Technical Note
Life-Cycle Cost Analyses of a New Steel for Bridges
Nader M. Okasha, Aff.M.ASCE1; Dan M. Frangopol, Dist.M.ASCE2;
Fred B. Fletcher3; and Alex D. Wilson, M.ASCE4
Abstract: This technical note presents the computations, results, and conclusions of an analytical investigation for comparing the life-cycle
cost (LCC) of a steel bridge component made of a new maintenance-free steel and the LCC of the same steel bridge component made of
conventional painted carbon steel with maintenance (repainting). An approach for the LCC analysis is presented both deterministically, where
different painting scenarios are considered, and probabilistically, where the uncertainties in the input variables are properly considered. Under
reasonable cost assumptions, it is demonstrated that the new steel, although initially more expensive, is indeed cost-effective after approximately 15 years. The LCC-effectiveness of the new steel increases over the service life of the bridge component. DOI: 10.1061/(ASCE)BE
.1943-5592.0000219. © 2012 American Society of Civil Engineers.
CE Database subject headings: Life cycles; Steel bridges; Maintenance; Corrosion; Coating.
Author keywords: Life-cycle cost; Steel; Maintenance; Corrosion; Painting; Bridge.
Introduction
A new candidate steel for bridges was developed by ArcelorMittal
in the 1990s. The steel, designated and codified as ASTM A1010,
is highly resistant to atmospheric corrosion. This behavior is particularly evident in microenvironments containing high levels of
chlorides such as locations of heavy deicing salt deposition and
along the seacoast. Conventional weathering steels, which provide
maintenance-free service in low-chloride microenvironments,
are unsuitable for bridges with severe chloride deposits; in this case
painted carbon steel bridge girders are necessary along with the
attendant frequent repainting maintenance costs. The A1010 steel
has been used to construct one innovative bridge in California and
two conventional plate girder bridges are being designed by the
Oregon Department of Transportation for erection in the next
few years.
Owing to its chemical composition, the manufacturing cost of
A1010 is considerably higher than that of carbon or weathering
steel. However, its corrosion resistance makes it able to last in structures for long periods (100–125 years, as considered in this study)
without the need for maintenance (i.e., repainting). Accordingly,
the feasibility of A1010 steel is judged on its lower life-cycle
cost (LCC) compared to that of painted carbon steel. The computation of the LCC for both steels requires considerations of the
1
Graduate Research Assistant, Dept. of Civil and Environmental
Engineering, ATLSS Center, Lehigh Univ., 117 ATLSS Dr., Bethlehem,
PA 18015-4729. E-mail: nao204@lehigh.edu
2
Professor and Fazlur R. Khan Endowed Chair of Structural Engineering
and Architecture, Dept. of Civil and Environmental Engineering, ATLSS
Center, Lehigh Univ., 117 ATLSS Dr. Bethlehem, PA 18015-4729 (corresponding author). E-mail: dan.frangopol@lehigh.edu
3
Principal Research Engineer, ArcelorMittal Global R&D, Coatesville,
PA 19320. E-mail: Fred.Fletcher@arcelormittal.com
4
Principal Research Engineer, ArcelorMittal Global R&D, Coatesville,
PA 19320. E-mail: Alex.Wilson@arcelormittal.com
Note. This manuscript was submitted on November 3, 2010; approved
on January 10, 2011; published online on January 12, 2011. Discussion
period open until June 1, 2012; separate discussions must be submitted
for individual papers. This technical note is part of the Journal of Bridge
Engineering, Vol. 17, No. 1, January 1, 2012. ©ASCE, ISSN 1084-0702/
2012/1-168–172/$25.00.
uncertainties inherent in future predictions, and these are best
handled by probabilistic procedures. Alternatively, different deterministic painting scenarios for a steel bridge component made from
painted carbon steel can be compared against the case of the same
bridge component made from A1010 steel.
