AASHTO Load Rating Provisions for Implements of Husbandry (2020)

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107 Protocols for Load Rating Bridges for Implements of Husbandry Introduction The increase of implements of husbandry (IoH) on public roads in both weight and number of trips is not uniform in all states. Some states face an increasing concern with these loads to the safety of bridges and a number of bridges have been collapsed due to these loads. On the other hand, some other states do not have this concern at all because of no or limited farming population. Furthermore, some states have state laws regarding IoH traveling on public roads but others do not. Therefore, these protocols have been developed for bridge owners to elect to adopt or not, depending on the situation within the jurisdiction. These protocols lay out a recommended procedure and related guidelines for planning, developing, and implementing a bridge load rating and permitting program for IoH if they are of concern to the bridge owner. Load rating herein is applicable to all bridge components, including both superstructure and substructure components of the bridge. Given the wide variety of situations in the states, the bridge owner may still modify these guidelines and/or skip certain steps recommended herein if deemed appropriate. The variation among states is seen in these aspects: 1. Legislation with regard to legalizing commercial vehicle weights and configurations. 2. Current permit system for overweight vehicles. 3. Current laws regarding IoH loads. 4. Bridges’ capacities for safe load carrying. 5. Available funding for bridge repair, rehabilitation, and replacement. 6. Other factors. Protocols recommended for IoH load rating of bridges can be categorized into the following steps: Step 1: Identification of Stakeholders Step 2: Identification of Bridges and IoH to Be Focused On and Potentially Impacted Upon by the Load-Rating/Permitting Program Step 3: Development of Load-Rating/Permitting Program for IoH Step 4: Development of Strategies for Implementation of Load-Rating/Permitting Program for IoH Step 5: Legislative Action If Needed Step 6: Implementation, Monitoring, and Further Enhancement The recommended steps are given in more detail as follows. Step 1: Identification of Stakeholders Identify current and potential stakeholders for a bridge load-rating program regarding IoH and possibly an associated permit program. They may include, but not be limited to, IoH owners, A P P E N D I X A

108 Proposed AASHTO Load Rating Provisions for Implements of Husbandry IoH renters, IoH users, farmers, IoH manufacturers, state and local bridge owners, state and local pavement owners, vehicle weight-enforcement agencies, legislators, the traveling public, and other truck drivers who may share roads with IoH vehicles. These parties may be affected by (1) the limitation on and access by IoH vehicles, (2) requirements on travel of IoH vehicles, (3) benefits brought by IoH such as economic development and/or reduced farming cost, etc. These parties may also need to be consulted in developing the load-rating procedure concerned herein. Step 2: Identification of Bridges and IoH to Be Focused On and Potentially Impacted Upon by the Load-Rating/Permitting Program Identify those bridges that may be impacted upon or influenced thereby. For example, these bridges may be of concern as a possible impact: to be load posted, restricted for use, rehabilitated, strengthened, and/or replaced, as well as those that are currently load posted and/or restricted for use, etc. Identify their characteristics, such as their ages, locations (on which roads and of which functional class), material type (e.g., timber), dimensions (number of available lanes, length, width, etc.), on which roadway systems (e.g., state or local, etc.), their conditions, current and potential safety issues, if any incidents of collapse have occurred involving IoH loads, if there have been such incidents nearby, etc. These vulnerable bridges need to be focused on in this step, so that such incidents like collapse will be prevented in the load-rating/permitting program to be successfully developed and practiced. A report on this step is required as a result of this step. If possible, an inventory of such bridges is recommended as part of its result. This inventory will be used later to verify or confirm possible impact when the load-rating program is tentatively developed in Step 3 and accordingly updated then. The report shall be periodically reviewed (e.g., on an annual basis) and such review documented, along with practice of the load-rating/permitting program. This vulnerable bridge inventory is also recommended to be reviewed periodically along with data collected and analyzed in practice of the load-rating/permitting system for needed improvement in the future, to monitor and enhance safety of this population of bridges being the weakest link in the infrastructure system within the jurisdiction. More specifically this process of identification of impacted bridges may be performed using computer-aided searches of the inventory based on predetermined criteria. These criteria should be developed by experienced bridge engineers familiar with the population of bridges in the jurisdiction in terms of their span types, material types, locations and routes carried, ages, load ratings versus current legal and other loads, weakest components and bridges, specific issues with these components and bridges, previous incidents and causes of bridge failure/collapse in the jurisdiction if any, especially those involved with IoH, possible failure/collapse prevention measures taken if applicable, etc. For example, these features may be potentially of vulnerability concern. 1. Older than 30 years of age without significant rehabilitation over past 10 years or longer. 2. Timber primary members, such as deck, beams, piers, abutments, etc. 3. Condition rating at or worse than 5. 4. Narrow width (inadequate for more than one lane). 5. Bridge sites that receive limited or no weight enforcement. 6. Weight posted. Note also that more specific screening using existing load ratings is a separate step covered in Step 3. Identify IoH populations that can be the focus of the load-rating/permitting program being developed if such data can be made available. The needed information may be collected from

Protocols for Load Rating Bridges for Implements of Husbandry 109 the stakeholders identified in Step 1. Consider categorizing the identified IoH into tiers with respect to axle weights, axle spacings, gauge widths, traffic volumes (frequency of appearance), etc. Within each tier they will be treated similarly for load-rating/permitting. See Step 3 for developing more details of the load-rating/permitting program for IoH loads. The goal of a load-rating/permitting program is to ensure bridge safety. As such, Step 2 is critical for the success of the load-rating/permitting program for IoH loads. The program should unambiguously state the purpose of the program and ensure that it can be reached. In other words, procedures and details of load rating/permitting may change over time in order to reach this purpose, but this purpose shall not change over time. Furthermore, periodical review and update of this step’s results (the report and inventory discussed previously) are parts of an effort to ensure bridge safety related to IoH loads, by constantly enhancing the load-rating/permitting program. This periodical review is particularly critical when IoH loads show a trend or potential to increase in severity and/or when bridges in the jurisdiction are observed deteriorating at a significant rate. Step 3: Development of Load-Rating/Permitting Program for IoH Consider working with the stakeholders identified in Step 1 in this development step. Possible ways of needed communication with the stakeholders include, but may not be limited to, face-to-face meetings, web conferences, conference calls, e-mails, announcements, flowcharts, newsletters, web pages, reports, letters, etc. Step 3.1: Load-Rating/Permitting Program Tier Structure Consider a framework of categorizing IoH vehicles into two or three tiers for a load-rating and possibly permitting program. For a three-tier system, Tier 1 represents the lower end of the IoH weight spectrum and is intended to cover a vast majority of current IoH loads, Tier 3 represents the higher end of the IoH weight spectrum, and Tier 2 includes those in between. Compared with Tier 1, Tiers 2 and 3 are meant to cover a much smaller percentage of current IoH population to travel on public roads at a very limited frequency. Tier 3 is also to accommodate possibly future IoH. Its statistics may be used to forecast future trends of IoH and shall receive close monitoring and attention because it can become critical to the jurisdiction’s bridge safety. Tier 1 is recommended to cover a vast majority of IoH vehicles currently demanding or having access to public roads and bridges. This tier will likely require a large amount of analysis work for load rating, and thus a carefully designed program is needed to minimize such a work load and more importantly to assure safe use of bridges in the jurisdiction, particularly for those bridges and IoH loads identified in Step 2 as being of concern. An appropriately selected model is recommended to envelope this tier of IoH so that load rating for individual IoH vehicles with respect to individual bridges can be avoided. For this purpose, consider a notional IoH load model in Figure A-1 as recommended in NCHRP Research Report 951 for Project 12-110 for the enveloping model; 115% of the federal bridge formula (FBF) may be used, per study of NCHRP Project 12-110 as a case. If deemed consistent and appropriate for the jurisdiction’s current practice, consider referring to this tier as legal IoH loads, routine permit IoH loads, etc. This reference should be consistent with the current overweight permit system being practiced in the jurisdiction. Otherwise, significant legislation work may be required and/or the current overweight permit system’s practice may need to be revised. However, any of them may become prohibitively costly in terms of needed funds and time.

