Bridge load rating involves performing a series of calculations synonymous with bridge design calculations in order to ...
2007 Structures Congress: New Horizons and Better Practices
© 2007 ASCE
Comparison of Load Factor Rating (LFR) to Load and Resistance Factor Rating (LRFR) of Prestressed Concrete I - Beam Bridges
. d e v r e s e r ts h irg ll ;a y l n o se u l a n sro e p r o F . E C S A t h g ir y p o C . 3 /1 9 1 / 8 0
n o s e ir a r b i L s sa n a rk A f O tiy sr e v i n U y b g r o . y r ra ib l e c s a m o fr d e d a lo n w o D
Authors:
Lei Zheng, Tennessee Technological University,
[email protected] Xiaoming Sharon Huo, Tennessee Technological University, P.O. Box 5015, Cookeville, TN 38501, Phone: 931-372-3188, Fax: 931-372-6239,
[email protected] Rebecca P. Hayworth, Federal Highway Administration, Nashville Division Office
ABSTRACT Bridge load rating involves performing a series of calculations synonymous with bridge design calculations in order to determine if a bridge is safe for public traffic loads. The AASHTO Load Factor Rating (LFR) is the currently used method in bridge load rating. The Load and Resistance Factor Fating (LRFR) is a new guide manual adopted by the American Association of State Highway and Transportation Officials (AASHTO) in 2001 for condition evaluation of highway bridges. The guide manual reflects the most current technologies and builds on the structural reliability approach inherent in specifications for Load and Resistance Factor Design (LRFD). In this paper, seven prestressed concrete bridges of moderate span length (50 - 117 ft) are analyzed and rated using the AASHTO LFR and AASHTO LRFR methods. The selected bridges include one straight simple span Bulb Tee-girder, three skewed simple span I-girder, and three skewed continuous multi-span I-girder bridges. The comparison study for the prestressed concrete I-section bridges reveals some differences between the rating results using LFR and new LRFR methodologies. The majority of load ratings achieved using the LRFR approach for the prestressed concrete bridges are governed by shear rather than flexure, which is a substantial difference from the LFR method where flexural ratings typically govern for all bridge types.
KEYWORDS Bridges, loads, ratings, load factors
INTRODUCTION In general, load rating is the determination of the safe load carrying capacity of a bridge. The highway bridges must be inspected periodically for maintenance reasons and to ensure bridge safety to the public. Along with the visual inspection, the load-carry capacity (bridge rating) mustBeginning be evaluated determine the maximum truck for loads onBridge the structure. withtothe April 2005 data collection theallowed National Inventory (NBI), the Federal Highway Administration (FHWA) allowed the inventory rating and operating rating to be reported as a Rating Factor (RF) using either the Load Factor Rating (LFR) method or Load
New Horizons and Better Practices
2007 Structures Congress: New Horizons and Better Practices
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© 2007 ASCE
and Resistance Factor Rating (LRFR) method. Prior to this change, the LFR method was the national standard for computing inventory and operating ratings reported to the NBI. The AASHTO Manual for Condition Evaluation of Bridges (LFR) served as a standard for bridge engineers to determine the physical condition, maintenance needs, and load capacity of highway bridges that are designed with the AASHTO Standard Specifications for several years. However, LFR did not provide a uniform level of safety. With the increasing implementation of the AASHTO LRFD Specifications around the nation and as more and more bridges are designed by using the LRFD, rating these bridges using LRFR becomes an important issue. One of the most challenging tasks facing department of transportation (DOT) and engineering firms is that engineers need to have a good understanding and confidence the new In LRFR ratings whenthe bridge rating from is transited from usingasLFR method to using LRFRon method. order to make transition LFR to LRFR painless as possible, the loading procedures were designed to appear to be as extension of the current LFR method.