The objective of this technical note is to deterministically and
probabilistically compare the LCC of a model steel bridge girder
fabricated from A1010 steel (maintenance-free) and the LCC of the
same bridge girder made of painted carbon steel with subsequent
maintenance by repainting.
Input Variables
The analysis is on the basis of the cost of a model steel bridge
girder, expressed in 2008 US dollars. The dimensions of the model
girder are given in the following.
For a bridge fabricator, the purchase price of carbon steel plate
was assumed to be $975 per metric ton. This is about the average
steel price in the United States from 1957 to 2007. The purchase
price for A1010 plate was assumed to be $2,265 per metric ton.
Both of these initial cost inputs are considered deterministic.
The cost of a typical fabricated carbon steel girder was given
by Ronnie Medlock (personal communication, 2009) to vary from
$1.50 to $1.55 per pound ($3,000–$3,100 per metric ton). This total
cost includes fabrication, initial painting, shop inspection, and
transportation. Hence, the total cost of a conventional painted steel
girder is assumed deterministically to be $1.525 per pound ($3,050
per metric ton).
The use of unpainted weathering steel rather than painted carbon
steel to fabricate a typical bridge girder reduces the total cost by
about 5% (Ronnie Medlock, personal communication, 2009). This
figure may be used to estimate the material-independent bridge
girder costs of fabrication, shop inspection, and transportation.
The other initial costs considered for the conventional steel, including fabrication, initial painting, shop inspection, and transportation
are found by subtracting the material cost from the total cost. The
result is reduced by 5% to obtain the other initial costs for the
A1010 steel product. It is herein assumed that the 5% reduction
in the total cost for weathering steel can be applied to the
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A1010 steel because it is also not painted. The other initial costs for
both steel types are also assumed to be equal and deterministic.
The typical cost for repainting the bridge girders was given by
Eric Kline (personal communication, 2009) as $12=ft2 . This cost is
considered in this study as a random variable modeled with a triangular distribution with a lower limit of $6=ft2 , a most probable
value of $12ft2 , and an upper limit of $18=ft2 [i.e., Tri(6, 12, 18)].
The repainting time-interval is considered as a random variable
modeled also with a triangular distribution Tri(10, 15, 20). This
time-interval reflects a microenvironment that is extremely severe
such as a coastal bridge. In less-severe microenvironments, the
repainting time-interval may be longer, especially with newly
developed paint systems.
The annual discount rate of money is also treated as a random
variable modeled with a uniform distribution with probable values
ranging from 0.00 to 0.03 [i.e., U(0.00, 0.03)].
Deterministic Life-Cycle Analysis
In this section, the overall life-cycle analysis approach is conducted
deterministically. Different realizations of the random variables
presented in the previous section are treated as different scenarios,
where in each scenario a limit value will be considered for each
random variable. Accordingly, the LCC is calculated by using
all combinations of limiting values for the random variables considered. The random variables are the repainting time-interval Tri
(10, 15, 20) years, the repainting cost Trið6; 12; 18Þ $=ft2 , and the
discount rate of money U(0.00, 0.03). One scenario would be, for
example, having a repainting time-interval of 10 years, a repainting
cost of 6 $=ft2 , and a discount rate of 0.03.
The computations of the LCC are conducted for a model bridge
girder. This model girder has the dimensions from a bridge in the
state of Wisconsin carrying US-51 and I-39 over the Wisconsin
River. The girder is composed of three plates, a top flange plate
with dimensions of 12-in. wide by 1=2 in: thick, a bottom flange
plate measuring 15-in. wide by 3=4 in: thick, and a web plate with
dimensions of 52-in. tall by 3=8 in: thick. The model girder has a
span of 80 ft.
