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Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations
REPORT 
This report is an archived publication and may contain dated technical, contact, and link information 

Publication Number: FHWAHRT11062 Date: November 2011 
Publication Number: FHWAHRT11062 Date: November 2011 
This chapter presents the computations performed and conclusions made with respect to an LCC analysis for unpainted corrosionresistant steel to be used in environments with high salt concentrations. As reported in chapters 3 and 4 of this report, ASTM A1010 steel is the only candidate in lieu of ASTM A588 weathering steel. The efforts to develop a steel cheaper than ASTM A1010 failed because the combination of strength and impact toughness required for fabrication of steel bridge members could not be achieved with the experimental Cr steels, although they were more corrosion resistant than ASTM A588 steel. Because ASTM A588 and other weathering steels do not develop a protective rust patina in the presence of high salt exposure, for those service environments, bridges made from weathering steels (or ASTM A36 carbon steel) must be painted and maintained by repainting at certain intervals. Its excellent corrosion resistance makes ASTM A1010 able to last in structures for long periods of time (100 to 125 years, as considered in this study) without the need for initial painting or maintenance (i.e., repainting). Accordingly, the feasibility of ASTM A1010 is gauged on its lower LCC compared to that of conventional painted bridge steel.
The approach taken in this study was to compare the LCC of a steel bridge component made of ASTM A1010 steel (maintenancefree) and the LCC of a steel bridge component made of conventional painted steel with maintenance (repainting). Computation of LCC for both cases was performed deterministically and by probabilistic procedures. The latter method takes into consideration the uncertainty of future cost components such as the repainting frequency and the associated maintenance cost elements.
The market price of steel is given in U.S. dollars per ton of steel. Steel prices are notoriously volatile, so performing a 125year cost analysis may be profoundly affected by the prices in effect at the time of bridge construction. To identify whether or not steel prices follow a longterm trend, either up or down in real terms, an analysis of the price of steel for the last 100 years was conducted. The analysis was based in large part on historical prices as reported by the United States Geological Survey (USGS). The USGS values for the average annual U.S. domestic steel price are the best estimate of the average price paid for conventional steel plate used in bridge construction over the years. It was concluded that $976 per 1 T (0.907 Mg) (in 2008 dollars) should be used as representative of the longterm average for conventional carbon or weathering bridge steel plate. This is the average from 1957 to 2007. The standard deviation of the cost of conventional steel is $167 per 1 T (0.907 Mg) (in 2008 dollars).
For estimating the price of ASTM A1010, a representative historical price was $1,300 per 1 T (0.907 Mg) (in 1998 dollars) higher for ASTM A1010 than for weathering steel plate. Accordingly, the unit cost of the ASTM A1010 steel used in the LCC analyses was $2,276 per 1 T (0.907 Mg) (in 2008 dollars).
To determine the cost of transforming the raw steel plate into a bridge girder, High Steel Structures, Inc. estimated that the 2008 price of a typical steel girder varied from $1.50 to $1.55 per 1 lb (0.454 kg). This includes fabrication, initial painting, shop inspection, and transportation. Use of weathering steel (unpainted) reduces this cost by about 5 percent. For purposes of this LCC analysis, the total delivered cost for a finished conventional steel girder was fixed at $1.525 per 1 lb (0.454 kg) (in 2008 dollars).
It was assumed that no girder replacements would be performed as part of the maintenance procedures. Maintenance consists only of repainting. The cost of repainting depends on the environment and different associated costs such as old paint removal, new paint application, cost of bridge closure during maintenance, and others. These costs were estimated by High Steel Structures, Inc., to be between 5 and 25 percent of the $1.525 per 1 T (0.907 Mg) total cost of a new girder.
For the probabilistic LCC analysis, a triangular distribution was assumed for all variable model inputs. The years from bridge fabrication to the first time of painting and the time interval between subsequent painting intervals was assumed to be a triangular distribution with a minimum repainting interval of 10 years, a mean of 15 years, and a maximum of 20 years. The designation Tri(10,15,20) represents these assumptions in the model. These values are thought to be realistic for the very high chloride service environments contemplated for the ASTM A1010 steel.
The cost for repainting of bridge girders was estimated by KTATator, Inc. as $12 per 1 ft^{2} (0.093 m^{2}). For the probabilistic LCC, this cost is treated as a triangular distribution with a lower limit of $6 per 1 ft^{2} (0.093 m^{2}), the most probable value of $12 per 1 ft^{2} (0.093 m^{2}), and an upper limit of $18 per 1 ft^{2} (0.093 m^{2}). The discount rate was assigned a uniform distribution with a range of 0 to 3 percent.
Computations of the LCC were conducted for an example bridge girder in figure 37. This 80ft (24.4m)long girder is from a bridge in Wisconsin carrying US51 and I39 over the Wisconsin River. The girder is composed of three plates: a top flange plate that is 12 x 0.5 inches (304.8 x 12.7 mm), a bottom flange plate that is 15 x 0.75 inches (381 x 19.05 mm), and a web plate that is 52 x 0.375 inches (1,320.8 x 9.53 mm).
Figure 37. Illustration. Example bridge girder 80 ft (24.4 m) long.
In performing the deterministic LCC, the variables presented in the previous section were treated deterministically in different scenarios, wherein each scenario employed a limit value for each variable. The random variables considered were the repainting timeinterval Tri(10,15,20) years, the repainting cost Tri(6,12,18) $/ft^{2}, and the discount rate of money U(0.00,0.03). For example, one combination would be having a repainting time interval of 10 years with a repainting cost of $6 per 1 ft^{2} (0.093 m^{2}) and a discount rate of 0.03.
The lifecycle computations are summarized in table 20. The girder weight was calculated to be 10,007 lb (4,543.18 kg), or 5.0035 T (4.5382 Mg). Thus, the steel cost for the model girders made from carbon steel and ASTM A1010 steel are $4,424.90 and $10,279.00, respectively.
The total fabricated cost of a new carbon steel girder, including the cost of the steel, is $1.525 per 1 lb (0.454 kg) times the weight, or $15,261. The total fabricated cost for a conventional painted girder should be reduced by 5 percent in the case of an unpainted girder (since there would be no costs associated with painting), and this would apply to an ASTM A1010 girder. Therefore, the shop fabrication costs (i.e., costs of welding, inspection, and transportation) for the ASTM A1010 steel would be estimated as ($15,261 x 0.95)  $4,424.90 = $10,073. The final cost of the ASTM A1010 steel model girder would be given by $10,279 + $10,073 = $20,352.
Table 20. Total model girder initial costs.
Cost 
Unit 
Assumption 
Carbon Steel 
ASTM A1010 Steel 
Unit cost 
$ per ton 