110 Proposed AASHTO Load Rating Provisions for Implements of Husbandry Tiers 2 and 3 are recommended to include those IoH vehicles beyond Tier 1 in weight. Tier 2 vehicles are less severe than Tier 3 but more than Tier 1, which may still require bridge- and IoH-specific load rating. As deemed appropriate, Tiers 2 and 3 may be combined into one tier for a two-tier system. Tier 3 is for very exceptional crossings of very limited bridges in the jurisdiction. They may correspond to the so-called super-overweight truck loads being practiced in some states, which are required to use only limited and specified routes during limited and specified time periods. Tier 3 will require individual load rating for the IoH vehicle and the bridges on the specified routes. More Details About Tier 1. The notional model enveloping Tier 1 vehicles (shown in Figure A-1 as an example) is intended to represent Tier 1 IoH vehicles and possibly others in Tier 2. It is also to be used to load rate bridges without using each individual IoH vehicle for each bridge. As a result, those bridges rated to be adequate to carry this notional load will be c) b) a) Figure A-1. Recommended notional model for IoH loads up to 115% of FBF: (a), (b), or (c), whichever induces maximum load effect; (a) and (b) for dual-wheel-steering-axle IoH, (c) for single-wheel-steering-axle IoH. Maximum axle load = 23 kips. Maximum gross vehicle weight = 92 kips.

Protocols for Load Rating Bridges for Implements of Husbandry 111 allowed to carry all Tier 1 IoH loads. In other words, Tier 1 IoH vehicles will not be required to be checked individually for load rating each bridge. Instead this is to be performed using computer-aided screening. More details of this screening are given in Step 3.2 on load-rating computation. Since Tier 1 is designed to represent a vast majority of current IoH population, this frame- work of multitier system will minimize the work load for IoH load rating. In addition, process- ing and approval for Tier 1 vehicles to have access to selected public roads and bridges (e.g., currently posted bridges may need to be excluded) can be fulfilled by other trained professionals than bridge engineers at a lower cost. If appropriate, a Tier 0 may be considered to cover those IoH that exceed FBF but induce load effects below the three AASHTO legal vehicles for load rating. Based on the definition of Tier 1 above, Tier 0 may become a subset of Tier 1. More Details About Tier 2. Tier 2’s upper limit may be determined with consideration to the following factors, if Tier 2 is not the most severe tier of the IoH load-rating/permitting program (in a three-tier system). If Tier 2 is the most severe tier (in a two-tier system), its upper limit may be open. 1. Consistency with current overweight permit system in the jurisdiction. 2. Bridge infrastructure’s current capacity in safe load carrying. 3. Enforcement strength or expected compliance when this new program is implemented. 4. Other possible factors special for the jurisdiction. For example, if 115% of FBF (or a similar upper limit for Tier 1) is accepted as legal load in the jurisdiction, then the upper limit for Tier 2 IoH vehicles may be considered to be set at the current annual permit upper limit and treated accordingly as such for processing, enforce- ment, etc. Or if 115% of FBF (or a similar upper limit for Tier 1) is accepted as annual permit loads, then the upper limit for Tier 2 IoH vehicles may be set at the current trip permit upper limit and treated accordingly as such for processing, enforcement, etc. These examples show that it is recommended to fit IoH loads into current categories of vehicle loads in the jurisdiction so that they will be treated accordingly in the current system with respect to bridge safety assurance and weight enforcement. This approach will also avoid possibly additional categories which likely will require additional attention, work, and funding. The upper limit for Tier 2 will also dictate how many bridges in the jurisdiction need to be restricted from access of Tier 2 vehicles. These loads are typically overweight according to FBF and their envelope represented by the upper limit may cause significant overstress in bridges in the jurisdiction, depending on their current safe load-carrying capacity. Apparently, the strength or effectiveness of weight enforcement can be a factor in deter- mining the upper limit of Tier 2. If Tier 2 loads are currently not allowed in the jurisdiction, predicting the strength of enforcement when Tier 2 is implemented in the future can be challenging. Thus, conservative estimation on such strength is advised. There may be other factors that need to be considered in determining Tier 2’s upper limit. Examples are as follows and they are not exhaustive. 1) Possible pressure from the legislation to allow further access of IoH loads to public roads. 2) Consideration of a more prudent approach to gradually increase exposure of bridges to IoH loads. 3) Local economy needs for allowing a specific type of IoH vehicle. It is recommended that the upper limit of Tier 2 loads be determined with consideration to the factors discussed herein. If a notional model is desired, it may be developed by consid- ering those IoH loads potentially to be covered in Tier 2 and then identify their enveloping

112 Proposed AASHTO Load Rating Provisions for Implements of Husbandry vehicle as the notional model. The recommended Tier 1 notional model in Figure A-1 may be considered in determining Tier 2’s notional model using a multiplying factor larger than 1.0 if the former configuration (its axle loads and axle spacings) is typical to targeted Tier 2 vehicles for the jurisdiction. Note that a notional model may not be needed when the number of IoH vehicles in Tier 2 is limited and their travels need to cross only a limited number of bridges in the jurisdiction. Individual Tier 2 vehicles will be load rated for each bridge in the jurisdiction. More Details About Tier 3. Tier 3 has an open end without upper limit. If the IoH load- rating/permitting program has only two tiers, then Tier 2 is open ended. These loads shall be rigorously reviewed for each bridge they intend to cross. As such, the number of such trips shall be controlled at a very low volume, in consideration to their higher potential of damaging and/or collapsing bridge spans in a jurisdiction, as well as the significant amount of required review work for permitting these loads. Step 3.2: Load-Rating Computations LRFR: Rating Equation. For LRFR of IoH loads, the following rating factor, RF, is recommended, consistent with the current AASHTO Manual for Bridge Evaluation (MBE): ( )( ) ( )( ) ( )( ) ( )( ) = − γ − γ ± γ γ + (1a) , RF C DC DW P LL IM IoH DC DW P LL IoH IoH IoH For the Strength-Limit States = j j jC Rc s n where the following lower limit shall apply: j j ≥ 0.85c s For the Service-Limit States: =C fR where jc = Condition factor js = System factor j = LRFD resistance factor RFIoH = Rating factor for IoH load C = Capacity fR = Allowable stress specified in the LRFD code Rn = Nominal member resistance (as inspected) DC = Dead-load effect due to structural components and attachments DW = Dead-load effect due to wearing surface and utilities P = Permanent loads other than dead loads LLIoH = IoH live load effect IMIoH = IoH dynamic load allowance γDC = LRFD load factor for structural components and attachments

