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Failure mechanism and retrotting strategy of transmission tower structures under ice load Qiang Xie a, b, , Li Sun a a Department of Building Engineering, Tongji Univ., Shanghai 200092, China b State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji Univ., Shanghai 200092, China abstract article info Article history: Received 16 March 2011 Accepted 3 February 2012 Available online 24 March 2012 Keywords: Transmission tower Subassemblage Ice load Diaphragm Retrotting Static test Failure mode An experimental study was conducted on two pairs of subassemblages of a typical 500 kV transmission tower of the same type as those suffered the most severe damage during ice disaster in South China in 2008. The objectives are to study the failure mechanism of transmission towers under extreme load of freezing rain and to investigate the pertinent retrotting strategy for increasing the load-carrying capacity of towers so as to prevent their col- lapse. The difference between specimens in each pair is that one had an additional diaphragm as measures of ret- rotting while the other did not. The mechanical behavior, failure mode, strain and deformation at critical points, of the specimens were studied. The test results revealed that buckling of the main leg was the predominant failure mode of structures. For the two subassemblages without diaphragm, the out-of-plane deformations in the joints of diagonal bracings were relatively large and the buckled main angle members exhibited apparent torsion, which signicantly decreased the load-carrying capacity of specimens. But for the two subassemblages with diaphragms, the out-of-plane deformations of cross-bracings were markedly inhibited by the added diaphragms and the buck- ling mode of the main member approached exural buckling without torsion. As a result, the ultimate strength was increased by 18.3% and 17.6% for the single-panel and double-panel tower subassemblages respectively. It shows that the addition of the diaphragm signicantly improved the mechanical performance of transmission towers by reducing the torsional effect on main members and inhibiting the out-of-plane deformation of diagonal braces. © 2012 Elsevier Ltd. All rights reserved. 1. Introduction High-voltage transmission towers are one important component of modern electrical power system. But due to the rapidly increased height and span, transmission tower-conductor coupling systems are more susceptible to natural disasters which have been more fre- quent and severe over the past few years. Taking China as an exam- ple, in earlier 2008, the Southern area suffered severe ice disasters. The power systems sustained serious damage due to the catastrophic freezing rain. According to released statistics, the gross number of col- lapsed and damaged towers with rating above 35 kV of State Grid Corporation of China and local electrical companies reached 7263 [1]. In 1998, one unprecedented ice storm struck the Montréal region of Canada on January 4 and continued until early January 10. Over those 80 h, the maximum thickness of freezing precipitation exceeded 100 mm. And totally, there were about 1000 transmission tower structures that were brought to failure. In addition, as reported by relevant literature, the power systems in many other countries including United States, Germany, United Kingdom, etc. were all sub- jected to serious ice disasters during past few years. In order to mitigate the damage caused by natural calamities, study on the failure mechanism and retrotting of tower structures is of great signicance and urgency. In practice, steel angles are commonly used as members of transmission tower. Due to the asymmetry of their cross sections, the stability of these angles would be a complex issue [2]. Over the past several decades, considerable studies have been carried out to capture the mechanical behavior of angles [3,4]. Kemp and Behncke [5] performed a series of 13 tests to investigate the property of cross-bracing systems in tower structure. It could be obtained that the end eccentricities caused by bolting one leg of each bracing to the main legs would signicantly inuence the displacement within the bracing system. Consequently, the intersection joints of tension and compression bracing system deected along the out-of-plane direction even at low loads and bending moments were then induced. At global structure level, Albermani and Kitipornchai [6] and Albermani et al. [7] established a nite element model which took the inuence of both geometric and material nonlinearities into account. The tower was modeled with beam-column and truss elements. The calculation results were found to agree well the corresponding test results. Based on the aforementioned ndings, some important design codes have been developed [8,9]. But unfortunately, there were some Journal of Constructional Steel Research 74 (2012) 2636 Corresponding author at: Department of Building Engineering, Tongji Univ., Shang- hai 200092, China. E-mail address: [email protected] (Q. Xie). 0143-974X/$ see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2012.02.003 Contents lists available at SciVerse ScienceDirect Journal of Constructional Steel Research

Failure mechanism and retrofitting strategy of transmission tower structures under ice load

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Page 1: Failure mechanism and retrofitting strategy of transmission tower structures under ice load

Journal of Constructional Steel Research 74 (2012) 26–36

Contents lists available at SciVerse ScienceDirect

Journal of Constructional Steel Research

Failure mechanism and retrofitting strategy of transmission tower structures underice load

Qiang Xie a,b,⁎, Li Sun a

a Department of Building Engineering, Tongji Univ., Shanghai 200092, Chinab State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji Univ., Shanghai 200092, China

⁎ Corresponding author at: Department of Building Enhai 200092, China.

