Protocols for Collecting and Using Traffic Data in Bridge Design (2011) / Chapter Skim
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From page 26... ...
A more robust reliability-based approach also is presented to consider the site-to-site variations in WIM data in the calibration of live loads. Some key issues and traffic parameters that influence the estimation of traffic statistics and the maximum load effect are summarized below.
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From page 27... ...
WIM data scatter for axles is different from gross weight scatter and is usually much larger. This axle scatter should be assembled separately from the equipment calibration and should be used to modify the measured axle loads.
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From page 28... ...
For LRFD bridge design it is not necessary to separate legal loads from routine permits because both are classified as unanalyzed truck loads that should be enveloped by the HL93 design loading. Protocols require that legal loads and routine permits be grouped under Strength I and heavy special permits be grouped under Strength II.
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From page 29... ...
The sensitivity analysis has demonstrated that small changes in the number of multiple-presence events do not have a significant effect on the estimated maximum load effect over the 75-year design life. Studies done using New York WIM data during this project show that there is a strong correlation between multiplepresence and ADTT.
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From page 30... ...
Draft Recommended Protocols for Using Traffic Data in Bridge Design Protocols recommended for collecting and using traffic data in bridge design can be categorized into the following steps: • Step 1: Define WIM data requirements for live-load modeling; • Step 2: Selection of WIM sites for collecting traffic data for bridge design; • Step 3: Quantities of WIM data required for load modeling; • Step 4: WIM calibration and verification tests; • Step 5: Protocols for data scrubbing, data quality checks, and statistical adequacy of traffic data; • Step 6: Generalized multiple-presence statistics for trucks as a function of traffic volume; • Step 7: Protocols for WIM data analysis for one-lane load effects for superstructure design; • Step 8: Protocols for WIM data analysis for two-lane load effects for superstructure design; • Step 9: Assemble axle load histograms for deck design; • Step 10: Filtering of WIM sensor errors/WIM scatter from Measured WIM histograms; • Step 11: Accumulated fatigue damage and effective gross weight from WIM data; • Step 12: Lifetime maximum load effect Lmax for superstructure design; and • Step 13: Develop and calibrate vehicular load models for bridge design. The steps to be followed are described in detail in the remainder of this chapter.
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From page 31... ...
. • Data needed for calibration of deck design load models include – Common axle configurations and axle weight distributions of legal trucks and permit trucks; – Frequencies of occurrences of common axle configurations; – Other multi-axle configurations with fixed and variable axles; – Headway information for side-by-side effects of axle groups or single axles; and – WIM scale calibration statistics for axle loads.
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From page 32... ...
Total Number of HighSpeed WIM Sites Number of WIM Sites on Interstates WIM Data Available for a Whole Year? California 1 WE 15 years 137 58 Yes Florida 5 SA 32 years 40 14 Yes Indiana 10 NC 15 years 52 24 Yes Michigan 11 NC 14 years 41 21 Yes Missouri 15 NC 10 years 13 7 Yes New Jersey 19 NE 13 years 64 14 Yes New York 8 NE 10+ years 21 11 Yes Ohio 4 NC 15 years 44 21 Yes Oregon 23 WE 8 years 22 18 Yes Texas 3 SG 21 years 18 6 Yes Table 9.
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From page 33... ...
Where WIM sites exist, verify that WIM data from all major truck routes within the area of interest are included. • The guidelines for selecting individual WIM sites should be as discussed above under Step 2.1.
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From page 34... ...
This includes a comparison of static axle weights with axle weights that are estimated from multiple vehicle passes with more than one vehicle. Assemble calibration statistics for a WIM site for filtration of sensor errors during the load modeling process (see Step 11)
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From page 35... ...
Step 5.3 Assess the Statistical Adequacy of Traffic Data The proposed protocols for calculating the maximum 75-year live-load effect, Lmax, is based on the WIM truck weight and truck traffic database assembled at various sites within the jurisdiction for which the Lmax estimates are required. The protocols are based on collecting truck weight and truck traffic 35
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From page 36... ...
Normal probability plots of truckload effects obtained from WIM data collected at several different sites have confirmed that the upper 5% of the data approaches a straight line with a regression coefficient R2 on the order of 0.97 to 0.99 indicating that the normal distribution does reasonably well model the upper tail of the truck load effect histograms. The slope and intercept of the regression fit of the upper tail on the normal probability plot can then be used to find the mean and standard deviation of the normal distribution.