Protocols for Load Rating Bridges for Implements of Husbandry 113 γDW = LRFD load factor for wearing surfaces and utilities γp = LRFD load factor for permanent loads other than dead loads = 1.0 γLL,IoH = IoH evaluation live load factor, depending on IoH tier For LLIoH, IMIoH, and γLL,IoH, NCHRP Research Report 951 for Project 12-110 provides more details for determining their values considering IoH vehicle loads. The remaining symbols in Eq.1a have been defined in current MBE. Depending on which tier of IoH load is being load rated, LLIoH and γLL,IoH will be accordingly selected. For Tier 1, LLIoH is computed using the recommended notional IoH model in Figure A-1 if adopted by the bridge owner for enveloping IoH vehicles up to 115% of FBF. For Tiers 2 and 3, LLIoH is computed using the IoH vehicle requesting access to public roads and bridges (likely through a permit application). γLL,IoH depends on the tier of IoH load. For Tier 1 IoH load, the live load factor is recom- mended to be the same as that for the legal load in the current MBE. For Tiers 2 and 3 IoH load, Table A-1 displays the recommended live load factor. For all three tiers, one-lane live load distribution is recommended, for low volume of IoH vehicles observed in weigh-in-motion data, with the built-in multiple presence factor 1.2 divided out. The bridge owner may decide to use two lanes or more as appropriate if significant IoH traffic is observed or anticipated. Notional Load Model. For 115% of FBF as the envelope for Tier 1 IoH loads, the notional load model in Figure A-1 is recommended to represent this tier for load rating. This model includes a tractor hauling an equipment unit as shown in Figure A-1a and A-1b. Figure A-1c is a unique IoH configuration with only one tire in the steering axle. The configuration of (a), (b), or (c) inducing the maximum load effect shall control. Table A-2 displays this IoH notional load’s relations with AASHTO HL93 and legal vehicles (Type 3, 3S2, 3-3, SU4 to SU7, and NRL) in terms of simple span maximum moment. This table is recommended (if the 115% of FBF upper limit in Figure A-1 is adopted) for screening bridges in the jurisdiction using their current load ratings in terms of these AASHTO loads for Tier 1 IoH vehicle loads, which represents the majority of current IoH that are to be accommodated. This screening will prevent bridge-by-bridge and vehicle-by-vehicle load rating, Type Frequency Loading Condition DFone- lane a ADTT (1 direction) Load Factor by IoH Weight Ratiob GVW / AL < 2.0 (kips/ft) 2.0 < GVW / AL < 3.0 (kips/ft) GVW / AL > 3.0 (kips/ft) Tier 2 Limited crossings (< 100 crossings per year) Mix with traffic One lane = 3,000 1.30 1.30 1.20 = 1,000 1.30 1.20 1.10 < 100 1.20 1.10 1.10 All Weights Tier 3 Single trip Mix with traffic One lane All ADTTs 1.10 NOTE: a DFone-lane = LRFD one-lane distribution factor with the built-in multiple presence factor 1.2 divided out and the modifying factor, MF, presented below to account for wider or narrower gauge width. b Implement of Husbandry Weight Ratio = GVW / AL; GVW = gross vehicle weight; AL = front-axle to rear-axle length. Uses use only the axles on the bridge. Table A-1. Live load factors for IoH Tiers 2 and 3.

114 Proposed AASHTO Load Rating Provisions for Implements of Husbandry 20 0.796 1.285 1.410 1.562 1.104 1.054 1.005 1.005 1.005 21 0.797 1.294 1.420 1.572 1.107 1.047 0.993 0.993 0.993 22 0.798 1.302 1.428 1.582 1.109 1.043 0.981 0.981 0.981 23 0.798 1.309 1.419 1.590 1.113 1.038 0.972 0.968 0.968 24 0.798 1.315 1.404 1.596 1.114 1.034 0.962 0.952 0.952 25 0.797 1.321 1.391 1.603 1.116 1.030 0.956 0.939 0.939 26 0.796 1.324 1.379 1.610 1.118 1.027 0.948 0.926 0.921 27 0.796 1.330 1.368 1.615 1.119 1.024 0.943 0.915 0.903 28 0.794 1.334 1.359 1.619 1.109 1.021 0.937 0.905 0.889 29 0.793 1.338 1.349 1.624 1.098 1.018 0.932 0.896 0.875 30 0.792 1.319 1.341 1.627 1.088 1.016 0.927 0.889 0.863 32 0.789 1.285 1.328 1.586 1.072 1.013 0.919 0.875 0.843 34 0.785 1.258 1.316 1.541 1.058 1.006 0.913 0.863 0.826 36 0.781 1.234 1.307 1.504 1.045 0.989 0.901 0.854 0.809 38 0.777 1.214 1.298 1.472 1.035 0.973 0.886 0.837 0.793 40 0.771 1.197 1.290 1.445 1.026 0.960 0.872 0.821 0.779 42 0.754 1.183 1.284 1.422 1.018 0.949 0.860 0.807 0.767 44 0.736 1.169 1.278 1.401 1.011 0.939 0.850 0.795 0.756 46 0.722 1.161 1.276 1.388 1.008 0.932 0.843 0.786 0.749 48 0.716 1.163 1.285 1.387 1.013 0.934 0.844 0.785 0.749 50 0.710 1.165 1.250 1.385 1.017 0.936 0.845 0.785 0.749 52 0.704 1.167 1.221 1.358 1.022 0.938 0.846 0.784 0.749 54 0.699 1.169 1.195 1.323 1.026 0.939 0.847 0.783 0.749 56 0.694 1.170 1.172 1.292 1.030 0.941 0.847 0.783 0.749 58 0.689 1.171 1.153 1.266 1.033 0.942 0.848 0.782 0.749 60 0.684 1.173 1.135 1.243 1.036 0.943 0.849 0.782 0.749 70 0.701 1.247 1.132 1.211 1.110 1.003 0.901 0.826 0.793 80 0.709 1.303 1.134 1.170 1.167 1.049 0.941 0.860 0.826 90 0.710 1.345 1.135 1.144 1.209 1.083 0.971 0.885 0.851 100 0.707 1.378 1.136 1.126 1.243 1.110 0.994 0.904 0.871 120 0.694 1.426 1.136 1.102 1.292 1.149 1.028 0.933 0.899 140 0.676 1.459 1.137 1.088 1.326 1.176 1.051 0.952 0.919 160 0.657 1.483 1.137 1.078 1.352 1.195 1.069 0.966 0.933 180 0.637 1.501 1.138 1.070 1.371 1.210 1.082 0.977 0.944 200 0.617 1.516 1.138 1.065 1.386 1.222 1.092 0.986 0.952 250 0.571 1.542 1.138 1.055 1.413 1.243 1.110 1.001 0.967 300 0.530 1.559 1.138 1.050 1.432 1.257 1.122 1.011 0.977 Span, IoH/ HL93 IoH/ Type3 IoH/ Type3S2 IoH/ Type3-3 IoH /SU4 IoH /SU5 IoH /SU6 IoH /SU7 IoH /NRLft Table A-2. Ratios of maximum simple span moment of recommended IoH notional load to AASHTO HL93 and legal vehicles.

Protocols for Load Rating Bridges for Implements of Husbandry 115 minimizing the majority of load-rating analysis work while accommodating the majority of IoH loads desiring access to public roads in the jurisdiction. In other words, a current load rating in terms of any of these AASHTO vehicles can be converted to an IoH rating using Table A-2. When this conversion is implemented in a computer software program, the entire population of bridges in the jurisdiction can be load rated efficiently against the notional model in Figure A-1 for Tier 1 IoH loads. This approach is also recommended in Step 2 in identifying vulnerable bridges in terms of current load rating. However, it is noted that load rating is only one of the parameters that need to be considered in identifying vulnerable bridges in Step 2. There are other factors that load rating is unable to quantify or represent, such as age, lack of maintenance, etc., which have been discussed in Step 2. If the bridge owner adopts a different threshold than 115% but must rate a vehicle model proportional to the configuration in Figure A-1, Table A-2 can still be used with a correspond- ing proportioning factor for this purpose. As such, this computer-aided screening approach may also be used in determining the upper limit for Tier 1 if 115% is not appropriate for the jurisdiction. By trying other values and observing how many bridges may become inadequate for Tier 1 IoH loads using Table A-2, an appropriate upper limit other than 115% can be determined for its acceptable number of bridges to become inadequate for Tier 1 IoH loads. There can be situations in which Table A-2 is not applicable, for example, when a member is not modeled as a longitudinal beam. A substructure member may fall into this category. A similar table may be accordingly developed for that specific member or that type of member. Dynamic Load Allowance. Dynamic load allowance IMIoH in Eq.1a shall be included as an additional fraction IIoH of the static load effect of LLIoH as defined in Eq.1a: = (2)IM I LLIoH IoH IoH where IIoH is 20% for IoH load, except for wood components. For wood components 15 years old or older, IIoH is recommended to be 20%. For wood components younger than 15 years, IIoH may be linearly interpolated to 0 when new (0 year of age). Live Load Distribution Factor/Method. For primary parallel members such as primary beams and slabs supporting a bridge span, the AASHTO LRFD Bridge Design Specifications (BDS) include provisions for distributing vehicular loads to these members for the maximum load effect in them. For beam-slab span types, the BDS girder live load distribution factors (DF) are for this purpose. For slab spans, equivalent strip widths (E) are prescribed in BDS for the same purpose. Both DF and E in BDS are for a gauge width (GW) of 6 ft for typical highway vehicles. For IoH vehicles, this GW varies from the typical 6 ft. It has been found in NCHRP Project 12-110 that the corresponding DFIoH and EIoH for IoH loads can be estimated as modified DFBDS and EBDS from the BDS as follows. = (3a)DF MF DFIoH BDS = (4a)E MF EIoH BDS where MF is the modifying factor given below for a number of span types relevant to IoH loads. More details of their derivations are documented in NCHRP Research Report 951 for Project 12-110. MF is presented for dual-wheel-steering-axle and single-wheel-steering-axle