LRFR AND LFR LOAD RATING The basic rating equation in the AASHTO LRFR manual is: C − γ DC DC − γ DW DW ± γ P P RF = γ L LL (1 + IM )
(1)
C = φ c ϕ s φR n ; φ c φ s ≥ 0.85
(2)
Where RF is the rating factor, C is the structural capacity, R n is the nominal member resistance (as inspected), DC is the dead-load effect of structural components and attachments, DW is the dead-load effect of wearing surfaces and utilities, P is the permanent loading other than dead loads, LL is the live-load effect, IM is the dynamic load allowance, γDC is the LRFD load factor for structural components and attachments, γDW is the LRFD load factor for wearing surfaces and utilities, γP is the LRFD load factor for permanent loads other than dead loads, γL is the evaluation live-load factor, ϕc is the condition factor, ϕs is the system factor, and ϕ is the LRFD resistance factor. LRFR dead load factors are dependent on bridge type, limit state and truck model type. LRFR load factors for dead load and live loads (LL) are shown in Table 1.
Bridge Type Limit State*
Strength I Prestressed Strength II Concrete Service III Service I
Design Load 6.4.3.2.1 Legal Load Permit Load Dead Load Dead Load 6.4.4.2.1 6.4.5.4.1 Inventory Operating DC DW LL LL LL LL 1.25
1.50
1.75
1.35
Table 6-5
-
1.25
1.50
-
-
-
Table 6-6
1.00
1.00
0.8
-
1.00
-
1.00
1.00
-
-
-
1.00
TABLE 1 LIMIT STATES AND LOAD FACTORS FOR LOAD RATING (FROM LRFR TABLE 6-1)
As stated in the current AASHTO Manual for Condition Evaluation of Bridges, the general expression used in LFR calculations is:
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RF =
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C − A1 D A2 L(1 + I)
(3)
Where C is the capacity of the member, D is the dead load effect on the member, L is the live load effect on the member, I is the impact factor, A 1 is the factor for dead loads, and A 2 is the factor for live load. LFR dead load factors are the same for all bridges and analysis types. LFR live load factor depends only on rating level. LFR load factors are shown in Table 2. Rating Level
A1
A2
Inventory Operating
1.3 1.3
1.3 2.17
TABLE 2 LFR LOAD FACTORS FOR LOAD RATING
One of the biggest differences between the LRFR method and the LFR method is the design live load models used to generate the live load effect. LRFR uses the HL-93 loading, which consists of the HS20/H20 truck and 0.64 kip/ft of lane loading, while LFR uses either the HS20/H20 truck or the HS20-44/H20-44 lane loading.
SELECTED BRIDGES Seven Tennessee bridges were selected and studied in this research for the comparison of LFR and LRFR results. The bridges selected are precast prestressed concrete bridges with varied structure parameters. These parameters included the number of spans and their lengths, beam spacing, beam depth, skew angle, slab thickness, and the presence of support diaphragms. Table 3 is the details of the selected bridges.
Bridge No. 1 2 3 4 5 6 7
Bridge Name
Bridge Type
Number of Spans
Total Bridge Length (ft)
Max. Span Length (ft)
Number of Beam Lines
Beam Spacing (ft)
Skew Angle (deg)
I-Beam
1
85
85
4
6.42
50
I-Beam
1
60
60
9
8.00
15
I-Beam
3
145
48.67
10
7.88
15
I-Beam
3
156
56
5
8.83
9.56
I-Beam
2
86
43
4
8.00
30
1
117
117
5
9.5
-15
1
108
108
4
7.75
0
Old Fifteenth Road over Gulf Fork Big Creek State Route 20 over One Mile Branch Shallowford Road over Friar Branch State Route 50 over C.S.X. Railroad State Route 116 over Cage Creek S. R. 31 over Big War Creek S. R. 69 over Turnbo
Bulb-Tee Beam Bulb-Tee
Creek
Beam
TABLE 3 SEVEN SELECTED BRIDGES INFORMATION
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BRIDGE RATINGS WITH LFR PROCEDURE
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The Virtis/Opis software package was used as the analysis tool in this study. Virtis is a bridge rating program, while Opis is a bridge design program. Bridge modeling for both programs is almost identical. Virtis/Opis has a shared database, which allows the user to save a single bridge model that can be used in both programs. To get LFR rating factors, all bridges were initially modeled in the Virtis program for the acquired TDOT bridge plans. The rating results for every bridge studied include inventory rating and operating rating. The lower load rating factor obtained from truck loading or lane loading is named as critical load rating factor. Rating factor greater than one indicates that the bridge is safe for the rating load. For simple span Prestressed concrete bridges, flexural service load rating, positive moment load rating, positive shear load rating and negative shear load rating were calculated with Virtis. The serviceability rating is based on concrete tension and compression stress check. The critical load rating factors of moment strength, shear strength, and flexural service in inventory and operating ratings are used in the comparison study. For continuous span bridges, flexural service load rating, positive moment load rating, negative moment load rating, positive shear load rating and negative shear load rating are included. Again, the smaller load rating factors for moment, shear, and service under inventory and operating ratings are chosen as the critical LFR rating factors.
