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Life Prediction of Electrical Power Transmission Towers
Conference Paper · January 2008
DOI: 10.1115/ESDA2008-59490
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Proceedings of the 9th Biennial ASME Conference on Engineering Systems Design and Analysis
ESDA08
July 7-9, 2008, Haifa, Israel
ESDA2008-59490
LIFE PREDICTION OF ELECTRICAL POWER TRANSMISSION TOWERS
(1)
Juan E. Salazar 1, 2
Department of Research and Postgraduate Studies
National Polytechnic University UNEXPO
Puerto Ordaz, Venezuela
E-mail: salazarj1@asme.org
ABSTRACT
This paper presents a study conducted to estimate the
remaining theoretical life of one type of 400 kV latticed steel
towers installed on a power transmission line in Venezuela. The
study focused on determining the structural behavior and
vibration characteristics of suspension towers on the fore
mentioned line, considering material loss of their structural
members due to atmospheric corrosion, in different design
conditions. For this purpose, a commercially available FEM
code was used to build models to perform structural and modal
analysis of the chosen type of tower, in order to determine load
effects in the structure (stress and deformation), natural
frequencies and mode shapes in each of the different design
states. Then, a simple methodology engineered as part of this
study leads to prediction of the tower’s service life based on an
allowable state of stress and deformation in the tower (direct
and vibration-induced) affected by different reliability factors
and taking into account corrosion effects and corrosion rates in
a particular environment along the transmission line.
Keywords: Latticed towers, power transmission
atmospheric corrosion, service life prediction, LRFD.
(2)
Jesus A. Mendoza 2,1
Center for Mechanical Design (CEDIMEC)
Department of Mechanical Engineering
National Polytechnic University UNEXPO
Puerto Ordaz, Venezuela.
For this reason, a grid of over 5,000 km of transmission
lines has been developed in order to service load centers across
the national geography, northeastern Colombia and northern
Brazil (see Fig. 1).
lines,
Figure 1. High voltage transmission lines in Venezuela.
1. INTRODUCTION
Despite the fact of being a producer of oil and natural gas,
some 70% of the electricity used in Venezuela comes from
hydropower sources located in the southern part of the country.
Most of this energy is supplied by a single utility company,
CVG EDELCA, running three hydroelectric plants along the
Low Caroni Basin with a combined capacity of over 15,000
MW.
Nevertheless, the main users of all this power are spread
along the Venezuelan coastline, in the northern part of the
country, where the more densely populated and industrialized
cities are located.
For the most part this power grid is located in rural areas in
between the cities, in constant interaction with different
environments and weather systems and with difficult access for
operations & maintenance purposes.
Visual inspections performed recently in several locations
along one of the transmission lines that make up the grid have
led to believe that some supporting structures of the line or
towers, may be deteriorating faster than expected (due mainly
to atmospheric corrosion) specially when compared to towers
of similar kind exposed to more severe environments, such as
marine.
Hence, there is reasonable doubt as to whether these
towers may have lost strength over the years due to corrosion
1
Copyright © 2008 by ASME
attack to a point where possibility exists for a catastrophic
failure of one or more towers sometime in the near future.
Furthermore, no information is available on what the expected
useful life of the towers would be given deterioration and
changes of environmental and climate conditions in the
different installation sites from the conditions assumed in the
original design.
In order to evaluate how much longer these structures may
stand complying with standardized reliability factors, a
complete study of the mechanical behavior of the towers
considering corrosion effects is proposed. The study was
conducted to estimate the remaining theoretical life of one type
of latticed steel towers installed in 1987 on a transmission line
running about 400 km from southern to central Venezuela, and
its results are presented in this paper.
conductors and hence larger support structures). The chosen
transmission line here is a 400 kV line, and the tower type
under study will be referred to as S/450 (see Fig. 2).
Figure 3 and Fig. 4 show line representations of the
selected 40 m tall S/450 tower. The development of the tower
configuration starts with the upper portion, which is designed
for the selected vertical and horizontal spacing of conductor
phases and electrical clearance around each conductor phase.
The lower portion of the tower determines the towers’ useful
height, which depends on the required clearance to ground, sag
of the conductors and extension or reduction of height
requested by tower spotting.