E-mail address: [email protected] (Q. Xie).

0143-974X/$ – see front matter © 2012 Elsevier Ltd. Aldoi:10.1016/j.jcsr.2012.02.003

a b s t r a c t

a r t i c l e i n f o

Article history:Received 16 March 2011Accepted 3 February 2012Available online 24 March 2012

Keywords:Transmission towerSubassemblageIce loadDiaphragmRetrofittingStatic testFailure mode

An experimental study was conducted on two pairs of subassemblages of a typical 500 kV transmission tower ofthe same type as those suffered themost severe damage during ice disaster in South China in 2008. The objectivesare to study the failure mechanism of transmission towers under extreme load of freezing rain and to investigatethe pertinent retrofitting strategy for increasing the load-carrying capacity of towers so as to prevent their col-lapse. The difference between specimens in each pair is that one had an additional diaphragm asmeasures of ret-rofitting while the other did not. Themechanical behavior, failuremode, strain and deformation at critical points,of the specimenswere studied. The test results revealed that buckling of themain legwas the predominant failuremode of structures. For the two subassemblages without diaphragm, the out-of-plane deformations in the jointsof diagonal bracingswere relatively large and the buckledmain anglemembers exhibited apparent torsion,whichsignificantlydecreased the load-carrying capacity of specimens. But for the two subassemblageswith diaphragms,the out-of-plane deformations of cross-bracingsweremarkedly inhibited by the added diaphragms and the buck-ling mode of the main member approached flexural buckling without torsion. As a result, the ultimate strengthwas increased by 18.3% and 17.6% for the single-panel and double-panel tower subassemblages respectively. Itshows that the addition of the diaphragm significantly improved the mechanical performance of transmissiontowers by reducing the torsional effect onmainmembers and inhibiting the out-of-plane deformation of diagonalbraces.

© 2012 Elsevier Ltd. All rights reserved.

1. Introduction

High-voltage transmission towers are one important componentof modern electrical power system. But due to the rapidly increasedheight and span, transmission tower-conductor coupling systemsare more susceptible to natural disasters which have been more fre-quent and severe over the past few years. Taking China as an exam-ple, in earlier 2008, the Southern area suffered severe ice disasters.The power systems sustained serious damage due to the catastrophicfreezing rain. According to released statistics, the gross number of col-lapsed and damaged towers with rating above 35 kV of State GridCorporation of China and local electrical companies reached 7263[1]. In 1998, one unprecedented ice storm struck the Montréal regionof Canada on January 4 and continued until early January 10. Overthose 80 h, the maximum thickness of freezing precipitationexceeded 100 mm. And totally, there were about 1000 transmissiontower structures that were brought to failure. In addition, as reportedby relevant literature, the power systems in many other countries

gineering, Tongji Univ., Shang-

l rights reserved.

including United States, Germany, United Kingdom, etc. were all sub-jected to serious ice disasters during past few years.

In order to mitigate the damage caused by natural calamities, studyon the failure mechanism and retrofitting of tower structures is of greatsignificance and urgency. In practice, steel angles are commonly used asmembers of transmission tower. Due to the asymmetry of their crosssections, the stability of these angles would be a complex issue [2].Over the past several decades, considerable studies have been carriedout to capture the mechanical behavior of angles [3,4]. Kemp andBehncke [5] performed a series of 13 tests to investigate the propertyof cross-bracing systems in tower structure. It could be obtained thatthe end eccentricities caused by bolting one leg of each bracing to themain legs would significantly influence the displacement within thebracing system. Consequently, the intersection joints of tension andcompression bracing system deflected along the out-of-plane directioneven at low loads and bending moments were then induced. At globalstructure level, Albermani and Kitipornchai [6] and Albermani et al.[7] established a finite element model which took the influence ofboth geometric and material nonlinearities into account. The towerwas modeled with beam-column and truss elements. The calculationresults were found to agree well the corresponding test results.

Based on the aforementionedfindings, some important design codeshave been developed [8,9]. But unfortunately, there were some

Page 2: Failure mechanism and retrofitting strategy of transmission tower structures under ice load

Fig. 1. The prototype transmission tower and test model (unit: mm).

Table 1Material property.

