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Axle load
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Axle load
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The axle load of a wheeled vehicle is the total weight bearing on the roadway for all wheels connected to a given axle. Axle load is an important design consideration in the engineering of roadways and railways, as both are designed to tolerate a maximum weight-per-axle (axle load); exceeding the maximum rated axle load will cause damage to the roadway or railway tracks.

Railway use

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On railways, a given section of tracks is designed to support a maximum axle load. The maximum axle load is determined by train speeds, weight of rails, density of sleepers and fixtures, amount and standard of ballast, and strength of bridges and earthworks. Higher operating speeds can be achieved by reducing axle loads and increased load-carrying capacity. Operating above the specified load can cause catastrophic failure of track components.[citation needed] The diameter of the wheels also affects the maximum axle load of a Talgo RD wagon.

United Kingdom

[edit]

The standard rail weight for British railways is now 113 lb/yd (56.1 kg/m). Before the 1990s, most diesel locomotives were built to a maximum axle load of 19 long tons (19.3 tonnes; 21.3 short tons) so the maximum locomotive weight was 76 long tons (77.2 tonnes; 85.1 short tons) for a four-axle locomotive and 114 long tons (115.8 tonnes; 127.7 short tons) for a six-axle one. Higher axle loads are now permitted, e.g. the Class 67 locomotive is a four-axle machine weighing 90 tonnes (88.6 long tons; 99.2 short tons), giving 22.5 tonnes (22.1 long tons; 24.8 short tons) on each axle.[citation needed]

Australia

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The Fortescue railway uses 68-kilogram-per-metre (140 lb/yd) rail on concrete sleepers and has a maximum axle load of 40 t (39 long tons; 44 short tons), which as of 2008 was the highest axle load of any railway in the world.[1] In 2011, it was proposed to increase the axle load of the railway to 42 tonnes (41 long tons; 46 short tons).[2][needs update][3]

Kenya

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In 2022, sixteen new metre-gauge locomotives were supplied by CRRC with axleloads of 12.5 tonnes, 14 tonnes, and 18 tonnes respectively.

Bridge loading

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Bridges may have to carry several locomotives or wagons at the same time. especially on longer spans; in that case they require separate calculation of maximum allowable axle load. A weak bridge may limit the axle load of the full line. Theodore Cooper developed the E10 loading system for calculating the strength of bridges.[citation needed]

Roadway use

[edit]
Further information: road wear

The term axle load is also applicable to trucks, and this context is made more complex by some trucks having more than two wheels per axle. The axle load remains the same, but the load borne by the individual wheels is reduced by having more contact area (more wheels, larger tires, lower tire pressure) to distribute the load.[4]

See also

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References

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[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Axle load

View on Grokipedia
from Grokipedia
Axle load is the total weight borne by a single of a wheeled , including both the vehicle's own mass and any or passengers it carries, distributed across the wheels connected to that axle. In , this measure is fundamental for assessing the impact of vehicles on , as it determines the static vertical force exerted on roads, bridges, or railway tracks per axle. For road vehicles, axle load is typically calculated as the portion of the gross supported by each axle configuration, such as single, , or tridem setups, while in railways, it represents the weight per axle derived from the total mass divided by the number of axles. The significance of axle load extends to pavement and track design, where excessive loads can accelerate wear, cracking, and structural failure, necessitating standards like the Equivalent Single Axle Load (ESAL) in road engineering to equate various configurations to a standard 18,000-pound (8,164 kg) single- load for predicting long-term damage. , federal regulations, such as those under the Federal-Aid Highway Amendments of 1974, limit single axles to 20,000 pounds (9,072 kg), tandem axles to 34,000 pounds (15,422 kg), and gross vehicle weight to 80,000 pounds (36,287 kg) on the Interstate System to protect and bridges. For railways, axle loads influence track strength and speed restrictions; European standards often cap them at 22.5 metric tons (24.7 short tons), while North American freight lines permit up to 35 metric tons (38.6 short tons) on heavy-haul routes to accommodate bulk cargo transport. Monitoring and enforcement of axle loads are critical for safety and efficiency, with technologies like weigh-in-motion systems used at ports and highways to detect overloads in real-time, preventing accidents and extending infrastructure lifespan. Overloading an axle can increase pavement deterioration exponentially—often by a factor related to the fourth power of the load—leading to higher maintenance costs and reduced service life. In railway contexts, higher axle loads enable greater freight capacity but require advanced materials and maintenance to mitigate risks like rail fatigue and derailments. Overall, axle load management balances economic demands for heavier vehicles with the need to sustain transportation networks.