976 
2265 
Girder weight 
Pounds 

10,007 
10,007 
Girder weight 
Tons 

4.5384 
4.5384 
Steel cost 
$ 

$4,424.90 
$10,279 
Fabricated painted girder cost 
$/lb 
$1.525 x weight 
$15,261 

Fabricated unpainted girder cost 
$/lb 
0.95 x $1.525 x weight 

$14,497.64 
Less carbon steel cost 
$ 


$4,424.90 
Plus ASTM A1010 steel cost 
$ 


$10,279 
Fabricated unpainted ASTM A1010 girder cost 
$ 


$20,352 
1 lb = 0.454 kg 1 T = 0.907 Mg Note: Empty cells are not relevant for the model calculations. 
The total cost for the ASTM A1010 steel is constant throughout the service life of the girder. LCC assumes that ASTM A1010 steel is maintenancefree. Therefore, throughout the life of the bridge, there will be no additional costs required related to the structural steel. In contrast, the total cost for the painted steel is constant only until the first repainting. Each time a repainting is performed, its cost must be added to determine the total running cost.
The repainting cost is calculated based on the steel surface area, which was determined for the model girder as 985 ft^{2} (91.61 m^{2}). Hence, the cost of repainting the model girder is Tri(6,12,18) $/ft^{2} x 985 ft^{2} = Tri(5,910, 11,820, 17,730)$.
The cost of repainting is also subject to a discount rate at each application time, t. The present cost of the kth repainting of the girder at t is as follows:
Where:
(C_{pv})_{k} = Present value of cost for the kth repainting of the girder.
C = Cost of repainting at time of application.
ν = Discount rate of money.
t = Time of application of the kth repainting.
Hence, at time t, the cumulative LCC of the conventional steel girder is computed as follows:
Where:
LCC(T) = Cumulative LCC of the conventional steel girder at time t.
C_{i} = Initial total cost (i.e., $15,261).
n = Number of repaintings performed until time n(t).
Consider the case where the repainting time interval is 20 years and the discount rate is 0 percent. Figure 38 shows the LCC for girders of both steels given the repainting cost of $6, $12, and $18 per 1 ft^{2} (0.093 m^{2}). It is clear that with this discount rate and repainting schedule, LCC of the painted carbon steel girder becomes higher than that of the ASTM A1010 steel after the first repainting, even with the lowest price considered for repainting. At 125 years, the LCC penalty for the painted carbon steel girder is between $30,000 and $100,000.
Figure 38. Graph. Change of the total cost with time assuming a repainting interval of 20 years and a discount rate of 0 percent.
Consider the case where the repainting time interval is 15 years and the discount rate is 0 percent. Figure 39 shows LCC for both girders given the repainting cost of $6, $12, and $18 per 1 ft^{2} (0.093 m^{2}). At 125 years, the LCC advantage of the ASTM A1010 girder is even larger. The cost advantage of the ASTM A1010 steel increases as the number of repaintings increases.
Figure 39. Graph. Change of the total cost with time assuming a repainting interval of 15 years and a discount rate of 0 percent.
Consider the case where the repainting time interval is 10 years, and the discount rate is 0 percent. Figure 40 shows LCC for a model girder of both steels given the repainting cost of $6, $12, and $18 per 1 ft^{2} (0.093 m^{2}). This is the most frequent repainting schedule considered. The curve representing the repainting cost of $18 per 1 ft^{2} (0.093 m^{2}) is the highest LCC among the cases considered. With this extreme case, the LCC of the painted carbon steel girder at 125 years is $225,000 compared to a LCC of $20,352 for a girder made from ASTM A1010.
Figure 40. Graph. Change of the total cost with time assuming a repainting interval of 10 years and a discount rate of 0 percent.
Consider the case where the repainting time interval is 20 years but the discount rate is 0.03 percent. Figure 41 shows LCC for girders of both steels given the repainting cost of $6, $12, and $18 per 1 ft^{2} (0.093 m^{2}). This is the least frequent repainting schedule considered. Under these assumptions, LCC of the painted carbon steel girder becomes higher than that of the ASTM A1010 steel after the first repainting only for the two higher prices considered ($12 and $18 per 1 ft^{2} (0.093 m^{2})) for repainting. With the lower bound price considered for repainting, the LCC cost of the carbon steel becomes higher than that of the ASTM A1010 steel only after the third repainting at year 60. The curve representing this case is the lowest LCC among the cases considered. LCC of the painted carbon steel girder is $22,000 compared to $20,352 for the ASTM A1010 steel girder at year 125.
Figure 41. Graph. Change of the total cost with time assuming a repainting interval of 20 years and a discount rate of 3 percent.
