Comparision Betn Euro Code ,Spain Code and AASHTO

8th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability PMC2000-308

Nowak, Park and Casas 1

RELIABILITY ANALYSIS OF PRESTRESSED CONCRETE BRIDGE GIRDERS: COMPARISON OF EUROCODE, SPANISH NORMA IAP AND AASHTO LRFD

A. S. Nowak, F. ASCE University of Michigan, Ann Arbor, MI 48109-2125

[email protected]

Chan-Hee Park YonseiUniversity, Seoul, Korea

[email protected]

J.R. Casas University of Catalonia, Barcelona, Spain

[email protected]

Abstract

The objective of this paper is to compare the reliability level of prestressed concrete bridge girders designed using three codes: Spanish Norma IAP-98 (1998), ENV 1991-3 Eurocode 1 (1994), and AASHTO LRFD (1998). Typical precast girders used in Spain are considered. Load and resistance parameters are treated as random variables. The statistical parameters are based on the available literature, test data and load surveys. Reliability indices are calculated by iterations. The results indicate that Eurocode is more conservative than the other two codes, and AASHTO LRFD is the most permissive code.

Intro duction

Recently, a considerable research effort has been devoted to bridge design and evaluation in Europe and in North America. However, the work has been carried out independently according to region-specific conditions. This study focuses on the comparison of the design codes for prestressed concrete bridge girders. The considered codes are: Spanish Norma IAP-98, Eurocode ENV 1991-3, and AASHTO LRFD. Five prestressed concrete bridges are selected. The structures were designed with typical Spanish precast concrete girders. Spans vary from 20m to 40m and girder spacing varies from 1.3m to 3.4m. For comparison, three versions of the selected structures are considered, with the load carrying capacity determined by the amount of prestressing strands according to Norma IAP-98, ENV 1991-3 and AASHTO LRFD 1994. The comparison criterion is structural reliability. Load and resistance are treated as random variables. The statistical models are based on the available literature. Ultimate limit state of flexural capacity (bending moment) is considered in this study. It should be noted that the serviceability limit state (tension stress in concrete) usually governs the design of prestressed concrete bridge girders.

mailto:[email protected]




Load Model The major load components for highway bridges are dead load, live load, dynamic load, environmental loads (temperature, wind, earthquake), and other loads (collision, braking). In this study, only the first three are considered. The load models are based on the available statistical data, surveys, inspection reports, and analytical simulations. The load variation is described by cumulative distribution function (CDF), mean value or bias factor (ratio of mean to nominal value), and coefficient of variation. Dead load is the gravity load due to the self-weight of structural and non-structural elements permanently connected to the bridge. Three components are considered: D1 = dead load due to factory made elements (precast concrete), D2 = dead load due to cast-in-place materials (concrete slab), and D3 = dead load due to asphalt overlay. All components of dead load are treated as normal random variables. The bias factor (ratio of mean to nominal), λ = 1.03, and coefficient of variation, V = 0.08, for D1, and λ = 1.05 and V = 0.10 for D2 (Nowak 1993). For asphalt wearing surface it is assumed that the mean thickness is 80mm and V = 0.30. Live load covers a range of forces produced by vehicles moving on the bridge. Truck surveys indicate that it is strongly site-specific, from geographical region to region, and even within a region. Both static and dynamic effects of live load are considered in this study. Effect of live load depends on many parameters including the span length, truck weight, axle loads, axle configuration, position of the vehicle on the bridge (transverse and longitudinal), number of vehicles on the bridge (multiple presence), girder spacing, and stiffness of structural members. There are considerable differences in the design values of live load specified by the three codes considered in this study. In the Spanish Code, the design live load consists of three axles of 200 kN each, superimposed with a uniform load of 4 kN/m2. The design dynamic load is specified as equal to 15% of the static live load. The design live load in Eurocode includes static and dynamic components. AASHTO specifies HL-93 loading which consists of a three axle truck superimposed with a uniform lane load of 9.3 kN/m. Dynamic load is specified as 0.33 of the truck load only, with no dynamic load applied to the lane load. AASHTO also specifies the girder distribution factor (GDF). For moments, GDF is a function of girder spacing, span length and stiffness of the girder,

GDF = 0.075 +

S2900

0.6SL

0.2 Kg

Lts3

0.1

(1)

where S = girder spacing (mm), L = span length (mm), ts = thickness of slab (mm), and Kg = stiffness parameter.


