Prediction Of Tower Failure.pdf

Engineering Failure Analysis 16 (2009) 1922–1928

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Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal

Failure analysis of transmission towers F. Albermani a,*, S. Kitipornchai b, R.W.K. Chan b a b

The University of Queensland, School of Engineering, St. Lucia QLD 4072, Brisbane, Australia City University of Hong Kong, Building and Construction Department, Hong Kong

a r t i c l e

i n f o

Article history: Received 11 October 2008 Accepted 16 October 2008 Available online 25 October 2008 Keywords: Buckling Structural failure Finite element analysis

a b s t r a c t This paper advocates the use of nonlinear methodology for structural failure analysis. This approach is used for structural failure prediction rather than forensic analysis. Failure prediction has been confirmed by the expensive full-scale testing of a new transmission tower design that collapsed during the test. Using this approach, tower designs can be easily modified and upgraded, which results in substantial savings in time and resources. Crown Copyright Ó 2008 Published by Elsevier Ltd. All rights reserved.

1. Introduction Overhead transmission lines play an important role in the operation of a reliable electrical power system. Transmission towers are vital components of the lines, and accurate prediction of tower failure is very important for the reliability and safety of the transmission system. Fig. 1 shows a collapsed transmission tower; when such failure takes place, it is usually a cascading failure involving a number of adjacent towers along the line. Repair is very costly, in the order of one million dollars per kilometre of the line, leaving aside other costs associated with power disruption and litigation. A substantial number of tower failures happen around the world, but they usually occur in remote areas with no loss of life and thus escape media attention. Latticed transmission towers are constructed using eccentrically connected angle section members. Proof-loading or the full-scale testing of towers has traditionally formed an integral part of tower design. Stress calculations for the tower are normally obtained from a linear elastic analysis, whereby members are assumed to be axially loaded and in the majority of cases to have pinned connections. In practice, such conditions do not exist and members are detailed to minimize bending stresses. Despite this, results from full-scale tower testing often indicate that the bending stresses in members could be as high as the axial stresses. A comparison of data from full-scale tests with predicted results using the current practice indicates that the behaviour of transmission towers under complex load conditions cannot be consistently predicted with present techniques. Furthermore, the available test data show considerable discrepancies between member forces computed from linear elastic truss analysis and measured values from full-scale tests. The paper describes a nonlinear analytical technique of predicting the transmission tower failure. The technique can be used to verify new tower designs and reduce or eliminate the need for full-scale tower testing. The method has been calibrated with results from full-scale tower tests with good accuracy both in terms of the failure load and the failure mode. The technique was recently used to predict the catastrophic failure of a new tower design. When a full-scale test of this tower was conducted, the tower experienced full collapse in close agreement with the nonlinear analysis predictions.

* Corresponding author. E-mail address: [email protected] (F. Albermani). 1350-6307/$ - see front matter Crown Copyright Ó 2008 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2008.10.001

F. Albermani et al. / Engineering Failure Analysis 16 (2009) 1922–1928

Fig. 1. A case of transmission tower failure.

Fig. 2. General thin-walled beam-column element.

Fig. 3. Single equation yield surfaces for angle structural sections.

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2. Nonlinear analysis In the proposed nonlinear analysis technique, the tower is modelled as an assembly of beam-column and truss elements. Linear, geometric and deformation stiffness matrices are used to describe the behaviour of a general thin-walled beam-column element in an updated Lagrangian framework (Fig. 2). This approach greatly reduces the number of elements required for accurate modelling of the nonlinear structural response [1,2]. A lumped plasticity approach coupled with the concept of a yield surface in force space is adopted for modelling the material nonlinearity [3]. The formex algebra approach is used for the automatic generation of data necessary for the analysis [4]. All of the members in the tower are modelled in the analysis, including secondary (nominal) bracing members. The technique accounts for both geometric and material nonlinearity. The geometric nonlinearity accounts for the effects of the accumulated stresses on the structural stiffness of the elements and the effect of the continuing changes in the geometry as the applied load is increased. The buckling of structural members can be detected during load application. The material nonlinearity accounts for the effect of combined stresses on the plastification of the element cross-section. Stress-resultant yield

Fig. 4. Isometric view of the generated tower model.

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surfaces (Fig. 3) and a lumped plasticity approach are used for this purpose [3]. The analysis can also incorporate nonlinear effects due to joint flexibility, bolt slippage and differential support settlement [5]. The analysis incorporates an incremental-iterative predictor–corrector solution strategy. Loads are applied in small increments, at each of which several iterations are performed to satisfy equilibrium, and the structural geometry is constantly updated. The solution method is equipped with a number of numerical strategies that enable the prediction of buckling or instability and tracing of the nonlinear load–deflection path. The described numerical simulation technique has been used to analyse self-supporting and guyed towers under various static load conditions [6,7]. Some of the towers modelled have subsequently been tested to failure. The predicted failure loads and failure modes have been in good agreement with those obtained from tests. 3. Failure prediction of a new tower design We were asked to conduct a nonlinear analysis of a new tower design for a 275 kV double circuit transmission line. The aim of the analysis was to predict the tower response under five static load conditions specified by the client. These conditions account for various aspects of loading expected during the tower operation, ranging from line stringing to double circuit angle termination with full wind load.