Fundamentals

Definition

The axle load of a wheeled is defined as the total static vertical force exerted on the supporting surface—such as a track or —by all wheels connected to a single , assuming the vehicle is in a horizontal position. This force represents the portion of the vehicle's overall weight that is transmitted through that specific axle to the below. The components contributing to axle load include the distribution of the vehicle's own weight (such as the , , and passengers) and any additional or carried by the . While the primary focus is on static components, dynamic influences like vehicle motion or uneven surfaces can temporarily amplify the effective load, though these are not part of the base static measurement. Axle loads are typically measured in units of tons (short tons of 2,000 pounds or metric tonnes of 1,000 kilograms internationally), kips (where 1 kip equals 1,000 pounds-force), or newtons for more precise calculations. Examples of axle configurations include a single , which typically supports two wheels (one on each side) and bears the load for that isolated unit; a in railway vehicles, consisting of a pivoting frame with two or more to distribute weight over multiple wheels; and tandem axles in trucks, where two closely spaced axles share the load to comply with weight limits while maximizing capacity.

Importance

Axle load plays a critical role in transportation , as excessive loads can lead to derailments, structural failures in , and increased risks by compromising stability and control. In operations, higher axle loads beyond design limits have been shown to heighten the potential for derailments due to amplified dynamic forces on tracks and wheels, particularly under high-speed or curved conditions. For road vehicles, overloading axles reduces braking efficiency and responsiveness, elevating the likelihood of rollovers and collisions, while also straining tires and suspension components to the point of failure. Economically, axle load management balances freight efficiency against infrastructure longevity, where higher allowable loads enhance capacity and reduce transportation costs per unit but accelerate on roads and rails, necessitating elevated expenditures. In rail freight, increasing axle loads from standard levels has demonstrated economic benefits through greater throughput on existing lines, yet it correlates with increased track degradation rates. Similarly, in roadway applications, optimized axle configurations allow for heavier payloads that lower operational expenses for shippers, but exceedances lead to premature pavement cracking and resurfacing needs, imposing substantial burdens. The significance of axle load extends to engineering design, influencing axle spacing to distribute forces evenly, suspension systems to absorb shocks and maintain contact, and material choices for durability in both vehicles and supporting structures. Proper load considerations ensure suspensions mitigate uneven , preventing excessive stress on components and enhancing overall system reliability. Environmentally, effective axle load distribution improves by minimizing and optimizing , thereby reducing from ; overloading, conversely, boosts fuel consumption and pollutant output due to heightened mechanical strain. Historically, axle load concepts emerged during 19th-century railway expansion, when early imposed loads around 10-15 tons per on nascent iron rails, prompting innovations in track to support growing freight demands. Post-World War II developments in heavy further elevated loads to over 30 tons in specialized rail systems, driven by industrial recovery and material advancements that enabled safer and more efficient bulk transport.

Engineering Aspects

Static and Dynamic Loads

The static axle load represents the vertical force imposed by a on the supporting rail or under stationary conditions or at negligible speeds, arising directly from the gravitational weight of the and its evenly distributed across the axles. This load is fundamentally the total multiplied by , divided by the number of axles, providing a baseline for structural design without motion-induced variations. In contrast, the dynamic axle load incorporates additional vertical forces that emerge during vehicle motion, exceeding the static component due to interactions between the vehicle and the . Key influencing factors include the speed of travel, which escalates oscillatory effects; irregularities in the track or profile, such as joints, corrugations, or settlements that introduce sudden inputs; the and of the vehicle's suspension system, which modulates energy transfer; and centrifugal forces acting in curved sections, altering load distribution. These elements collectively amplify contact forces at the wheel-rail or wheel-road interface, with dynamic loads often reaching 1.5 to 2 times the static value at elevated speeds on imperfect surfaces. The underlying physics of these dynamic effects stems from Newton's second law applied to the vertical oscillations within the vehicle-track system, where track irregularities and speed-induced accelerations produce inertial forces that superimpose on the static gravitational load, modeled through coupled mass-spring-damper dynamics. High-frequency -rail interactions, excited by wavelengths of 30–300 mm in corrugations or sleeper spacing, lead to resonant amplifications when frequencies align with system natural modes (e.g., 50–1000 Hz for track components), intensifying short-term peak stresses that can cause immediate impacts like unloading. Over longer durations, these oscillations contribute to cumulative , differentiating dynamic loads' role in transient versus sustained material degradation. Dynamic axle loads are measured using strain gauges affixed to rails or integrated into instrumented wheelsets, which detect vertical force variations in real time at sampling rates up to 200 Hz, often filtered to isolate motion-related components from static baselines. Techniques like wheel impact load detectors further quantify peaks from irregularities, enabling assessment of short-term overload risks (e.g., up to 200% increases) against long-term stress accumulation that informs thresholds, with data collected over operational routes to validate amplification under varying conditions.