This type of towers are built with structural angle shapes
(single or double), of low carbon steel, galvanized, and bolted
together in the arrangement shown in Fig. 3.
2. TRANSMISSION TOWERS
2.1. Basic description
Of the different types of structures in a transmission line,
the present study will focus on self-supporting suspension
towers. These, unlike other types of towers (such as angle or
dead-end towers) are made to stand only tension from the
conductors and little or no torsion loads may be applied to
them. The conductor phases pass through and are suspended
from an insulator support point at the tower so that – in normal
operating condition – horizontal tension from the conductors
applied at the transverse faces at both sides of the tower is
always balanced.
L50x4
L50x5
L65x5
L65x6
L65x7
L75x7
L75x8
L90x7
L100x8
L100x10
Figure 3. Structural members in an S/450 tower.
Figure 2. Actual 400 kV transmission tower, type S/450.
The capacity of the line, in terms of voltage carried,
determines the size of a tower (higher voltages mean larger
2.2. Structural loading
In terms of loading, several national and international
standards classify the various types of loads transmission
towers must stand. ANSI and ASCE standards distinguish
between the events that produce the loads and the resulting
loads in the components of the towers [1]. They refer to loads
only as direct forces applied on the towers and classify the load
producing events as weather-related, accidental and
construction & maintenance (C&M) events.
2
Copyright © 2008 by ASME
In short, transmission towers are subject to loads in three
directions: vertical, longitudinal and transverse; whether in
normal or extraordinary conditions. Vertical loads include own
weight of the assembly, weight of the conductor phases and
insulators and weight of maintenance workers.
Figure 4. Tower geometry and load carrying faces.
Horizontal loads are applied in two directions, namely
transverse and longitudinal, which are respectively
perpendicular and parallel to the transport direction of the
transmission line (see Fig. 4). Force decomposition is also used
to distribute loads applied to the structures at an angle (e.g.
wind pressure).
Load classification is helpful in the present study when
identifying the type of events and working conditions assumed
in the original S/450 design of 1987. Fourteen load cases were
formulated at that time (see Table 7 in the appendix), covering
all types of load producing events. All of them were input in
the computer simulations of this project and take into account
load from events plus own weight of the assembly and weight
of the conductor phases and shield wires.
Even though designing a tower from scratch is not the aim
of this study, thorough care should be given at fully
understanding the nature of loading of the structure (and its
response to all type of loads) in order to apply new-tower
analysis procedures on an old deteriorated tower when
verifying its integrity after several years of continuous service,
as will be described in the next section.
3. SOLUTION APPROACH
Current standardized tower design is very much reliabilitybased and does not directly deal with the issue of service life
and how it is affected by interactions of the structures with the
environment [1-6]. There are provisions in the different
standards to increase the design factors for the towers in an
attempt to lower the chances of them failing in a given period.
This overdesign is meant to compensate for other effects
like corrosion of the structures, not specifically covered in the
calculation procedures (as would be the case for wind and other
weather-related events). So if any prediction is to be made on a
towers’ life, a methodology is to be set that can help
management decide on major maintenance programs, and
partial or total replacement of the structures in a transmission
line, taking into account all aspects related to their behavior.
In this spirit, a practical methodology was engineered as
part of this project to predict the theoretical life of a tower
based on verification of its structural integrity at different
stages of corrosion.
A commercially available finite elements method (FEM)
code was used to this purpose, and a single geometric model of
40 m tall S/450 towers was built to perform structural and
modal analyses of this type of tower. Structural analyses are run
to find out what is the limit state of corrosion a tower can stand
without one of its members failing to a critical load producing
event, while modal analyses are run to find out what the
vibration response of the tower is in that limit state, and how it
compares to known data for actual towers.
In order to find out what the limit state is, defined by the
maximum material loss due to corrosion, an iterative solution
scheme is adopted.
In the first cycle, the original (design) condition of the
towers is assessed by calculating the general distribution of
stress and deformation, as well as the natural frequencies and
mode shapes of the tower in that state. Stress results in the
models from already factored loads of the original design are
compared against the nominal strength calculated for each
member as per the current ANSI/ASCE standard [1], which is
based on the AISC-LRFD procedure [3]. Using the FEM model
simplifies this checking process, as only critical structural
members are really needed to be studied in detail.