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From page 37... ...
For each WIM site with refined time stamp data, the cumulative frequencies for side-by-side, staggered, and following events are obtained for headway separation from 0 ft to 300 ft in 20-ft increments. Report multiple-presence probabilities for each day for each site as a function of daily truck count and headway separations or gap.
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From page 38... ...
. By studying the occurrence of multiple trucks within a given headway separation at WIM sites with accurate time stamps, the effects of multiple trucks on a span can be simulated for WIM sites without accurate time stamps.
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From page 39... ...
Step 7. Protocols for WIM Data Analysis for One-Lane Load Effects for Superstructure Design (Single Events and Following Events)
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From page 40... ...
Step 7.2 Following Truck Events for Superstructure Design When Accurate Truck Arrival Time Stamps are Available Load effects for following trucks may be obtained directly from the WIM data where accurate time arrival stamps are collected together with truck weight data. The load effects analysis is performed with the following trucks in their proper relative positions.
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From page 41... ...
5. With the randomly selected truck pair separated by the randomly selected headway separation, maximum load effects can be calculated in the same manner as for trucks with accurate time stamps and measured headway separation (Step 7.2)
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From page 42... ...
5. With the randomly selected truck pair separated by the randomly selected headway separation, maximum load effects can be calculated in the same manner as for trucks with accurate time stamps and measured headway separation (Step 8.1)
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From page 43... ...
Step 8.4 Assemble Two-Lane Load Effects Histograms for Strength I and Strength II • Assemble normalized load effects frequency histograms for two-lane load effects for Strength I and Strength II in narrow bins of 0.02 increments. • These will constitute the two-lane measured load effects histograms without any filtering for WIM sensor errors (see Step 10)
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From page 44... ...
Because main member load effects are influenced by the weight and spacing of several axles, some of the axle weight errors will cancel out and thus the overall error may have a lower standard deviation than that for individual axles. For example, for the calibration data of the same I-87 site studied above, the maximum moment effect of the calibration truck for a 60-ft simple span beam would be equal to 275.4 kip-ft, if the actual axle weights and axle spacings were used.
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From page 45... ...
Because the error may depend on various random factors related to the WIM system's characteristics and truck/structure/WIM system dynamic interaction as well as some truck features including tire size and pressure, the calibration factor is a random variable that relates the measured WIM data results to the "true" weight through the following equation: x xm r= ( )
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From page 46... ...
If the bin sizes for the histogram of the actual weight xr and that of the measured weight xm are taken to be the same, so that Δz = Δ(zy) , then Equation 20 can be expressed as Thus, given the histogram of the measured WIM data, xm, and the probability distribution of the calibration factor, , the integration of Equation 19 for all possible values of xr = z can be executed numerically using software tools.
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From page 47... ...
Generally, a Gumbel fit can be executed on the tail of the short-term maximums for statistical projections. An alternative to the convolution approach consists of using a Monte Carlo simulation to obtain the maximum load effect.
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From page 48... ...
This procedure should be executed on the raw data prior to calculating Lmax. Step 12.2.1 Protocols for Calculating Maximum Load Effect Lmax The process begins by assembling the WIM truck weight data and load effects for single-lane events and two-lane events and filtering the data for WIM sensor errors.
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From page 49... ...
Figure 19 gives a schematic representation of the Monte Carlo simulation, which follows the procedure described in the following steps: 1. Assemble the data representing the filtered load effects for the trucks in the drive lane into a histogram labeled Bin I
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From page 50... ...
In the AASHTO LRFD calibration, the overall live-load COV was taken as 20%. • Method II: If the variability in the WIM data is much greater than that assumed in the calibration, then the entire LRFD 50 .
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From page 51... ...
If r is relatively r L from WIM data projections for two-lmax 2 = anes L used in existing LRFD calibrationmax for two-lanes ( ) 31 r L from WIM data projections for one-lmax 1 = ane L used in existing LRFD calibrationmax for one-lane ( )
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From page 52... ...
For example, the data from Florida show a COV for the moments of simple span bridges under one-lane loadings that varies from 32.5% for the 20-ft simple spans to 22.3% for the 200-ft simple spans. These COVs for site to site must be augmented by the COVs for the other variables that control the maximum load including within site variability, the effect of the dynamic allowance factor, load distribution factor, and WIM data sample size, leading to much higher overall COV for the live load than the 20% used during the AASHTO LRFD calibration.
