with a lattice steel tower Fig. 7. Top view of the site during the experiment Fig. 8. Tower foundation Fig. 9. Displacements of the observed nodes in X direction Fig. 10. Displacements of the observed nodes in Z direction Fig. 11. Deformed tower shape after the experiment – view from the front (left) and the base (right) Fig. 12. Deformed leg shape – view from the left side (left) and the base (right) Fig. 13. Deformed leg shape – view from the front (left) and the base (right) Fig. 14. Nodal displacements between sections S-6(S-4) and S-5 Fig. 15. Deformed leg shape – view from the inside of the tower Fig. 16. Plastic deformation measurements of the leg in section S-5, units are mm Fig. 17. Deformed shape of the diagonal bracings in section S-5 Fig. 18. Deformed shape of the diagonal bracing (view along the element) Fig. 19. A joint connecting the leg with the diagonal bracings Fig. 20. Cracked L-section element Fig. 21. L-section crack at the cross section with the bolt hole Fig. 22. Standard assumption of the tower legs geometrical division
S-4
S-5
S-6
6000 5000 5000 500
S-7
6000
S-3
6000
S-2
6000
S-1
1500
6000
+ 40,5m n.p.t
1850
+ 42,0m n.p.t
4900
Fig. 1. View of the tower, static scheme, 3D view for sections S-6 and S-7
Fig. 2. Legs and diagonal bracing joints details
Fig. 3. Attachment of the cable-climbing ladder to the tower legs
Fig. 4. Diaphragm view (left and right elevations)
Fig. 5. Steel diaphragm during the assembly process (left) and the experiment (right)
(h = 41,23 m) C Longitudinal section diaphragm
(h = 30,25 m) B F load cell wire cable
(h = 19,25 m) A
towing truck z D (h = 1,78 m) 118,96 m x
120,41 m
Top view towing truck
x
y
Fig. 6. Experiment test site with a lattice steel tower
Fig. 7. Top view of the site during the experiment
Fig. 8. Tower foundation
110 100 90 80 70 60 F [kN] 50 40 30 20 10 0
0
100
200
300
400
500 point A
600
700
800
point B
900 1000 1100 1200 1300 1400 point C
Fig. 9. Displacements of the observed nodes in X direction
ux [mm]
110 100 90 80 70 60 F [kN] 50 40 30 20 10 0 -10
0
10
20
30 point A
40
50 point B
60
70
80
point C
Fig. 10. Displacements of the observed nodes in Z direction
90
100 uz [mm]
110
Fig. 11. Deformed tower shape after the experiment – view from the front (left) and the base (right)
Fig. 12. Deformed leg shape – view from the left side (left) and the base (right)
Fig. 13. Deformed leg shape – view from the front (left) and the base (right)
Fig. 14. Nodal displacements between sections S-6(S-4) and S-5
Fig. 15. Deformed leg shape – view from inside of the tower
Fig. 16. Plastic deformation measurements of the leg in section S-5, units are mm
Fig. 17. Deformed shape of the diagonal bracings in section S-5
Fig. 18. Deformed shape of the diagonal bracing (view along the element)
Fig. 19. A joint connecting the leg with the diagonal bracings
Fig. 20. Cracked L-section element
Fig. 21. L-section crack at the cross section with the bolt hole
L
L1 L1
Fig. 22. Standard assumption of the tower legs geometrical division
Highlights
1. All the results described in the paper are obtained via full scale pushover test of the 40 meters high telecommunication tower. As far as author of this study is informed, no prior experiments have been conducted for this type of telecommunication tower. 2. The mechanism of failure for the structure of the high complexity has been revealed. 3. Formulation of the conclusion for the effective slenderness ratio that is necessary for the bearing capacity approximation has been proposed.
