National Cooperative Highway Research Program Research Articles

Development of a Practical Procedure for Data-Driven Weigh-in-Motion Equipment Calibration Scheduling to Assure Data Accuracy and Consistency over Time

Weigh-in-motion (WIM) technology is a traffic monitoring technology that highway agencies use to obtain information about the weight, axle loading, and configuration of heavy vehicles moving at operational speed. To ensure high-quality WIM data, the Federal Highway Administration (FHWA) recommends regular calibration of WIM equipment. This study addresses the need to optimize the allocation of the limited resources that agencies have for WIM equipment calibration by developing a procedure for data-driven calibration scheduling. This was accomplished through an analysis of WIM measurement errors from test truck data collected during field performance validation and calibration events and an analysis of monthly changes in truck weight and axle loading characteristics, based on WIM data collected between calibration events. The analysis results were used to draw conclusions on the functional performance of different WIM sites. The study also demonstrates how the newly developed National Cooperative Highway Research Program (NCHRP) WIM Data Quality Assurance Analysis Tool can be used to compute truck weight and axle loading parameters and visualize data analysis results using four case studies: two WIM sites with piezo quartz sensors in asphalt pavements and two WIM sites with bending plate sensors in concrete pavements. This paper provides a practical procedure and recommendations that highway agencies can use to develop data-driven WIM calibration schedules that will ensure consistent high-quality WIM data for sites managed by an agency with the aid of the NCHRP WIM Data Quality Assurance Analysis Tool.

MASH TL-3 Evaluation of the Hawaii Department of Transportation 34 in. Tall Aesthetic Bridge Rail with Pedestrian Rail and Sidewalk Options

Recommended guidelines were provided for the shape and size of aesthetic features added to roadside barriers in National Cooperative Highway Research Program Report No. 554, but limited full-scale crash testing has been performed on barriers with aesthetic features, especially in combination with sidewalks and pedestrian railings, each of which may contribute to increased propensity for vehicle snag, vehicle instabilities, and occupant risk metrics. A Hawaii Department of Transportation (HDOT) bridge rail design with vertical faces and aesthetic recessed panels was evaluated to Manual for Assessing Safety Hardware (MASH) TL-3 impact conditions in three configurations: stand-alone; in combination with a pedestrian handrail installed on the back side of the barrier system; and in combination with a pedestrian rail and 6 ft long x 6 in. tall sidewalk. The 34 in. tall aesthetic concrete bridge rail consisted of segments measuring 11 ft long at upstream and downstream ends and three 22 ft long, consecutive interior segments. MASH test designation Nos. 3-10 and 3-11 were performed on the stand-alone system and with the sidewalk and pedestrian rail, and test designation 3-11 was performed on the system on level terrain with handrail. Results indicated that the HDOT 34 in. tall aesthetic concrete bridge rail was crashworthy in all of the configurations evaluated.

Progression of e-ticketing implementation for state transportation agencies for asphalt materials

E-ticketing, which has been promoted by the Federal Highway Administration (FHWA) “every day counts” (EDC) initiative, utilizes software applications to digitally track and store information regarding highway construction materials paid by state transportation agencies (STAs) by weight in unit bid contract structures. STAs often face implementation barriers such as institutional inertia, or the resistance by stakeholders to adopt changes from the status quo, including new technologies. The purpose of this paper is to determine the progression of STA e-ticketing policy adoption, specifically with a focus on asphalt paving operations, due to the COVID-19 pandemic. To accomplish this research effort, previous FHWA data, National Cooperative Highway Research Program (NCHRP) data, and other literatures are reviewed to determine an implementation baseline. Additional data is collected from the American Association of State Highway and Transportation Officials Committee on Construction to gain current feedback from STAs and their highway contractor partners after the COVID-19 pandemic. Additionally, a case study featuring the Kentucky Transportation Cabinet (KYTC), the Kentucky Association of Highway Contractors (KAHC), and the Plantmix Asphalt Industry of Kentucky (PAIKY) is performed to provide more in-depth analysis. The major finding includes a statistically significant result indicating increased implementation of e-ticketing for asphalt operations within the last two years, along with noting benefits including employee safety, task loading, and project documentation along with concerns regarding cellular connectivity and procurement responsibilities. These findings indicate the importance of STAs investing in partnership with contractors to improve stakeholder buy-in before proceeding towards e-ticketing adoption.

