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Reliability analysis of prestressed concrete bridge girders:

comparison of Eurocode, Spanish Norma IAP and

AASHTO LRFD

Andrzej S. Nowaka,*, Chan-Hee Parkb, Juan R. Casasc

aDepartment of Civil and Environmental Engineering, University of Michigan, 2340 G.G. Brown Building,2350 Hayward, Ann Arbor, MI 48109-2125, USA

bYonsei University, Seoul, South KoreacSchool of Civil Engineering, Technical University of Catalonia, Barcelona, Spain

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 moreconservative than the other two codes, and AASHTO LRFD is the most permissive code.# 2002 Elsevier

Science Ltd. All rights reserved.

Keywords: Girder bridge; Prestressed concrete; Design code; Reliability; Target reliability

1. Introduction

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 pre-stressed concrete bridge girders. The analysis is performed for typical Spanish bridge girders,

therefore, the considered codes are: Spanish Norma IAP-98 [1], Eurocode ENV 1991–3 [2], and

AASHTO LRFD [3].

Five prestressed concrete bridges are selected. The structures were designed with typical Spanish

precast concrete girders, presented in Fig. 1. Spans vary from 20 to 40 m and girder spacing varies

from 1.3 to 3.4 m as shown in Table 1. For comparison, three versions of the selected structures are

0167-4730/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved.P I I : S 0 1 6 7 - 4 7 3 0 ( 0 2 ) 0 0 0 0 7 - 3

Structural Safety 23 (2001) 331–344www.elsevier.com/locate/strusafe

* Corresponding author. Tel.: +1-734-764-9299; fax: +1-734-764-4292.

E-mail address: [email protected] (A.S. Nowak).

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Fig. 1. Prestressed concrete bridge girders considered in this study.

332 A.S. Nowak et al. / Structural Safety 23 (2001) 331–344

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considered, with the load carrying capacity determined by the amount of prestressing strands

according to the three considered design codes.

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 with the following limit state

function,

g ¼ R Q ð1Þ

where R=resistance, and Q=total load effect.

The total load is a sum of several components including,

Q ¼ D þ L þ I ð2Þ

where D=dead load, L=live load, and I =dynamic load (impact).It should be noted that the serviceability limit state (tension stress in concrete) usually governs

the design of prestressed concrete bridge girders.

2. 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 bycumulative 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), l=1.03, and coefficient of

variation, V =0.08, for D1, and l=1.05 and V =0.10 for D2 [4]. For asphalt wearing surface it is

assumed that the mean thickness is 80 mm and V =0.30 [4].

Table 1

Selected prestressed concrete girder bridges

Bridge no. Span (m) Girder spacing (m) Girder type Number of girders

1 20 1.76 Leopardo 7

2 25 1.32 Pantera 9

3 30 2.02 Jabali 6

4 35 3.36 Rinoceronte 4

5 40 1.44 Bisonte 8

A.S. Nowak et al. / Structural Safety 23 (2001) 331–344 333

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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 configura-tion, 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 [1], the design live load consists of three axles of 200

kN each, superimposed with a uniform load of 4 kN/m2. The spacing of axles and wheels is

shown in Fig. 2. The design dynamic load is specified as equal to 15% of the static live load.

The design live load in Eurocode [2] is shown in Fig. 3. It is assumed that the specified live load

includes static and dynamic components.

Fig. 2. Design live load model specified in Spanish Code [1]. Concentrated forces are superimposed with a uniform

load of 4 kN/m2.

Fig. 3. Design live load specified by Eurocode [2]; Q=300 kN for Lane 1, Q=200 kN for Lane 2, Q=100 kN for Lane

3, and q=9 kN/m2 for Lane 1, q=2.5 kN/m2 for Lanes 2 and 3.