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From page 53... ...
32 surface, DC is the dead load effect for the components and attachments and Ln is the live-load effect of the HL93 load including dynamic allowance and load distribution factor. According to the LRFD specifications φ =1.0 for the bending moment capacities of steel and prestressed concrete members, γDW = 1.50, γDC = 1.25.
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From page 54... ...
If all the random variables representing the resistance, dead load, and live load follow Gaussian (normal) probability distributions, the reliability index, β, can be calculated as follows: Where the mean of the total dead load is given by the COV of the total dead load is and the standard deviations are obtained as The AASHTO LRFD was calibrated so that all bridge members designed using the specified load and resistance factors produce a uniform level of risk expressed in terms of a reliability index β equal to a preset target value βtarget.
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From page 55... ...
. • The models used to obtain the statistical data on the mean values and COVs of the moment and shear capacity of steel composite and prestressed concrete members, as well as the dynamic amplification factors and load distribution factors used during the AASHTO LRFD calibration, are still valid.
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From page 56... ...
It is important to note that there are no β calculations or database of loads/load effects used for the calibration of decks in the LRFD available for use in this project. One reasonable approach to calibration of deck design loads is to assume the present LRFD safety targets are adequate for the strength design of decks and establish new nominal loads for axles based on recent WIM data.
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From page 57... ...
from field measurements on typical steel and prestressed concrete bridges is still valid. Therefore, for the loading of a single permit vehicle, the live-load COV becomes The reliability index conditional on the arrival of two side-by-side permits on the bridge can then be calculated using Equation 40 where R – is the mean resistance when the bridge member is designed for two side-by-side permits and LL –– is the live-load effect on the beam due to two sideby-side permits.
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From page 58... ...
The final number of random trucks alongside a permit will be Where Pside-by-side is the percentage of side-by-side events that depend on the ADTT and Np is the number of permits within the return period of interest. The maximum live-load effect is obtained from Where P is the load effect of the permit truck, DFP is the distribution factor for the load P, Lmax NR is the maximum load effect of random trucks for NR events which correspond to the 1-year return period applicable for the Strength II case, DFR is the distribution factor for the random load, and IM is the impact factor for side-by-side events.
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From page 59... ...
Requests for WIM data needed for the studies were sent out to certain selected states based on the national survey findings. The requirements for selection of WIM sites were for WIM data for a whole year (2006 or 2005)
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From page 60... ...
The scrubbed WIM data were passed through various quality control checks. The quality control checks established in Step 5.2 were employed for each WIM site studied.
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From page 61... ...
. Appendix C contains the GVW histograms for all other WIM sites studied in this task.
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From page 62... ...
One-Lane Load Effects (Step 7.1) The load effects of each truck individually were calculated for eight span lengths from 20 ft to 200 ft for both simple spans and two-span continuous spans.
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From page 63... ...
The load effects of the simulated multiple-presence events were calculated as for the single truck events. For the purpose of design, in consideration of distribution factors, load effects were segregated into one-lane and two-lane; one-lane load effects are those due to a single truck as well as two trucks in the same lane, while two-lane load effects are those due to two trucks in adjacent lanes.
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From page 64... ...
Appendix C contains the load effect histograms for all other WIM sites studied in this task. Since it is unlikely that two trucks traveling in the same lane will be separated by less than 60 ft, the load effects histograms for the one-lane events are very similar to the single-truck load effects histograms; that is, they display the typical bi-modal shape.
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From page 65... ...
The effective gross weight of the truck population was still used for the GVW of this fatigue truck. Table 24 shows the effective gross vehicle weight, in kips, used in calculating K for each directional WIM site studied in this task.
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From page 66... ...
Lmax was calculated for all 5 load effects, 8 span lengths, and 47 directional WIM sites, and segregated by one-lane and two-lane events. The results of the calculation of Lmax based on the data assembled from several WIM sites are provided in Tables 25 through 29 for different span lengths.
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From page 67... ...