Framework for Integrating the Reliability of the Inspection Technique into Risk-Based Inspection Practice

In compliance with recent (2022) federal legislation found in the Code of Federal Regulations Part 650 Subpart C, risk-based inspection (RBI) practices for determining inspection intervals for highway bridges are now permitted. The RBI approach allows for a systematic assessment of risk and prioritizes inspection resources where they are most needed. However, to ensure an optimal level of safety and serviceability, it is necessary to utilize reliable inspection techniques in conjunction with an appropriate inspection interval, as emphasized by National Cooperative Highway Research Program (NCHRP) Report 782. Utilizing ineffective inspection techniques may lead to uncertainty about the element’s condition and thus increase the risk associated with the component. Therefore, this paper proposes a framework that integrates a new factor, called the inspection effectiveness factor (IEF), into the RBI process to rationally estimate the inspection interval considering the reliability of the inspection technique. The inspection interval in the proposed approach is determined based on the damage mode, associated likelihood, consequences, and effectiveness of the inspection technique, offering a rational approach for decision-makers in estimating the inspection interval of bridges and identifying appropriate inspection techniques for different defects. The effectiveness of the proposed method is validated through experts’ judgment. In addition, the proposed approach is demonstrated through a case study utilizing historical inspection reports.

Numerical modeling and simulation of cable barriers under vehicular impacts on a sloped median

Cable barriers are flexible barrier systems that are commonly used as median barriers in the United States for their general effectiveness and low installation and maintenance costs. The current cable median barrier (CMB) adopted by the North Carolina Department of Transportation was previously evaluated on flat terrain and found to satisfy the requirements of the National Cooperative Highway Research Program Report 350. Under in-service conditions (i.e., on a sloped median), the current CMB failed to stop small passenger cars in many incidents. The new roadside safety standard, Manual for Assessing Safety Hardware (MASH), recommends that CMBs be tested and/or evaluated on sloped medians. However, conducting full-scale crash tests on sloped median is extremely difficult and few experimental studies exist. In this study, finite element simulations were used to evaluate the performance of the current CMB design on a 6H:1V sloped median under MASH Test Level 3 conditions. To address the issue of vehicle underriding on the current CMB, two retrofit designs were developed and also evaluated on the sloped median. Two MASH compliant vehicles, a 1996 Dodge Neon and a 2006 Ford F250, were used to evaluate all three CMBs from both frontside and backside and with two initial impact points. The MASH exit-box criterion, MASH Evaluation criteria A, D, and F, vehicular responses, exit angles, and residual velocities were used to evaluate the CMB performance for structural adequacy, occupant risk, and post-impact trajectories. The simulation results showed that one of the retrofit designs could improve the CMB performance on a sloped median at MASH Test Level 3 conditions.