Sampled angle(mm)

Yielding strength(MPa)

Ultimate strength(MPa)

L36×3 340 410L36×3 320 500L56×4 340 440L56×4 295 430L30×4 260 355L30×4 250 340L50×5 285 420L50×5 270 415

27Q. Xie, L. Sun / Journal of Constructional Steel Research 74 (2012) 26–36

potential shortcomings in their original versions, which were exempli-fied by many collapse accidents of in-service towers. Therefore somenotable studies have been conducted to find the shortcomings. Alamand Santhakumar [10] carried out the loading test on a 34 m-high trans-mission towerwith a capacity of 220 kV. They found that the buckling ofleg and cross-arm bottom members would bring the tower to failure.Moon et al. [11] conducted an experimental study on one tower subas-semblage to examine the failure mode of structures under wind load.The test result showed that the main leg buckled under the bendingmoment causedby eccentric compression and unbalanced deformation.

Based on the above research work, some retrofitting strategies havebeen proposed to improve wind-resistant performance of transmissiontowers. Albermani et al. [12] considered the feasibility of adding dia-phragm to strengthening tower structures. They found that simple

a) single-panel

Fig. 2. Schematic drawing of two pa

diaphragm bracing systems could be very effectively used in theupgrading of older transmission towers. Xie et al. [13,14] conductedboth static and dynamic analysis of independent towers as well astower-conductor coupling system. The results showed that adding dia-phragm significantly improved the mechanical performance and thusincreased load-carrying capacity of the structure under strong wind.

It should be pointed out that the studywork presented beforemainlyfocused on failure mode and retrofitting of tower structures under windload. But according to the field investigation, the failure pattern of struc-tures under ice load was remarkably different from that under windload. Furthermore, although the ice load has been greatly increased inrelevant design codes, the arrangement principle of diaphragm (hori-zontal bracings) was not explicitly stipulated [15]. In this paper, twopairs of tower subassemblages were fabricated and tested under simu-lated ice load. The failure mechanism of transmission tower structuresdesigned by current code under ice loadwas captured. The effect of add-ing diaphragm and its physical mechanism was investigated.

2. Test program

2.1. Test specimens

A 500 kV high-voltage transmission tower of height 48.5 m, whichwas illustrated in Fig. 1, was chosen for the research. This kind of lat-ticed tower structures which was widely employed in Chinese powersystem suffered the greatest damage during the ice disasters in SouthChina in 2008. It should be noted that, according to the field

b) two-panel

ir subassemblages (unit: mm).

Page 3: Failure mechanism and retrofitting strategy of transmission tower structures under ice load

Fig. 3. Schematic drawing of equivalent load.

28 Q. Xie, L. Sun / Journal of Constructional Steel Research 74 (2012) 26–36

investigation, most of the collapses of tower structures were causedby the failure of some specific panels in the tower body. Meanwhile,it was found that the overturning moment of towers increased byless than 5% while considering second order effect under uniformlydistributed ice load [16]. So tests of subassemblages could be viewedas indicative of the overall behavior of the tower structures and theinfluence of second order effect will not be significant.

In this program, the specified panelswere extracted and scaled to twopairs of subassemblages. Because of the space limitation of the laboratory,the two single-panel specimens were scaled to 2/3 in dimension whilethe two double-panel specimenswere to 1/2. The single-panel specimenswere designed to minimize the influence of the size effect while thedouble-panel specimens were to take the non-rigid effect of the end re-straints into account. The two specimens in each pair of subassemblageswere identical in geometry but one specimen had an additional dia-phragm installed at the joints of cross-bracings, as shown in Fig. 2. Themain leg, diagonal and redundant members of the single-panel structurewere L56×4, L36×3 and L25×3, respectively. As to the double-panelones, the corresponding members were L50×5, L30×4 and L20×3, re-spectively. The diaphragm of both subassemblages consisted of onlyL30×4 steel angles. All angles of the subassemblages had the same slen-derness ratio as their counterparts of the prototype structure.

2.2. Material properties

Thematerial properties of steel anglememberswere obtained by con-ducting uniaxial tension tests on coupons, which were cut from the aux-iliary angles of the same batch as those used in specimen fabrication.

a) south elevation

Fig. 4. Test

For each type of angle, two coupons were machined and tested.Table 1 presented the measured material properties of four types ofangles which were used for main legs, diagonal bracings and dia-phragms. In addition, because the redundant members were toosmall to cut and their stresses were very small during loading tests,property measuring of these angles was omitted.

2.3. Testing apparatus

The tested tower subassemblage was fixed at the bottom and theloads applied on the subassemblage were simulated to be the lateralwind load, ice load and gravity load of the tower structure. Asshown in Fig. 3, the lateral wind load on the structure led to both mo-ment Mw and lateral force Pw, and the self-weight and ice load weremodeled as the vertical load Gi. Based on the principle of “equiva-lence”, unequaled vertical load G1, 2 were exerted on the oppositesides of the structure to simulate Mw and Gi. Obviously, G1,2 equaledGi+Mw/L and Gi−Mw/L separately. The Pw represents the equivalentstatic wind load which was calculated by considering the wind speed5 m/s as stipulated in the design code [15]. The influence of icing ac-cretion on wind load coefficient was also taken into consideration.