116 Proposed AASHTO Load Rating Provisions for Implements of Husbandry implements of husbandry. Figures A-1a and A-1 b are typical examples of the former, and Figure A-1c is of the latter. In the following regression relation equations, GW is IoH gauge width in feet, S is beam spacing in feet, L is span length in feet, tS is deck thickness in inches, Nb is number of beams in the bridge-span cross section, W is bridge-span width, I is the moment of inertia for the beams in inch4, and b is width of prestressed concrete box beam in feet. When the gauge width is variable in an implement of husbandry, GW is to be computed as follows as a weighted average GW: ∑ ∑ =         GW GW LoadEffect LoadEffect i i N i j j N where N = Total number of axles on the span for the maximum load effect of interest GWi = Gauge width of Axle i on the span for the maximum load effect of interest LoadEffecti = Load effect of Axlei for the maximum load effect position All load effects herein, including those of the total vehicle (Σ jNLoadEffectj) and individual axle (LoadEffectj , j = 1, 2, . . . , N) are calculated using the beam line theory in the longitudinal direction. (a) MF for dual-wheel-steering-axle implements of husbandry R1 in MF below is equal to 1.15 for GW ≤ 6 ft and 0.85 for GW > 6 ft. MF for Spans of Steel Beams Supporting Reinforced Concrete Deck—Case (a) of Table 4.6.2.2.1-1 in BDS: For interior longitudinal beam moment with DFBDS in BDS Table 4.6.2.2.2b-1: = −     1 0.301 6 (5)1MF R Ln GW For exterior longitudinal beam moment in LRFD Design Table 4.6.2.2.2d-1: = −         1 0.887 6 (6)1 0.870 MF R Ln GW GW L For interior longitudinal beam shear in LRFD Design Table 4.6.2.2.3a-1: = −         1 0.509 6 14 (7)1 0.60 MF R Ln GW S For exterior longitudinal beam shear in LRFD Deign Table 4.6.2.2.3b-1: = −         1 0.640 6 15 (8)1 0.50 MF R Ln GW S

Protocols for Load Rating Bridges for Implements of Husbandry 117 The application ranges for Eqs. 5 to 8 are 3.5 ≤ S ≤ 14 (ft) 5.5 ≤ ts ≤ 14 (in.) 20 ≤ L ≤ 150 (ft) 4 ≤ Nb ≤ 11 5 ≤ GW ≤ 12 (ft) MF for Spans of Steel Beams Supporting Timber Deck—Case (a) of Table 4.6.2.2.1-1 in BDS: For interior longitudinal beam moment in LRFD Design Table 4.6.2.2.2b-1: = −         1 0.499 6 (9)1 0.310 MF R Ln GW GW L For exterior longitudinal beam moment in LRFD Design Table 4.6.2.2.2d-1: = −     1 0.263 6 (10)1MF R Ln GW For interior longitudinal beam shear in LRFD Design Table 4.6.2.2.3a-1: = −                 1 0.134 6 14 6 (11)1 0.12 1.10 0.15 MF R Ln GW L t GW t s s For exterior longitudinal beam shear in LRFD Design Table 4.6.2.2.3b-1: = −             1 0.334 6 (12)1 0.76 0.44 MF R Ln GW t GW S GW s The application ranges for Eqs. 9 to 12 are 1.5 ≤ S ≤ 6 (ft) 3 ≤ ts ≤ 10 (in.) 20 ≤ L ≤ 140 (ft) 5 ≤ Nb ≤ 23 5 ≤ GW ≤ 12 (ft) MF for Spans of Timber Beams Supporting Timber Deck—Case (l) of Table 4.6.2.2.1-1 in BDS: For interior longitudinal beam moment in LRFD Design Table 4.6.2.2.2b-1: = −     1 0.340 6 (13)1MF R Ln GW For exterior longitudinal beam moment in LRFD Design Table 4.6.2.2.2d-1: = −     1 0.376 6 (14)1MF R Ln GW

118 Proposed AASHTO Load Rating Provisions for Implements of Husbandry For interior longitudinal beam shear in LRFD Design Table 4.6.2.2.3a-1: = −             1 0.362 6 6 9 (15)1 0.51 0.17 MF R Ln GW t Ss For exterior longitudinal beam shear in LRFD Design Table 4.6.2.2.3b-1: = −             1 0.284 6 6 9 (16)1 0.67 0.79 MF R Ln GW t Ss The application ranges for Eqs. 13 to 16 are 0.7 ≤ S ≤ 6 (ft) 3 ≤ ts ≤ 10 (in.) 20 ≤ L ≤ 45 (ft) 5 ≤ Nb ≤ 30 850 < I < 12,000 (in4) Beam’s moment of inertia 5 ≤ GW ≤ 12 (ft) MF for Spans of Prestressed Concrete I-Beams Supporting Reinforced Concrete Deck—Case (k) of Table 4.6.2.2.1-1 in BDS: For interior longitudinal beam moment in LRFD Design Table 4.6.2.2.2b-1: = −         1 0.650 6 (17)1 0.50 MF R Ln GW S L For exterior longitudinal beam moment in LRFD Design Table 4.6.2.2.2d-1: = −         1 0.531 6 (18)1 0.40 MF R Ln GW S L For interior longitudinal beam shear in LRFD Design Table 4.6.2.2.3a-1: = −         1 0.863 6 12 (19)1 0.25 MF R Ln GW S For exterior longitudinal beam shear in LRFD Design Table 4.6.2.2.3b-1: = −         1 0.526 6 12 (20)1 0.34 MF R Ln GW S The application ranges for Eqs. 17 to 20 are 3.5 ≤ S ≤ 14 (ft) 5.5 ≤ ts ≤ 11 (in.) 20 ≤ L ≤ 150 (ft) 4 ≤ Nb ≤ 8 5 ≤ GW ≤ 12 (ft)

Protocols for Load Rating Bridges for Implements of Husbandry 119 MF for Spans of Prestressed Concrete Box Beams Supporting Reinforced Concrete Deck— Case (f) of Table 4.6.2.2.1-1 in BDS: For interior longitudinal beam moment in LRFD Design Table 4.6.2.2.2b-1: = −     1 0.198 6 (21)1MF R Ln GW For exterior longitudinal beam moment in LRFD Design Table 4.6.2.2.2d-1: = −     1 0.179 6 (22)1MF R Ln GW For interior longitudinal beam shear in LRFD Design Table 4.6.2.2.3a-1: = −     1 0.147 6 (23)1MF R Ln GW For exterior longitudinal beam shear in LRFD Design Table 4.6.2.2.3b-1: = −     1 0.097 6 (24)1MF R Ln GW The application ranges for Eqs. 21 to 24 are 3 ≤ S ≤ 5 (ft) 5 ≤ ts ≤ 6 (in.) 20 ≤ L ≤ 120 (ft) 7 ≤ Nb ≤ 13 5 ≤ GW ≤ 12 (ft) MF for Spans of Reinforced Concrete T-Beams, Case (e) of Table 4.6.2.2.1-1 in BDS: For interior longitudinal beam moment in LRFD Design Table 4.6.2.2.2b-1: = −         1 3.281 6 (25)1 1.48 MF R Ln GW S L For exterior longitudinal beam moment in LRFD Design Table 4.6.2.2.2d-1: = −     1 0.238 6 (26)1MF R Ln GW For interior longitudinal beam shear in LRFD Design Table 4.6.2.2.3a-1: = −             1 3.097 6 6 (27)1 1.87 0.93 MF R Ln GW GW S L For exterior longitudinal beam shear in LRFD Design Table 4.6.2.2.3b-1: = −         1 0.321 6 (28)1 1.53 MF R Ln GW S L