Maximum Lmax values for Indiana. Load Effect 20 40 60 80 100 120 160 200 1-Lane 1.687 1.679 1.666 1.674 1.678 1.796 1.989 2.010 2-Lane 2.255 2.156 1.930 1.935 2.025 2.031 1.954 1.856 1-Lane 1.683 1.689 1.790 1.781 1.957 2.083 2.158 2.133 2-Lane 2.309 2.135 2.054 2.097 2.104 2.093 1.981 1.861 1-Lane 1.618 1.659 1.660 1.646 1.626 1.791 1.955 2.012 2-Lane 2.237 2.182 1.979 1.989 2.034 2.035 1.973 1.873 1-Lane 1.905 1.816 2.164 1.972 1.733 1.466 1.240 1.186 2-Lane 2.059 2.490 1.911 1.353 1.228 1.193 1.118 1.015 1-Lane 1.711 1.702 1.853 1.839 1.940 1.920 1.824 1.764 2-Lane 2.260 2.086 2.054 2.069 2.071 1.864 1.635 1.467 Maximum Lmax Values of 10 Directional WIM Sites in Mississippi Span (ft)
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From page 68... ...
68 Load Effect 20 40 60 80 100 120 160 200 1-Lane 1.718 1.844 1.793 1.647 1.524 1.463 1.313 1.190 2-Lane 1.966 1.763 1.598 1.557 1.600 1.611 1.559 1.462 1-Lane 1.742 1.694 1.648 1.578 1.515 1.454 1.345 1.260 2-Lane 1.996 1.655 1.706 1.776 1.785 1.759 1.666 1.554 1-Lane 1.688 1.741 1.798 1.674 1.570 1.479 1.331 1.233 2-Lane 1.937 1.698 1.579 1.561 1.609 1.612 1.575 1.490 1-Lane 1.642 1.605 1.206 0.864 0.941 0.966 0.906 0.850 2-Lane 1.567 2.028 1.536 1.098 0.978 0.993 0.952 0.838 1-Lane 1.666 1.706 1.670 1.569 1.447 1.242 1.057 0.966 2-Lane 1.951 1.605 1.682 1.732 1.733 1.560 1.356 1.224 Maximum Lmax Values of 8 Directional WIM Sites in Texas Span (ft) M-simple V-simple M-positive M-negative V-center Table 29.
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From page 69... ...
Lmax for 2-lane/Lmax for one-lane for moments and shear of simple spans.
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From page 70... ...
Lmax vs. ADTT for one-lane simple span moment.
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From page 71... ...
Lmax vs. ADTT for one-lane simple span shear.
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From page 72... ...
Maximum r values for California. Load Effect 20 40 60 80 100 120 160 200 1-Lane 2.200 1.904 1.692 1.697 1.663 1.637 1.564 1.463 2-Lane 1.184 1.059 1.074 1.075 1.064 1.056 1.029 0.991 1-Lane 2.402 2.045 1.997 1.886 1.789 1.798 1.673 1.585 2-Lane 1.153 1.132 1.123 1.053 1.007 1.033 1.028 1.010 1-Lane 2.079 1.797 1.446 1.307 1.163 0.996 0.854 0.798 2-Lane 1.088 1.074 0.789 0.721 0.671 0.613 0.576 0.508 Maximum r Values of 9 Directional WIM Sites in Florida Span (ft)
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From page 73... ...
Load Effect 20 40 60 80 100 120 160 200 1-Lane 1.298 1.244 1.262 1.268 1.281 1.392 1.604 1.634 2-Lane 1.064 0.921 0.839 0.849 0.896 0.907 0.896 0.859 1-Lane 1.368 1.373 1.455 1.402 1.529 1.707 1.798 1.823 2-Lane 1.089 0.979 0.925 0.928 0.923 0.951 0.926 0.895 1-Lane 1.500 1.397 1.731 1.630 1.444 1.222 1.033 0.988 2-Lane 0.903 1.038 0.831 0.604 0.553 0.537 0.504 0.457 Maximum r Values of 10 Directional WIM Sites in Mississippi Span (ft) M-simple V-simple M-negative Table 34.
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From page 74... ...
Calculation of nominal resistance, Rn, using current LRFD for a sample of typical composite steel bridges. Prestressed Concrete Dead Loads HL-93 Required Nominal Resist.
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From page 75... ...
Since in this case the Rn value for two lanes is higher than that obtained for one-lane loading, the two-lane case governs the design. Similar calculations can be executed to find the required nominal bending moment capacity of steel and prestressed concrete bridges having different span lengths and beam spacings.
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From page 76... ...
included the uncertainties in estimating the lane distribution factor, which was associated with a COV equal to VDF = 8% based on field measurements on typical steel and prestressed concrete bridges. This information is used in Equations 35 and 36 to find the mean value of the live load and the COV.
