The method, however, has a problem of determining optimal starting effect interval for tail histogram curve fitting of crossing rate. At present, the problem is generally solved using the approach proposed by Cremona. But the approach is essentially subjective in computing procedure. To solve these issues, this paper develops a new method of determining optimal starting interval for tail histogram fitting. Instead of direct application of the Kolmogorov theory to crossing rate histogram, the new method starts analysis with the sample empirical distribution of effect at arbitrary time in stochastic process.
Towards actual brazilian traffic load models for short span highway bridges
By characteristics analysis of Kolmogorov distribution variable, it figures out whether the stochastic process variable complies with the hypothesis of the Rice's theory or the fitting curve tails with its theoretical curve identification of optimal starting interval. Unable to display preview. Download preview PDF. Skip to main content.
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Calgaro, J. Introduction aux Eurocodes. Google Scholar. Caprani, C. Probalistic analysis of highway bridge traffic loading. Doctoral Dissertation, University College Dublin. CrossRef Google Scholar. Cremona, C. Crespo-Minguill, N. Croce, P.
Ditlevsen, O. Enright, B. Flint, A. Span lengths range from 10 m to 40 m for simply supported and continuous systems, and from 2. Figure 6 illustrates a typical grid numerical model used for static analyses, where T-beams and cross beams are represented by frame elements. In order to obtain the critical internal forces produced by the simulated traffic, it was developed a computational tool that works in two steps [ 6 ]:. In order to generate values for the random variables, Monte Carlo technique is employed;.
Effects caused by the generated loading are recorded in certain sections those indicated in Table 6 at each time step. The maximum effect at each loading cycle is also registered. At the end of simulation the process recorded effects are summarized in histograms. According to O'Connor and O'Brien [ 16 ], four different traffic situations should be analyzed: traffic jams, mixed flow, free flow and emergencies.
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In small spans, critical load cases are due to heavy vehicles crossing and are affected by dynamic amplification factor. In large spans, however, critical load cases are due to simultaneous presence of several vehicles on structures in congested or mixed flow, with little or no dynamic amplification [ 11 ]. As the structures considered herein have maximum length of 40 m, congested and mixed flow situations were not analyzed. In free flowing, the time between vehicles is modeled as a random variable. Traffic is generated at each lane independently; correlations between random variables of the same vehicles in different lanes with same direction may be important [ 17 ], but weren't taken into account.
Traffic simulations were performed for a total of 30 days. The simulator checks if, at the current instant of time, there is at least one vehicle with at least one axle on the bridge. If so, the computational tool calculates the desired effects at the reference sections. Structural analysis ceases when all vehicles in all lanes have already travelled along the bridge; then histograms are produced for every considered effect.
Time between vehicles was modeled by a gamma distribution [ 11 ]. The adoption of this distribution is suggested in the case of the process of vehicles arrival be idealized as a Poisson process. Due to lack of information, it was adopted a coefficient of variation equal to 0. The simulation does not take into account acceleration, braking or lateral displacements. In the structural analysis the force exerted by each tire is modeled by a concentrated load and the effects due to each load are calculated using influence surfaces. The traffic simulator was validated through some tests that demonstrated its accuracy [ 6 ].
The transverse location of passing vehicles in opposite senses of traffic direction pictured in Figure 7 , named scenario 1, is the most frequent scenario for one carriageway typical bridge with two traffic lanes centered along its axis; most of the heavy vehicles pass along the longitudinal axis of each lane.
However, taking girder L1 as a reference for ultimate limit state design situation, the worst load case occurs for the traffic of vehicles out of the lanes marked along the pavement. Thus, many possibilities are opened for traffic on bridges. For the wider bridge deck considered in this work a variety of traffic situations are depicted in Figure 8 as scenarios 2 to 9, all of them for free flowing traffic of vehicles.
It should be observed in this figure that the transverse distribution of lanes, shoulders and clearances differ from the actual situation in existing bridges [ 11 ]. Nevertheless it is considered in order to achieve the worst transverse load distributions, the vehicles traveling on the border lane or shoulder of the bridge deck, close to the lateral barrier or guard-rail.