S1350-6307(15)00148-X http://dx.doi.org/10.1016/j.engfailanal.2015.04.017 EFA 2565
To appear in:
Engineering Failure Analysis
Received Date: Revised Date: Accepted Date:
6 February 2015 22 April 2015 23 April 2015
Please cite this article as: Szafran, J., An experimental investigation into failure mechanism of a full-scale 40 meters high steel telecommunication tower, Engineering Failure Analysis (2015), doi: http://dx.doi.org/10.1016/ j.engfailanal.2015.04.017
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An experimental investigation into failure mechanism of a full-scale 40 meters high steel telecommunication tower Jacek Szafran Department of Structural Mechanics, Chair of Reliability of Structures, Faculty of Civil Engineering, Architecture and Environmental Engineering, Lodz University of Technology, Al. Politechniki 6, 90-924 Łódź, Poland email: [email protected], tel. 48-42-631-35-64
Abstract: The main objective of this paper is to present and discuss failure mechanism, failure mode, as well as plastic deformation of a lattice telecommunication tower obtained during a full-scale pushover test. The manuscript consists of a detailed description of the tested structure and the experimental site. Displacements of particular nodes of the tower are presented as a function of the external load. The main conclusion is that the rigidity of joints between particular elements, which depends on thickness and diameter of connecting flanges and number and quality of bolts, determines the failure mode of the compressed tower legs. In the article, values of axial forces under compression, taken directly from the conducted test, were compared with the standard buckling resistance. On the basis of this comparison, discussion about the effective slenderness factor has been generated, and the proper determination of this coefficient has been proposed. Keywords: failure mechanism, buckling, plastic deformation, structural failures, breaking load, code of practice, deflection
1. Introduction Experiments on full-scale engineering structures, although difficult to perform because of, both technical and financial reasons, can produce results that are impossible to obtain in a different way. Structure response searching in the context of, e.g. stresses, strains, displacements, and last but not least, failure mechanism and failure mode, may help enrich the knowledge about structures like lattice towers. Steel lattice towers are extensively utilized in telecommunication industry as supporting structures providing services such as telephoning, wireless internet or television. The more pressing the mobile networking needs of today’s customers are, the more requirements are being imposed on telecommunication devices which, in turn, causes repetitive replacements, upgrades, and modernizations. Antennas and radio units which get attached to telecommunication towers have different shapes, dimensions and weight. They are installed at various heights which considerably alters forces distribution of a supporting structure as well as carrying capacity of tower elements. Taking into consideration constant change of operating conditions, there is recurring need of determining bearing capacity of such structures. Due to the advancements in telecommunication engineering, including a growing number of new technological solutions, the scientists and civil engineers also contribute to the effort of meeting the new demands with numerous scientific publications devoted to problems in the field of telecommunication structures.. As an example of current state of knowledge of high, slender engineering structures and, in particular, of their dynamic behavior and fatigue, the works of Repetto and Solari [1, 2] may be mentioned. One of the most practical and comprehensive scientific manuscripts dealing with communication structures is one written by Smith [3].The author thoroughly elaborates on utilization of structures of that type, taking into account a variety of design aspects: meteorological parameters, strength, fatigue, and etc., where the conclusions coming from structural failures of masts and towers caused by external loads are particularly important. One type of load that determines cross-section size of particular elements of steel lattice towers is obviously wind load. The effect that the wind has on various engineering structures is a subject of many research articles. The comparison of results taken directly from wind tunnel tests and those predicted by Eurocode [4] for a slender tower structure can be found in [5]. Various problems in design, and analysis of telecommunication structures in particular, were published in [6] by Travanca et al. From the standpoint of engineering practice, a significant problem was tackled: the comparison of standards’ records and definitions from various codes of practice, which change over time, with their impact on subsequent estimation of