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From page 77... ...
For the maximum moment of the sample of simplespan bridges studied in this report, Equations 37 and 38 will yield the mean and standard deviation values provided in Tables 36 and 37 for the bending moment of simple-span composite steel and prestressed concrete bridges. Calculation of Reliability Index and Calibration of Live-Load Factor The adjustment of the live-load factors requires the calculation of the reliability index for different values of the live-load factor γL.
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From page 78... ...
The differences are mainly due to the legal truck weight limits or exemptions and the permit overload frequencies and weight regulations that may vary from state to state. For example, if the Lmax values generated from the Florida WIM data sites are used as input for the live-load modeling, the reliability index values shown in Tables 42 and 43 are obtained.
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From page 79... ...
Reliability index calculation for bending moment of simple span composite steel bridges based on California WIM data. 60 4 1564 1794 125 144 576 34 447 362 60 64 3.78 5.32 60 6 1940 2281 155 183 695 44 567 476 76 84 3.80 5.40 60 8 2280 2732 182 219 802 52 675 583 91 103 3.82 5.45 60 10 2644 3206 212 256 939 64 776 684 105 121 3.80 5.45 60 12 3011 3681 241 295 1087 77 870 782 117 138 3.78 5.43 120 4 5955 6614 476 529 3180 187 949 904 134 153 3.45 4.35 120 6 7064 8016 565 641 3656 215 1193 1181 169 200 3.53 4.51 120 8 8064 9307 645 745 4084 245 1414 1440 200 244 3.57 4.61 120 10 9180 10709 734 857 4629 285 1618 1686 229 286 3.58 4.64 120 12 10333 12144 827 972 5223 331 1811 1923 256 326 3.56 4.64 200 4 15304 16701 1224 1336 9221 545 1630 1611 228 258 3.28 4.00 200 6 17902 19898 1432 1592 10541 620 2035 2095 285 335 3.36 4.17 200 8 20253 22834 1620 1827 11730 699 2401 2547 336 408 3.41 4.28 200 10 22958 26115 1837 2089 13247 808 2740 2977 384 476 3.41 4.32 200 12 25783 29507 2063 2361 14895 934 3059 3390 428 542 3.40 4.32 Span Spacing Ave.
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From page 80... ...
Reliability index calculation for bending moment of simple span prestressed concrete bridges based on Florida WIM data. 60 4 1356 1602 136 160 346 28 566 425 151 134 2.25 4.02 60 6 1770 2134 177 213 474 38 718 558 192 177 2.27 4.02 60 8 2163 2646 216 265 604 48 855 683 229 216 2.30 4.02 60 10 2572 3171 257 317 756 61 982 802 263 254 2.32 4.01 60 12 2989 3704 299 370 923 74 1102 916 295 290 2.34 3.99 120 4 4396 5099 440 510 1741 117 1201 1036 315 269 2.69 4.01 120 6 5726 6742 573 674 2325 160 1510 1354 397 351 2.71 4.00 120 8 6853 8179 685 818 2797 199 1789 1651 470 429 2.71 4.01 120 10 8087 9718 809 972 3375 247 2048 1934 538 502 2.72 3.99 120 12 9446 11378 945 1138 4063 301 2292 2205 602 572 2.72 3.96 200 4 12306 13796 1231 1380 6265 377 2120 1851 565 498 2.82 3.78 200 6 15810 17938 1581 1794 8123 500 2648 2407 706 648 2.83 3.79 200 8 18999 21753 1900 2175 9814 614 3123 2926 833 788 2.83 3.79 200 10 22444 25812 2244 2581 11743 749 3565 3420 950 921 2.83 3.78 200 12 26416 30389 2642 3039 14096 906 3980 3894 1061 1049 2.82 3.74 Span Spacing Ave.
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From page 81... ...