All of the specimens were tested under combined constant lateralequivalent static wind load and monotonously increased ice load. Asillustrated in Fig. 4, during loading process, the specimens were total-ly constrained by the rigid foundations which were fixed to thegrooves of testing pedestal with anchor bolts. The constant lateralload (Pw) was applied by one pair of 200 kN oil jacks. These two oiljacks were fixed on a reaction frame at the height of 5 m, and werecarefully calibrated to make sure that the forces they applied wereidentical and synchronized. Meanwhile, the monotonous increasedloads (G1, G2) in vertical direction were applied by two pairs of500 kN hydraulic jacks at the top four corners through two paralleldistribution beams with two corners along one side and the othertwo along the opposite side.

The loading setups for the single-panel and double-panel subassem-blageswere the same. During loading process, the lateral load Pwwouldbe firstly increased up to 2 kN, then decreased to zero tomake sure thatthe subassemblages as well as all the instruments were serviceable.Then the lateral load (Pw) was increased to the stipulated value andkept constant. Afterwards the vertical load was applied monotonicallyuntil the structure failed. The difference between the value of G1 andG2 was maintained as invariable.

b) east elevation

setup.

Page 4: Failure mechanism and retrofitting strategy of transmission tower structures under ice load

b) arrangement of displacement-transducers

a) arrangement of strain gauges

Fig. 5. Layout of measurements.

Fig. 6. Location of strain gauges in compression side of single-panel structure withoutdiaphragm.

29Q. Xie, L. Sun / Journal of Constructional Steel Research 74 (2012) 26–36

2.4. Measurements

The load cells attached to the head of each jack was used to mea-sure the instantaneous value of the load. For all the subassemblages,strain gauges were arranged on sections where large stress wouldoccur, as shown in Fig. 5(a). During loading tests, the four sides ofeach structure were named as A-1, A-2, B-1 and B-2, respectively. Re-garding the main leg members in A-1 side, i.e. where G1 were loaded,four strain gauges were glued on the measured sections. Taking Sec-tion No. 6 of double-panel tower subassemblage without diaphragmsfor instance, two of the gauges (Nos. 21 and 23) would be placed atthe middle points on the outer-surface of two legs of the anglewhile two others (Nos. 22 and 24) at the inner-surface. As to the di-agonal members, there were two gauges placing on the outer-surface of measured sections. Because the stresses of redundantmembers were expected to be much smaller, no gauge was placedon them.

In order to capture the load–displacement behavior, for every sub-assemblage, three pairs of LVDTs, were arranged at the positionwhere G1, G2 and Pw were applied to record the corresponding defor-mation. Furthermore, LVDTs were also arranged at the joints of diag-onal bracings to monitor the out-of-plane deformations as shown inFig. 5(b).

In the single-panel subassemblage without diaphragm, 8 straingauges were mounted at the Section No. 2. Four strain gauges intwo pairs were located at the 1/3 and 2/3 points, respectively, of thetwo legs on the outer-surface while four others at the same positionsbut on the inner-surface, as shown in Fig. 6.

3. Experimental behavior of specimens

3.1. Experimental behavior of specimens without diaphragm

The subassemblageswithout diaphragm, both the single-panel andthe double-panel, behaved in brittlemanner. Up to being fully laterallyloaded, the structures were still in elastic range and the deformationand strain were very small. Then the vertical load began to be gradu-ally exerted. At about 30% of the ultimate load, slippage of bolts inthe connection area could be observed while the deformations ofangle members were still not obvious. When the vertical load reached85% of the ultimate load, the out-of-plane deformations of cross-bracings were found to be distinct and to increase rapidly. And thenshortly the structure failed as the main leg buckled suddenly. Forboth single-panel and double-panel structures, the deformations ofdiagonal bracings were much apparent, as illustrated by Figs. 7 and 8.

3.2. Experimental behavior of specimens with diaphragm

The subassemblages with diaphragm, both single-panel anddouble-panel, behaved in relatively ductile manner. Until being fullylaterally loaded, the structures were at elastic stage, and the deforma-tion and strain of all members were much small. At about 50% of theultimate vertical load, slippage of bolts in the connection area couldbe observed and the continuous ‘bang’ sound could be heard. The de-formation of both main leg and diagonal bracings was still very small.When the vertical load was up to about 85% of its maximum value,the deformations of main legs were found to be noticeable. The out-of-plane deformations of cross-bracings were not obvious. As theload became larger and larger, the structure failed as the main legbuckled suddenly, as shown in Figs. 9 and 10. Comparing with thecorresponding subassemblages without diaphragm, both for single-panel and double-panel ones, the deformations of diagonal bracingswere much smaller.