Fig. 5. Top, front and right views of the generated tower model.

Table 1 Specified load cases for full-scale test of the tower. Case No.

Description

Transverse (kN)

1 2 3 4 5 Wind

Single circuit stringing Double circuit stringing 90° Deviation with full transverse wind Double circuit line termination with full transverse wind Double circuit angle termination with full transverse wind Full transverse wind

409.6 382.5 1613 (+824.8 = 2437.8) 205.5 (+824.8 = 1030.3) 912.5 (+824.8 = 1737.3) 824.8

Longitudinal (kN)

Vertical (kN)

246.9 382.5

725.7 872.4 296.4 162.1 162.1

0 952.1 685.3 0

0

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The design was for a self-supporting lattice tower with a 14  14 m square base and a height of 73 m from the ground. All members in the tower were structural steel angle sections with grades of 250 or 345 MPa. The self-weight of the tower was 615 kN. A finite element model with 5244 degrees-of-freedom simulating the tower was generated to account for every single member in the tower. The model is shown in Fig. 4 and 5, where T, L and V shown in Fig. 4 indicating the transverse, longitudinal and vertical directions respectively. Geometric and material nonlinear analysis of the tower was conducted under each of the five specified load conditions. A summary of these conditions is presented in Table 1. Under each condition, the self-weight was applied first, followed by incremental application of the specified load until the tower reached its ultimate capacity under that particular condition. The predicted tower response under each load condition is presented in terms of a load–displacement curve. The location used to monitor the displacement is at the tip of the right earth-wire arm indicated as ER in Fig. 4. The load is described in terms of a load factor, k, which represents the ratio of the applied load during the analysis to the specified ultimate design load for the particular load case. When k = 1.0, the tower is subjected to the full specified ultimate design load shown in Table 1. Nonlinear analysis shows that the design is adequate under load conditions 1–4, with the tower reaching an ultimate load factor k of between 1.06 and around 1.2. The loading tree for condition 5 is shown in Fig. 6. This load condition presented a serious problem. The nonlinear analysis revealed that the tower would collapse at a load factor of k = 0.96. The collapse would be initiated by the elastic buckling of a hip bracing member (a nominal bracing type) at the lower part of the tower, which would lead to buckling of the main diag-

Fig. 6. Loading tree for load case 5.

Fig. 7. Load–deflection curve at ER in the transverse direction, TER, under load case 5.

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onal bracing member in the second panel from the ground (compression axial force in this member is around 300 kN). Once this member buckled, the tower’s compression leg, which has a compression axial force of close to 5000 kN, would buckle as well, resulting in full collapse of the tower. The predicted load–displacement curve under this load condition is shown in Fig. 7 and the predicted deformed shape of the tower at collapse is shown in Fig. 8.

Fig. 8. Magnified tower deflected shape at collapse under load case 5.

Fig. 9. Full-scale intact tower at the testing station prior to test.

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Fig. 10. Full-scale test of the tower under loading condition 5: (a) start of the test; (b) tower collapsing during the test.

When these results were reported to the client, it was revealed to us then that a full-scale testing of the tower had been conducted two weeks previously. The tower successfully passed the full-scale test under load conditions 1–4 (as predicted by the nonlinear analysis), but experienced a catastrophic collapse during the full-scale test under load condition 5. The collapse took place as the load was incremented from 95% to 100% of the design ultimate load (nonlinear analysis predicted collapse at k = 0.96). Video footage of the full-scale test was given to us that show the dramatic tower collapse during the test. The footage is in close agreement with the collapse scenario predicted by the nonlinear analysis. Fig. 9 shows the intact tower erected at the testing station and Fig. 10 is a screen capture of the tower at the beginning of the test and during the collapse. 4. Conclusion A nonlinear analysis technique for transmission tower structures has been presented in this paper. The proposed technique can be used to accurately predict structural failure, with our predictions confirmed by the results of an expensive full-scale test. Given this accuracy, the technique can be used for failure analysis and prediction, and for design upgrades and modifications. Use of the technique will result in tremendous savings in resources, and will reduce the need for the full-scale testing that is customary in the transmission industry. References [1] [2] [3] [4] [5] [6] [7]

Albermani F, Kitipornchai S. Nonlinear analysis of thin-walled structures using least element/member. J Struct Eng ASCE 1990;116(1):215–34. Albermani F, Kitipornchai S. Nonlinear analysis of transmission towers. Eng Struct 1992;14(3):139–51. Albermani F, Kitipornchai S. Elasto-plastic large deformation analysis of thin-walled structures. Eng Struct 1990;12(1):28–36. Albermani F, Kitipornchai S, Chan SL. Formex formulation of transmission tower structures.. Int J Space Struct 1992;7(1):1–10. Kitipornchai S, Albermani F, Peyrot AH. Effect of bolt slippage on the ultimate strength of latticed structures. J Struct Eng ASCE 1994;120(8):2281–7. Albermani F. Design verification of guyed transmission tower using nonlinear analysis. Int J Space Struct 1997;12(1):43–50. Albermani F, Kitipornchai S. Numerical Simulation of structural behaviour of transmission towers. Thin-Walled Struct 2003;41(2-3):167–77.