Moreover, the first cycle gets completed when natural
frequencies calculated for this design state are compared
against frequency values known to cause failure of
transmission towers due to galloping1 and other weather-related
vibration
phenomena.
Direct
and
vibration-induced
deformations are also checked here.
1
Wind-induced self-excited motion of overhead transmission lines. It
may cause such serious problems as short circuits due to the
entanglement of lines, snapping of the line-to-line spacers and the
breakage of transmission towers.
3
Copyright © 2008 by ASME
At this point, the concept of “lifetime series” is introduced
to denote several stages of increasing corrosion affecting the
tower. For each series, a set of cross-section properties results
from an allowed thickness loss for all structural members.
They have been named to match the type of steel angle – in
each series – reaching the minimum thickness of 3 mm required
by norm for tower members exposed to general atmospheric
corrosion2 (see Table 1).
used to build Venezuela’s corrosivity map [10] was selected to
obtain corrosion and environmental data for lifetime prediction.
This station was spotted on the path of the 400 kV transmission
line under study, in an industrial setting, and its location
showed to have more severe conditions for tower deterioration
than most of the other parts of the country the power line goes
through (mainly rural inland areas).
Table 1. Lifetime series. Preliminary.
4. TOWER MODELING
For analysis purposes a tower may be represented by a model
composed of members interconnected at joints. Members are
normally classified as primary and secondary. Primary
members form the triangulated system that carries the loads
from their application points down to the tower foundations.
Secondary members are used to provide intermediate bracing
points to the primary members and thus reduce unsupported
length. They can be easily identified on drawings as members
inside a triangle formed by primary members.
To this day, latticed towers are analyzed mostly as ideal
trusses made up of straight members with pin connections. In
those first-order linear elastic analyses only tension or
compression and displacement is produced in the joints, and
moments in members due to eccentric loads, distributed wind
loads or assembly eccentricities are usually not taken into
account, even though they may affect member selection.
Special attention should be given to this traditional
assumption that structural members are to stand axial loads
only, for it has been proven in the past that as assembly angles
between secondary and primary members are smaller, the
secondary member does not fully support the primary member,
making the arrangement less rigid and producing moments in
the primary members [11]. In addition, joints between
secondary and primary members also introduce moments that
must be taken into account as they may produce premature
failure of the tower [12].
Furthermore, the effects of bolt slippage and local bolt
deformation on joint flexibility, and the bending stiffness of the
angle members are also ignored in the traditional approach.
These have been known to cause discrepancies between the
predicted and actual structural response when comparing
results from linear elastic programs and deflections and
rnember axial forces measured in transmission towers [13].
Due to these reasons, the structure has been considered in
this study as a space truss, modeled using uniaxial finite
elements with tension, compression, and bending capabilities,
to simulate the actual rigidity of tower joints. The same elastic
beam elements were also used in modal analyses.
A view of the tower upper body in Fig. 5 shows the
featured mesh for this project. It is comprised of 5,606 finite
elements and 4,921 nodes, and is the result of a mesh
convergence study performed for both static and modal
analyses of the tower.
Series
L50 series
L65 series
L75’ series
L75 series
Allowable thickness loss (mm)
1.0
2.0
2.5
3.0
Calculation of load effects (as described for the first cycle)
will continue for each series until a series is reached where one
or several structural members in the FEM model fails to
comply with the ASCE-LRFD condition that,
φ Rn > QD
(1)
Where,
Rn: Nominal Strength (MPa), for the particular member
φ : Strength Factor, affected by the exclusion limit3 e and
its statistical variation, for the chosen component reliability
QD: Load effect: Stress (MPa), affected by Load Factor γ ,
for the chosen transmission line reliability factor
Then, an intermediate series is to be introduced between
the last successful one and the one failed. If this first
intermediate series results in failure, a second intermediate
series is to be introduced and so on until a successful one is
reached, that will define the ultimate limit state.