Page 5: Failure mechanism and retrofitting strategy of transmission tower structures under ice load

Fig. 7. Failure phenomena of single-panel subassemblage without diaphragm.

30 Q. Xie, L. Sun / Journal of Constructional Steel Research 74 (2012) 26–36

4. Test result analysis of the specimens without diaphragm

4.1. Strain–load curves of the main leg members

In this paper, the ultimate strengths of single-panel subassem-blages without and with diaphragm are marked as fuos and fuw

s , respec-tively. Similarly, the corresponding values of double-panelsubassemblages are marked as fuo

t and fuwt . Fig. 11 shows the curves

of vertical load (G1) versus strain of the main leg of the single-panel

Fig. 8. Failure phenomena of double-pane

structure, at critical sections numbered as 6 and 7 (Fig. 6). Fromboth (a) and (b), it can be found that the relationship between thestrain value of each gauge and the vertical load was approximatelylinear at early stage. But at about 50% of the ultimate load fuo

s , thestrains measured at the inner-surface and those at the outer-surfacebegin to deviate from each other. When the load increased andreached its peak value, the strain curves bifurcate immediately,which indicates the buckling of the main leg members. The failurehappened suddenly and showed evident brittleness. Meanwhile, it

l subassemblage without diaphragm.

Page 6: Failure mechanism and retrofitting strategy of transmission tower structures under ice load

Fig. 9. Failure phenomena of single-panel subassemblage with diaphragm.

0 200 400 600 800 1000 1200 1400 1600 18000

20

40

60

80

100

120

P/k

N

0

20

40

60

80

100

120

P/k

N

ε/10-6

0 200 400 600 800 1000 1200 1400 1600 1800ε/10-6

a) section-6

b) section-7

suddenly ascend

begun to bifurcate

57 58 59 60

0.5f suo

0.5f suo

suddenly descend

begun to bifurcate

suddenly ascend

suddenly descend 61 62 63 64

Fig. 11. Load–strain curves of critical sections of single-panel subassemblage withoutdiaphragm.

31Q. Xie, L. Sun / Journal of Constructional Steel Research 74 (2012) 26–36

should be noted that the behavior of Section 6 and Section 7 is notidentical. For Section 6, the strains at the outer-surface abruptly in-creased. On the contrary, the counterpart strains at the inner-surface suddenly decreased. As to Section 7, only the strain at theouter-surface of one leg of the angle increased while the other threeones at the section all suddenly decreased.

Similarly, Fig. 12 presents the vertical load (G1) versus straincurves of the main leg of the double-panel structure, at critical sec-tions also numbered as 6 and 7 (Fig. 5). Obviously, the case is quitesimilar to that of the single-panel structure. For both two sections,

Fig. 10. Failure phenomena of double-panel subassemblage with diaphragms.

four curves began to fall into two groups and to deviate from eachother when the load is up to about 50% of its maximum value fuo

t .And when the structure reached its ultimate limit state, the two sec-tions also behaved differently. For Section 6, the strains measured atthe outer-surface suddenly increase. By contrast, the strains at theinner-surface suddenly decrease. For Section 7, only gauge No. 25which was placed at the outer-surface of one leg rapidly increases.All other three ones snap back immediately.

In order to capture the feature of behavior of themain legmembersunder ice load, 8 strain gauges were arranged at Section 2 of thesingle-panel structure (Fig. 6). The 8 curves were presented inFig. 13(a). Meanwhile, strains being recorded by the gauges at differ-ent loading stages were shown in Fig. 13(b). From Fig. 13(a), it couldbe observed that at early stage (below 50% of the ultimate load), thestrains at both the inner and outer surfaces are almost identical, mean-ing that the main leg members were approximately in axial loadingstate. But as the vertical load was increasing to 60% of the ultimatestrength, in Fig 13(b), the strains near the edge of the angle, i.e. ofGauges 5, 6, 11 and 12, develop more rapidly than those of Gauges 7,8, 9 and 10. At the limit state, the strains of Gauges 11 and 12 increasegreatly with their final values 17% higher than those of Gauges 5 and 6installed at the corresponding position of another leg, which meansthat the torsion had remarkably affected the behavior of the member.Themuch small and relatively uniform strain distributionmeasured atthe positions close to the connection of the two legs of the anglefurther shows that the influence of secondary moment as well as thetorsion is significant and cannot be neglected.