Calculation Methods

The static axle load represents the portion of a vehicle's total weight borne by an individual axle under stationary conditions, assuming even distribution. For vehicles with symmetrically loaded axles, the basic simplifies to axle load equals total divided by the number of axles. This approach provides a preliminary estimate but often overgeneralizes for multi-axle configurations where weight is unevenly distributed due to placement or vehicle design. To account for weight distribution, engineers apply the moment equilibrium principle, treating the vehicle as a rigid body in static balance. The load on a specific axle is calculated as the product of the total weight and the horizontal distance from the center of gravity to that axle, divided by the wheelbase (the distance between the front and rear axles). For the front axle, this yields: Front Axle Load=Total Weight×Distance from CG to Rear AxleWheelbase\text{Front Axle Load} = \frac{\text{Total Weight} \times \text{Distance from CG to Rear Axle}}{\text{Wheelbase}} The rear axle load follows analogously by swapping the distance term. This method ensures compliance with load limits by optimizing positioning during or loading. Dynamic axle loads exceed static values due to motion-induced effects like suspension response, irregularities, and centrifugal forces in curves, necessitating impact factors to amplify base calculations. Dynamic effects in curves include load transfer due to centrifugal forces, which can cause significant variation between inner and outer wheels, depending on superelevation, speed, and radius. In practice, axle loads are measured using weighbridges, which are fixed platforms with load cells capturing total or per-axle weights as vehicles pass slowly, or portable axle scales placed under individual wheels for field verification. These tools achieve accuracies within 1-2% when calibrated, enabling on-site enforcement and design validation. Software simulations, such as finite element models integrated with programs, further assist in load balancing by iterating cargo distributions to minimize axle overloads during prototype development. Errors in axle load calculations often arise from uneven cargo distribution, which can introduce significant variances compared to assumed uniform loading. Calibration standards, such as those outlined in NIST Handbook 44, mitigate measurement inaccuracies by requiring periodic verification against known test weights, ensuring tolerances below 0.1% for legal scales. Adherence to these protocols prevents compounding errors in dynamic scenarios, where uncalibrated sensors may overestimate impacts by up to 15%.

Railway Applications

Standards and Limits

Axle load standards in railways are primarily governed by international bodies such as the (UIC), which provides guidelines for standard gauge networks (1435 mm). UIC standards typically limit axle loads to 20-25 tonnes for conventional freight operations, with variations based on track category; for instance, category A tracks support up to 22.5 tonnes at speeds up to 100 km/h, while higher categories allow up to 25 tonnes under controlled conditions. As of April 2025, UIC updated its loading guidelines to support up to 25-tonne standards in . These limits ensure compatibility across interconnected networks and promote safe for . Historically, axle load limits have evolved significantly to accommodate growing freight demands and technological advancements in track infrastructure. In the early , typical axle loads ranged from 10-15 tonnes, constrained by lighter rails and designs. By the mid-20th century, improvements in production and track engineering pushed limits to 20 tonnes or more, and by the , heavy-haul lines routinely handle 30 tonnes or greater per axle, reflecting a fourfold increase over a century. Key factors influencing these standards include , rail weight, and train speed, as they directly affect structural integrity and stability. Standard gauge tracks with heavier rails, such as UIC60 profiles weighing 60 kg/m, can support higher axle loads—up to 25 tonnes—compared to lighter 40-50 kg/m rails limited to 16-20 tonnes. Higher speeds necessitate lower limits to mitigate dynamic effects, with UIC guidelines reducing permissible loads above 120 km/h. Safety margins are integral to these standards, incorporating factors for dynamic loads that can increase effective axle forces by 20-50% due to track irregularities, suspension characteristics, and speed. Certification processes for locomotives and wagons require rigorous verification, including static weighbridge tests, dynamic simulations, and compliance audits against UIC leaflets or equivalent norms, ensuring vehicles do not exceed rated limits under operational conditions. Global trends emphasize raising axle load limits to boost capacity and efficiency without proportional infrastructure expansion, particularly in freight corridors. For example, as of 2025, North American Class I railroads have adopted 32.5- axle loads as standard for heavy-haul services, enabling longer trains and reduced operational costs while maintaining safety through upgraded rails and monitoring. This shift aligns with broader efforts, such as UIC initiatives for 25-30 standards in , verified via established calculation methods for load distribution.