Finally, theoretical lifetime of S/450 towers is estimated in
the ultimate limit state using the value for the amount of
corrosion loss in thickness per year for both coated and
uncoated structural members, known as corrosion rate. A
separate calculation is required in both cases, as corrosion rates
differ from zinc (in the galvanizing coating) to iron in the bare
steel angles (after all coating has corroded).
Coating thickness of the tower steel angles was taken from
the mandatory standard for galvanized members of latticed
towers, ASTM A123 [9], choosing the minimum value in the
ranges set for structural shapes and plates thicker than 4 mm.
Corrosion rates were obtained using the geographic
mapping method. Specifically, one of the monitoring stations
2
Type of corrosion where the metal surface corrodes uniformly across the
exposed area. Field exposure results indicate the corrosion form of zinc or zinc
coated steel (or galvanized) is this general corrosion or uniform corrosion [8].
3
Percentage of components not surviving materials test at loads equal to
their nominal strength. It accounts for nonuniformity of material properties
from the manufacturers, as actual strength is considered to be a random variable
affected by statistical variations.
4
Copyright © 2008 by ASME
Table 3. Natural vibration frequencies f. Ultimate state.
Mode - f (Hz)
1 2.5899
2 2.9687
3 3.1167
4 4.8184
5 6.1001
6 8.8025
7 9.8128
8 9.9492
9 10.934
10 11.293
Mode - f (Hz)
11 13.703
12 14.173
13 14.429
14 14.658
15 16.006
16 16.573
17 16.939
18 17.541
19 18.123
20 19.133
Mode - f (Hz)
21 19.238
22 19.520
23 19.567
24 19.589
25 19.648
26 19.667
27 19.668
28 19.763
29 19.772
30 19.805
Mode - f (Hz)
31 20.103
32 20.193
33 20.411
34 20.895
35 21.033
36 21.227
37 21.399
38 21.499
39 21.645
40 21.746
Figure 5. Meshed upper body of an S/450 tower model.
5. RESULTS
In determining S/450 tower behavior, all load cases in the
original design were analyzed (see Table 7). For simplicity of
presentation, only sample contour graphs and representative
information will be shown in this section for the most critical
load case, 1B, both at the original design condition and at the
ultimate limit state. Nevertheless, verification checks leading to
determination of the final lifetime series will be discussed in
detail.
5.1. Modal analysis
One hundred natural frequencies f of S/450 towers were
calculated in the models for every design condition. In one
hand, frequency values ranged from 2.15–35.78 Hz for the
original design condition, whilst on the other hand they ranged
from 2.15–34.43 Hz for the ultimate limit state.
The results for the first 40 modes of the original design and
the ultimate state may be observed in Table 2 and Table 3,
respectively.
m1)
m2)
Table 2. Natural vibration frequencies f. Original design.
Mode - f (Hz)
1 2.1572
2 2.4694
3 2.9368
4 4.6904
5 5.9144
6 8.6268
7 9.0896
8 9.2150
9 10.882
10 10.965
Mode - f (Hz)
11 13.159
12 13.466
13 14.045
14 14.823
15 16.405
16 17.082
17 17.500
18 17.911
19 18.503
20 19.182
Mode - f (Hz)
21 19.246
22 19.440
23 19.527
24 19.560
25 19.684
26 19.711
27 19.762
28 19.782
29 20.099
30 20.438
Mode - f (Hz)
31 20.505
32 20.576
33 20.807
34 21.407
35 21.680
36 21.737
37 21.963
38 22.516
39 22.538
40 22.597
m3)
m4)
Figure 6. First four vibration mode shapes. Original design.
5
Copyright © 2008 by ASME
Figure 6 shows the deformed shapes of the structure for its
first four vibration modes. Even though mode shapes are
similar when comparing the original design condition to the
ultimate limit state, deformation results in each of these
conditions differ an average 50%, as may be seen for an
example vibration mode in Fig. 7 and Fig. 8.
Figure 7. Deformation (m), resultant (XYZ), original design,
mode 3.
Figure 8. Deformation (m), resultant (XYZ), ultimate state,
mode 3.