Page 7: Failure mechanism and retrofitting strategy of transmission tower structures under ice load

a) section-6

b) section-7

0 200 400 600 800 1000 1200 1400 1600 18000

20

40

60

80

100

120

P/k

N

0

20

40

60

80

100

120

P/k

N

ε/10-6

0 200 400 600 800 1000 1200 1400 1600 1800ε/10-6

0.5f ,tuo suddenly ascend

suddenly descend

21 22 23 24

begun to bifurcate

suddenly descend

suddenly ascend

begun to bifurcate

0.5f tuo

25 26 27 28

Fig. 12. Load–strain curves of critical sections of double-panel subassemblage withoutdiaphragm.

0 200 400 600 800 1000 1200 1400 1600 1800

ε/10-6

0

20

40

60

80

100

120

P/k

N

a) load-strain curve at section-2

b) strains at different loading stages

5 6 7 8 9 10 11 12

5 6 7 8 9 10 11 12 130

200

400

600

800

1000

1200

1400

1600

ε(10

-6)

Number of strain gauge

20%× fs

uo

40%× fs

uo

60%× fs

uo

80%× fs

uo

90%× fs

uo

fs

uo

Fig. 13. Strain of critical section of single-panel subassemblage without diaphragm.

32 Q. Xie, L. Sun / Journal of Constructional Steel Research 74 (2012) 26–36

4.2. Out-of-plane deformations of the subassemblages

Fig. 14 shows the typical curves of the vertical load (G1) versus theout-of-plane deformations of the subassemblages. For the single-panel subassemblage, it can be found that the curve maintained ap-proximately linear till about 85% of the ultimate load. Then thecurve abruptly deflects and become horizontal. This obvious plateauas marked in Fig. 14(a) shows that the deformation begins to increaserapidly as the load keeps almost constant. When the deformation be-came nearly doubled, the curve ascends again in a smaller stiffnessthan the initial one till the structure failed. The maximum deforma-tion reaches more than 12 mm. The case of the double-panel subas-semblage is similar. But even from the initial stage, the relationshipbetween load and deformation begins to deviate from linearity. Thewhole curve can be divided into a series of small plateaus, as shownin Fig. 14(b). The peak value is up to nearly 5 mm. From this, it canbe concluded that for structures without diaphragm, the out-of-plane deformation of cross-bracings will become considerable evenunder lower load, due to the lack of inhibiting mechanism.

5. Comparative analysis of the test results analysis of the speci-mens with and without diaphragm

5.1. Strain–load curves of the main leg members

Fig. 15 compares the strain–load behavior and failure modes of themain leg members in the single-panel structures with and without

diaphragm. In the early stage, both structures, with and without dia-phragm, behaved linearly. In Fig. 15(a), the curves of the two specimensalmost overlapped, showing that adding diaphragm will not increaseaxial stiffness of the main leg members substantially. But in the laterstage, themechanical behavior of the two subassemblages exhibits nota-ble difference. For the structure without diaphragm, as the vertical loadreached its peak value fuo

s , the strain of the outer-surface and inner-surface bifurcates forthwith. Meanwhile, the sudden increase of thestrains means that the whole structure lost load-carrying capacity thor-oughly. The failure happened without warning. On the other hand, forthe structure with diaphragm, as the load reached about 90% of the ulti-mate strength fuw

s , the slopes of all four curves begin to decrease gradual-ly and thus the strain increase more rapidly. Then after the curves wentthrough a plateau, the main leg members failed.

The failure modes of the two specimens are also of great difference.For the subassemblage without diaphragm, as evidenced by Fig. 15(b),buckling of themain anglemembers is accompaniedwith apparent tor-sion. But after the diaphragm was added, the torsion effect has beeninhibited significantly, as illustrated in Fig. 15(c). It can be concludedthat the failure pattern has been transited from flexural–torsional buck-ling of the specimen without diaphragm to approached flexural buck-ling of the specimen with diaphragm. The ultimate capacity of thespecimen with diaphragm increased consequently. These observationsare consistent with the test results.

Fig. 16 compares the load–strain behavior and failure modes ofthe main leg members in the double-panel structures. Obviously,the case is very similar to that of the single-panel structures. InFig. 16(a), the load–strain curves of the specimen without diaphragm

Page 8: Failure mechanism and retrofitting strategy of transmission tower structures under ice load

-2 0 2 4 6 8 10 120

20

40

60

80

100

120

"plateau"

P/k

N

D/mm

D/mm0 1 2 3 4 5 6 7 8

0

20

40

60

80

100

P/k

N

"plateaus"

a) single-panel

b) two-panel

Fig. 14. Out-of-plane deformation of subassemblages without diaphragms.