Lane moments due to live load and dynamic load were calculated for the considered three codes, and each value was multiplied by the corresponding live load factor, which is 1.50 for the Spanish Code, 1.35 for Eurocode, and 1.75 for AASHTO. The values of design live load moments per girder were also calculated according to the considered three codes. Each value corresponds to live load moment per lane (lane width is 3.6 m) and it is normalized by AASHTO design live load. The live load factors are included (1.35 for ENV 1991-3, 1.50 for IAP-98 and 1.75 for AASHTO. The statistical model for live load was derived using the approach developed by Nowak (1993), Nowak and Hong (1991) and Park at al. (1998). Extreme load effects are calculated for a one year period. It is assumed that the mean maximum annual live load follows the extreme type I (Gumbell) distribution. The truck data base was taken from the available literature and actual field surveys. The live load model in Spain is based on analytical simulations of the traffic (Crespo and Casas 1997). Two levels of traffic density were considered, a high volume traffic with an average daily truck traffic (ADTT) of 6,000 trucks per day (two lanes and one direction) and a low volume traffic with ADTT of 2,000 trucks per day. The live load model for AASHTO was based on the truck survey in Ontario, Canada (Nowak 1994). The cumulative distribution functions (CDF) of the gross vehicle weight (GVW) were prepared for the Spanish and Ontario traffic. For each surveyed truck, the maximum lane moment was calculated using influence lines, for simple span bridges with spans from 20m through 40m. The CDF of moments were extrapolated to obtain the statistical parameters (the means) of the maximum live load effect for extended periods of time for Ontario and Spanish trucks. The corresponding bias factors for the maximum annual lane moment were calculated and the nominal (design) live load is taken as specified by the AASHTO. The uncertainty in bridge analysis and girder distribution factor is expressed in terms of a bias factor, λ, and coefficient of variation, V. Field measurements indicate that the actual load distribution is more uniform than what can be analytically predicted. For girder ��

girder distribution factors based on more sophisticated methods, (e.g., finite elements and !�� "�� # �� $� %� �� !��

distribution factor can be treated as a normal random variable (Kim and Nowak 1997) and (Kim 1996). The dynamic load, I, can be measured in terms of dynamic load factor (DLF), e.g. as the ratio of dynamic strain and static strain (or deflection). DLF is a function of three parameters: road surface roughness, bridge dynamics and vehicle dynamics (suspension system). The statistical parameters for the dynamic load model were derived analytically in (Hwang and Nowak 1991) and then they were confirmed by field tests in (Nassif and Nowak 1995) and (Kim and Nowak 1997). It was observed that DLF decreases for heavy vehicles. The mean DLF is 0.15 for a single truck and 0.10 for two side-by-side trucks. The coefficient of variation is 0.80.


Resistance Model Resistance is a variable representing the load carrying capacity. Resistance can be affected by uncertainties in strength of materials, dimensions and analysis. For prestressed concrete girders, the statistical parameters were derived by Nowak, Yamani and Tabsh (1994), � ��&��$&�%�� !��variable. The minimum required resistance, Rmin, is defined by each design code, and, for given loads, D, L and I, and load and resistance factors, it can be calculated from the design formula, Rmin = [αD D +αL�'()�*+� (2) where αD is dead load factor, αL��,�� Values of load and resistance factors specified in the considered codes are given in Table 1. Table 1. Load and Resistance Factors Load & Resistance Spanish Eurocode AASHTO Factors .D1 1.35 1.35 1.25 .D2 1.35 1.35 1.25 .D3 1.35 1.35 1.50 .L 1.50 1.35 1.75 3 0.88 0.88 1.00

Reliability Analysis Reliability analysis is performed for prestressed concrete bridge girders designed � ��!�� -��.��"��/��

a function of probability of failure, PF , (Melchers 1987 and Thoft-Christensen 1982), ��– Φ-1(PF) (3) where, Φ-1 is inverse standard normal distribution function. An iterative procedure is used to calculate the reliability index as described by Rackwitz and Fiessler (1978) and Nowak (1995). Live load is the most site-specific variable. For


comparison, the computations were carried out for the live load models based on the Spanish data and Ontario truck surveys. The bias factor for the maximum annual live load was calculated with the coefficient of variation of 0.18. Finally, reliability indices corresponding to the considered codes are plotted in Fig.1, with AASHTO live load model based on the Ontario data, Spanish Code and Eurocode based on the Spanish data.