Reliability index calculation for bending moment of simple span composite steel bridges based on Indiana WIM data. 60 4 1564 1794 125 144 576 34 508 376 62 50 3.34 5.40 60 6 1940 2281 155 183 695 44 644 495 79 65 3.35 5.50 60 8 2280 2732 182 219 802 52 767 606 94 80 3.36 5.55 60 10 2644 3206 212 256 939 64 881 711 107 94 3.36 5.55 60 12 3011 3681 241 295 1087 77 988 812 121 107 3.34 5.53 120 4 5955 6614 476 529 3180 187 1137 888 162 100 3.05 4.46 120 6 7064 8016 565 641 3656 215 1430 1161 203 131 3.10 4.64 120 8 8064 9307 645 745 4084 245 1695 1415 241 160 3.13 4.76 120 10 9180 10709 734 857 4629 285 1940 1657 275 187 3.13 4.80 120 12 10333 12144 827 972 5223 331 2170 1890 308 214 3.12 4.80 200 4 15304 16701 1224 1336 9221 545 1999 1598 264 190 2.99 4.04 200 6 17902 19898 1432 1592 10541 620 2496 2078 329 247 3.05 4.22 200 8 20253 22834 1620 1827 11730 699 2944 2526 389 301 3.09 4.34 200 10 22958 26115 1837 2089 13247 808 3360 2952 444 351 3.09 4.37 200 12 25783 29507 2063 2361 14895 934 3752 3362 495 400 3.08 4.38 Span Spacing Ave.
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From page 82... ...
The results show that the average reliability index values vary considerably from state to state as a function of the average Lmax values, the liveload case that governs, and the site-to-site variability expressed in terms of the COV of Lmax. Also, the results reflect that current WIM data indicate that one-lane loadings are often dominating the safety of bridge members due to the lower number of sideby-side events and the lower load effects produced by these events when compared to the data used during the calibration of the AASHTO LRFD.
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From page 83... ...
• The average reliability index for the span lengths and beam spacings considered is on the order of βave = 3.07 with a minimum value of β = 2.74 and a maximum value of β = 3.40. • Using a live-load factor γL = 1.35 for Strength II produces an average reliability index of βave = 3.07 for a single permit on the bridge.
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From page 84... ...
from field measurements on typical steel and prestressed concrete bridges, is still valid. Therefore, for the loading of a single permit vehicle, the live-load COV becomes The reliability index, conditional on the arrival of two side-by-side permits on the bridge, can then be calculated using Equation 40 where R – is the mean resistance when the bridge member is designed for two side-by-side permits and LL ––– is the live-load effect on the beam due to two sideby-side permits.
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From page 85... ...
• Increasing the span length leads to lower reliability index values. • The average unconditional reliability index for the span lengths and beam spacings considered is on the order of βave = 4.62 with a minimum value of β = 4.30 and a maximum value β = 4.91 • The higher reliability index obtained for the two side-by-side permits as compared to the single permit is primarily due to 85 Composite steel Reliability index, Span (ft)
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From page 86... ...
The maximum live-load effect expected within this 1-year period will be due to the heaviest of these 12.5 random trucks combined with the effect of the permit. Table 52 gives the LmaxNR values for the maximum moment effect on simple spans obtained for the maximum of 12.5 events for single lanes for WIM data collected at six California sites.
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From page 87... ...
LRFD did not specifically address deck components in the calibration. In the protocols developed in this study, the nominal axle loads derived using WIM data are used instead 87 Composite steel Reliability index, Span (ft)
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From page 88... ...
non-permit traffic using permit records, it was decided to group all trucks with six or fewer axles in the Strength I calibration. The high r values (r is defined as Lmax WIM data/Lmax LRFD calibration data)
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From page 89... ...
. Statistics SingleSingle SingleTandem TandemTandem All Others Event Count 13124 29735 16306 1801 Mean All Events 21.585 32.535 43.445 63.314 Std Dev All Events 4.994 10.486 14.111 17.759 COV All Events 0.231 0.322 0.325 0.280 Mean Top 20% Events 29.141 47.916 64.044 87.483 Std Dev Top 20% Events 3.345 4.509 6.522 8.462 COV Top 20% Events 0.115 0.094 0.102 0.097 Mean Top 5% Events 33.655 54.181 72.988 99.089 Std Dev Top 5% Events 3.003 4.094 5.088 7.489 COV Top 5% Events 0.089 0.076 0.070 0.076 99th Percentile 34 54 74 102 Table 55.
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From page 90... ...
Truck Sorting Strategies Based on State Permit Regulations The previously noted sorting strategies were implemented using permit rules and recent WIM data. For each state with the selected WIM sites (Indiana, California, and Florida)
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From page 91... ...
10 State Legal Trucks Illegal Trucks Annual (Routine) Permits Trip Permits All valid permit trucks grouped in Strength II.