The life-cycle computations were performed as follows. First,
the weight of the girder was calculated. Because the volume of
the girder is calculated to be 0:5781 m3 and the density of steel
is 7:85 metric ton=m3 , the weight of the girder is 4.5384 metric tons
or 5.0027 (short) tons. Accordingly, the material costs for the
model girders are calculated for the conventional steel and for
the A1010 steel, respectively, as
Material cost of girder; conventional steel ¼ $975 × 4:5384
¼ $4;424:
Material cost of girder; A1010 steel ¼ $2;265 × 4:5384
¼ $10;279
The total initial cost of the model painted carbon steel girder is
calculated to be
1:525 × 10;007:1 ¼ $15;261:
The other costs for the A1010 steel girder are:
Other initial costs; A1010 steel ¼ 15;261 × 0:95 4;424:9
¼ $10;073:
Accordingly, the total cost of the model A1010 steel girder is
Total initial cost; A1010 steel ¼ 10;279 þ 10;073 ¼ $20;352
This total cost for the A1010 steel girder is constant throughout
the service life of the bridge. However, the total cost for the painted
carbon steel girder is constant only until the first repainting is performed. Each time the girder is repainted, the repainting cost must
be added to determine the total cost. The repainting cost is a function of the surface area of the model girder which is calculated to be
985 ft2 . Hence, the cost of repainting of this girder is
Cost of repainting ¼ Trið6; 12; 18Þ $=ft2 × 985 ft2
¼ Trið$5;910; $11;820; $17;730Þ
The cost of repainting is subjected to a discount rate at each
application time t. The present cost of the kth repainting of the
girder at time t is
ðC PV Þk ¼
C
ð1 þ νÞt
ð1Þ
where ðC pv Þk = the present value of the cost for the kth repainting of
the girder, C = the cost of repainting at time of application, ν = the
discount rate of money, and t = the time of application of the kth
repainting.
Consider the case where the repainting time-interval is 20 years,
and the discount rate is 0.00. Fig. 1(a) shows the LCC for girders
made from both steels given the repainting cost of 6, 12, and
18 $=ft2 . With this discount rate and repainting schedule, the LCC
of the conventional steel girder becomes higher than that of the
A1010 steel after the first repainting, even at the lowest value considered for repainting cost. At 125 years, the difference is considerably large.
Consider the case where the repainting time-interval is 15 years,
and the discount rate is 0.00. Fig. 1(b) shows the LCC for the girder
in both steels given the repainting cost of 6, 12, and 18 $=ft2 . At
125 years, the difference is also considerably large. In fact, this
difference increases as the number of repainting actions increases.
Consider the case where the repainting time-interval is 10 years,
and the discount rate is 0.00. Fig. 1(c) shows the LCC for the girder
in both steels given the repainting cost of 6, 12, and 18 $=ft2 . This
is the most frequent repainting schedule considered. The curve representing the repainting cost of 18 $=ft2 is the highest LCC among
the cases considered. With this extreme case, the LCC of the conventional steel girder at 125 years is many times higher than that of
the A1010 steel.
Next, consider the case where the repainting time-interval is
20 years, but the discount rate is 0.03. Fig. 1(d) shows the LCC
for the girder in both steels given the repainting cost of 6, 12,
and 18 $=ft2 . This is the least frequent repainting schedule considered with the highest discount rate. It is clear that with this discount
rate and repainting schedule that the LCC of the conventional steel
girder becomes higher than that of the A1010 steel after the first
repainting and only with the two higher prices considered (12 and
18 $=ft2 ) for repainting. With the lower bound price considered for
repainting, the LCC cost of the conventional steel becomes higher
than that of the A1010 steel only after the third repainting at year
60. The curve representing this case is the lowest LCC for the
painted carbon steel girder among the cases considered. Even in
this case, the LCC of the painted carbon steel girder is higher than
that of the A1010 steel girder at year 125.