120 Proposed AASHTO Load Rating Provisions for Implements of Husbandry The application ranges for Eqs. 25 to 28 are 3.5 ≤ S ≤ 14 (ft) 4.5 ≤ ts ≤ 12 (in.) 20 ≤ L ≤ 90 (ft) 4 ≤ Nb ≤ 14 5 ≤ GW ≤ 12 (ft) MF for Spans of Reinforced Concrete and Timber Slab, Cases (a), (b), and (c) of LRFD Design Table 4.6.2.3-1 For interior longitudinal strip equivalent width E in LRFD Design Equation 4.6.2.3-1: = −     1 1 0.155 6 (29) 1 MF R Ln GW For edge longitudinal strip equivalent width in LRFD Design 4.6.2.1.4b: = 1 (30)MF The application ranges for Eqs. 29 to 30 are 25 ≤ ts ≤ 45 (in.) 20 ≤ L ≤ 60 (ft) 12 ≤ W ≤ 28 (ft) 5 ≤ GW ≤ 12 (ft) (b) MF for single-wheel-steering-axle implements of husbandry R2 in MF below is equal to 1.05. MF for Spans of Steel Beams Supporting Reinforced Concrete Deck—Case (a) of Table 4.6.2.2.1-1 in BDS: For interior longitudinal beam moment with DFBDS in BDS Table 4.6.2.2.2b-1: =             0.726 14 (31)2 0.233 0.071 0.225 MF R L W L S L For exterior longitudinal beam moment in LRFD Design Table 4.6.2.2.2d-1: 1.015 6 0.233 0.111 0.018 (32)2 0.228 MF R GW S L GW L =     −     +     +       For interior longitudinal beam shear in LRFD Design Table 4.6.2.2.3a-1: =             1.035 6 (33)2 0.261 0.059 0.396 MF R GW S L S GW For exterior longitudinal beam shear in LRFD Deign Table 4.6.2.2.3b-1: =             1.045 6 (34)2 0.334 0.050 0.198 MF R GW L S GW S

Protocols for Load Rating Bridges for Implements of Husbandry 121 The application ranges for Eqs. 31 to 34 are 3.5 ≤ S ≤ 14 (ft) 5.5 ≤ ts ≤ 14 (in.) 20 ≤ L ≤ 150 (ft) 4 ≤ Nb ≤ 11 6 ≤ GW ≤ 10 (ft) MF for Spans of Steel Beams Supporting Timber Deck—Case (a) of Table 4.6.2.2.1-1 in BDS: For interior longitudinal beam moment in LRFD Design Table 4.6.2.2.2b-1: =         + −     − +     −                   1.118 6 0.094 0.559 0.00222 0.240 6 0.175 (35)2 0.151 0.039 MF R GW S L GW L L t t GW s s For exterior longitudinal beam moment in LRFD Design Table 4.6.2.2.2d-1: =                 1.736 1 (36)2 0.050 0.235 0.091 0.053 MF R S L S S GW S ts For interior longitudinal beam shear in LRFD Design Table 4.6.2.2.3a-1: 1.542 0.0437 6 0.337 9 0.0204 (37)2MF R GW S GW S = −     −     −         For exterior longitudinal beam shear in LRFD Design Table 4.6.2.2.3b-1: =         1.166 9 (38)2 0.160 0.087 MF R S S GW The application ranges for Eqs. 35 to 38 are 1.5 ≤ S ≤ 6 (ft) 3 ≤ ts ≤ 10 (in.) 20 ≤ L ≤ 140 (ft) 5 ≤ Nb ≤ 23 6 ≤ GW ≤ 10 (ft) MF for Spans of Timber Beams Supporting Timber Deck—Case (l) of Table 4.6.2.2.1-1 in BDS: For interior longitudinal beam moment in LRFD Design Table 4.6.2.2.2b-1: 1.088 6 (39)2 0.298 0.022 0.012 MF R GW GW L GW ts =             For exterior longitudinal beam moment in LRFD Design Table 4.6.2.2.2d-1: =                     1.141 9 6 (40)2 0.064 3 0.114 0.114 0.105 0.307 MF R S GW Lt I S L S t s s

122 Proposed AASHTO Load Rating Provisions for Implements of Husbandry For interior longitudinal beam shear in LRFD Design Table 4.6.2.2.3a-1: =         1.232 9 (41)2 0.035 0.074 MF R S GW S For exterior longitudinal beam shear in LRFD Design Table 4.6.2.2.3b-1: =         − 1.199 9 (42)2 0.045 0.098 MF R GW S S The application ranges for Eqs. 39 to 42 are 0.7 ≤ S ≤ 6 (ft) 3 ≤ ts ≤ 10 (in.) 20 ≤ L ≤ 45 (ft) 5 ≤ Nb ≤ 30 850 < I < 12,000 (in4) Beam’s moment of inertia 6 ≤ GW ≤ 10 (ft) MF for Spans of Prestressed Concrete I-Beams Supporting Reinforced Concrete Deck—Case (k) of Table 4.6.2.2.1-1 in BDS: For interior longitudinal beam moment in LRFD Design Table 4.6.2.2.2b-1: =             1.132 1 (43)2 0.198 0.025 0.150 MF R L GW L S L For exterior longitudinal beam moment in LRFD Design Table 4.6.2.2.2d-1: =             1.259 1 (44)2 0.184 0.204 0.164 MF R S GW L S L For interior longitudinal beam shear in LRFD Design Table 4.6.2.2.3a-1: =             3.013 1 (45)2 0.239 0.662 0.597 MF R S GW L S L For exterior longitudinal beam shear in LRFD Design Table 4.6.2.2.3b-1: =         1.297 6 (46)2 0.399 0.264 MF R GW GW S The application ranges for Eqs. 43 to 46 are 3.5 ≤ S ≤ 14 (ft) 5.5 ≤ ts ≤ 11 (in.) 20 ≤ L ≤ 150 (ft) 4 ≤ Nb ≤ 8 6 ≤ GW ≤ 10 (ft)

Protocols for Load Rating Bridges for Implements of Husbandry 123 MF for Spans of Prestressed Concrete Box Beams Supporting Reinforced Concrete Deck— Case (f) of Table 4.6.2.2.1-1 in BDS: For interior longitudinal beam moment in LRFD Design Table 4.6.2.2.2b-1: =             0.967 (47)2 0.157 0.0238 0.176 MF R S GW L S t S s For exterior longitudinal beam moment in LRFD Design Table 4.6.2.2.2d-1: =                     1.323 1 (48)2 0.358 0.514 0.316 0.272 2 0.165 MF R L GW L GW b b t L bds For interior longitudinal beam shear in LRFD Design Table 4.6.2.2.3a-1: =         1.229 (49)2 0.077 0.103 MF R S GW L S For exterior longitudinal beam shear in LRFD Design Table 4.6.2.2.3b-1: MF R b GW b 1.193 12 (50)2 0.069 0.191 =         The application ranges for Eqs. 47 to 50 are 3 ≤ b ≤ 5 (ft) 5 ≤ ts ≤ 6 (in.) 2.25 ≤ d ≤ 3.5 (ft) 20 ≤ L ≤ 120 (ft) 7 ≤ Nb ≤ 13 6 ≤ GW ≤ 10 (ft) MF for Spans of Reinforced Concrete T-Beams, Case (e) of Table 4.6.2.2.1-1 in BDS: For interior longitudinal beam moment in LRFD Design Table 4.6.2.2.2b-1: =             0.975 1 (51)2 0.193 0.038 0.111 MF R L GW L S L For exterior longitudinal beam moment in LRFD Design Table 4.6.2.2.2d-1: =         0.968 (52)2 0.125 0.023 MF R S GW L GW For interior longitudinal beam shear in LRFD Design Table 4.6.2.2.3a-1: =                 0.747 14 (53)2 0.058 0.392 0.136 0.229 MF R L S S S GW t S s