33Q. Xie, L. Sun / Journal of Constructional Steel Research 74 (2012) 26–36

descended suddenly as soon as the load reached its peak value fuot ,

symbolizing that the structure failed completely. But for its counter-part, up till to about 90% of the ultimate strength fuw

t , the structure ri-gidity starts to decrease and the strains exhibit a rapid increase. Thenwith the vertical load reaching its maximum, the curves tend to behorizontal rather than descending immediately, which once againverifies that adding diaphragm can improve the deformability of thestructure.

0 400 800 1200 1600 20000

20

40

60

80

100

120

140

P/k

N

ε/10-6

fsuo

f suw

a) load-strain curves b) fa

9 10 11 12 57 58 59 60

without diaphragm with diaphragm

0.9f suw

Fig. 15. Comparison of failure mode of main mem

From Fig. 16(b) and (c), it is obvious that the buckling mode wasalso transited from flexural–torsional buckling of the specimen with-out diaphragm to approached flexural buckling of the specimen withdiaphragm, the same as that for the single-panel specimens.

5.2. Load–strain behavior of diaphragm member

As being substantiated, the diaphragms can significantly improvethe mechanical performance of the main leg members as well as theglobal structure. But the mechanical characteristics of themselvesshould also be investigated. Fig. 17 presents the strain–load curvesof the diaphragm members in the single-panel structure. FromFig. 17(a), it can be found that during the whole loading process,the strains of the angle in the diaphragm were very small. Their max-imum values never exceeded 120με. Meanwhile, from the compari-son of the strains of the main leg members with those of thediaphragm members (Fig. 17(b)), it can be observed that the strainof a typical main leg member increased linearly once the verticalload was applied. On the other hand, the strain in a typical diaphragmmember was almost zero till being loaded to about 60% of the ulti-mate load. And just from then, its value begins to increase slowly.As the structure failed, the maximum strain in diaphragm memberis only about 6% of that of the main leg member.

5.3. Out-of-plane deformations of the subassemblages

For structures without diaphragm, due to the lack of inhibitingmechanism, the out-of-plane deformations at the joints of diagonalbracings will be considerable. This characteristic has a great impact onthe failure pattern of the structure. In transmission towers, the mainleg members are employed as the primary compression memberswhile the diagonal bracings are used to provide lateral constraint. Asthe out-of-plane deformation increases continuously, the loading stateof the bracings will be translated from approached axial compressionto compression-bending. Then due to the second-order effect, the de-formation tends to increase more and more rapidly, as exemplified inFig. 14. Consequently, the constraint effect on themain legwill be great-ly weakened. Hence the effective lengths of the main leg members willbe increased.

But after adding diaphragm, the out-of-plane deformation is con-trolled to an acceptable degree. Here, the maximum deformation ofsingle-panel specimens without and with diaphragm is marked as(duos ) and (duws ), respectively. The corresponding values of double-panel specimens are marked as (duot ) and (duwt ). Fig. 18 compares thebehavior of the structures with and without diaphragm. Regarding thesingle-panel structure, it can be observed that when the vertical load

ilure without diaphragm c) failure with diaphragm

bers in single-panel tower subassemblages.

Page 9: Failure mechanism and retrofitting strategy of transmission tower structures under ice load

0

20

40

60

80

100

120P

/kN

0 400 800 1200 1600 2000

ε/10-6

f tu0

f tuw

a) load-strain curves b) without diaphragm c) with diaphragm

0.9ftuw

21 22 23 24 5 6 7 8

without diaphragm with diaphragm

Fig. 16. Comparison of failure mode of main members in double-panel tower subassemblages.

34 Q. Xie, L. Sun / Journal of Constructional Steel Research 74 (2012) 26–36

reached about 85% of the ultimate load of the specimen without dia-phragm, the deformation increases significantly and rapidly. And thewhole structure suffered failure shortly then. The value of duos reachednearly 13 mm. However, after adding the diaphragm, the correspond-ing values of duws almost never exceeded 0.5 mm.

-120 -90 -60 -30 0 30 60 900

20

40

60

80

100

120

140

P/k

N

ε/10-6

0 20 40 60 80 100 120 140-200

0

200

400

600

800

1000

1200

1400

1600

1800

P/kN

a) strain of diaphragm

b) comparison between strain behaviour of diaphragm and main leg

ε/10

-6

5556

0.60fsuw

fsuw

diaphragm

main-leg

Fig. 17. Strain behaviors of diaphragm in single-panel subassemblage.