Regional Variations

In the , maximum axle loads on the railway network vary by route, typically up to 25 tonnes, with some sections permitting 25.4 tonnes under guidelines for compatibility with mixed passenger and freight traffic. These limits accommodate diverse train formations, including intermodal and bulk freight, while ensuring infrastructure integrity on lines upgraded post-1960s rationalization efforts that prioritized lighter, more efficient operations. Australia's standard gauge network generally permits axle loads up to 25 tonnes at speeds of 80 km/h, supporting efficient interstate freight movement. On heavy-haul lines in the region, such as those operated by Fortescue Metals Group for transport, loads exceed 30 tonnes—reaching 40 tonnes or more since the early —to maximize payload on dedicated mineral routes. In , the legacy metre-gauge railway operates with axle loads of 18-20 tonnes, constrained by colonial-era that limits capacity for heavier freight. The (SGR) project, operational since 2017, has upgraded sections to support 25-tonne axle loads, enabling faster and higher-volume cargo transport from to inland hubs. Across other regions, the and adhere to (AAR) standards allowing 25-32.5 tonnes on heavy-haul lines, facilitating vast commodity flows like and . In , the Technical Specifications for Interoperability (TSI) set a conventional limit of 22.5 tonnes, though high-speed lines like those for trains impose exceptions with lower loads around 17 tonnes to maintain stability at velocities over 300 km/h. China's network standards 23-25 tonnes per axle, with rapid expansions since the enabling heavy-haul corridors to test 30-tonne loads for increased freight efficiency. These variations reflect adaptations to local economics, with higher loads in resource-rich areas boosting throughput and revenue—such as Australia's Pilbara lines handling over 900 million tonnes of iron ore annually—while lower limits in mixed-traffic networks prioritize safety and maintenance costs.
RegionTypical Axle Load (tonnes)Track Type/GaugeEconomic Impact Example
United Kingdom25.4Standard (1435 mm)Supports £10B+ annual freight value on mixed lines, but limits heavy bulk to road alternatives.
Australia (Standard)25Standard (1435 mm)Enables 80 km/h interstate hauls, reducing logistics costs by 20-30% vs. road.
Australia (Heavy-Haul)30-40Standard (1435 mm)Pilbara ore exports exceed 900 million tonnes/year, contributing AUD 100B+ to GDP.
Kenya (Metre-Gauge)18-20Metre (1000 mm)Handles 5M tonnes freight annually, but upgrades needed to compete with ports.
Kenya (SGR)25Standard (1435 mm)With a designed capacity of 22 million tonnes per year; actual volumes reached approximately 7.5 million tonnes in 2025, cutting transport time by 50% and costs by 40%.
US/Canada25-32.5Standard (1435 mm)Heavy-haul moves 40% of freight ton-miles, saving USD 50B+ in energy vs. trucks.
Europe22.5 (conventional); 17 (high-speed)Standard (1435 mm)Freight share at 18% of inland transport, with TSI harmonization aiding €500B market.
China23-25 (standard); 30 (heavy-haul)Standard (1435 mm)Handles 4B tonnes freight/year, enhancing logistics efficiency.