BRIDGE RATINGS WITH LRFR PROCEDURE Bridge rating with LRFR was conducted using Opis/Virtis design/rating software. Currently, Opis is capable of performing LRFD design, but Virtis has not been updated for LRFR rating. To obtain the LRFR rating results, a less direct approach was taken. Although load factors for LRFD and LRFR are different, both LRFD LRFR apply the same procedures for determining effects on bridges. Therefore, for a and given bridge member, LRFR and LRFD should haveload the same values for unfactored dead load effect, unfactored live load effect and resistance. Thus Opis could be used as a tool in performing LRFR calculations for HL-93 design loads. Once the bridge model was completed in Virtis, the model was opened in Opis using the shared database. Some additional fields required completion in Opis such as LRFR/LRFD live load distribution factors. Then, the bridge models could be analyzed in Opis program. The values unfactored dead load effect, unfactored live load effect and resistance for each bridge were determined from the Opis run. Finally, a LRFR rating factor could be determined by entering these values into the LRFR load rating equation.
RESULTS AND DISCUSSION The LRFR and LFR rating results for flexure, shear and serviceability are given in this section. The controlling load ratings are presented for Inventory and Operating conditions separately. LFR Rating Results
The LFR control rating results were listed in Table 4. In general, the LFR load ratings for simple span I-beam prestressed concrete bridges are governed by flexural service in inventory level and
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2007 Structures Congress: New Horizons and Better Practices
© 2007 ASCE
by shear and moment strengths in operating level. The rating factors for continues spans are controlled by shear strength rather than moment strength in both inventory and operating level. Bridge No. . d e v r e s e r ts h irg ll ;a y l n o se u l a n sro e p r o F . E C S A t h g ir y p o C . 3 /1 9 1 / 8 0
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1 2 3 4 5
Rating Factor 1.17 1.12 1.04 0.51 1.35
6 7
0.92 1.2
Inventory Limit State Service Service Shear Shear Shear Service Service
Girder Interior Interior Interior Interior Interior
Rating Factor 2.4 2.14 1.74 0.87 2.25
Interior Interior
2.3 2.04
Operating Limit State Moment Shear Shear Shear Shear Shear Shear
Girder Interior Interior Interior Interior Interior Interior Interior
TABLE 4 CONTROL LFR RATING FACTORS
LRFR Rating Results
The LRFR control rating results were listed in Table 5. At inventory level, all the simple span prestressed concrete bridges were governed by flexural service. For the three continuous bridges, two of them were governed by moment strength and one by shear strength. At operating level, four of seven bridges were governed by moment strength at exterior girder while the rest three by shear strength at interior girder. Bridge No.
1 2 3 4 5 6 7
Rating Factor 1.063 0.723 1.41 1.022 1.582 0.769 1.028
Inventory Limit State Service Service Moment Moment Shear Service Service
Girder Exteriors Exteriors Exteriors Exteriors Interiors Exteriors Exteriors
Rating Factor 1.5 1.374 1.827 1.324 20.51 1.445 1.636
Operating Limit State Shear Moment Moment Moment Shear Shear Moment
Girder Interiors Exteriors Exteriors Exteriors Interiors Interiors Exteriors
TABLE 5 CONTROL LRFR RATING FACTORS
Comparison of LRFR and LFR
The comparison of Table 4 with Table 5 showed that most of the LRFR controlling ratings appeared at exterior beams while most of the LFR controlling ratings existed at interior beams. This distinction is mainly due to the differences of live load moment distribution factors between LRFR procedure and LFR procedure. It appears that LRFR produces larger live load moment distributions on exterior beams than LFR. Figure 1 and Figure 2 illustrate the LFR and LRFR rating factors for moment strength in inventory and operating level, respectively. The rating results from LRFR and LFR procedures were very similar. The difference between the two sets of rating results is around 10% or less.