carrying capacity of the structures with emphasis being placed on existing object evaluation. This problem seems to be particularly significant for telecommunication towers due to changing nature of their load conditions (technological requirements). Additionally, the subject of tower strengthening and upgrading, where maintaining an object in a fair condition over years is concerned, is extremely valid. It is not uncommon that these objects are utilized for several dozen years. Hence the constant need for modernization, renovation, or upgrading to fulfill the above requirements [7]. The replacement of structure’s elements with ones of larger cross-sections, manufacturing additional truss elements or adding weight to the foundations are very common, exemplary attempts of upgrading telecommunication support structures. Reliability modeling is the next aspect of research and development in this branch of engineering. The requirements concerning the reliability are included in [8]. They impose a structural design process which ensures compliance with top quality standards. Computational probabilistic analysis and reliability assessment of steel telecommunication towers subjected to material and environmental uncertainty can be found in author’s previous works [9-12] and book of Kamiński [13]. One of more interesting and challenging problems is either analytical or numerical determination of carrying capacity of steel tower elements made of cold-rolled or hot-rolled L-sections. In particular, it involves the determination of support conditions influence, load applying manner, failure mechanism, and failure modes which results in carrying capacity estimation. Many scientific publications tackle the problem of structural elements behavior and their plastic deformation in particular [14]. An analysis of such elements often used in steel structures may involve full 3D behavior; consideration of axial, bending and shearing actions; various slenderness ratios; loading and displacement eccentricities. The comparison of numerical calculations with a full-scale destructive test may be found in the work of Lee and McClure [15]. The manuscript elaborates on highly relevant aspects of structures composed of hot-rolled single angle shapes with eccentric connections and, most importantly, allows for comparison of the obtained numerical results with full-scale, destructive test data. The authors of [15] should be also noted for pointing out that, in the context of mechanical security where the assessment of modes of failures and the confinement of failure are key, it becomes important to predict the actual strength and failure mechanism of such towers with a reasonable accuracy for failure scenarios in both static and dynamic regimes. Some consideration about non-local and local buckling and their influence on overall stability of truss and arched structures can be found in [16, 17]. The use of FEM
analyses with the experimental study findings considerably extends the knowledge of buckling phenomenon for structures’ elements. 2. Experimental, full-scale test 2.1. Experimental study objective One of the main objectives of the experiment was to reveal failure mechanism and failure mode of the 40 meters high, steel, lattice telecommunication tower under breaking load. The experiment has been conducted in such a manner that the external load was exerted on the tower and the maximum compression forces in its legs were created. It was achieved by applying the load in the least favorable direction for a tower of a triangular cross-section causing the maximum value of the compression stresses at one of the legs. Particular attention was paid to the observation of the tower legs behavior. One of the goals of the performed test was the determination of their buckling resistance. Another purpose was to determine the nature of destruction of diagonal bracings comprising hot-rolled angle sections. For these purposes, a tower of a complex structure and specific bearing elements was chosen. 2.2 Tower description The tower is a 40 meter lattice structure with a triangular cross-section. It is divided into seven sections. The sections may be classified into two types, with convergent and parallel legs. The bottom part of the tower (up to 34th meter) forms a pyramid frustum of convergence of 5%. The centerline dimension is 4.90 m at its base and 1.50 m at the top. The upper part of the tower is a parallelepiped of a height equal to 6.0 m with the cross-section of an equilateral triangle of side length equal to 1.50 m. Geometric division of sections and their heights, the layout of elements in two bottom sections as well as the structure of the tower under average exploitation are shown in Fig. 1. The general construction manner of particular sections shall be presented as the following: the legs were made with round solid bars, the diagonal bracing members with hot-rolled single angles, both symmetric and non-symmetric. The profiles of particular tower elements are presented in Tab. 1 below:
Section S-1 S-2 S-3 S-4 S-5 S-6 S-7
Legs Ø 65 Ø 65 Ø 65 Ø 80 Ø 80 Ø 90 Ø 90
Diagonal bracings ∟60x60x6 ∟60x60x6 ∟60x60x6 ∟60x60x8 ∟90x60x8 ∟90x60x8 ∟90x60x8
Tab. 1. Selected tower element profiles, units are mm Intersections of the diagonal bracings (of type X) are made with a spacer and a single bolt. The joints of the diagonal bracing and legs were realized with gusset plates and bolts (two for a node). The legs at the connections of individual sections of the structure were made using round plates (connecting flanges) welded at their ends and an adequate number of bolts as presented in Fig. 2. Data concerning individual joints, thickness and size of the flanges, and the number and type of bolts in individual sections were presented in Tab. 2. Section
S-1 S-2 S-3 S-4 S-5 S-6 S-7
Diameter of lower/upper connecting flange 180/180 180/180 200/180 220/200 230/220 260/230 270/260
Thickness of lower/upper connecting flange 25/25 25/25 30/25 30/30 30/30 35/30 35/35
Bolts in lower/upper connecting flange
Number of bolts in joint
M16x75(8.8)/M16x75(8.8) M16x75(8.8)/M16x75(8.8) M16x85(8.8)/M16x75(8.8) M20x85(8.8)/M16x85(8.8) M20x85(8.8)/M20x85(8.8) M24x100(8.8)/M20x85(8.8) M24x100(8.8)/M24x100(8.8)
6 6 6 6 6 6 6