Infrastructure Impacts

Higher axle loads in railway operations significantly accelerate wear on track components, primarily through increased rail fatigue and the development of corrugation. Rail fatigue arises from repeated cyclic loading at the wheel-rail interface, leading to crack initiation and that can result in defects such as shelling or transverse fissures. Studies using three-dimensional fatigue models indicate that total rail fatigue life, defined up to a 20% transverse defect, is approximately proportional to the wheel load raised to the power of -2, meaning doubling the load roughly quarters the life under typical conditions. Corrugation, characterized by periodic wave-like patterns on the rail surface, is exacerbated by higher loads due to intensified flow and dynamic vibrations, particularly on curves and in heavy-haul lines. Railway bridges must be designed to accommodate maximum anticipated loads, incorporating live load factors to account for dynamic effects like impact and . In standards such as the American Railway Engineering and Maintenance-of-Way Association (AREMA) Manual, bridges are typically designed using Cooper E80 loading, which simulates heavy freight trains, with load factors in Load Factor Design (LFD) reaching 1.75 times the static live load for primary strength checks. This ensures structural integrity against , shear, and , though historical incidents highlight risks from underestimating combined loads; for instance, early 20th-century bridge collapses in were linked to inadequate provisions for increasing train weights. Elevated axle loads necessitate more frequent and intensive activities, including rail grinding to restore profiles and mitigate , as well as renewal to counteract degradation from higher stresses. Cost models demonstrate that doubling loads can approximately double track damage rates, inversely halving component life and escalating annual expenses by 50-100% depending on volume. Grinding intervals may shorten from every 1-2 million gross tons to under 1 million, while tamping and undercutting become essential every 5-10 years in heavy-haul sections to maintain geometry and stability. To mitigate these impacts, railways adopt heavier rail sections exceeding 60 kg/m, which provide greater resistance to bending and wear under high loads, alongside concrete sleepers that offer superior durability over timber in distributing forces to the ballast. Advanced monitoring systems, including axle load sensors embedded in tracks or wayside detectors, enable real-time detection of overloads and predictive maintenance, reducing unplanned outages. In heavy-haul corridors like those in North America and Australia, infrastructure upgrades incorporating these measures—such as rail replacements and sensor networks—have reduced downtime by up to 30% while extending asset life.

Roadway Applications

Regulations and Enforcement

In the United States, the (FHWA) establishes baseline axle load limits for trucks on the , setting a maximum of 20,000 pounds for a single and 34,000 pounds for a tandem group, with an overall gross cap of 80,000 pounds for a standard five- configuration. These federal standards, which apply nationwide to federally funded highways, serve as the minimum requirements, but individual states may impose stricter limits or allow variations through special permits. For instance, overweight permits issued by state departments of transportation enable vehicles to exceed these thresholds for specific routes, often requiring route restrictions, escort vehicles, or time-of-travel limitations to mitigate strain. As of 2025, legislative proposals in the U.S. seek to raise the gross limit to 91,000 pounds on certain configurations, potentially affecting axle load distributions and requiring assessments. The further regulates multi- configurations by linking total weight to axle spacing, calculated as W = 500 [ (L N) / (N-1) + 12 N + 36 ], where W is the allowable weight in pounds, L is the distance in feet between the outer s of a group, and N is the number of s in the group; this ensures even load distribution to prevent bridge damage. In the , Directive 96/53/EC governs heavy goods vehicles, permitting up to 10 tonnes on a single non- and 11.5 tonnes on a , with tandem s allowed up to 18 tonnes, though some member states enforce stricter 10.5-tonne limits per to protect road networks. Proposed amendments to Directive 96/53/EC aim to accommodate heavier electric vehicles by increasing allowances, such as up to 2-4 tonnes for zero-emission trucks' gross weight and up to 12.5 tonnes on rear s to offset battery mass, though these remain under negotiation as of 2025. Enforcement of these regulations relies on technologies like weigh-in-motion (WIM) systems, which use embedded road sensors to measure axle loads and gross weights of moving vehicles at speeds up to highway limits, enabling real-time screening without stopping traffic. Portable scales and fixed weigh stations supplement WIM for precise verification, with violations resulting in fines scaled to the excess weight—for example, many U.S. states impose penalties starting at $0.01 to $0.05 per pound over the limit, escalating to thousands of dollars for severe overruns. Historically, these frameworks originated with the Federal-Aid Highway Act of 1956, which first standardized national axle limits at 18,000 pounds for singles and 32,000 pounds for tandems to support the Interstate System's construction, with subsequent revisions in 1975 and 1983 raising them to current levels. Compliance is facilitated by onboard weighing systems integrated into truck chassis, which provide drivers with real-time axle and gross weight data via digital displays and alerts, helping avoid violations and optimize payloads. Internationally, the International Road Transport Union (IRU) advocates for of axle load standards across borders, promoting consistent limits and permit reciprocity to streamline cross-border freight while aligning with environmental goals like adoption.