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From page 92... ...
The total gross weight may be calculated by the following federal bridge formula and then compared to the established weight limits listed above. where: W = The overall gross weight on any group of two or more consecutive axles, to the nearest 500 lbs, L = The distance between the extreme of any group of two or more consecutive axles, and N = The number of axles in the group under consideration, except that two consecutive sets of tandem axles may carry a gross load of 34,000 lbs each, providing the first and last axles of the consecutive sets of tandem axles are at least 36 ft or more apart.
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From page 93... ...
For California, it is about 30% higher. This means that California has more annual permits or illegal loads with number of axles greater than seven, which were being 93 Maximum r Values, Strength I IN WIM Sites CA WIM Sites FL WIM Sites Sorting Variation 9544 9532 9512 Site 0003 Site 0059 Site 0072 9919 9926 9936 Str.
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From page 94... ...
. The last three columns of Table 61 show the averages for all WIM sites by span length and load effect for easy comparison.
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From page 95... ...
20 ft 60 ft 120 ft 20 ft 60 ft 120 ft 20 ft 60 ft 120 ft 20 ft 60 ft 120 ft Based on # Axles Baseline M-simple 18 18 14 21 5 10 28 0 1 0 6 8 17 # Axles 6 or less V-simple 13 29 4 16 29 0 0 3 5 10 20 M-negative 40 44 11 29 37 1 15 9 8 28 30 P1 M-simple 15 11 11 3 6 20 0 0 0 5 6 11 # Axles 7 or less V-simple 15 10 20 2 11 20 0 0 2 4 7 14 M-negative 31 36 10 19 30 0 7 8 6 19 25 P2 M-simple 12 8 10 0 1 4 0 0 0 4 3 5 # Axles 8 or less V-simple 12 8 17 0 2 6 0 0 0 4 3 8 M-negative 15 24 33 3 7 14 0 0 4 3 10 17 P3 M-simple 22 28 33 5 13 32 4 1 6 7 14 24 # Axles 5 or less V-simple 21 20 32 4 21 34 1 4 9 5 15 25 M-negative 32 40 48 14 35 41 2 23 14 11 33 35 Based on GVW P4 40 38 49 19 30 53 34 28 42 26 32 48 GVW 84 or less 44 37 55 22 39 57 32 36 48 27 37 53 52 63 65 31 62 64 29 59 54 30 61 61 P5 35 31 40 12 23 45 30 25 35 22 27 40 GVW 100 or less 39 27 45 14 32 50 29 32 41 23 30 45 45 55 58 24 53 57 25 49 46 24 52 54 P6 27 19 26 9 18 37 20 21 26 16 19 30 GVW 120 or less 28 17 35 11 24 39 22 24 29 17 22 34 34 44 49 16 40 47 18 35 33 16 40 43 P7 18 11 13 6 10 26 9 6 14 10 9 18 GVW 150 or less 20 11 22 6 15 28 7 11 18 8 12 22 25 33 35 11 25 36 9 20 20 11 26 30 Based on State Permit Regulations P8 52 53 55 50 52 62 46 40 52 47 48 56 Legal 54 48 59 51 56 63 45 47 54 48 50 58 57 63 67 49 63 67 40 59 58 44 62 64 P9 38 41 38 47 51 56 23 26 27 32 39 40 Legal & Annual 37 1 1 33 35 49 54 55 25 29 23 34 39 38 34 33 30 49 51 55 23 17 14 35 34 33 P10 0 -3 0 0 0 3 1 0 1 0 0 Legal & Illegal 0 -4 0 0 1 1 0 2 0 0 0 -4 -3 0 0 0 2 12 7 0 3 1 P11 0 0 0 0 0 0 0 3 0 0 1 All but Trip Permits 1 0 0 0 0 0 2 4 0 1 1 0 0 0 0 0 1 7 6 0 2 2 P12 0 0 0 0 0 0 0 0 0 0 0 All Trucks 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Average for CA Average for IN Average for FL Strength I Definition Load Effect Average r Differential Values (percentage) for Strength I Average for CA, IN,FL 26 21 M-simple V-simple M-negative M-simple V-simple M-negative M-simple V-simple M-negative M-simple V-simple M-negative M-simple V-simple M-negative M-simple V-simple M-negative M-simple V-simple M-negative M-simple V-simple M-negative M-simple V-simple M-negative 0 0 0 0 0 0 0 Table 61.