Tab. 2. Data concerning leg joints of individual tower sections, units are mm The tower was equipped with a climbing - cable ladder. The ladder is attached at every section to the tower legs with two angle braces and bolts (Fig. 3). In order to determine the mechanical properties of the structural steel tensile testing of the 14 specimens (5 for L-sections and 9 for full round bars), according to standard [19], were performed. Mechanical properties obtained during the laboratory tests are listed in Tab. 3. Mechanical properties Young modulus Lower yield strength Upper yield strength Tensile strength
Tab. 3. Mechanical properties of structural steel
Values L-sections 205,0GPa 323,6 MPa 333,8 MPa 447,0 MPa
Legs round bars 203,3 GPa 284,7 MPa 290,0 MPa 467,4 MPa
2.3 Full-scale experiment Full-scale experiments are the type of scientific and engineering effort which allows for understanding of authentic behavior of a structure under ultimate load. As mentioned in [15], experimental tests are frequently used as a validation procedure in the development process of numerical models. Taking engineering structures into account, the complexity level, scale, and nonlinearities of any kind are considerably large making it impossible to give analytical solutions in most structural problems. Thus, in engineering practice, approximated numerical formulae and elements of lower complexity levels are being used. As one can see, it may be concluded that conducting full-scale tests, although particularly difficult, laborious, and most of all, costly, cannot be overstated enough. There is apparent need for testing with those features provided. Taking the above into consideration, as well as analyzing the tower structure described in 2.2, the tested tower undeniably complies with all the requirements above. The experiment was carried out in November, 2014. As it is known to the author of this manuscript, no prior experiments have been conducted for this type of telecommunication towers. There are about 2000 such structures in Poland, which was the reason for choosing this particular type of the tower. In order to conduct the test, the structure was provided with a diaphragm to which external load was applied. It was designed, constructed and welded to the legs of the tower especially for the experiment. Its steel elements, their dimensions, and attachment manner were designed to apply the pulling force to the whole cross-section of the tower rather than a single joint connecting the bracings and legs. Such application of load results in the most unfavorable load distribution for a tower structure of a triangular cross-section. The technical solution of the diaphragm is depicted in Fig. 4. The element during assembly and testing is presented in Fig. 5. The experiment consisted of slow line pulling action with one end of the line attached to the diaphragm described above and the other to a towing truck. The load was being increased in steps. It was caused by the intermediate necessity of geodetic measurements at individual tower nodes. A load cell measuring the force in the line was located right at the diaphragm. The testing site is presented in Fig. 6 (scheme) and Fig. 7 (photo taken during the experiment). The tower along with specially laid foundation constituted its main part. The structure was attached to a steel frame equipped with special anchors enabling fixing into the foundation. Everything got loaded with pavement slabs of dimensions 3.0 x 1.5 x 0.15 meters which summed up to the total weight of about 108 tons. The
mass of the foundation and the geometrical dimensions were determined beforehand on the basis of tower stability calculations as well as on an analysis of over a dozen towers of the same type and height. As the comparative analyses indicated, the total mass of the foundation of existing towers with height equal to 40 meters amounted to, with ground above, 60-100 tons. The foundation of the tower prepared for the test is depicted in Fig. 8. 3. Failure mechanism of the tower Yielding of one of the compressed towers legs at section S-5 is presented in the movies which can be accessed
online
at
https://www.youtube.com/watch?v=qtLBw_RumVA&feature=youtu.be
and
https://www.youtube.com/watch?v=abDk-VRVTmc&feature=youtu.be. During the test, the changing values of the external force were controlled and recorded. The data of the measurements of the external load were gathered every 1.7 s. The measuring device was synchronized with special computer software which correlated the data from the load cell and electric resistance strain gauges placed on the elements of the structure. The leg plastic deformation occurred when the force recorded in the line reached about 108.7 kN. It is worth noting that the loss of stability occurred in the leg of section S-5 where the diameter of the round bar was equal to 80 mm. In the recorded movie mentioned above, the failure mechanism and plastic large deformations of particular elements of the tower can be observed. The buckling of the leg occurred along the plane parallel to the wall opposite to that bar which indicates that, in accordance with the assumptions of the experiment, the force applied to the transverse cross-section of the structure remained alongside the bisector of the angle between the walls of the tower. In the movie - the displacement of individual nodes and tower deflection may be observed best if compared with the initial position of the structure. 3.1 Tower nodes displacements Geodetic measurements of the displacements of structure nodes are highlighted in Fig. 9 and Fig. 10. It should be emphasized that the measurements were taken for two different locations of the total station theodolite. Arithmetic average of measurement values (planes X and Z of nodes A, B, and C) are shown in Tab. 4.