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AASHTO [3] specifies HL-93 loading which consists of a three axle truck superimposed with a

uniform lane load of 9.3 kN/m as shown in Fig. 4. Dynamic load is specified as 0.33 of the truck

load only, with no dynamic load applied to the lane load. AASHTO [3] also specifies the girder

distribution factor (GDF). For moments, GDF is a function of girder spacing, span length andstiffness of the girder,

GDF ¼ 0:075 þ S

2900

0:6S

L

0:2K g

Lt3s

0:1

ð3Þ

where S =girder spacing (mm), L=span length (mm), ts=thickness of slab (mm), and K g=stiff-

ness 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 theSpanish Code [1] 1.35 for Eurocode [2] and 1.75 for AASHTO [3]. For comparison, the ratio of

factored lane moments is plotted in Fig. 5. The denominator is the factored lane load moment

specified by AASHTO [3].

The values of design live load moments per girder were also calculated according to the con-

sidered three codes and the results are shown in Table 5 together with dead load. Each value

corresponds to live load moment per lane (lane width is 3.6 m) and it is normalized by AASHTO

[3] design live load. The live load factors are included (1.35 for Eurocode [2], 1.50 for the Spanish

Code [1] and 1.75 for AASHTO [3].

The statistical model for live load was derived using the approach developed by Nowak [4],

Nowak and Hong [5], and Park et al. [6]. Extreme load effects are calculated for a one year per-

iod. The cumulative distribution function (CDF) of moments due to trucks in the survey can beapproximated by a normal distribution, in particular this applies to the upper tail of CDF [4].

Therefore, it is assumed that the mean maximum annual live load follows an 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 [7].

Two levels of traffic density were considered, a high volume traffic with an average daily truck

traffic (ADTT) of 6000 trucks per day (two lanes and one direction) and a low volume traffic with

ADTT of 2000 trucks per day. The live load model for AASHTO [3] was based on the truck

survey in Ontario, Canada [8]. The cumulative distribution functions (CDF) of the gross vehicle

Fig. 4. Live load specified by AASHTO [3], HL-93 loading.


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weight (GVW) are shown in Fig. 6 for the Spanish and Ontario traffic. The CDFs are plotted on

the normal probability paper. The vertical scale is the inverse standard normal distribution

function.

For each surveyed truck, the maximum lane moment was calculated using influence lines, forsimple span bridges with spans from 20–40 m. The CDF of moments were extrapolated to obtain

the statistical parameters (the means) of the maximum live load effect for extended periods of

time, as shown in Fig. 7 for Ontario trucks and in Fig. 8 for the Spanish trucks. The corre-

sponding bias factors for the maximum annual lane moment are plotted in Fig. 9. The nominal

(design) live load is taken as specified by the AASHTO [3].

The uncertainty in bridge analysis and girder distribution factor is expressed in terms of a bias

factor, l, and coefficient of variation, V . Field measurements indicate that the actual load dis-

tribution is more uniform than what can be analytically predicted [9,10]. For girder distribution

factors based on simplified methods [Eq. (3)], l=0.93 and V =0.12. For girder distribution

factors based on more sophisticated methods, (e.g. finite elements and grid analysis), l

=0.98 andV =0.07 [11]. Recent field tests confirmed that the girder distribution factor can be treated as a

normal random variable [9,10].

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 [12], and then they were

confirmed by field tests by [13] and [9]. 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 standard

deviation of DLF is 0.08, therefore the coefficient of variation is 0.80 [9,13].

Fig. 5. Ratio of factored design live load moments per lane (including DLF) and AASHTO [3] moment, for lane

width=3.6 m.


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Fig. 6. CDF of gross vehicle weight.


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Moments due to dead load components for the selected bridges are given in Table 2.

3. Resistance model

Resistance is a variable representing the load carrying capacity. It can be affected by uncer-

tainties in strength of materials, dimensions and analysis. The type of distribution is based on

observed shape of CDFs for prestressing steel and concrete. Resistance is considered as a product

Fig. 7. CDFs of moment due to Ontario trucks/AASHTO [3] design moments and extrapolations.


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of three factors representing strength of materials, dimensions and analysis, therefore, it is log-

normally distributed [14]. For prestressed concrete girders, the statistical parameters were derived

by Nowak et al. [15], l=1.05 and V =0.075.

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 ¼ D þ L L þ I ð Þ½ = ð4Þ

Fig. 8. CDFs of moment due to Spanish Trucks/AASHTO [3] design moments and extrapolations.


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where D is dead load factor, L is live load factor and is resistance factor.Values of load and resistance factors specified in the considered codes are given in Table 3. The

calculated Rmin, are shown in Table 4.

4. Reliability analysis

Reliability analysis is performed for prestressed concrete bridge girders designed according to

the considered codes. The reliability index, , is defined as a function of probability of failure, PF ,

[16],

Fig. 9. Bias factors for the moment per girder (including DLF) for the Ontario truck data and Spanish truck data, with

the nominal moment corresponding to AASHTO [3].

Table 2

Design dead load and live load moments per girder (kN m)

Bridge no. D1 D2 D3 L+I

Spanish Eurocode AASHTO

1 344 432 162 1162 1770 1124

2 594 505 189 1280 1890 1229

3 1478 1113 418 2230 3430 2057

4 2434 2526 1000 4380 6313 3563

5 2979 1410 531 2610 3870 2345


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Table 3

Load and resistance factors

Bridge no. Spanish Eurocode AASHTO

D1 1.35 1.35 1.25

D1 1.35 1.35 1.25

D1 1.35 1.35 1.50

L 1.50 1.35 1.75

0.88 0.88 1.00

Table 4

Minimum required resistance, Rmin

Bridge no. Spanish Eurocode AASHTO

1 3420 4154 3180

2 4158 4875 3808

3 8417 9878 7465

4 16,609 18,827 13,935

5 11,997 13,485 10,387

Fig. 10. Reliability indices for Ontario truck traffic.


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Fig. 11. Reliability indices for Spanish truck traffic.

Fig. 12. Reliability indices for region specific truck traffic.


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¼ 1 PF ð Þ ð5Þ

where, 1 is inverse standard normal distribution function.

An iterative procedure is used calculate the reliability index as described by Rackwitz andFiessler [17] and Nowak [14]. 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 results obtained for the Ontario truck survey data are plotted in Fig. 10. The bias factor for

the maximum annual live load is taken from Fig. 9, with the coefficient of variation of 0.18.

Reliability indices calculated using the maximum annual live load based on Spanish traffic

simulations are shown in Fig. 11. The bias factor is also taken from Fig. 9.

Finally, reliability indices corresponding to the considered codes are plotted in Fig. 12, with

AASHTO [3]) live load model based on the Ontario data, and Spanish Code [1] and Eurocode [2]

based on the Spanish data.As mentioned earlier, the serviceability limit states govern the design. Therefore, the actual

reliability indices for the ultimate limit states are considerably higher than calculated values.

5. Conclusions

The reliability analysis is performed for prestressed concrete bridge girders designed according

to three codes: Spanish Norma IAP-98 [1], Eurocode [2], and AASHTO [3]. The load and resis-

tance 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 clearthat Eurocode [2] is the most conservative one, and AASHTO [3] is the most permissive code. The

actual =7.0–8.0 for Eurocode, =5.1–6.8 for Spanish Code [1], and =4.5–4.9 for AASHTO [3].

For the Eurocode [2] and Spanish Code [1], the largest values of b are for the span of 35 m, and

decreases for shorter span lengths. AASHTO [3] provides the most uniform reliability level.

Acknowledgements

The research presented in this paper has been partially sponsored by the NATO Cooperative

Research Program which is gratefully acknowledged.

References

[1] Spanish Norma IAP-98. Actions in highway bridges. Road Directorate, Spanish Ministry of Public Works,

Madrid, 1998.

[2] Eurocode ENV 1991–3. Eurocode 1: Basis of Design and Actions on Structures. Part 3: Traffic Loads on Bridges.

Final draft—August 1994.

[3] AASHTO LRFD Bridge Design Specifications. American Association of State Highway and Transportation

Officials, Washington, DC, 1998.


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