Missouri Bridge Rating by LRFR and LFR: MoDOT Comparative Study

During my graduate studies at the University of Missouri-Kansas City (UMKC), I conducted bridge load rating research under the guidance of Professor Ganesh Thiagarajan alongside senior colleagues Bao Tran and Ronald Cheruiyot. The research was part of a Missouri Department of Transportation (MoDOT) project investigating the transition from the existing Load Factor Rating (LFR) methodology toward Load and Resistance Factor Rating (LRFR) for highway bridge load rating and posting.

As part of the research team, my primary focus was the reinforced concrete (RC) bridge portion of the study. I evaluated a dataset of 99 reinforced concrete bridges across Missouri, performing comparative LFR and LRFR analyses using AASHTOWare Bridge Rating (BrR). The analysis included Missouri legal vehicles, AASHTO legal vehicles, and Specialized Hauling Vehicles (SHVs), with the objective of understanding how the change in rating methodology could affect rating results and bridge load-posting decisions.

This article provides a summary of the research background, load-rating methodologies, vehicle models, BrR analysis, data-processing approach, and key findings from the reinforced concrete bridge portion of the study.

MoDOT Load Rating Research Background

The Missouri Department of Transportation has historically used the Load Factor Rating (LFR) methodology for evaluating bridge load capacity and determining load-posting requirements. With the adoption of the AASHTO Manual for Bridge Evaluation (MBE) and the broader implementation of Load and Resistance Factor Rating (LRFR), there was a need to understand how LRFR results would compare with MoDOT's existing LFR-based practice.

This transition is particularly important because load-rating methodologies do not simply produce a numerical capacity. Their results can directly affect whether a bridge requires a weight restriction or load posting.

Previous research in other states had generally shown that LRFR could produce lower rating factors than LFR and could result in additional bridge postings. However, those results could not be directly applied to Missouri because Missouri has its own bridge inventory, legal vehicle configurations, commercial-zone policies, and posting procedures.

The objective of this research was therefore to conduct a Missouri-specific comparison of LFR and LRFR and investigate how LRFR could be implemented while maintaining a load-posting policy consistent with MoDOT's existing practice. The broader study evaluated both reinforced concrete and prestressed concrete bridges; my portion focused specifically on the 99 reinforced concrete bridges.

Load Rating Principles: LFR vs. LRFR

Bridge load rating evaluates the ability of an existing structure to safely carry specified live loads. The primary result is the Rating Factor (RF), which represents the available structural capacity relative to the live-load demand.

In simplified form:

Rating Factor (RF) = (Capacity − Dead Load Effect) / Live Load Effect

The corresponding Rating Load can then be determined from the rating factor and the gross vehicle weight of the rated vehicle.

Under LFR, bridge capacity is evaluated at Inventory and Operating rating levels. MoDOT uses a posting level between these two levels, with its existing LFR posting procedure based on 86% of the Operating-level rating.

LRFR uses a different framework based on factored loads and resistance factors and includes different rating stages, including design load rating, legal load rating, and permit load rating. For this research, the primary focus was the legal load rating, because the objective was to evaluate the capacity of existing Missouri bridges for actual legal vehicle configurations and determine the implications for load posting.

Missouri State Legal Trucks & AASHTO Legal Vehicles

The analysis included several categories of live-load models to determine whether Missouri's existing legal vehicles could adequately represent other vehicles used for bridge load rating.

1. Missouri Department of Transportation (MoDOT) State Vehicles

The statewide Missouri legal vehicles evaluated were:

• H20L – Single-Unit Legal Truck

• MO3S2 – Combination Legal Truck

Missouri also uses commercial-zone legal vehicles:

• CZSU – Commercial Zone Single-Unit Truck

• CZRT – Commercial Zone Combination Truck

These vehicles were evaluated according to the load configurations and requirements established in Missouri's bridge inspection and rating procedures.

2. AASHTO Legal Loads & Specialized Hauling Vehicles

The study also evaluated the AASHTO legal vehicles:

• Type 3

• Type 3S2

• Type 3-3

In addition, the research included Specialized Hauling Vehicles (SHVs):

• SU4

• SU5

• SU6

• SU7

Including these vehicles was important because one objective of the study was to determine whether MoDOT's primary legal vehicle models could be used to envelop the rating demands of AASHTO legal vehicles and SHVs when developing an LRFR-based posting procedure.

Analysis of 99 Missouri Reinforced Concrete Bridges Using AASHTOWare BrR

The reinforced concrete portion of the research evaluated 99 existing RC bridges provided by MoDOT. The bridge sample represented a range of construction periods, span configurations, span lengths, and bridge characteristics across Missouri.