Deformation values from the modal analyses are one order
of magnitude smaller than those obtained in the structural
analyses for the more severe stress conditions (see Fig. 9 and
Fig. 12); leading to the preliminary conclusion that vibrationinduced deformation is not considered to be a threat to the
structural integrity of the towers under the conditions studied.
On the other hand, approximate natural frequencies of
conductor vibration for ordinary aeolian motions are 3-150 Hz,
for sub conductor oscillations 0.15-10 Hz, and for galloping
0.08-3 Hz (Appendix F in ref. [2]). Out of these three, the latter
is the event with greater potential to cause the most structural
damage, so natural frequencies obtained in this study are
compared to the galloping range to find that the first frequency
calculated in the models is way above the initial value for
which the phenomenon usually occurs.
In addition, wind induced oscillations may originate for
individual members of the tower rather than for the whole
structure (as would be the case of study here). This type of
vibration may be initiated by vortex shedding and/or aerolastic
instability but, given its arrangement, latticed towers present a
complex aerodynamic shape to the wind such that consistent
vortex shedding that could cause complete oscillation of the
structure over a prolonged period is very unlikely to happen.
Therefore, it is fair to say from all of these results that the
structures are not likely to fail due to vibration-related
phenomena, which occur mainly when frequency of the
conductors’ motion matches one of the natural frequencies of
the towers.
5.2. Structural analysis
Results presented here will primarily focus on stress
verification according to standards, since there are no
established limits of deflections for structural members in
transmission tower applications (pp. 37 in ref. [1]).
Deformation results are useful as reference when
comparing the original design condition to the ultimate limit
state, having in mind the fact that no catastrophic failure has
occurred involving an S/450 tower in over 20 years, and hence
the original design is considered to represent the more
conservative condition in this study. Figure 9 and Fig. 12 serve
to this purpose, and values observed in the pictures let draw the
conclusion that no failure of the towers is expected due to short
circuiting of the conductor phases and shield wires, neither
from tower deformation from external loads nor from
vibration-induced deformation, since the greatest value
obtained (for the ultimate state) is about 18 cm at the cross-arm
of the 40 m tall tower, with the smallest separation between
conductor phases and shield wires being of 2.6 m.
As for stress, results from the first calculation cycle –
model of the original condition – vary depending on the type of
member being analyzed. Verification checks are made for each
member against nominal strength as described in Table 8 of the
appendix, selecting the appropriate formula according to
restraint conditions, when in tension, and slenderness ratio
6
Copyright © 2008 by ASME
when in compression. Tension and compression from bending
are also checked.
The general stress distribution for the most severe
scenarios obtained for the original design state show that most
members are stressed below their nominal strength values;
whether in direct stress or bending stress, as observed in Fig.
10 and Fig.11. In the case of tension, few members reach the
peak value of 228 MPa, mostly primary members restrained in
such a way that their nominal strength equals the materials
yield strength Fy. As for the rest of components (the majority of
secondary members) their nominal strength equals the reduced
yield strength 0.9Fy of 225 MPa yet their calculated stress in
the models fall in the range of 46 to 107 MPa.
It is important to note for strength comparison purposes
that whilst most of the tower secondary members and some
primary members are made of ASTM A36 steel (Fy= 250 MPa
and Fu=360 MPa), there are an important number of primary
members made of ASTM A570, gr. 50 steel (Fy= 345 MPa and
Fu=510 MPa). In both cases double member arrangements are
also found, which are taken into account in the verification
checks as well.
In the case of compressed members, even though most of
them show calculated stress values in the range of -75 to -135
MPa, posing no risk to the structural integrity of the tower,
those subject to the highest compression need to be precisely
identified in the model results database and studied in detail, in
order to anticipate the effects of local buckling which might
start in individual members but may eventually trigger failure
of the entire structure [14].
Figure 10. Direct stress (Pa), original condition.
From the first cycle, these critical members of the tower
are identified. They are the primary members connecting the
left lower haunch with the first body extension (Fig. 12a), in
the case of tension, and the primary member connecting the
third extension with the front right leg (Fig. 12b). Once these
members are known, iterative calculations start for all lifetime
series, following the procedure described in the previous
section.
Figure 9. Deformation (m), resultant (XYZ), original design.