Consider the case where the repainting time interval is 15 years and the discount rate is 3 percent. Figure 42 shows LCC for the two girders assuming repainting costs of $6, $12, and $18 per 1 ft^{2} (0.093 m^{2}). With this discount rate and repainting schedule, LCC of the painted carbon steel girder also becomes higher than that of the ASTM A1010 steel after the first repainting only with the two higher prices considered ($12 and $18 per 1 ft^{2} (0.093 m^{2})) for repainting. However, with the lower bound price considered for repainting, the LCC cost of the carbon steel becomes higher than that of the ASTM A1010 steel after the second repainting at year 30. This is because as the repainting time t decreases, LCC increases (see equation 1).
Figure 42. Graph. Change of total cost with time assuming a repainting every 15 years and a discount rate of 3 percent.
Finally, consider the case where the repainting time interval is 10 years, and the discount rate is 3 percent. Figure 43 shows LCC for the painted carbon steel girder and the ASTM A1010 girder, given the repainting cost of $6, $12, and $18 per 1 ft^{2} (0.093 m^{2}). Again, with this discount rate and repainting schedule, LCC of the carbon steel girder also becomes higher than that of the ASTM A1010 steel after the first repainting, with the two higher prices considered ($12 and $18 per 1 ft^{2} (0.093 m^{2})) for repainting. In the case of the lowerbound price for repainting, the LCC cost of the conventional steel becomes higher than that of the ASTM A1010 steel after the second repainting at year 20. After 125 years, the total cost of the ASTM A1010 girder remains $20,352, while the painted carbon steel girder ranges between $31,000 and $64,000.
Figure 43. Graph. Change of the total cost with time assuming a repainting interval of 10 years and a discount rate of 3 percent.
The uncertainties associated with the variables of repainting interval, repainting cost, and discount rate are introduced in the LCC analysis by employing a probabilistic analysis. To take into account all the possible realizations of these variables, a Monte Carlo simulation with 500,000 samples was performed. In this approach, 500,000 values were generated for 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 LCC analysis was performed in a similar manner to that in the previous section. As a result, 500,000 LCC profiles were generated. It should be noted that this simulation was performed only for the painted steel girder because LCC of the ASTM A1010 steel girder was 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 quintiles. In this study, the mean was considered. At each point in time, the mean from all 500,000 generated LCC profiles (at that point in time) was computed. The result was a mean LCC profile for the painted carbon steel girder. This profile is presented in figure 44. Also presented in the figure is the LCC cost of the ASTM A1010 steel girder, which is the total initial $20,352 cost constant over time.
Figure 44. Graph. Change of the mean total cost with time for the conventional painted carbon steel girder and the unpainted ASTM A1010 steel girder.
A probabilistic comparison between LCC of the model girder fabricated from both steels is based on the probability in a particular year of service that the cost of the conventional painted steel girder, C_{conv}, is higher than the cost of the ASTM A1010 steel girder, C_{A1010}. This probability is computed in equation 3, and the results are shown in figure 45.
Using this probabilistic analysis, during the first 10 years, there is 0 percent probability that the ASTM A1010 steel girder is cheaper than the conventional painted steel. However, starting in about year 12, the probability that the ASTM A1010 steel girder is cheaper increases rapidly, and the 50 percent probability occurs at year 15. By the 20th year of service, the probability is over 90 percent that the ASTM A1010 steel girder is cheaper, and it becomes almost certain that the ASTM A1010 steel girder is cheaper than the conventional steel after 40 years.
Figure 45. Graph. Probability that C_{conv} is higher than C_{A1010} with time.
The LCC analysis presented above is based on the best estimates of costs and paint longevity for a severe local environment as of 2010. Actual data should be used by fabricators and State transportation departments to determine LCCs for specific bridge locations and conditions. The methodology described above is recommended for comparing the LCCs of using a maintenancefree (no girder repainting) steel for a plate girder bridge. Note that costs associated with maintenance closures are not included in this approach, so this methodology is considered to be conservative.