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2007 Structures Congress: New Horizons and Better Practices
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However, the moment strength ratings for exterior beam showed that LFR load rating factors were significantly higher than that of HL-93 LRFR at both inventory and operating level. At inventory, LFR for the moment ratings of exterior beams were 17.04% - 57.50% higher than that of LRFR. At operating, Rating factors of LFR were 50.86% - 96.66% higher than that of LRFR. One explanation to the discrepancy is the specified design loads in the two procedures are quite different. The larger design live load and larger live load distribution factor for exterior beams seem to have larger impacts on the rating results of exterior beams. 2
2.5 LRFR
LRFR
LFR r
to c a F g in t a R
LFR
2
1.5
r o tc a 1.5 F g in t 1 a R
1
0.5
0.5 0
0
1234567
1234567
Bridge Number
Bridge Number
(a) for Interior Beam
(b) for Exterior Beam
FIGURE 1 RATING FACTORS FOR MOMENT AT INVENTORY LEVEL 3.5
4 LRFR
3
LRFR
3.5
LFR r o t
r 2.5 o t c a 2 F g n 1.5 ti a R 1
LFR
3
c 2.5 a F g 2 in t a 1.5 R
1
0.5
0.5 0
0
1234567
1234567
Bridge Number
Bridge Number
(a) for Interior Beam
(b) for Exterior Beam
FIGURE 2 RATING FACTORS FOR MOMENT AT OPERATING LEVEL
Figure 3 and Figure 4 show the comparison of the LFR and LRFR rating factors for shear strength in inventory and operating level, respectively. The results for shear strength ratings of exterior beams were more widely scattered than those for moment. For the three continuous span bridges and one of the four simple span bridges, shear rating factors for LRFR were higher than that of LFR, the differences scattered from 22% to 54% at inventory and from 0.22% to 40.28% at operating level. For the rest of the three simple span bridges, shear rating factors for LFR were higher than that of LRFR, the difference between LRFR and LFR were from 26% to
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39% at inventory level and from 56.23% to 85.81% at operating level. There could be several reasons for the scattering, such as live load effect and shear resistance. The LRFR design live load and load factors are quite different with the ones in LFR, which would contribute the discrepancy in comparison. In addition, the LRFR employs a new shear design approach for prestressed concrete members. The new shear strength could directly affect the rating results with LRFR. . d e v r e s e r ts h irg ll ;a y l n o se u l a n sro e p r o F . E C S A t h g ir y p o C . 3 /1 9 1 / 8 0
n o s e ir a r b i L s sa n a rk A f O tiy sr e v i n U y b g r o . y r ra ib l e c s a m o fr d e d a lo n w o D
2.5
3 LRFR
LRFR
2
2.5
LFR
r to c a F1.5 g n ti 1 a R
LFR
r o t 2 c a F g1.5 n ti a 1 R
0.5
0.5 0
0
1234567
1234567 Bridge Number
Bridge Number
(a) for Interior Beam
(b) for Exterior Beam
FIGURE 3 RATING FACTORS FOR SHEAR AT INVENTORY LEVEL 3.5
3.5 LRFR
LRFR
3
3
LFR
r 2.5 to c a
r 2.5 to c a
F g 2 n it 1.5 a R 1
F 2 g n ti 1.5 a R 1
0.5
0.5
0
LFR
0 1234567
1234567 Bridge Number
Bridge Number
a) for Interior Beam
(b) for Exterior Beam
FIGURE 4 RATING FACTORS FOR SHEAR AT OPERATING LEVEL
It has been observed that the difference between LFR and LRFR strength ratings at inventory level were smaller than that at operating level. For example, for bridge #1, the difference between LFR and LRFR moment strength rating was 17% at inventory level while the difference became 50% at operating level. This difference is attributed to the live load factors used in LRFR and LFR procedures. The live load factors in Inventory for LRFR and LFR are 1.35 and 1.3, respectively, and the live load factor in operating for LRFR and LFR are 1.75 and 2.17, respectively. As shown, the live load factors in inventory for both procedures are very close, but