Force in line [kN] 0 20 30 40 52 60 65 70 75 80 85 90 95 100 105
Point A X 0
Point B
Point C
Z
X
Z 0 3 7 6 6 8
X 0
Z 0
34 58 82 115 134
0 0 0 0 7 6
0 56 97 138 193 226
72 128 180 250 298
4 3 7 9 9
148 166 183 204 229 268
6 3 4 2 3 5
251 282 311 349 391 455
10 12 12 11 12 8
330 370 410 464 518 608
13 20 19 19 21 16
324 449
-10 -26
549 750
34 48
735 1012
49 83
588
-30
975
71
1320
101
Tab. 4. Displacements of monitored structure nodes, all measurements are given in mm Due to the elastic characteristic of the line, the force recorded in the line decreased each time the pulling effort by the towing truck paused. Therefore, the results obtained are approximated with an accuracy of around 1.0 kN. One significant observation concerns the displacement along Z axis of node A which was at the top of the leg that lost its stability. The buckling effect itself started when the force in the line was reaching around 90kN. A change of displacement direction was the sign that the buckling eventually started leading to the stability loss of the bar. Since then, the displacements of all the measuring points increased dramatically. During the process of line pulling, the back edge of the foundation started to rise. Taking into account the mass and the geometry, such a behavior revealed a truly global effort of the tower. The vertical displacement of the back edge of the foundation is presented in Tab. 5 below.
External load [kN] 0 40 73 80 85 90 95 100 105 110
Vertical displacement of the foundation [mm] 0 0 10 10 10 40 60 120 170 190
Tab. 5. Vertical displacement of foundation with corresponding force in line Deformed state of the tower after the experiment is shown in Fig. 11, the front view (left) and the base view (right). The difference in the impact of bending on the upper part of the structure (above S-5) and the rest of the tower, and the state of the leg after the stability loss may be observed. Fig.12 depicts how the displacement of the leg bar occurred – the main plastic deformations can be found in the compressed leg of section S-5. Most importantly, the rotation of the cross-sections of the legs does not occur at joints. It also happens not only in the buckled leg of section S-5, but also at the legs of neighboring sections, S-4 and S-6, which is particularly visible in Fig. 13. The stiffness and thickness of the connecting flanges, the number of bolts, and the attachment manner of neighboring diagonal bracing elements determine the character of the stability loss. The plastic hinges of the legs under ultimate load occurred below the node connecting sections S-6 and S-5, as well as above the node connecting sections S-4 and S-5, which is precisely shown in Fig. 14. In Fig. 15, the deformed state of the leg is shown from the view inside of the tower. Measured deformations of individual leg cross-sections in section S-5 are presented in Fig. 16. It may be noticed that the largest plastic deformations occurred on plane XZ. The plastic hinges were located at ¼ and ¾ of the span of the section wherein larger deformations were observed for a cross-section located above, at ¾ of the span. The fact worth noting is that, for the lower cross-section, the maximum displacements of 70 mm occurred on the plane YZ. It should be mentioned that the measured values were recorded after the disassembly of all tower elements took place. Therefore, the deformations are shown on the plot from the start of the leg, which results from the fact that the disassembly of bolts in connecting flanges of particular tower legs caused rotation of these elements and loss of elastic deformations.