Characterization of Motorcycle Encroachments in the U.S

In 2020, there were 5,579 motorcyclist fatalities in the U.S., which is the highest on record. Despite accounting for only 3% of registered vehicles, motorcycles are involved in 42% of fatal guardrail impacts. Roadside safety hardware testing guidelines are outlined in the Manual for Assessing Safety Hardware (MASH) for passenger vehicles and large trucks but these procedures do not include any motorcycle impacts. Although international test procedures for roadside hardware prescribe motorcycle crash tests, it is not known if the prescribed test conditions reflect the conditions at which motorcycles depart the roadway in the U.S. A better understanding of the characteristics of motorcycles departing the roadway in the U.S. is needed before the development of motorcycle crash tests. This study used the National Cooperative Highway Research Program (NCHRP) 17-88 database to compare the encroachment and impact characteristics of motorcycles, passenger vehicles, single-unit trucks, and tractor-trailer trucks. Motorcycles were found to have a similar distribution of impact angles to passenger vehicles, with an 85th percentile of 24 degrees. The median and 85th percentile impact angle was found to be shallower for tractor-trailer trucks compared with motorcycles and passenger vehicles. Additionally, large trucks and motorcycles were found to roll over at a higher frequency than passenger vehicles. During the first event, almost 80% of motorcycles were upright. By the second event, almost 50% of motorcyclists were separated from the motorcycle. This indicates that a large percentage of riders lose contact with the motorcycle during the first event and are separated during any subsequent events. Based on these results, future motorcycle-barrier tests should consider an upright configuration and an impact angle of 24 degrees.

Use of High-Resolution Signal Controller Data to Measure Transit Signal Priority Performance: A Case Study in the Boston Region

Automated traffic signal performance measures (ATSPMs) have been developed to organize data within a traffic signal, which will then be used to evaluate and monitor signal timing strategies. Past research has summarized the use of ATSPMs for performance-based management of a traffic signal system. The National Cooperative Highway Research Program Research Report 954 focused on many measures useful for general traffic, but did not consider transit agencies as specific stakeholders. ATSPMs do provide insights into measuring the number of preemption events, and the percentage of transit vehicles arriving on green, but additional information is needed to determine the effectiveness of transit signal priority or other transit preferential treatment strategies. This paper proposes a method for evaluating transit performance at signalized intersections more fully using the high-resolution data available within modern traffic signal controllers. The addition of transit-specific inputs within the ATSPM enumerations is used to produce transit-specific signal performance measures designed to be useful to practitioners. The methodology can be followed by other agencies seeking to enhance the capabilities of existing automatic vehicle location systems to further describe the performance at each signalized intersection. By incorporating transit into the ATSPM system, an agency can better assess the delay of buses, which can contribute to schedule adherence, on-time performance, and overall bus service. The methodology is presented as a prototype for further development and adaptation to individual agency objectives and data sources.

Effect of Specimen Fabrication Variables on the Measured Mechanical Properties of Asphalt Mixtures Tested in the Asphalt Mixture Performance Tester (AMPT)

Abstract The scope of this research involves the evaluation of the effects of specimen preparation variables—mixing temperature, binder time at mixing temperature, mixer type, mixing time, loose mix conditioning temperature, loose mix conditioning depth, loose mix stirring, mold loading, placement in mold, additional time at compaction temperature before loading in mold, gyratory specimen height, and test specimen air voids—on tests such as the Dynamic Modulus and Flow Number conducted using the Asphalt Mixture Performance Tester (AMPT). The initial testing program to evaluate the precision of the Dynamic Modulus and Flow Number tests (described in National Cooperative Highway Research Program Report 702) indicated that “specimen fabrication is a major component of the between-laboratory variability” for both tests. The expected outcome of this study was that AMPT users—Federal Highway Administration (FHWA), state user agencies, and industry—understand the importance of proper specimen preparation and the effect of specimen preparation variables on the results obtained from the AMPT Dynamic Modulus and Flow Number tests. The use of AMPT Dynamic Modulus at 20°C is the most sensitive portion of the modulus-time curve and can provide a general idea of sample preparation impact on other mixture tests. This information comes at critical timing as the United States begins to implement performance-engineered mixture designs, balanced mixture designs, and performance-based pay factors. Based on the findings of the study, recommendations may be made regarding changes to specimen preparation procedures, which are expected to produce more reproducible test results.