In scenarios 3, 5, 7 and 9, lanes are located on the right, as close as possible to girder L1, while the shoulders are clustered on the left of the deck, to represent emergency or temporary construction situations. In scenarios 1 to 5, vehicles travel in two traffic lanes, according to original design assumption, while in scenarios 6 to 9 the carriageway is divided in 3 lanes to conform to traffic growth. All these situations are feasible only to the wide slabs Figure 5b since the traffic lanes are all 3.
The scenarios considered herein intend to envelop all possible free flowing and emergency situations foreseen during lifetime of these typical RC bridges. However, the total number of commercial vehicles on the highway is greater than the number of records because i some vehicles avoid the weighing station, mainly due to legal limit weight surplus and ii the records were not obtained continuously since the weighing station closes in peak times until the queue of trucks is reduced to a few hundred meters.
Considering this "adjustment factor" the actual commercial vehicle ADTT in this database is estimated equal to 7, trucks and buses. This value is called reference flow RF and includes heavy traffic in all the three lanes of the considered highway. Due to lack of available recent traffic data collected directly in the lanes, the proportion of total traffic supported by each lane has to be estimated.
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Table 7 shows the distribution of total flow among lanes given by some authors, for two traffic lanes in the same direction. In Getachew [ 18 ] and Prat [ 11 ] the proportions were estimated from detailed traffic studies performed respectively in roads of France and Sweden; O'Brien and Enright [ 17 ] refer to data collected on Netherlands A and Czech Republic B highways.
The adopted proportions of total flow supported by each lane in each scenario are summarized in Table 8.
Study on Fatigue Traffic Loading for Highway Bridges in China
For Eurocode 1 load models calibration, the target values were taken with a return period of 1, years, to ensure a small probability of excess in effects' values: 0. This choice was made to limit the likelihood of several exceedances of the serviceability limit state during lifetime. To set the return period for the extrapolations of static effects one should take into account that a very large return period is not representative [ 8 ] because the traffic probably will not remain with the same settings.
The rapidly changing technology causes distortion of the load pattern in long-term violating the stationarity of these random processes which partially invalidates the large return periods, unlike natural phenomena such as wind speeds and river floodings.
On the other hand, the extrapolation is being held for random unmeasured but indirectly modeled quantities - the internal forces - which can generate errors, so that for safety conservatively large return periods must be adopted [ 11 ]. Considering both aspects a return period of years was adopted for target values calculation in simulations according to scenarios 1, 2, 4, 6 and 8, which do not include relocation of lanes.
As scenarios 3, 5, 7 and 9 refer to special situations, simulations under these configurations were carried out with a return period of 10 years. In all cases traffic growth was not taken into account for the extrapolation. These values are shown in the third column of Table 8. For the critical static effects shown in Table 6 , the following steps were accomplished in order to obtain the corresponding characteristic values:. These characteristic values were took as representative of each static effect;.
Among all vehicle classes shown in traffic composition Table 1 and Figure 2 , those which effectively contribute to the extreme static effects are 2S3, 3S3, 3T4, 3T6 and 3I3; all of them are susceptible to high values of GVW.
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In short spans, up to 10 m, the presence of tridem axles from classes 2S3 and 3S3 govern the extreme effects. As the span lengths increase, also increase the likelihood of longer and heavier vehicles from classes 3I3, 3T4, 3T6 and 3M6 pass on the bridges with all axes simultaneously acting at multiple sections of the girders.
Although classes 3T6 and 3M6 are quite infrequent in the traffic composition, they correspond to the longest trucks and the biggest GVW among all classes from Figure 2 ; this could explain its importance in static effects' extreme values. Each wheelbase and axle load of these trucks is shown in Table 9. Figure 9 illustrates the instant of time when these vehicles generate the largest bending moment at mid-span of girder L1. Figure 10 shows the histogram of positive bending moments for the simply supported 20 m span bridge with wide deck, the Weibull distribution fitted to this histogram and its distribution of extremes, whose mode is equal to kNm.