Figure 11. Bending stress (Pa), -Y side, original condition.
7
Copyright © 2008 by ASME
recalculated for each series due to material loss, stress in the
model tends to increase to the point where catastrophic failure
of a critical member is almost certain, thus disregarding the
series L75 as a reliable design condition.
1st
extension
Haunch
a)
a
b)
Figure 12. Direct stress (Pa) in critical members, original
condition. a) Max. tension, b) Max. compression.
In all cases, general stress distribution tends to have a
similar pattern, and critical members are nearly in the same
locations, if member material and arrangement are taken into
account (as would be expected, since all models shown are for
the same loading condition).
Figure 14. Direct stress (Pa), ultimate limit state.
Figure 13. Deformation (m), resultant XYZ, ultimate state.
Figures 13 to 15 show sample results for the ultimate limit
state arrived at after iterating from the first lifetime series L50
to the last L75. In this last series stress values peaked in general
but for critical members in particular, as may be observed from
comparison checking in Table 4.
It is evident from this table that while nominal strength
tends to decrease very little as cross-section properties are
Figure 15. Bending stress (Pa), +Z side, ultimate limit state.
8
Copyright © 2008 by ASME
Table 4. Nominal compressive strength Fa and model
compressive stress LS1 in critical members (MPa).
Series
Leg member, L100x10A
L
Elem.
(cm) r (cm)
Fa
LS1
Dif. %
Orig.
4407-10
153
3.04
306,82
256
-17%
L50
4407-10
153
3.00
305,79
202
-34%
L65
4407-10
153
2.60
292,80
230
-21%
L75’
4407-10
153
2.50
288,54
263
-9%
L75
4407-10
153
2.30
278,29
265
-5%
Series
Haunch member, 2L65x5
L
Elem.
(cm) r (cm)
Fa
LS1
Dif. %
Orig.
3414-21
227
2.63
235,26
235
0.1%
L50
3414-21
227
2.59
234,80
197
-16%
L65
3414-21
227
2.55
234,32
222
-5%
L75’
3414-21
227
2.54
234,19
207
-12%
L75
3414-21
227
2.52
233,94
408
74%
This led to the introduction of the intermediate series L75’
which complied with the reliability requirement set forth in Eq.
(1). As example, it may be noted from Fig. 14 and Fig. 16 that
whilst most of the critical primary member in compression
coming down from the tower body extension to the leg is in the
stress range of 210 to 282 MPa, a revision at the model results
database showed that none of the members exceeds the nominal
strength (calculated for individual slenderness ratios of each
member).
Figure 16. Direct stress (Pa), ultimate limit state (L75’).
Critical member detail.
Once again, contour graphics for all series showed that, in
general, only few secondary members reach the ultimate
strength. In some cases, database revision showed that only one
of several finite elements simulating a structural member
exceeds Fu (whether in tension or compression from direct or
bending stress), which suggests the presence of localized stress
concentration problems that have been solved in the past using
localized reinforcements without compromising structural
integrity of the tower [15].
As for the bending stress, it is worth mentioning that for all
lifetime series, and especially for the ultimate limit state L75’,
there are a number of members exceeding strength of low
carbon steel. They are located in the bridge area of the tower
and even though built in A570 steel it is anticipated that for the
ultimate limit state they will require local reinforcement in
order to reduce the risk of potential failure.
Such a failure might originate from a change in loading
conditions, as actual loads are really probabilistic in nature,
meaning that loads considered in this study could be
underestimated, resulting in a reliability level that is not
entirely according to reality [14].
Nevertheless, the methodology and tools set forth in this
study allow for general use of the model with application of
different load scenarios and adjustment of reliability levels for
verification purposes. This way, generalization of the results
obtained may assist management in decision taking.
5.3. Reliability assessment
From results of the structural analysis it is fair to say that
the ultimate limit state represents a safe working condition of
the tower, in light of the reliability level set in the original
design. In both conditions, fulfillment of the requirement in Eq.
(1) was checked, that is, reduced nominal strength of
components (φ Rn) must always be greater than load effects
(QD) from increased loads.