Pavement Design Considerations

In pavement design, axle loads are a critical factor in predicting structural and determining required thicknesses for layers. The of Equivalent Single Axle Load (ESAL) standardizes mixed impacts by converting various axle configurations into equivalents of a standard 18-kip (80 kN) single axle, which serves as the baseline for damage assessment over the pavement's . Damage from axle loads follows the , where pavement deterioration is proportional to the axle load raised to the (damage ∝ load⁴), emphasizing that small increases in load can exponentially amplify on flexible pavements. This principle underpins load equivalency factors in methods, allowing engineers to equate diverse axles to the standard ESAL for cumulative prediction. The American Association of State Highway and Transportation Officials (AASHTO) incorporates this into its 1993 Guide for of Pavement Structures through the flexible pavement performance equation, which estimates the allowable number of ESALs (W₁₈) a pavement can withstand before reaching terminal serviceability: log⁡10W18=ZRS0+9.36log⁡10(SN+1)−0.20+log⁡10(ΔPSI4.2−1.5)0.4+1094(SN+1)5.19+2.32log⁡10MR+8.07\log_{10} W_{18} = Z_R S_0 + 9.36 \log_{10} (SN + 1) - 0.20 + \frac{\log_{10} \left( \frac{\Delta PSI}{4.2 - 1.5} \right)}{0.4 + \frac{1094}{(SN + 1)^{5.19}}} + 2.32 \log_{10} M_R + 8.07 Here, Z_R is the standard normal deviate for reliability, S_0 is the combined standard error, SN is the structural number of the pavement layers, ΔPSI is the change in present serviceability index, and M_R is the subgrade resilient modulus; material constants like layer coefficients (a_i) and drainage factors (m_i) influence SN to reflect site-specific conditions. Pavement structures are designed as layered systems—typically subgrade, granular base, and asphalt surface—where thicknesses are scaled according to projected ESALs accumulated over a standard 20-year design period to ensure adequate load distribution and resistance. For instance, higher ESAL projections necessitate thicker asphalt layers (often 4-12 inches) and stabilized bases to mitigate stress, with the structural number SN balancing material properties and thicknesses against expected . Heavy vehicles, such as trucks comprising about 10% of volume, account for 80-90% of pavement damage due to their concentrated loads, underscoring the need for strategies like optimized spacing to reduce peak stresses. Regulations establishing maximum allowable loads help inform these designs by capping ESAL inputs for economic planning. Recent advancements address limitations of empirical models through the Mechanistic-Empirical Pavement Design Guide (MEPDG), with implementations via updated AASHTOWare Pavement ME Design software (version 2.6 as of 2025), which integrates dynamic axle load effects, climate variations (e.g., temperature and moisture on material stiffness), and probabilistic distress predictions for more precise layered thickness optimization. This approach refines ESAL-based inputs with mechanistic simulations of stress-strain responses, enhancing longevity forecasts under variable conditions.

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  57. https://ops.fhwa.dot.gov/freight/publications/brdg_frm_wghts/
  58. https://eur-lex.europa.eu/EN/legal-content/summary/authorised-maximum-dimensions-and-weights-for-trucks-buses-and-coaches.html
  59. https://www.europarl.europa.eu/legislative-train/theme-a-european-green-deal/file-revision-of-the-weights-and-dimensions-directive
  60. https://www.fhwa.dot.gov/policyinformation/knowledgecenter/wim_guide/wim_guidebook_part2_070918_%28508_compliant%29.pdf
  61. https://oversize.io/regulations/oversize-overweight-fines-by-state
  62. https://nap.nationalacademies.org/read/10382/chapter/3
  63. https://www.vpgonboard.com/products/truckweigh/
  64. https://www.iru.org/system/files/European%2520Commission%2520proposal%2520to%2520amend%2520the%2520EU%2520rules%2520on%2520weights%2520and%2520dimensions.pdf
  65. https://pavementinteractive.org/reference-desk/design/structural-design/1993-aashto-flexible-pavement-structural-design/
  66. http://www.wispave.org/wp-content/uploads/dlm_uploads/WAPATechBulletinPavementStructureDesign.pdf
  67. https://www.fhwa.dot.gov/publications/research/infrastructure/pavements/asphalt/HMA.pdf
  68. https://blog.ucs.org/dave-cooke/trucks-cause-the-lions-share-of-road-damage-and-their-industry-wants-you-to-keep-paying-for-it/
  69. https://www.gao.gov/assets/ced-79-94.pdf
  70. https://www.michigan.gov/-/media/Project/Websites/MDOT/Business/Construction/Pavement-Operations/ME-Pavement-Design/User-Guide-for-ME-Pavement-Design.pdf?rev=521090cecf3a4af48b71cea1f3c1304f
  71. https://www.fhwa.dot.gov/pavement/materials/hmec/pubs/module_e/participant_workbook.pdf
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