Consider the case where the repainting time-interval is 15 years,
and the discount rate is 0.03. Fig. 1(e) shows the LCC for the girder
in both steels given the repainting cost of 6, 12, and 18 $=ft2 . With
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4
14
(b)
x10
Girder
repainting at
20 yrs int
Total cost (2008$)
12
12$/ft2
Repainting cost=18$/ft
2
6
6$/ft2
4
Girder
repainting at
15 yrs int
Repainting cost=18$/ft 2
10
8
6$/ft2
6
0
25
50
75
100
0
125
0
25
(d)
4
Total cost (2008$)
Total cost (2008$)
Girder
repainting at
20 yrs int
3.5
12$/ft2
1
100
125
x10
ν = 0%
Repainting cost=18$/ft2
15
75
4
4
Girder
repainting at
10 yrs int
50
Time from construction (years)
x10
20
A1010
Conventional
Time from construction (years)
25
12$/ft2
2
A1010
Conventional
(c)
ν = 0%
4
2
0
x10
12
10
8
4
16
14
ν = 0%
Total cost (2008$)
(a)
6$/ft2
5
ν = 3%
18$/ft2
12$/ft2
3
2.5
Repainting cost=6$/ft 2
2
A1010
A1010
0
(e)
Conventional
Conventional
0
25
50
75
100
Time from construction (years)
1.5
125
(f)
4
x10
ν = 3%
12$/ft2
18$/ft2
3
Repainting cost=6$/ft2
50
75
100
ν = 3%
12$/ft2
5
4.5
18$/ft2
4
3.5
Repainting cost=6$/ft 2
A1010
2
Conventional
25
125
2.5
A1010
2
100
3
2.5
0
Girder
repainting at
10 yrs int
5.5
4
3.5
75
4
6
Total cost (2008$)
Total cost (2008$)
4.5
50
x10
6.5
Girder
repainting at
15 yrs int
25
Time from construction (years)
5
1.5
0
125
1.5
Conventional
0
Time from construction (years)
25
50
75
100
125
Time from construction (years)
Fig. 1. Change of the total cost with time given discount rate ¼ 0% and repainting interval (a) 20 years, (b) 15 years, and (c) 10 years; and given
discount rate ¼ 3% and repainting interval (d) 20 years, (e) 15 years, and (f) 10 years
this discount rate and repainting schedule, the LCC of the painted
carbon steel girder is also higher than that of the A1010 steel after
the first repainting with the two higher prices considered (12 and
18 $=ft2 ) for repainting. However, with the lower bound price
considered for repainting, the LCC cost of the painted carbon
steel becomes higher than that of the A1010 steel after the second
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(a)
x104
(b)
7
1
0.9
Monte Carlo
500,000 samples
Prrobability of (Cconv > C A1010)
Mean total cost (2008$)
6
5
4
Conventional
3
A1010
2
15 20) years
Repainting time - interval =Tri(10
10,15,20)
Repainting cost = Tri(6,12,18) $/ft 2
Discount rate of money = U(0.00,0.03)
Unit cost of conventional steel = 975 $/ton
Unit cost of A1010 steel = 2,265 $/ton
1
0
0
25
50
75
100
0.8
0.7
0.6
Monte Carlo
500,000 samples
0.5
0.4
0.3
Repainting
p
g time-interval=Tri(10,15,20)
( , , ) yyears
Repainting cost = Tri(6,12,18) $/ft2
Discount rate of money = U(0.00,0.03)
Unit cost of conventional steel = 975 $/ton
Unit cost of A1010 steel = 2,265 $/ton
0.2
0.1
125
0
0
25
Time from construction (years)
50
75
100
125
Time from construction (years)
Fig. 2. Change over time of (a) the mean total cost for the conventional steel and the A1010 unpainted steel; and (b) the probability that the cost of
conventional steel girder, C conv , is higher than the A1010 steel girder, C A1010
repainting at year 30. This is because as the repainting time t
decreases, the LCC increases [Eq. (1)].
Finally, consider the case where the repainting time-interval is
10 years, and the discount rate is 0.03. Fig. 1(f) shows the LCC for
the girder in both steels given the repainting cost of 6, 12, and
18 $=ft2 . Again, with this discount rate and repainting schedule,
the LCC of the painted carbon steel girder is also higher than that
of the A1010 steel after the first repainting with the two higher
prices considered (12 and 18 $=ft2 ) for repainting. With the lower
bound price for repainting, the LCC cost of the painted carbon steel
becomes higher than that of the A1010 steel after the second repainting at year 20.