In this study, loads have been increased by a γ factor of 1.2
and the strength factor φ was considered to be 1, as the original
design was made by the ASD procedure [4] without factoring
component strength. This yields a component reliability factor
of 1, with an exclusion limit of 2-10% and a statistical variation
of 10-20%.
These values make this calculation fall in the category of a
non-critical transmission line (e.g. a line that is not the single
source of power for an area), as defined by the ASCE standard
(pp. 11 in ref. [1]).
Then, for the chosen load factor of 1.2, interpolation of
values in Table 5 yields a reliability factor for the original
design LRF of 2.66 which corresponds to a return period RP of
133 years, greater than the base period for calculating a tower
in the ASCE standard [2].
Moreover, no breakage failure is expected in the ultimate
limit state L75’, since peak stress exceeding the material’s
ultimate strength Fu is only reached in a critical member for the
extreme lifetime series L75 (see table 4).
Table 5. Load factors to adjust component reliability
Line reliability factor, LRF
Return period, RP
Load factor, γ
9
1
50
1.0
2
100
1.15
4
200
1.3
8
400
1.4
Copyright © 2008 by ASME
Even though it is implied form the standard that towers are
calculated to stand for at least 50 years (see Tabe 5), the return
period RP does not define the tower’s service life for itself but
rather affects selection of reliability factors, as it is related to
the probability of an event occurring that could exceed the
nominal loads. A greater RP means this probability is smaller
(and therefore the tower design is considered to be more
reliable).
5.4. Lifetime prediction
Finally, service life of the towers is defined by the
corrosion rates selected for the transmission line and the
structural condition in each limit state. For the steel substrate
(Fe) and galvanizing coating (Zn) of structural members these
are 23.0 and 2.73 µm/year, respectively.
From a combined analysis of corrosion rates and allowable
thickness loss, useful life of galvanizing coating in structural
members of S/450 towers is estimated in 31 years for all
lifetime series, which is not yet complete. Useful life of the
bare substrate (the unprotected metal surface after all coating
has been lost) is estimated for corrosion of the allowable
thickness loss in all lifetime series. Results are showed in Table
6.
Table 6. Theoretical service life for different limit states
Series
L50
L65
L75’
L75
Thickness
loss (mm)
Coating
Zn (years)
Substrate
Fe (years)
1,0
2,0
2,5
3,0
31
31
31
31
43
87
109
130
Service life
(years)
74
118
140
161
6. CONCLUSIONS
• Theoretical service life of S/450 towers, based on its
original loading condition and calculated through the
simulated reduction of structural members’ thickness below
the minimum standard, is approximately 140 years.
• In light of the ASCE-LRFD method, original S/450 design
is considered to be reliable and overdimensioned,
compensating the lack of a strength reliability factor with a
high load factor associated with a high line reliability
factor.
• Methodology and tools from this study allow for general
use of the model with application of different load
scenarios and adjustment of reliability levels for
verification purposes, either for existing tower evaluation
for upgrade/replacement or for new designs.
7. ACKNOWLEDGMENTS
The authors wish to gratefully acknowledge collaboration from
the Transmission Projects Division of CVG EDELCA, for
providing us with valuable technical data during precommissioning of this project, and FUNDACITE-BOLIVAR
for providing a grant to partially fund this work.
8. REFERENCES
[1] ANSI/ASCE Standard 10-97: Design of latticed steel
transmission structures, 1997, American Society of
Civil Engineers (ASCE). Reston, VA.
[2] ASCE Manuals and Reports on Engineering Practice
Nº 74. Guidelines for Electrical transmission Line
Structural Loading, 1991, American Society of Civil
Engineers (ASCE). New York, NY.
[3] Manual of steel construction. Load & Resistance
Factor Design, 1994, American Institute of Steel
Construction (AISC). Chicago, IL.
[4] Manual of steel construction. Allowable Stress Design,
1973, American Institute of Steel Construction (AISC).
New York, NY.
[5] Chen Wai-Fah, ed., 1999, Structural Engineering
Handbook. CRC Press. Boca Raton, FL. Chap. 2 and
15.
[6] Marne, D., 2002, National Electrical Safety Code
(NESC) Handbook. McGraw-Hill. New York, NY.