This value is equal to the extrapolated value obtained by the probability level using the parent Weibull distribution and is taken as the characteristic value of the static bending moment. The ratio between the characteristic value and the maximum value reached by the simulation in 30 days equals 1. One can check, assuming linear static behavior, that extrapolation leads to physically feasible results.
This ratio, multiplied by the GVWs of the trucks that generated the greatest static bending moment within 30 days of traffic simulation Table 9 , results in these "new" GVWs: Retaining the same relative positions shown in Figure 9 , this new combination of trucks would generate a bending moment equal to kNm.
Both GVWs are smaller than its upper limits: Comparison between the obtained characteristic static effects and those generated by the brazilian live load models. In Figures 11 to 16 the representative extreme values of the static effects shown in continuous lines , which are caused by the traffic of real vehicles, are compared to those produced in the same structural models see Figure 6 by the live load models prescribed in the Brazilian codes NB-6 and NBR shown in dashed lines.
Only the static effects produced by these live loads were considered as they were not multiplied by the impact factor. Figures 11 to 13 refer to the narrow bridge deck ND configuration designed with the old load model from NB-6 while Figures 14 to 16 are related to the wide deck bridge WD designed according to the current live load from NBR Figures 11 and 14 illustrate the variation with the span length of the maximum shear forces in simply supported span Figure 11 a and 14 a and continuous spans Figure 11 b and 14 b bridges.
Figures 12 and 15 show comparisons in terms of positive bending moments for each one of the same structural systems. Negative bending moments in continuous and cantilever spans are shown in Figures 13 and It can be seen in these figures that the static effects generated by the real traffic of vehicles as calculated according to the procedures described herein are in general greater than those produced by the past and current Brazilian standards load models. It is noticeable that the current Brazilian code gives conservative values only for the negative bending moment in 30 m and 40 m continuous spans with wide bridge deck Figure 16 a.
These results show that Brazilian code load models may not reproduce adequately the real traffic of heavy vehicles and may, in many cases, be non-conservative. The dynamic effects and the modeling of uncertainties must be taken into account for a final conclusion on this matter. It can still be noted in Figures 11 to 16 that the curves related from one side to the real traffic of heavy vehicles and from the other side to load models are in general divergent with increasing span length, particularly in the case of bending moments.
This indicates that the safety margin of the Brazilian load models is not uniform for all span lengths and structural systems. It is outlined in this paper the main results obtained in the first stage of the work performed towards the development of new live load models which aim to simulate the effects caused by the real traffic loads on existing two girders short span bridges, typical of Brazilian roadways comprising two lanes single carriageway.
The lack of a large number of WIM records was got around by establishing a database which brought together measurements from weighing stations and idealized traffic scenarios.
Applied traffic simulation techniques allow for scenarios of multiple vehicles on the bridges and provided the histograms of the selected critical effects. Then Weibull distributions were fitted to these histograms from which the characteristic static effects were calculated by extrapolations according to the return period defined for the traffic scenarios. In each structure the representative values of the critical static effects were considered as the highest characteristic values among all traffic scenarios.
It was observed from the traffic simulations that in short spans up to 10 m the passage of tridem axles from classes 2S3 and 3S3 governed the extreme effects. In larger spans the critical effects were caused by the simultaneous presence of longer and heavier vehicles once all their axles can be located simultaneously on the bridge deck. In most cases the static effects generated by real traffic, as calculated according to the procedures described herein, are higher than those produced by the load models from Brazilian design codes without multiplying them by the dynamic amplification factor.
The current Brazilian code NBR gives conservative values only for the negative bending moment in 30 m and 40 m continuous spans with wide bridge deck. The negative bending moments in cantilever spans produced by this code live load model are significantly lower than the extreme ones generated by the traffic of heavy vehicles. A great number of bridges with narrow decks designed under the NB-6 code are still in full service.