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From page 96... ...
Another helpful sensitivity index is the change in r values from P8 to P9 where annual permits are added to state legal loads and from P8 to P10 where illegal loads are added to state legal loads. Table 63 also illustrates the influence of illegal trucks in driving high r values.
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From page 97... ...
For both California and Florida, the influence of illegal trucks on r values was far more significant than that of annual permits. Detailed Review of Strength I r Differential Results One WIM site from each state has been selected for a more in-depth review and discussion and will serve as representative examples of the other sites for each state.
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From page 98... ...
Sorting Variation Load Effect 20 60 120 20 60 120 Baseline M-simple 0.94 1.03 0.97 5.61 9.88 25.49 V-simple 1.07 1.10 1.01 4.56 12.81 23.76 M-negative 1.05 0.82 0.55 8.50 30.75 37.88 P1 M-simple 0.99 1.06 1.09 0.65 7.70 16.57 V-simple 1.09 1.13 1.13 3.30 10.69 14.14 M-negative 1.12 0.97 0.63 1.95 17.92 28.59 P2 M-simple 0.99 1.08 1.12 0.58 5.90 13.89 V-simple 1.09 1.14 1.16 3.21 9.69 12.08 M-negative 1.13 1.04 0.66 1.56 12.15 25.04 P3 M-simple 0.94 0.90 0.81 5.94 21.05 37.70 V-simple 1.07 0.97 0.93 4.72 22.78 29.61 M-negative 1.02 0.81 0.48 10.49 31.15 45.09 P12 M-simple 1.00 1.14 1.30 0.00 0.00 0.00 V-simple 1.13 1.26 1.32 0.00 0.00 0.00 M-negative 1.14 1.18 0.88 0.00 0.00 0.00 Table 65. California Site 0059 r differentials for Group I
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From page 99... ...
. Load Effect Strength I r Values r Differential = (r12 - rx)
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From page 100... ...
The following sorting variations will be discussed under Group III: • P8: Strength I = state legal trucks, • P9: Strength I = state legal trucks and annual permits, • P10: Strength I = state legal trucks and illegal trucks, and • P11: Strength I = state legal trucks, illegal trucks, and annual permits. In Table 70 and Figure 46, Group III results (based on state permit regulations)
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From page 101... ...
Sorting Variation Load Effect Strength I r Values r Differential = (r12 - rx) / r12 x 100% Span Length (ft)
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From page 102... ...
SortingVariation Load Effect 20 60 120 20 60 120 P8 M-simple 0.74 0.65 0.58 61.38 60.76 69.05 V-simple 0.76 0.70 0.62 63.42 66.70 70.39 M-negative 0.72 0.51 0.33 60.89 68.00 71.18 P9 M-simple 0.80 0.74 0.76 58.27 55.65 59.12 V-simple 0.85 0.79 0.78 59.37 62.64 62.67 M-negative 0.73 0.67 0.46 60.20 58.14 59.73 P10 M-simple 1.91 1.67 1.86 -0.04 -0.06 -0.07 V-simple 2.09 2.11 2.10 -0.04 -0.04 -0.06 M-negative 1.85 1.59 1.15 -0.04 -0.07 -0.07 P11 M-simple 1.91 1.67 1.86 0.00 0.00 0.00 V-simple 2.08 2.11 2.10 0.00 0.00 0.00 M-negative 1.84 1.59 1.15 0.00 0.00 0.00 P12 M-simple 1.91 1.67 1.86 0.00 0.00 0.00 V-simple 2.08 2.11 2.10 0.00 0.00 0.00 M-negative 1.84 1.59 1.15 0.00 0.00 0.00 Table 70. Indiana Site 9544 r differentials for Group III.
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From page 103... ...
The r differential results for P8 were the highest. This signifies that the biggest difference in r values occurs when only state legal loads are included in Strength I or illegal loads, trip permits, and annual permits are excluded.
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From page 104... ...
Using a state's permit and weight regulations as in P11 to group trucks into Strength I and Strength II is considered more rational, and more precise, when using national WIM data. • A sensitivity analysis of r values shows that Group III results (based on state permit regulations)
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From page 105... ...
to group trucks into Strength I and Strength II is considered the most precise and rational approach, when using national WIM data. Variation P11 includes state legal trucks, illegal trucks, and annual (routine)
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Key Terms
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