0

1

2

3

4

5

6

7

8

9

0 10 20 30 40 50

Simple Span Moment

Euro-codeSpainUS-LRFD

Rel

iabilit

y In

dex

, β

Span (m)

Figure 1. Reliabili ty Indices for Region Speci fic Truck Tr affic. Conclusions The reliability analysis is performed for prestressed concrete bridge girders designed according to three codes: Spanish Norma IAP-98, Eurocode and AASHTO. The load and resistance parameters are treated as random variables, and the statistical parameters are taken from the available literature, test data and survey results. The calculated reliability indices vary considerably for the three considered codes. It is clear that Eurocode is the most conservative one, and AASHTO is the most permissive ��.�� ,�� " ��/��$��-#�� &��-6.8 ��0��-��1�&-4.9 for AASHTO. For the Eurocode and Spanish Code, the ��!�� ,�� &�� !��

AASHTO provides the most uniform reliability level. Ackn owled gments The research presented in this paper has been partially sponsored by the NATO Cooperative Research Program, which is gratefully acknowledged.


References AASHTO LRFD Bridge Design Specifications. American Association of State Highway and

Transportation Officials, Washington, DC, 1998. Casas, J., “Are Prestressed Highway Bridges Safe?”, IABSE Structural Engineer International, in print. Crespo, C. and Casas, J.R., “A Comprehensive Traffic Load Model for Bridge Safety Checking”,

Structural Safety, Vol. 19, No. 4, 1997, pp. 339-359. ENV 1991-3 Eurocode 1: Basis of Design and Actions on Structures. Part 3: Traffic Loads on Bridges.

Final draft – August 1994. Hwang, E-S. and Nowak, A.S., "Simulation of Dynamic Load for Bridges", ASCE Journal of Structural

Engineering, Vol. 117, No. 5, (1991) pp. 1413-1434. Kim, S-J. and Nowak, A.S., “Load Distribution and Impact Factors for I-Girder Bridges”, ASCE Journal of

Bridge Engineering, Vol. 2, No. 3, August 1997, pp. 97-104. Kim, S-J., “Bridge Evaluation Based on Field Measurements”, Doctoral Dissertation, University of

Michigan, December 1996. Melchers, R.E., “Structural Reliability Analysis and Prediction”, Ellis Horwood Limited, John Wiley &

Sons, New York, 1987. Nassif, H. and Nowak, A.S., 1995, "Dynamic Load Spectra for Girder Bridges", Transportation Research

Record, No. 1476, pp. 69-83. Norma IAP-98, “Actions in Highway Bridges”, Road Directorate, Spanish Ministry of Public Works,

Madrid, 1998. Nowak, A.S. and Hong, Y-K., "Bridge Live Load Models", ASCE Journal of Structural Engineering, Vol.

117, No. 9, (1991) pp. 2757-2767. Nowak, A.S., 1993, "Live Load Model for Highway Bridges", Journal of Structural Safety, Vol. 13, Nos.

1+2, December, pp. 53-66. Nowak, A.S., 1994, "Load Model for Bridge Design Code", Canadian Journal of Civil Engineering, Vol.

21, pp. 36-49. Nowak, A.S., 1995, "Calibration of LRFD Bridge Code", ASCE Journal of Structural Engineering, Vol.

121, No. 8, pp. 1245-1251. Nowak, A.S., Yamani, A.S. and Tabsh, S.W., 1994, "Probabilistic Models for Resistance of Concrete

Bridge Girders", ACI Structural Journal, Vol. 91, No. 3, pp. 269-276. Park, C.H., Nowak, A.S., Das, P.C. and Flint, A.R., “Time-Varying Reliability Model of Steel Girder

Bridges”, Proc. Institution of Civil Engineers, Structures and Buildings, Thomas Telford Publishing, Vol. 128, Issue 4, Nov. 1998, pp. 359-367.

Rackwitz, R. and Fiessler, B., 1978, "Structural Reliability under Combined Random Load Sequences",

Computer and Structures, 9, (1978) pp. 489-494. Thoft-Christensen, P. and Baker, M.J., Structural Reliability Theory and Its Applications, Springer-Verlag,

(1982) p. 267.

Comparision Betn Euro Code ,Spain Code and AASHTO

Documents

Transcript of Comparision Betn Euro Code ,Spain Code and AASHTO