[7] Wilson, E., 2002, Three-dimensional static and
dynamic analysis of structures.
Computers and
Structures, Inc. Berkeley, CA.
[8] Zhang, X.G., 1996, Corrosion and Electrochemistry of
Zinc, Plenum, New York, NY. Parts available online at
http:// www.galvinfo.com:8080/zclp/
[9] ASTM Standard A 123/A 123M-00: Standard
Specification for Zinc (Hot-Dip Galvanized) Coatings
on Iron and Steel Products, 2000, American Society
for Testing and Materials. West Conshohocken, PA.
[10] Morcillo, M., Almeida, E., Rosales, B., Uruchurtu, J.
and Marrocos, M., eds., 2002, Corrosión y protección
de metales en las atmósferas de Iberoamérica. Parte I –
Mapas de Iberoamérica de corrosividad atmosférica
(Proyecto MICAT, XV.1/CYTED). Iberoamerican
Program of Science and Technology for Development.
Madrid, Spain.
[11] Roy, S., Fang, S., and Rossow, E., 1984, “Secondary
stresses on transmission tower structures”. Journal of
Energy Engineering. 110 (2). pp 157-172.
[12] Knight, G. and Santhakumar, A., 1993, “Joint effects
on behavior of transmission towers”. Journal of
Structural Engineering. 119 (3). pp 698-712.
[13] Kroeker, D., 2000, “Structural analysis of transmission
towers with connection slip modeling”. Master of
Science thesis. University of Manitoba. Winnipeg,
Canada.
[14] Albermani, F. and Kitipornchai, S., 2003, “Numerical
simulation of structural behaviour of transmission
towers”. Thin-Walled Structures. 41 (12). pp. 167-177.
[15] Prasada Rao, N., Mohan, S.J. and Lakshmanan, N.,
2005, “Lessons from premature failure of cross arms in
transmission line towers during prototype testing”.
Proc. 10th NAFEMS World Congress. Malta.
10
Copyright © 2008 by ASME
9. APPENDIX
Table 7. Load cases in S/450 design.
Case N°
1A
1B
1C
2A, 2A1
2B, 2B1
2C
3A, 3A1
3B, 3B1
3C
3D
Description
Distributed wind pressure on one face (T), 193 kg/m2
Distributed wind pressure on both faces (TD+LD), 145 kg/m2
Distributed wind pressure on one face (L), 193 kg/m2
Shield wire installation at either side (left, 2A; right, 2A1)
Conductor phase installation at either side (left, 2B; right, 2B1)
Conductor phase installation at the center
Shield wire breakage at either side (left, 3A; right, 3A1)
Conductor phase breakage at either side (left, 3B; right, 3B1)
Conductor phase breakage at the center
Simultaneous breakage of both shield wires and all three conductor phases
Direction
Transverse
Transv.+Long.
Longitudinal
Vertical
Vertical
Vertical
Longitudinal
Longitudinal
Longitudinal
Longitudinal
Table 8. ANSI/ASCE 10-97 component nominal strength.
Stress state
Description
Tension
Equal leg angle, bolted in both legs, at both ends
Tension
Equal leg angle, bolted in one leg
Ft = 0.9 Fy
Bending
Extreme fiber in tension
Fb = Fy
Bending
Extreme fiber in compression
Fb = Fy
Compression
Max. slenderness ratio*: KL ≤ C ; C = π
c
c
r
2E
Fy
KL L for
L
=
0 ≤ ≤150.
r r
r
Compression
Max. slenderness ratio*: KL > C ; C = π
c
c
r
2E
Fy
KL L for
L
=
0 ≤ ≤150.
r r
r
Nominal Strength Rn
Ft = Fy
⎡ 1 ⎛ KL r ⎞2 ⎤
⎟⎟ ⎥ Fy
Fa = ⎢1 − ⎜⎜
⎢⎣ 2 ⎝ Cc ⎠ ⎥⎦
Fa =
π 2E
(KL r )2
* For angles with a width to thickness ratio w/t <25. Where,
L: unbraced length of the structural member
r: radius of gyration of the weakest axe
K: Effective length coefficient
11
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