One observation, captured also in the attached movie, is that tower legs, not bracing elements are crucial in determination of reliability of a structure as understood in the serial reliability system. It is worth underlining that the deformation of the diagonal bracings of section S-5 occurred at the time of the yielding of the compressed leg. The effects of that deformation can be observed in Fig. 17 and Fig. 18.The main cause of the deformation of L-section diagonal bracings is the vertical displacement of gusset plates located at the center of the section. At the moment of adoption of a large deformation state, deflection of those plates occurs, which causes bending of bracing elements. That way a very complex load state is created. Apart from an eccentric (due to attachment manner) compression and relative tension, a moment which bends bracing elements is created by the buckling behavior of the leg. Deformed gusset plates at joints of L-sections of section S-5 are presented in Fig. 19 and Fig. 20. The confirmation of the thesis concerning diagonal bracing bending can be witnessed in Fig. 21. A crack in material occurred near one bolt hole. It was also caused by the element attachment manner which involved two bolts. 3.2 Standard buckling resistance versus experimental compression in the tower legs According to standard [18], buckling resistance of a compression member in a lattice tower should be determined as: N b,Rd
Af y , M1
(1)
where is the reduction factor for the relevant buckling mode, A is the cross section of the tower element, f y is the yield strength, and M 1 is the partial safety factor.
The most important issue in calculations of the buckling resistance of the tower elements is the proper determination of . For constant axial compression in members of a constant cross section the reduction factor should be calculated as follows:
1 2 2 eff
(2)
,
where
2 0,5 1 eff 0,2 eff .
(3)
In formula (3) is the imperfection factor equal to 0.49 for full round rods and eff is the effective slenderness ratio defined by:
eff k
, 1
(4)
where k is the effective slenderness factor, is the slenderness for the relevant buckling mode defined in [18], and 1 93.9 235 f y . In order to complete the presentation of the standard calculation procedure, the buckling resistance of the tower legs in section S-7 and S-6 is introduced below. All the parameters, both geometrical and mechanical, are collected In Tab. 6. Standard definition of the geometrical division of legs is presented in Fig. 22. Length of the leg members:
L 600 cm
Distance between the diagonal bracing members and both ends of the legs:
L1 300 cm
Diameter of the leg member:
d 9 cm
Cross sectional area:
A 63.6 cm 2
Moment of inertia
J 321.9 cm 4
Radius of gyration:
i 2.25 cm
Grade of steel
S 235 E 210 GPa
Standardized value of the Young’s modulus: Standardized value of the yield strength (reduced because of the thickness of the element): Partial safety factor:
f y 215 MPa
M1 1
Tab. 6. Geometrical and mechanical parameters of the tower legs in sections S-6, S-7 Considering the slenderness of leg members for the analyzed tower that are braced symmetrically, the following formula should be implemented:
L1 300 133.3. i 2.25
(5)
Effective slenderness factor k for the leg members of the analyzed tower is equal to 1.0 according to the definition given in standard [18].Taking that value into account, the effective slenderness ratio is equal to:
eff 1.0
133.3 93.9 235 215
1.36.