Probabilistic Life-Cycle Analysis
In this section, the uncertainties associated with the random variables are introduced in the life-cycle analysis. To take into account
all the possible realizations of these random variables, a Monte
Carlo simulation with 500,000 samples was performed. Accordingly, 500,000 random values are generated from each random
variable according to its probability density function. A sample
comprises one of the values generated from each random variable.
For each sample, the life-cycle analysis is performed in a similar
manner to that in the previous section. Hence, 500,000 LCC profiles were generated for the statistical and probabilistic analysis. It
is noted that this simulation was only performed for the conventional painted carbon steel girder. The LCC of the A1010 steel
girder is considered deterministic and constant throughout the service life of the bridge.
To represent the simulation outcomes, several descriptors can be
used, such as the mean or quantiles. In this technical note, the mean
is considered. At each point in time, the mean from all 500,000
generated LCC profiles (at that point in time) is computed. The
result is a mean LCC profile for the conventional steel girder. This
profile is presented in Fig. 2(a). Also presented in the figure is the
LCC cost of the A1010 steel girder which is held constant over time
at the total initial cost.
Because the final objective of this technical note is a probabilistic comparison between the LCC of the girder made from both
steels, it is considered that the most appropriate approach to conduct this comparison is to study the probability that the cost of the
conventional painted carbon steel girder, C conv , is higher than the
cost of the A1010 steel girder, C A1010 . This probability is computed
as
Probability of ðC conv > C A1010 Þ
¼
number of samplesðC conv > C A1010 Þ
total number of samples
ð2Þ
and the results are shown in Fig. 2(b). According to this probabilistic analysis, the conventional painted carbon steel girder has the
lower LCC. Starting in year 10 there is some probability that the
A1010 steel girder has a lower LCC. By year 15, it is equally probable that the A1010 steel has a lower LCC. At year 20, it is 90%
probable that the lower LCC comes from using A1010 steel. After
the 40th year it becomes almost certain that the A1010 steel is
the most cost-effective. Thereafter, the LCC-effectiveness of the
A1010 steel increases over the service life of the bridge.
Conclusions
In this technical note, the computations, results, and conclusions
of an analytical investigation for comparing the LCC of a model
steel bridge girder made of a maintenance-free steel designated
by ASTM as A1010 and the LCC of the same model girder made
of conventional painted carbon steel that requires maintenance
(repainting) are represented. The feasibility of the A1010 steel
is judged on its lower LCC compared to that of conventional steel.
A deterministic analysis was conducted, where several scenarios
were considered to compute the LCC of the steel bridge girder in
both steels. The deterministic analysis shows that with the upper
bound LCC extreme case having the highest frequency of repainting (10 years interval), the lowest discount rate (0%), and the highest repainting cost ($18=ft2 ), the LCC of the conventional painted
carbon steel girder at 125 years is many times higher than that of
the A1010 steel. Also, with the lower bound extreme case having
the lowest frequency of repainting (20 years interval), the highest
discount rate (3%), and the lowest repainting cost ($6 b=ft2 ), the
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LCC cost of the conventional steel becomes higher than that of the
A1010 steel after the third repainting at year 60.
A probabilistic analysis was also conducted. It is concluded
from the results of the probabilistic analysis that the A1010 steel
is indeed cost-effective over the long run. The LCC-effectiveness
of the A1010 steel product increases over the service life of the
bridge. In fact, in this example, even so during the first 10 years
there is 0% probability that the A1010 steel girder is cheaper than
the conventional steel, it becomes almost certain that the A1010
steel girder is cheaper than the conventional steel girder after about
40 years.
Acknowledgments
The support of the U.S. Federal Highway Administration through
contract DTFH61-07-00008, “Improved Corrosion Resistant Steel
for Highway Bridge Construction”, is gratefully acknowledged.
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