The bridge models were provided as AASHTOWare BrR (.xml) working models and were analyzed using AASHTOWare Bridge Rating v7.1. Rather than creating simplified theoretical bridge models, the research used existing bridge-rating models, allowing the comparison to reflect actual bridge characteristics and rating conditions.

For each vehicle, multiple rating configurations were evaluated, including:

• Impact with one lane loaded

• Impact with multiple lanes loaded

• Non-impact with one lane loaded

• Non-impact with multiple lanes loaded

Every existing and current girder in the bridge models was evaluated using both LFR and LRFR rating templates. The BrR analyses generated rating factors, rating loads, governing limit states, and governing locations for each vehicle and structural component.

Data Processing and Comparative Analysis

Because the analysis generated a large amount of bridge-rating data, the research team used an Excel-based DataCollector tool developed with VBA to consolidate the individual BrR results into a single dataset.

I then used the collected rating results to perform the comparative analysis between LFR and LRFR. Rating factors were determined by identifying the minimum value across the four rating modes for each bridge and vehicle. The resulting dataset allowed the research to examine:

1. LFR versus LRFR rating factors

2. LFR versus LRFR rating loads

3. Governing structural elements

4. Governing limit states and locations

5. Differences in load-posting requirements

6. The ability of MoDOT legal vehicles to envelop AASHTO legal vehicles and SHVs

This analysis moved the research beyond a simple comparison of rating equations and focused on the practical consequences of implementing LRFR within Missouri's existing bridge-management framework.

Research Findings & Conclusions

The comparison of the 99 reinforced concrete bridges demonstrated several important differences between LFR and LRFR.

Rating Factor Comparison

For the primary MoDOT legal vehicles, LRFR generally produced lower rating factors than LFR.

The average results for the RC bridge sample were approximately:

*The commercial-zone results were based on a very small sample of only two RC bridges and were therefore treated cautiously.

For H20L, MO3S2, and SU5, the LRFR rating factors were approximately 11% lower on average than the corresponding LFR values.

Governing Structural Elements

The research also examined which structural components controlled the bridge ratings.

Under LFR, interior girders were the most frequent governing structural elements. Under LRFR, interior girders continued to control the majority of ratings; however, the proportion of cases governed by exterior girders increased from approximately 11% under LFR to 14% under LRFR.

This shift is important from a practical engineering perspective because it demonstrates that changing the rating methodology can change not only the numerical rating factor but also which structural component controls the evaluation.

Load Posting Comparison

The difference in rating methodology also affected the number of bridges requiring posting.

Using the proposed LRFR thresholds and the existing LFR posting threshold, the analysis indicated that the number of RC bridges requiring posting for the H20L vehicle increased from 33 under LFR to 49 under LRFR.

For the MO3S2, CZSU, and CZRT vehicles, the number of bridges requiring posting did not change under the proposed LRFR thresholds.

Overall, the RC bridge analysis indicated that LRFR resulted in approximately 16% more bridges requiring posting than LFR under the evaluated conditions.

Proposed LRFR Posting Thresholds for Reinforced Concrete Bridges

A major professional application of the research was the development of proposed LRFR thresholds and posting factors that could allow MoDOT legal vehicles to envelop the demands of AASHTO legal vehicles and Specialized Hauling Vehicles.

For the reinforced concrete bridge sample, the research proposed:

These thresholds were developed from the numerical comparison of the 99 RC bridges and were intended to provide a practical basis for transitioning MoDOT's posting procedure toward LRFR while maintaining an appropriate relationship with the existing LFR-based practice.

Engineering Significance

This research demonstrated that transitioning from LFR to LRFR involves more than replacing one rating equation with another. For an existing bridge inventory, the change can influence rating factors, governing structural elements, rating loads, and ultimately load-posting decisions.

By evaluating a statewide sample of existing reinforced concrete bridges using actual BrR models and multiple legal and specialized vehicle configurations, the research provided a Missouri-specific basis for evaluating the practical effects of LRFR implementation.

My work on the reinforced concrete bridge portion of the study combined bridge load-rating theory, AASHTO/MoDOT requirements, AASHTOWare BrR modeling, large-scale engineering data processing, statistical comparison, and practical load-posting evaluation.

The resulting analysis contributed to recommendations for LRFR posting thresholds that could support MoDOT's transition from its existing LFR-based practice toward an LRFR-based bridge load-rating framework.

For more discussion on superstructure modeling and bridge layout standards, see the guide on Layout Length vs. Span Length in Bridge Design.