As to the double-panel structures, even from the initial loadingstage, the deformation of the subassemblage without diaphragm in-creased fast. At the ultimate limit state, the maximum deformation

0 20 40 60 80 100 120 140 160-2

0

2

4

6

8

10

12

14

D/m

m

P/kN

0 20 40 60 80 100 120-1

0

1

2

3

4

5

6

D/m

m

P/kN

a) single-panel

b) two-panel

dsuo

dsuw

without diaphragm

with diaphragm

dtuo

with diaphragm

without diaphragm

dtuw

Fig. 18. Comparison of the out-of-plane deformation of the diagonal bracing joints.

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35Q. Xie, L. Sun / Journal of Constructional Steel Research 74 (2012) 26–36

duot was up to nearly 5 mm. However, for its counterpart structure,

owing to the function of the diaphragm, the corresponding valueduwt was controlled within 0.7 mm.It could be summarized that for both the single and double-panel

specimens, the amplitude of the out-of-plane deformation could bereduced substantially about 96% and 86% of that of the structureswithout diaphragm, respectively. But it should be noted that, interms of the single-panel subassemblage, the favorable effect of dia-phragm might be amplified for that the non-rigid effect of structureswas not be taken into account.

5.4. Deformation–load behavior of main-leg member in specimen

Fig. 19 compared the deformation–load behaviors of two pairs ofspecimens. Obviously, the ultimate load-carrying capacity of thestructures with diaphragm had been increased greatly. For thesingle-panel specimens, the maximum load is improved from109 kN to 129 kN (Fig. 19(a)). For the double-panel specimens, thepeak value of the vertical load is increased from 85 kN to 100 kN(Fig. 19(b)). Therefore, it can be obtained that the maximum capaci-ties are enhanced by 18.3% and 17.6%, for the single and double-panel subassemblages, respectively. But it should be noted that themaximum values of the deformation of both the single and double-panel structures did not have a marked change.

0 2 4 6 8 10 12

0 2 4 6 8 10

0

20

40

60

80

100

120

140

P/k

N

0

20

40

60

80

100

120

P/k

N

D/mm

D/mm

a) single-panel

b) two-panel

with diaphragm

without diaphragm

without diaphragm

with diaphragm

Fig. 19. Comparison of deformation–load curves in the tests.

6. Discussion on the physical mechanism for favorable effect ofdiaphragm

Based on the experimental study on two pairs of tower subassem-blages presented in this paper, the most notable function of dia-phragms is to inhibit the out-of-plane deformation of diagonalmembers. Some important notions of consequent favorable effect ofdiaphragms are summarized as follows:

1. The main legs should be braced effectively under heavy ice load.Thus the effective length of themain legs,which served as the prima-ry compressionmembers of the tower, will be reduced. The ultimateload which the global structure could sustain is then increased.

2. The additional torsional effect that diagonal members bring to themain legs can be inhibited substantially, and the buckling mode ofmain leg members will be transited from flexural–torsional bucklingfor the structurewithout diaphragm to approached flexural buckling.This feature would improve the ductility and load-carrying capacityof the main members as well as the global structure.

3. The stability of diagonal members will be maintained as the stabil-ity performance of the main legs has been improved. This pointwill in turn render diagonal members more effective in terms ofproviding lateral restraint to main legs.

4. Adding diaphragms can be viewed as a practical strategy for theretrofitting for existing towers as well as ice-resistant design ofnew tower structures.

7. Summary and conclusions

Two pairs of tower subassemblages, were fabricated and staticallytested under simulated ice load in this research. One pair specimenswere single-panel, while the other is double-panel. The effect of theaddition of the diaphragm on the failure mode, behavior and capacityof the subassemblage is investigated. Based on the experimental in-vestigation, following conclusions could be drawn:

1. Buckling of the main leg members was the overriding failure modeof the structures without diaphragm. For both the single anddouble-panel subassemblages, the out-of-plane deformations atthe joints of diagonal bracings were considerable and the torsionin the main leg angles is apparent.

2. The structures with diaphragmwould also fail due to the buckling ofthe main leg members. But the notable difference is that the specificfailure mode, load-carrying capacity and ductility of both the singleand double-panel specimens had been enhanced significantly.

3. The physical mechanism of the favorable effect from the dia-phragm is that it can inhibit the out-of-plane deformation of diag-onal braces as well as the torsion effect of main angles.

4. It is proposed that sufficient diaphragms should be added in eachpanel of latticed transmission tower structures. The arrangementprinciple should be determined by considering load-carry capacityand deformability simultaneously.

Acknowledgments

This work was financially supported by the National Natural ScienceFoundation of China under Grant No. 50778135, Fok Ying Tung EducationFoundation for Young Scientists underGrantNo. 114021andS&TProgramof State Grid Corporation of China. All sponsors are gratefully acknowl-edged. Any opinions, findings, conclusions and recommendations pre-sented in this paper are those of the writers and do not necessarilyreflect the views of the sponsors.

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