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the interval between the load factors in operating for LRFR and LFR is much larger. This larger interval leads to a larger difference between the rating factors at operating level. Figure 5 illustrates the LFR and LRFR rating factors for service at inventory level. The results for flexure service at inventory level showed the similar trends as that of moment strength. LFR load rating factors were from 20.62% to 70.12% higher than that of LRFR. . d e v r e s e r ts h irg ll ;a y l n o se u l a n sro e p r o F . E C S A t h g ir y p o C . 3 /1 9 1 / 8 0
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2.5
3.5 LRFR
2
LRFR
3
LFR
r o t c a1.5 F
r 2.5 o t c
g n it a R
g n 1.5 ti a R 1
a F
1
0.5
LFR
2
0.5
0
0 1234567
1234567 Bridge Number
Bridge Number
a) for Interior Beam
(b) for Exterior Beam
FIGURE 5 RATING FACTORS FOR SERVICE AT INVENTORY LEVEL
No other trends were found when comparing LRFR to LFR design ratings. This can be expected because the LFR procedures were not calibrated and designed for uniform reliability in the same manner that the LRFR procedures are. As made evident in the development of LRFD, the comparison of a calibrated code versus an uncalibrated code generally produces scattered results.
CONCLUSIONS: Seven Tennessee bridges were selected and studied in this research for the comparison of LFR and LRFR. Ratings on moment and shear strength were performed in inventory and operating levels and rating for serviceability was performed only in inventory level. The rating results were presented separately for flexure strength, shear strength and serviceability. Based on results of the seven prestressed concrete I beam bridges, the following conclusions can be drawn: • Most of the LRFR critical ratings appeared at exterior beams while most of the LFR critical ratings existed at interior beams. The distinction is mainly due to LRFR utilizes a larger distribution factor on live load moment for exterior girders than the LFR procedure. • The results for moment strength showed that LFR load rating factors were higher than that of LRFR at both inventory and operating levels. The ratings for shear strength were more widely scattered than those for moment with some LRFR ratings are higher and some LFR ratings are higher. The results for flexure service at inventory level showed that LFR load rating factors were higher than that of HL-93 LRFR. •
The difference between LFR and LRFR strength ratings at inventory level were smaller than that at operating level. This difference is attributed to the different live load factors used in LRFR and LFR procedures.
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REFERENCES [1]
American Association of State Highway and Transportation Officials. AASHTO LRFD Bridge Specifications. 3nd Ed. Washington, D.C: AASHTO, 2004.
Design
[2] American Association of State Highway and Transportation Officials, Manual for Condition Evaluation and Load and Resistance Factor Rating (LRFR) of Highway Bridges, Washington, D.C: AASHTO, 2003. . d e v r e s e r ts h irg ll ;a y l n o se u l a n sro e p r o F . E C S A t h g ir y p o C . 3 /1 9 1 / 8 0
[3] Jaramilla, B., Huo, S., "Looking to Load and Resistance Factor Rating", Public Roads, Vol. 69, No 1, July/August 2005, p 58-65. [4] Mertz, D. R. “Load Rating By Load and Resistance Factor Evaluation Method” June 2004. [5] Minervino, C., Sivakumar, B., Moses, F., Mertz, M., and Edberg, W., "New AASHTO Guide Manual for Load and Resistance Factor Rating of Highway Bridges", Journal of Bridge Engineering, Vol. 9, No. 1, January 2004: p 43-54. [6] Rogers, B. J., Jauregui, D. V., "Load rating of prestressed concrete girder bridges comparative analysis of load factor rating and load and resistance factor rating", Transportation Research Record, n 1928, Design of Structures 2005, 2005, p 53-63. [7] Moses, F. “Calibration of Load Factors for LRFR Bridge Evaluation, NCHRP Report No. 454” Transportation Research Board, 2001.
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