Objective Geographic Information System-Based Context Classification Approach Using Nationally Available Data

For decades the functional classification system (FCS) has guided roadway planning and design in the U.S.A. However, the FCS has a narrow focus, is auto centric, and because of its reliance on a binary classification scheme it lacks the resolution needed to develop context-sensitive designs. National Cooperative Highway Research Program (NCHRP) Report 855, An Expanded Functional Classification for Highways and Streets, introduced an expanded context classification system that supports more integrative and context-adapted roadway designs. This system was subsequently adopted in the seventh edition of the Policy of Geometric Design for Highways and Streets ( Green Book). Transitioning from the FCS to context classification entails a major shift in design practices. The context sets expectations for each setting and informs project development. Despite its advances, NCHRP Report 855 lacks guidance on quantitative measures for performing roadway classification. This paper resolves this issue by presenting an objective geographic information system (GIS)-based process transportation agencies can adopt to define contexts and weave context classification into the entire project development process. The proposed classification is based on measures that can be computed using readily available data, such as the TIGER/Line roadway data, U.S. Census urban-area data, U.S. Census population and employment data at the tract level, building polygon data, and GIS-derived intersection and street data. The application process outlined here provides the basic steps for implementing context classification at the state, regional, or project level.

Effect of Binder Chemistry and Related Properties on the Low-Temperature Performance Parameters of Asphalt Binders

The current Superpave™ performance grading specifications were developed under the Strategic Highway Research Program during the 1990s. Since the implementation of these specifications, the petroleum industry, and in turn asphalt binder formulation and production processes, have changed to a great extent owing to various factors, including improving yields and margins. Therefore, there is a need to evaluate and characterize evolving asphalt binder technologies through chemical-, rheological-, and performance-based approaches and to understand the relationships between these various aspects. This paper provides a robust method to characterize the effects of the binder crude source, compositional chemistry, crude oil processing, and modification type, as well as the thermal properties, on the low-temperature performance parameters (e.g., glass transition, crystallization properties, Δ Tc, asphalt binder cracking device [ABCD] Tcr, etc.). As a part of the National Cooperative Highway Research Program 9-60 effort, this work was aimed at providing a robust binder guideline tool for asphalt and additive suppliers, and the asphalt community in general. The experimental matrix includes 50 binders carefully selected based on input from road authorities, researchers, past experience from the field, crude source variability, type of chemical processing involved, modifier type, and so forth. Characterization efforts included tests such those using a bending beam rheometer, an ABCD, the SAR-AD tool composition, and differential scanning calorimetry for asphalt binders at various aging conditions. The outcome of this research sheds new light on binder formulation and manufacturing, especially that related to low-temperature pavement performance.

Optimization of stone matrix asphalt mixture design based on fracture mechanics approach

Low-temperature cracking is one of the most common pavement distresses that occurred in a short period of service life and is known as premature distress. Stone matrix asphalt (SMA) with gap gradation, which has high strength and rutting performance, should also perform well against low-temperature cracking. So in this research, the criteria of SMA mixture design based on the National Cooperative Highway Research Program (NCHRP) 9–8 were optimized in a way so that SMA has the best performance against low-temperature cracking. Therefore, the optimization process was carried out using the response surface method (RSM) considering the combined effect of compaction energy (Ndesign) and binder content as mixture design factors. The fracture evaluation was done based on stress and energy. So critical stress intensity factor (KIC) and critical fracture energy (Gf) were used as fracture evaluation parameters. After conducting the tests and analyzing the results, it was found that 6.09 % binder with Ndesign = 78 leads to a design with a desirability of 0.869, which passed all the NCHRP 9–8 criteria of the mixture design in line with the maximum fracture performance.

Evaluating Pedestrian Service of the New Super Diverging Diamond Interchange on Three Case Study Sites in Denver, Colorado

Ensuring safe and comfortable conditions for pedestrians necessitates specific strategies at intersections and service interchanges where traffic and pedestrians interact in complex ways with other modes of transportation. This study aims to investigate pedestrian performance at the new Super Diverging Diamond Interchange (Super DDI) using real-world locations (i.e., I-225 and Mississippi Ave, I-25 and 120th Ave, and I-25 and Hampden Ave in Denver, