Euro-SiBRAM’2002 Prague, June 24 to 26, 2002, Czech Republic
Session 3
INTRODUCTION
The development of rational design and evaluation criteria for bridges requires the development of efficient load models. Load parameters are random variables, depending on uncertainties in loads, load distribution factors, prediction of future loads, and so on. The actual measurements indicate that loads are site-specific and component-specific. The statistical load models are based on the test data, measurements and simulations. The paper is focused on dead load, live load, dynamic load, extreme load events and their combinations.
Extreme events include scour, earthquake and collision loads. In the past, each extreme event was considered separately, and combinations were considered as a conservative simultaneous occurrence of these events. There is a need for the development of rational design criteria for combination of scour, vessel collision and earthquake. These extreme events often govern the design. Simultaneous occurrence of scour and ship collision may result in a dominating load combination. Calibration of the new bridge design codes covered mostly the basic design combinations with dead load and live load. Extreme loads and their combinations could not be considered in the calibration because the statistical data and methodology were not available.
DEAD LOAD AND LIVE LOAD
Dead load is the gravity load due to the self weight of the structural and non structural elements permanently connected to the bridge. Because of different degrees of variation, it is convenient to consider three components of dead load: weight of factory made elements (steel, precast concrete members), weight of cast-in-place concrete members, and weight of the wearing surface (asphalt). All components of dead load are treated as normal random variables. The statistical parameters were derived in conjunction with the development of the OHBDC (1979, 1983 and 1992) and AASHTO LRFD (1994 and 1998), bias factor is 1.03-1.05 and coefficient of variation is 0.08-0.10 (Nowak 1995 and 1999).
Live load covers a range of forces produced by vehicles moving on the bridge. It includes the static and dynamic components. The static live load is considered first. The 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 (slab and girders). The effect of these parameters is considered separately.
The development of live load model is essential for a rational bridge design and/or evaluation code. The model developed by Nowak and Hong (1991) and Nowak (1993 and 1999) was based on the results of truck survey performed by the Ontario Ministry of Transportation. It covered 9,250 selected trucks (only trucks which appeared to be heavily loaded were measured and included in the data base). The uncertainties involved in the analysis are due to limitations and biases in the survey. The available data base is small compared to the actual number of heavy vehicles in a 75 year life time. It is also reasonable to expect that some extremely heavy trucks purposefully avoided the weighing stations. A considerable degree of uncertainty is caused by unpredictability of the future trends with regard to configuration of axles and weights.
The data base includes truck configuration (number of axles and axle spacing) and weights (axle loads and gross vehicle weight). For each truck in the survey, bending moments and shear forces were calculated for a wide range of spans. Simple spans and continuous two equal spans are considered. For each span length, a cumulative distribution function (CDF) was determined for the considered internal forces (positive moment, negative moment, and shear). The maximum moments and shears for various time periods were determined by extrapolation. The bias factors in terms of the HS20 live load (AASHTO 1996) were between 1.65 and 2.10. The HS20 live load is a three axle vehicle: 45 kN, 145 kN and 145 kN, with axle spacings of 4.3m. For spans longer than about 40m, HS20 consists of a uniformly distributed load of 9.3 kN/m and a concentrated force of 81 kN. The coefficients of variation for the maximum truck moments and shears can be calculated by transformation of CDF. Each function can be raised to a certain power, so that the calculated earlier mean maximum moment (or shear) becomes the mean value after the transformation. The slope of the transformed CDF determines the coefficient of variation. For 75 year maximum values it is 0.11 for most spans.
The maximum one lane moment or shear is caused either by a single truck or two (or more) trucks following behind each other. For a multiple truck occurrence, the important parameters are the headway distance and degree of correlation between truck weights. The maximum one lane effect (moment or shear) is derived by Monte Carlo simulations. The analysis of two lane loading involves the distribution of truck load to girders. For moment in an interior girder, AASHTO code specifies a girder distribution factor (GDF) as a function of girder spacing. The comparison of AASHTO (1996) GDF's with the results of the structural analysis is carried out using the finite element method (FEM) indicates that code specified values are overly conservative in most cases, except of short spans and short girder spacing. Recent field tests indicate that the actual GDF's are even smaller than analytical results (Kim and Nowak 1997; Eom and Nowak 2001). For two lane bridges, the load analysis involves the determination of the load in each lane and load distribution to girders. The effect of multiple trucks can be calculated by superposition. The maximum effects can be calculated using Monte Carlo simulations.
ADTT (average daily truck traffic) is an important parameter of live load. The observations indicate a considerable site-specific variation of the number of vehicles and percentage of trucks. The live load moments for multilane bridges with various ADTT's can be derived by simulations. The maximum 75 year moment for a single lane is considered as a reference value. For multiple lanes, moment per lane is lower than that value. For two lanes, the ratio of the per lane moment and the maximum single lane moment is 0.85. For three lanes, the probability of a simultaneous occurrence of very heavy trucks in all three lanes is even smaller. Accordingly, the ratio of per lane moment and reference value is 0.70. For four lanes, the ratio is 0.50. For other ADTT's (in one direction), the probabilities of simultaneous occurrence of multiple trucks are different than for ADTT = 1,000. Therefore, the per lane moments are also different. The moment ratios determined by simulations of multilane traffic are listed in Table 1.
Table 1. Multilane Live Load Factors
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ADTT Number of lanes
(in one direction) 1 2 3 4 or more
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100 1.15 0.95 0.65 0.55
1,000 1.20 1.00 0.85 0.60
5,000 1.25 1.05 0.90 0.65
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DYNAMIC LOAD
The dynamic load model is a function of three major parameters: road surface roughness, bridge dynamics (frequency of vibration) and vehicle dynamics (suspension system). An analytical procedure was developed by Hwang and Nowak (1991) for simulation of the dynamic load on girder bridges. It was observed that dynamic deflection is almost constant and it does not depend on truck weight. Therefore, the dynamic load, as a fraction of live load, decreases for heavier trucks. For the maximum 75 year values, the corresponding dynamic load does not exceed 0.15 of live load for a single truck and 0.10 of live load for two trucks side-by-side. The coefficient of variation of dynamic load is about 0.80. The results of the simulations indicate that DLF values are almost equally dependent on road surface roughness, bridge dynamics and vehicle dynamics. The actual contribution of these three parameters varies from site to site and it is very difficult to predict.
Field tests were performed to verify the analytical results (Nassif and Nowak 1995; Kim and Nowak 1997, Eom and Nowak 2001). The results clearly indicate that the dynamic load factor (DLF) decreases for heavier trucks. In Fig. 1, DLF is plotted vs. static strain. These are the results of measurements on five steel girder bridges located in Michigan. Larger static strain corresponds to heavier vehicles. These values were measured on the girders that carried the maximum load.
EARTHQUAKE
Effect of earthquake is a time-varying load. It is a function of ground (bedrock) acceleration, structural system specific parameters, and component-specific parameters. The major statistical parameters of ground acceleration are magnitude and frequency of occurrence (rate or probability of occurrence in a specified time interval). The actual acceleration is strongly site-specific (geographical location, soil condition) and the structural response is also component-specific. The dynamic analysis of seismic behavior may require the consideration of non-linear models. Therefore, the prediction of structural response to an earthquake is very difficult and involves a considerable degree of uncertainty. Earthquake loading can be represented as a product of three variables representing variation in the ground acceleration, uncertainty in transition from load (ground acceleration) to load effect in a component (moment, shear forces, axial force), and variation due to approximate method of structural analysis.
Static Strain (10-6)
Fig. 1. Dynamic Load Factor versus Static Strain
For the United States, various building codes and specifications use the rate of return to determine the design event load. This is typically presented in a form of bedrock acceleration contour map with the actual magnitudes being a function of the design codes specified return period. In the AASHTO codes, the design values are presented in a contour maps (bedrock accelerations) derived using a probabilistic analysis methodology similar to that presented above. However, it is important to note that the risk level (return period) associated with earthquake is not consistent with other load components. In particular, this applies to selection of return period and factored load and load combinations.
SCOUR EFFECT
Scour is not considered a load, however, it can have a considerable effect on bridge performance because of load re-distribution. In addition, from a statistical point of view, occurrence of scour is similar to other extreme events in that it is a time-varying condition that can be represented by a PDF. Scour is the major cause of bridge failures in the United States. The approach to design and evaluation with regard to scour is presented in FHWA publications: Evaluating Scour at Bridges (Hydraulic Engineering Circular No. 18, 1993) and Stream Stability at Highway Structures (Hydraulic Engineering Circular No. 20, 1991).
There are three types of scour: (1) long-term channel degradation (or aggradation), (2) contraction scour, and (3) local scour. Occurrence and magnitude of scour can be affected by a flood event. The following definitions of scour will be used: local scour refers to severe erosion around the abutment and piers, contraction scour refers to scour caused by the constriction to the stream caused by bridge approach embankments, local and contraction scour occur under the bridge and are usually refilled after the flooding event, and therefore can be referred to as short-term, temporary, or transient scour, long-term channel degradation refers to scour across the entire waterway breadth (this is a long-term scour degradation problem that increases in depth with time, and it occurs regardless of the bridge).
VESSEL COLLISION
Similar to earthquake loading, vessel collision can also be statistically represented by a time varying product of three variables representing variation in the vessel collision force, variation due to uncertainty in transition from load (vessel collision) to load effect in a component (moment, shear forces, axial force), and variation due to approximate method of structural analysis. The major parameters which directly affect the vessel impact force are: type (barge ship), displacement tonnage, and speed. However, the actual collision force is also dependent on site-specific parameters that include: waterway characteristics and geometry; vessel and/or barge configurations; and bridge type and geometry. Expected collision forces can vary widely, however, typical values are 250-750 kN for a drifting empty barge; 15,000 kN for a barge under power; and 250,000 kN for a ship under power (Nowak and Knott 1996; AASHTO 1991).
LOAD COMBINATIONS MODEL
A load combination is defined as an effect of a simultaneous occurrence of two or more load components (Nowak and Collins 2000). The basic background for modeling load combinations in bridges is needed to create a reference frame to compare the existing load combination models used in highway bridges to what they should be based on the available statistical data. The description focuses on the load combinations, basic parameters of a load combination, discussion of time variation, and selection of the design values.
Total load, Q, can be considered as a sum of load components: DL = dead load, LL = live load, EQ = earthquake, CV = vessel collision, and SC = scour effect. This notation for the loads is based on the AASHTO LRFD (1998) code. All load combinations involve dead load. For combination of DL, LL and dynamic load, the model is presented by Nowak (1993 and 1999). For load combinations with extreme load events, the analysis requires the evaluation of the return periods for combined effect and component events. In addition, current bridge design methods and analysis models may be inadequate for extreme design. In the past, designers were aware of the need to design for these extreme events, but comprehensive codes and rational design models were not available. As a result, the design of bridges for extreme events can vary broadly throughout the United States.
For load combinations including extreme load events, Nowak and Knott (1996) proposed to consider:
(a) extreme EQ + long term SC + average LL
(b) normal speed CV + long term SC + average LL
(c) drifting barge CV + short term SC
As a long-term solution, it is recommended that a full probability-based calibration be performed leading to the development of an expert system. Monte Carlo is recommended as an efficient simulation procedure.
CONCLUSIONS
The basic load combination for highway bridges is dead load, live load and dynamic load. Statistical models are summarized for dead load, live load, and dynamic load. Multiple presence of trucks is considered in lane and side-by-side. The parameters which affect the analysis include headway distance and degree of correlation (with regard to weight). The frequency of occurrence is a site-specific parameter. It is modeled on the basis of the available observations. The maximum values are determined by simulations. For two lane bridges, the maximum 75 year effect is caused by two side-by-side maximum two month trucks, with fully correlated weights. The two month truck is about 0.85 of the 75 year truck. The presented live load model has been used in the development of the new LRFD (load and resistance factor design) codes in the United States and Canada. Extreme loads that are important for bridges include earthquake, scour and vessel collision. These are strongly time-varying loads. A load combination is proposed as an intermediate solution for use in the bridge design code.
REFERENCES
[1] AASHTO, "Standard Specifications for Highway Bridges", American Association of State Highway and Transportation Officials, Washington, DC., 1996.
[2] AASHTO, “Guide Specification and Commentary for Vessel Collision Design of Highway Bridges”, Am. Assoc. of State Highway and Transp. Officials, Washington, D.C., 1991.
[3] AASHTO, ”LRFD Bridge Design Specifications and Commentary”, American Association of State Highway and Transportation Officials, Washington D.C., 1998.
[4] Eom, J. and Nowak, A.S., “Live Load Distribution for Steel Girder Bridges”, ASCE Journal of Bridge Engineering, Vol. 6, No. 6, 2001, pp. 489-497.
[5] FHWA, “Stream Stability at Highway Structures”, Hydraulic Engineering Circular No. 20, Federal Highway Administration, McLean, VA., 1991.
[6] FHWA, “Evaluating Scour at Bridges”, Hydraulic Engineering Circular No. 18, Federal Highway Administration, McLean, VA., 1993.
[7] Hwang, E-S. and Nowak, A.S., 1991, "Simulation of Dynamic Load for Bridges", ASCE Journal of Structural Engineering, Vol. 117, No. 5, pp. 1413-1434.
[8] 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.
[9] Nassif, H. and Nowak, A.S., "Dynamic Load Spectra for Girder Bridges", Transportation Research Record, No. 1476, 1995, pp. 69-83.
[10] Nowak, A.S., 1993, "Live Load Model for Highway Bridges", Journal of Structural Safety, Vol. 13, Nos. 1+2, December, pp. 53-66.
[11] Nowak, A.S., "Calibration of LRFD Bridge Design Code", NCHRP Report 368, Transportation Research Board, Washington, D.C., 1999.
[12] Nowak, A.S., "Calibration of LRFD Bridge Code", ASCE Journal of Structural Engineering, Vol. 121, No. 8, 1995, pp. 1245-1251.
[13] Nowak, A.S. and Knott, M.A., “Extreme Load Events and Their Combinations”, National Conference on Design of Bridges for Extreme Events, Atlanta, GA, December, 1996.
[14] Nowak, A.S. and Collins, K.R., “Reliability of Structures”, McGraw-Hill, New York, 2000.
[15] Nowak, A.S. and Hong, Y-K., 1991, "Bridge Live Load Models", ASCE Journal of Structural Engineering, Vol. 117, No. 9, pp. 2757-2767.
[16] OHBDC, "Ontario Highway Bridge Design Code", Ministry of Transportation, Downsview, Ontario, Canada, 1st Edition 1979, 2nd Edition 1983, 3rd Edition 1992.