124 Proposed AASHTO Load Rating Provisions for Implements of Husbandry For exterior longitudinal beam shear in LRFD Design Table 4.6.2.2.3b-1: =         0.987 14 (54)2 0.307 0.112 MF R S S GW The application ranges for Eqs. 51 to 54 are 3.5 ≤ S ≤ 14 (ft) 4.5 ≤ ts ≤ 12 (in.) 20 ≤ L ≤ 90 (ft) 4 ≤ Nb ≤ 14 6 ≤ GW ≤ 10 (ft) MF for Spans of Reinforced Concrete and Timber Slab, Cases (a), (b), and (c) of LRFD Design Table 4.6.2.3-1 For interior longitudinal strip equivalent width E in LRFD Design Equation 4.6.2.3-1: 0.618 1 (55)0.137 0.160 2 MF GW L GW R ( )=         For edge longitudinal strip equivalent width in LRFD Design 4.6.2.1.4b: = 1 (56)MF The application ranges for Eqs. 55 to 56 are 25 ≤ ts ≤ 45 (in.) 20 ≤ L ≤ 60 (ft) 12 ≤ W ≤ 28 (ft) 6 ≤ GW ≤ 10 (ft) LFR: For LFR of IoH loads, the following rating factor, RF, is recommended, consistent with current MBE: ( ) = − +1 (1b) 1 2, RF C A D A L I IoH IoH IoH IoH where RFIoH = The rating factor for the IoH live load–carrying capacity. The rating factor multiplied by the rating vehicle in tons gives the rating of the structure C = The capacity of the member D = The dead-load effect on the member. For composite members, the dead-load effect on the noncomposite section and the dead-load effect on the composite section need to be evaluated when the allowable stress method is used LIoH = The IoH live load effect on the member IIoH = The IoH impact factor to be used with the live load effect A1 = Factor for dead loads A2,IoH = Factor for IoH live load, depending on IoH tier

Protocols for Load Rating Bridges for Implements of Husbandry 125 For LIoH, IIoH, and A2,IoH, NCHRP Research Report 951 for Project 12-110 provides more details of determining their values for IoH vehicle load. The remaining symbols in Eq. 1b have been defined in current MBE. Depending on which tier of IoH load is being load rated, LIoH and A2,IoH will be accordingly selected. For Tier 1, LIoH is computed using the recommended notional IoH model in Figure A-1 if adopted by the bridge owner for enveloping IoH up to 115% of FBF. For Tiers 2 and 3, LIoH is computed using the IoH vehicle requesting access to public roads and bridges (likely through a permit application). The live load factor A2,IoH depends on the tier of IoH load. For Tier 1 IoH load, it is the same as that for the legal load, namely A2,IoH = 2.17 for the inventory rating and A2,IoH = 1.30 for the operating rating. For Tiers 2 and 3 IoH load, A2,IoH =2.06 for the inventory rating and A2,IoH = 1.24 for the operating rating. For all tiers, one-lane live load distribution is used, for the low volume of IoH vehicles observed in weigh-in-motion data used in NCHRP Project 12-110 in calibrating live load factor. For a specific site with more significant volume of IoH vehicles, the bridge owner may decide to use two lanes or more as appropriate if significant IoH traffic is observed or anticipated. Notional Load Model. For 115% of FBF as the envelope for Tier 1 IoH loads, the notional load model in Figure A-1 is recommended to represent this tier for load rating, which includes a tractor hauling an equipment unit as shown in Figure A-1a and A-1b. Figure A-1c is a unique IoH configuration with only one tire in the steering axle. The one inducing a more severe load effect shall control. Table A-2 displays this IoH notional load’s relations with AASHTO HL93 and legal vehicles (Type 3, 3S2, 3-3, SU4 to SU7, and NRL) in terms of simple span maximum moment. This table is recommended (if 115% of FBF is adopted) for screening bridges in the jurisdiction using their current load ratings in terms of these AASHTO loads for Tier 1 IoH vehicle loads, which represents the majority of current IoH that are to be accommodated. This screening will prevent bridge-by-bridge and vehicle-by-vehicle load rating, minimizing the majority of load-rating analysis work while accommodating the majority of IoH loads desiring access to public roads in the jurisdiction. In other words, a current load rating in terms of any of these AASHTO vehicles can be converted to IoH rating using Table A-2. When this conversion is implemented in a computer software program, the entire population of bridges in the jurisdiction can be load rated efficiently against the notional model in Figure A-1 for Tier 1 IoH loads. This approach is also recommended in Step 2 in identifying vulnerable bridges in terms of current load rating. However, it is noted that load rating is only one of the parameters that needs to be considered in identifying vulnerable bridges in Step 2. There are other factors that load rating is unable to quantify or represent, such as age, lack of maintenance, etc., which have been discussed in Step 2. If the bridge owner adopts a different threshold other than 115% but still proportional to the configuration in Figure A-1, Table A-2 can still be used with a corresponding proportioning factor for this purpose. As such, this computer-aided screening approach may also be used in determining the upper limit for Tier 1 if 115% is not appropriate for the jurisdiction. By trying other values and observing how many bridges may become inadequate for Tier 1 IoH loads using Table A-2, an appropriate upper limit other than 115% can be determined for its acceptable number of bridges to become inadequate for Tier 1 IoH loads. Dynamic Load Allowance. Dynamic load allowance IIoH in Eq. 1b shall be included, as an additional fraction of the static load effect of LIoH. IIoH is computed according to current MBE

126 Proposed AASHTO Load Rating Provisions for Implements of Husbandry for LFR but is capped at 20% for IoH load, except wood components. For wood components 15 years old or older, IIoH is recommended to be also capped at 20%. For wood components younger than 15 years, IIoH may be linearly interpolated. Live Load Distribution Factor/Method. For primary parallel members such as primary beams and slabs supporting a bridge span, the AASHTO Standard Specifications for Highway Bridges (SSHB) includes provisions for distributing vehicular loads to these members for the maximum load effect in them. For beam-slab span types, the SSHB girder live load distribution factors (DF) are for this purpose. For slab span types, equivalent strip widths (E) are prescribed in SSHB for the same purpose. Both DF and E in SSHB are for a gauge width (GW) of 6 ft for typical highway vehicles. For IoH vehicles, this GW varies from the typical 6 ft. It has been found in NCHRP Project 12-110 that the corresponding DFIoH and EIoH for IoH loads can be estimated as modified DFSSHB and ESSHB from the SSHB as follows. = (3b)DF MF DFIoH SSHB = (4b)E MF EIoH SSHB where MF is the modifying factor given below for a number of span types relevant to IoH loads. More details of their derivations are documented in NCHRP Research Report 951 for Project 12-110. MF is presented for both dual-wheel-steering-axle and single-wheel-steering- axle implements of husbandry. Figure A-1a and A-1b are typical examples of the former, and Figure A-1c is of the latter. In the following regression relation equations, GW is IoH gauge width in feet, S is beam spacing in feet, L is span length in feet t, tS is deck thickness in inches, Nb is number of beams in the bridge-span cross section, W is bridge-span width, I is the moment of inertia for the beams in inch4, and b is width of prestressed concrete box beam in feet. When the gauge width is variable in an implement of husbandry, GW is to be computed as follows as a weighted average GW: ∑ ∑=         GW GW LoadEffect LoadEffect i i j j N i N where N = Total number of axles on the span for the maximum load effect of interest GWi = Gauge width of Axle i on the span for the maximum load effect of interest LoadEffecti = Load effect of Axle i for the maximum load effect position All load effects herein, including those of the total vehicle (Σ jNLoadEffectj) and individual axle (LoadEffectj, j = 1, 2, . . . , N) are calculated using the beam line theory in the longitudinal direction. (a) MF for dual-wheel-steering-axle implements of husbandry R1 in MF below is equal to 1.15 for GW ≤ 6 ft and 0.85 for GW > 6 ft. MF for Spans of Steel Beams Supporting Reinforced Concrete Deck in Article 3.23.2 of SSHB: For interior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB = −     1 0.301 6 (57)1MF R Ln GW