(6)
Using all the previously determined values, the buckling resistance of the analyzed leg members can be defined as:
N b,Rd
0.36 63.6 104 215 103 492.3 kN . 1
(7)
The maximal compression forces obtained during the experiment for the value of the external load equal to 108.7 kN are collected in Tab. 7; in fact, this is the breaking load for this particular structure. Measuring point located on tower legs at: middle of section S-7 top of section S-7 bottom of section S-6 middle of section S-6 top of section S-6
Experimental compression forces [kN] 521.3 461.0 756.5 654.3 410.2
Tab. 7. Experimental compression forces in the tower legs in sections S-7, S-6 There is quite significant scatter of the results. In the opinion of the author, the reference values of the axial forces shown in Tab. 7 are for centers of individual sections, which are 521.3 kN for section S-7 and 654.3 kN for S-6. Taking into account that the legs in both sections, S-7 and S-6, have the same diameter and the same system of diagonal bracing (resulting in the same L1 parameters), it can be concluded that the greater value can be treated as buckling resistance of such elements. It should be underlined that the loss of the stability of the tower leg took place in section S-5, not in S-7 or S-6, where the axial compression forces were measured. Therefore it can be assumed that “real” buckling resistance is greater than 654.3 kN for these particular leg members. In order to compare the results of the axial compression forces, taken directly from the experiment with the standard buckling resistance, the values of N b,Rd as a function of
effective slenderness factor k are
presented in Tab. 7. Effective slenderness factor k
Standard buckling resistance N b,Rd [kN]
0.95 0.90 0.85 0.80 0.75 0.70
527.9 569.0 623.2 661.9 713.5 768.2
Tab. 7. Standard buckling resistance of the tower leg members in sections S-7 and S-6 as a function of the effective slenderness factor Is worth noting that for the determination of the buckling resistance, mechanical parameters like Young’s modulus or yield strength were taken from the standard assumption for the particular grade of steel: S235 in
this case. There are significant differences between standardized values of these parameters and ones obtained during the laboratory tests (see Tab.3 and Tab.6). Higher values of the mechanical steel properties have, without any doubt, additional and positive influence on the “real” buckling resistance of the tower legs. That’s why, in opinion of the author, comparable value of the standard N b,Rd to experimental axial forces is the one obtained for slenderness factor k equal to 0.85.Taking that assumption into account, one can compare the experimental force during the compression of the tower legs equal to 654.3 kN and standard buckling resistance (obtained for k 0.85) equal to 623.2 kN. Achieving the experimental results allowed for comparison with the analytical ones based on the standard assumptions. 4. Conclusions and perspectives The manuscript presents the results of a full-scale, push-over test of a 40 meters high lattice telecommunication tower. The focus has been placed on the overall behavior of the structure under the ultimate load. One of the purposes of the experiment was to reveal the failure mechanism and failure mode. This goal has been achieved. The buckling of the leg member in section S-5 of the tower has been registered. After observing progress of the displacements increase, plastic deformations and, above all, failure mode of the tower leg member, one can conclude that joints between particular sections of the tower determine the form of the stability loss. Connecting flanges at both ends of the leg remained rigid, whereas cross-sections of the full round rods above and below these nodes underwent the plastic deformation. It confirms that the rigidity of the connections resulting from the flange thickness, number and diameter; and bolts quality is significantly higher than the rigidity of the leg members. A comparative analysis of the axial compression forces in the tower legs and standard buckling resistance have been presented. The results of N b,Rd calculations using standard procedure are significantly lower than the ones obtained experimentally.
It is worth pointing that standard procedure of buckling resistance
determination does not take into account quality of joints of particular tower legs. The value of buckling resistance, what was proven during the experiment, depends not only on the diagonal bracing distance between the elements, cross-sectional area of the legs, and mechanical properties of the material, but on the quality of the joints as well. Consequently, it is postulated that effective slenderness factor k should take the value of about 0.85 in buckling resistance analysis in the context of the standard records.
The results shown in the article demonstrate a significant raise of the back edge of the foundation under ultimate load. It can be concluded that, for this particular case, the buckling of the tower leg occurred before the loss of the stability of the foundation, which have caused overturning of the structure. It is worth underlining that, for other practical realizations (e.g. for lower values of the foundation mass or other geometrical properties), this behavior can be completely different which can cause stability loss of the foundation(s). The results of the conducted experiment will foster development of behavior analyses of similar steel telecommunication towers, which concerns mainly carrying-capacity analyses of already existing structures with a prospect of telecommunication equipment addition. In such cases, nonlinear analysis like the one carried out in work [20] is planned to be conducted. Moreover, knowing the results of an experiment with a full-scale structure, it is further planned to develop a numerical model for predicting structural failure. Behavior of diagonal bracing elements will be the next aspect subjected to computer simulation. In L-section modeling with complex strain state and complex geometric nonlinearities, aspects involving number and disposition of bolts, edge effects and tightening torque will be examined as given in [21]. As observed during the experiment, the elements suffer damage at the point where they are connected to legs, the fact which will also have to be taken into consideration in future perspectives. 5. Acknowledgements The author of this document would like to express his deepest gratitude to T-Mobile Poland S.A. whose financial support made this project possible. He would like to express his gratefulness to Mr. Michał Wójcicki. Acknowledgements should be given to Professors Kazimierz Rykaluk at Wrocław University of Environmental and Life Sciences and Marcin Kamiński at Lodz University of Technology for their support in the research project.