Protocols for Load Rating Bridges for Implements of Husbandry 127 For exterior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: = −         1 0.887 6 (58)1 0.870 MF R Ln GW GW L For interior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: = −         1 0.509 6 14 (59)1 0.60 MF R Ln GW S For exterior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: = −         1 0.640 6 15 (60)1 0.50 MF R Ln GW S The application ranges for Eqs.57 to 60 are 3.5 ≤ S ≤ 14 (ft) 5.5 ≤ ts ≤ 14 (in.) 20 ≤ L ≤ 150 (ft) 4 ≤ Nb ≤ 11 5 ≤ GW ≤ 12 (ft) MF for Spans of Steel Beams Supporting Timber Deck in Article 3.23.2 of SSHB: For interior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: = −         1 0.499 6 (61)1 0.310 MF R Ln GW GW L For exterior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: = −     1 0.263 6 (62)1MF R Ln GW For interior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: = −                 1 0.134 6 14 6 (63)1 0.12 1.10 0.15 MF R Ln GW L t GW t s s For exterior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: = −             1 0.334 6 (64)1 0.76 0.44 MF R Ln GW t GW S GW s The application ranges for Eqs. 61 to 64 are 1.5 ≤ S ≤ 6 (ft) 3 ≤ ts ≤ 10 (in.) 20 ≤ L ≤ 140 (ft) 5 ≤ Nb ≤ 23 5 ≤ GW ≤ 12 (ft)

128 Proposed AASHTO Load Rating Provisions for Implements of Husbandry MF for Spans of Timber Beams Supporting Timber Deck in Article 3.23.2 of SSHB: For interior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: = −     1 0.340 6 (65)1MF R Ln GW For exterior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: = −     1 0.376 6 (66)1MF R Ln GW For interior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: = −             1 0.362 6 6 9 (67)1 0.51 0.17 MF R Ln GW t Ss For exterior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: = −             1 0.284 6 6 9 (68)1 0.67 0.79 MF R Ln GW t Ss The application ranges for Eqs. 65 to 68 are 0.7 ≤ S ≤ 6 (ft) 3 ≤ ts ≤ 10 (in.) 20 ≤ L ≤ 45 (ft) 5 ≤ Nb ≤ 30 850 < I < 12,000 (in4) Beam’s moment of inertia 5 ≤ GW ≤ 12 (ft) MF for Spans of Prestressed Concrete I-Beams Supporting Reinforced Concrete Deck in Article 3.23.2 of SSHB: For interior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: = −         1 0.650 6 (69)1 0.50 MF R Ln GW S L For exterior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: = −         1 0.531 6 (70)1 0.40 MF R Ln GW S L For interior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: = −         1 0.863 6 12 (71)1 0.25 MF R Ln GW S

Protocols for Load Rating Bridges for Implements of Husbandry 129 For exterior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: = −         1 0.526 6 12 (72)1 0.34 MF R Ln GW S The application ranges for Eqs. 69 to 72 are 3.5 ≤ S ≤ 14 (ft) 5.5 ≤ ts ≤ 11 (in.) 20 ≤ L ≤ 150 (ft) 4 ≤ Nb ≤ 8 5 ≤ GW ≤ 12 (ft) MF for Spans of Prestressed Concrete Box Beams Supporting Reinforced Concrete Deck in Article 3.23.2 of SSHB: For interior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: = −     1 0.198 6 (73)1MF R Ln GW For exterior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: = −     1 0.179 6 (74)1MF R Ln GW For interior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: = −     1 0.147 6 (75)1MF R Ln GW For exterior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: = −     1 0.097 6 (76)1MF R Ln GW The application ranges for Eqs. 73 to 76 are 3 ≤ S ≤ 5 (ft) 5 ≤ ts ≤ 6 (in.) 20 ≤ L ≤ 120 (ft) 7 ≤ Nb ≤ 13 5 ≤ GW ≤ 12 (ft) MF for Spans of Reinforced Concrete T-Beams in Article 3.23.2 of SSHB: For interior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: = −         1 3.281 6 (77)1 1.48 MF R Ln GW S L

130 Proposed AASHTO Load Rating Provisions for Implements of Husbandry For exterior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: = −     1 0.238 6 (78)1MF R Ln GW For interior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: = −             1 3.097 6 6 (79)1 1.87 0.93 MF R Ln GW GW S L For exterior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: = −         1 0.321 6 (80)1 1.53 MF R Ln GW S L The application ranges for Eqs. 77 to 80 are 3.5 ≤ S ≤ 14 (ft) 4.5 ≤ ts ≤ 12 (in.) 20 ≤ L ≤ 90 (ft) 4 ≤ Nb ≤ 14 5 ≤ GW ≤ 12 (ft) MF for Spans of Reinforced Concrete and Timber Slab in Article 3.24.3.2 and 3.24.8 of SSHB: For interior longitudinal strip equivalent width E in Article 3.24.3.2 of SSHB: = −     1 1 0.155 6 (81) 1 MF R Ln GW For edge longitudinal strip equivalent width E in Article 3.24.8 of SSHB: = 1 (82)MF The application ranges for Eqs. 81 to 82 are 25 ≤ ts ≤ 45 (in.) 20 ≤ L ≤ 60 (ft) 12 ≤ W ≤ 28 (ft) 5 ≤ GW ≤ 12 (ft) (b) MF for single-wheel-steering-axle implements of husbandry R2 in MF below is equal to 1.05. MF for Spans of Steel Beams Supporting Reinforced Concrete Deck in Article 3.23.2 of SSHB: For interior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: =             0.726 14 (83)2 0.233 0.071 0.225 MF R L W L S L

Protocols for Load Rating Bridges for Implements of Husbandry 131 For exterior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: =     −     +     +      1.015 6 0.233 0.111 0.018 (84)2 0.228 MF R GW S L GW L For interior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: =             1.035 6 (85)2 0.261 0.059 0.396 MF R GW S L S GW For exterior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: =             1.045 6 (86)2 0.334 0.050 0.198 MF R GW L S GW S The application ranges for Eqs. 83 to 86 are 3.5 ≤ S ≤ 14 (ft) 5.5 ≤ ts ≤ 14 (in.) 20 ≤ L ≤ 150 (ft) 4 ≤ Nb ≤ 11 6 ≤ GW ≤ 10 (ft) MF for Spans of Steel Beams Supporting Timber Deck in Article 3.23.2 of SSHB: For interior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: 1.118 6 0.094 0.559 0.00222 0.240 6 0.175 (87)2 0.151 0.039 MF R GW S L GW L L t t GW s s =         + −     − +     −                   For exterior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: =                 1.736 1 (88)2 0.050 0.235 0.091 0.053 MF R S L S S GW S ts For interior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: = −     −     −         1.542 0.0437 6 0.337 9 0.0204 (89)2MF R GW S GW S For exterior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: =         1.166 9 (90)2 0.160 0.087 MF R S S GW

132 Proposed AASHTO Load Rating Provisions for Implements of Husbandry The application ranges for Eqs. 87 to 90 are 1.5 ≤ S ≤ 6 (ft) 3 ≤ ts ≤ 10 (in.) 20 ≤ L ≤ 140 (ft) 5 ≤ Nb ≤ 23 6 ≤ GW ≤ 10 (ft) MF for Spans of Timber Beams Supporting Timber Deck in Article 3.23.2 of SSHB: For interior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: =             1.088 6 (91)2 0.298 0.022 0.012 MF R GW GW L GW ts For exterior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: 1.141 9 6 (92)2 0.064 3 0.114 0.114 0.105 0.307 MF R S GW Lt I S L S t s s =                     For interior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: =         1.232 9 (93)2 0.035 0.074 MF R S GW S For exterior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: =         − 1.199 9 (94)2 0.045 0.098 MF R GW S S The application ranges for Eqs. 91 to 94 are 0.7 ≤ S ≤ 6 (ft) 3 ≤ ts ≤ 10 (in.) 20 ≤ L ≤ 45 (ft) 5 ≤ Nb ≤ 30 850 < I < 12,000 (in4) Beam’s moment of inertia 6 ≤ GW ≤ 10 (ft) MF for Spans of Prestressed Concrete I-Beams Supporting Reinforced Concrete Deck in Article 3.23.2 of SSHB: For interior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: =             1.132 1 (95)2 0.198 0.025 0.150 MF R L GW L S L For exterior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: =             1.259 1 (96)2 0.184 0.204 0.164 MF R S GW L S L

Protocols for Load Rating Bridges for Implements of Husbandry 133 For interior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: =             3.013 1 (97)2 0.239 0.662 0.597 MF R S GW L S L For exterior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: =         1.297 6 (98)2 0.399 0.264 MF R GW GW S The application ranges for Eqs. 95 to 98 are 3.5 ≤ S ≤ 14 (ft) 5.5 ≤ ts ≤ 11 (in.) 20 ≤ L ≤ 150 (ft) 4 ≤ Nb ≤ 8 6 ≤ GW ≤ 10 (ft) MF for Spans of Prestressed Concrete Box Beams Supporting Reinforced Concrete Deck in Article 3.23.2 of SSHB: For interior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: =             0.967 (99)2 0.157 0.0238 0.176 MF R S GW L S t S s For exterior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: =                     1.323 1 (100)2 0.358 0.514 0.316 0.272 2 0.165 MF R L GW L GW b b t L bds For interior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: =         1.229 (101)2 0.077 0.103 MF R S GW L S For exterior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: =         1.193 12 (102)2 0.069 0.191 MF R b GW b The application ranges for Eqs. 99 to 102 are 3 ≤ b ≤ 5 (ft) 5 ≤ ts ≤ 6 (in.) 2.25 ≤ d ≤ 3.5 (ft) 20 ≤ L ≤ 120 (ft) 7 ≤ Nb ≤ 13 6 ≤ GW ≤ 10 (ft)

134 Proposed AASHTO Load Rating Provisions for Implements of Husbandry MF for Spans of Reinforced Concrete T-Beams in Article 3.23.2 of SSHB: For interior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: =             0.975 1 (103)2 0.193 0.038 0.111 MF R L GW L S L For exterior longitudinal beam moment with DFSSHB in Article 3.23.2 of SSHB: =         0.968 (104)2 0.125 0.023 MF R S GW L GW For interior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: =                 0.747 14 (105)2 0.058 0.392 0.136 0.229 MF R L S S S GW t S s For exterior longitudinal beam shear with DFSSHB in Article 3.23.2 of SSHB: =         0.987 14 (106)2 0.307 0.112 MF R S S GW The application ranges for Eqs. 103 to 106 are 3.5 ≤ S ≤ 14 (ft) 4.5 ≤ ts ≤ 12 (in.) 20 ≤ L ≤ 90 (ft) 4 ≤ Nb ≤ 14 6 ≤ GW ≤ 10 (ft) MF for Spans of Reinforced Concrete and Timber Slab, in Articles 3.24.3.2 and 3.24.8 of SSHB: For interior longitudinal strip equivalent width E in Article 3.24.3.2 of SSHB: ( )=         0.618 1 (107)0.136 0.160 2 MF GW L GW R For edge longitudinal strip equivalent width E in Article 3.24.8 of SSHB: = 1 (108)MF The application ranges for Eqs. 107 to 108 are 25 ≤ ts ≤ 45 (in.) 20 ≤ L ≤ 60 (ft) 12 ≤ W ≤ 28 (ft) 6 ≤ GW ≤ 10 (ft) Step 3.3: Screening Bridge Inventory for Tier 1 IoH Loads The notional load in Figure A-1 is to envelop Tier 1 IoH loads. It can be used to screen bridge inventory against Tier 1 loads without bridge-by-bridge and vehicle-by-vehicle analysis for load rating. This is facilitated by Table A-2 that provides ratios of simple span maximum moment of the recommended notional load to other AASHTO legal vehicles and the HL93.

Protocols for Load Rating Bridges for Implements of Husbandry 135 As a simplified example, consider a 48-ft simple bridge span, with an LRFR rating factor of 0.94 for its interior beams as primary members, referring to the AASHTO legal load, for which Type3 controls span moment for rating. Use IM = 20% (instead of 33% for other highway loads) and an MF = 0.85 (15% lower than the AASHTO LRFD live load distribution factor) deemed to be applicable for the observed gauge widths of IoH in the jurisdiction, the rating for Tier 1 can be estimated as follows for screening purposes. =     + +         =             = 1 2 3 1 1 1 0.94 1 1.163 1.33 1.20 1 0.85 1.05 1 3RF RF Table RatioforIoHoverType IM IM MF Tier IoH Type HighwayLoad IoH Step 3.4: Bridge Posting If Needed If a bridge is load rated below the legal load of the jurisdiction for IoH, it may be considered to be posted for load restriction. Consider developing a posting policy for IoH consistent with current posting policy, or new legislation may need to be developed. It is recommended that the posting sign include (a) axle weight limit, (b) tandem weight limit, and (c) gross weight limit. The posting signage needs to comply with the requirements set forth in FHWA’s Manual on Uniform Traffic Control Devices (MUTCD). Step 4: Development of Strategies for Implementation of Load-Rating/Permitting Program for IoH Perform an impact study based on the decisions made in Step 3. Consider including the following items for an impact study. 1. Identify those bridges that are unable to carry Tier 0 and Tier 1 loads enveloped by the notional load model adopted by the agency according to the guidelines in Step 3. 2. Determine the actions possibly needed for those concerned bridges identified in Item 1, which may include but not be limited to, bridge posting, enforcement effort increasing, bridge strengthening, etc. 3. Estimate associated impact costs for implementing the actions in Item 2. 4. Evaluate the availability of funds to cover the estimated cost. When Item 4’s result is beyond the foreseeable budget, the load-rating/permitting program being developed will need to be revised for it to be implementable. This may translate to iteration of Steps 2 and 3. Develop a proposed flowchart for the load-rating/permitting process, including indication of responsible offices for each function that needs to be carried out. Also consider includ- ing needed reviews and trainings to ensure success. Identify the needed tools for successful realization for each function in the process, such as route maps for certain IoH loads, etc. Estimate the cost for each function and the entire process. Develop a plan for following up monitoring to gather information of implementation and long-term practice. The gathered information will help quantitative evaluation of the load- rating/permitting program for IoH. It will assist in future decision making for enhancing the program. Estimate the cost for such monitoring and information gathering. The impact study results may lead to iteration of Steps 2 and 3, in order to revise the decisions on a load-rating/permitting program and to make it implementable.

136 Proposed AASHTO Load Rating Provisions for Implements of Husbandry Consider communicating the load-rating/permitting program design and impact study results with the identified stakeholders. Receive and study their comments and feedback. Make needed revisions or fine tuning. Ensure funding if needed when finalizing. Step 5: Legislative Action If Needed Identify items decided in Steps 3 and 4 that require new legislation. Accordingly, prepare to assist the legislature in passing new legislation. This may include, but not be limited to, organiz- ing needed legislative hearings, preparing material to assist a legislature in understanding the issues and associated costs, answering questions from the legislature, etc. Step 6: Implementation, Monitoring, and Further Enhancement Consider implementing a subprogram as part of the load-rating/permitting program to further collect data and perform analysis beyond successful commencement of the program designed in the previous steps. Decide on which data to collect (e.g., IoH vehicles requesting travel, to travel on which roads, their requested frequencies and/or durations, etc.), how often to review gathered data (e.g., every 6 months or 12 months), reporting structure (e.g., to the state bridge engineer, the supervising engineer, head of agency, legislature, etc.), and needed types of recommendation based on the data analysis for future improvement of the current load-rating/ permitting program. For instance, for Tiers 2 and 3 in the three-tier program or Tier 2 in the two-tier program, it could be helpful to gather data on what types of IoH, roads, and bridges were used, in which time periods/seasons they were used, for what durations, for what purposes or usages, etc. Such data could help develop expectations for future IoH loads and their demands. Such expectations may trigger future enhancement changes to the load-rating/permitting program.