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FIGURE CAPTIONS Fig. 1. View of the tower, static scheme, 3D view for sections S-6 and S-7 Fig. 2. Legs and diagonal bracing joints details Fig. 3. Attachment of the cable-climbing ladder to the tower legs Fig. 4. Diaphragm view (left and right elevations) Fig. 5. Steel diaphragm during the assembly process (left) and the experiment (right) Fig. 6. Experiment test site with a lattice steel tower Fig. 7. Top view of the site during the experiment Fig. 8. Tower foundation Fig. 9. Displacements of the observed nodes in X direction Fig. 10. Displacements of the observed nodes in Z direction Fig. 11. Deformed tower shape after the experiment – view from the front (left) and the base (right) Fig. 12. Deformed leg shape – view from the left side (left) and the base (right) Fig. 13. Deformed leg shape – view from the front (left) and the base (right) Fig. 14. Nodal displacements between sections S-6(S-4) and S-5 Fig. 15. Deformed leg shape – view from the inside of the tower Fig. 16. Plastic deformation measurements of the leg in section S-5, units are mm Fig. 17. Deformed shape of the diagonal bracings in section S-5 Fig. 18. Deformed shape of the diagonal bracing (view along the element) Fig. 19. A joint connecting the leg with the diagonal bracings Fig. 20. Cracked L-section element Fig. 21. L-section crack at the cross section with the bolt hole Fig. 22. Standard assumption of the tower legs geometrical division
S-4
S-5
S-6
6000 5000 5000 500
S-7
6000
S-3
6000
S-2
6000
S-1
1500
6000
+ 40,5m n.p.t
1850
+ 42,0m n.p.t
4900
Fig. 1. View of the tower, static scheme, 3D view for sections S-6 and S-7
Fig. 2. Legs and diagonal bracing joints details
Fig. 3. Attachment of the cable-climbing ladder to the tower legs
Fig. 4. Diaphragm view (left and right elevations)
Fig. 5. Steel diaphragm during the assembly process (left) and the experiment (right)
(h = 41,23 m) C Longitudinal section diaphragm
(h = 30,25 m) B F load cell wire cable
(h = 19,25 m) A
towing truck z D (h = 1,78 m) 118,96 m x
120,41 m
Top view towing truck
x
y
Fig. 6. Experiment test site with a lattice steel tower
Fig. 7. Top view of the site during the experiment
Fig. 8. Tower foundation
110 100 90 80 70 60 F [kN] 50 40 30 20 10 0
0
100
200
300
400
500 point A
600
700
800
point B
900 1000 1100 1200 1300 1400 point C
Fig. 9. Displacements of the observed nodes in X direction
ux [mm]
110 100 90 80 70 60 F [kN] 50 40 30 20 10 0 -10
0
10
20
30 point A
40
50 point B
60
70
80
point C
Fig. 10. Displacements of the observed nodes in Z direction
90
100 uz [mm]
110
Fig. 11. Deformed tower shape after the experiment – view from the front (left) and the base (right)
Fig. 12. Deformed leg shape – view from the left side (left) and the base (right)
Fig. 13. Deformed leg shape – view from the front (left) and the base (right)
Fig. 14. Nodal displacements between sections S-6(S-4) and S-5
Fig. 15. Deformed leg shape – view from inside of the tower
Fig. 16. Plastic deformation measurements of the leg in section S-5, units are mm
Fig. 17. Deformed shape of the diagonal bracings in section S-5
Fig. 18. Deformed shape of the diagonal bracing (view along the element)
Fig. 19. A joint connecting the leg with the diagonal bracings
Fig. 20. Cracked L-section element
Fig. 21. L-section crack at the cross section with the bolt hole
L
L1 L1
Fig. 22. Standard assumption of the tower legs geometrical division
Highlights
1. All the results described in the paper are obtained via full scale pushover test of the 40 meters high telecommunication tower. As far as author of this study is informed, no prior experiments have been conducted for this type of telecommunication tower. 2. The mechanism of failure for the structure of the high complexity has been revealed. 3. Formulation of the conclusion for the effective slenderness ratio that is necessary for the bearing capacity approximation has been proposed.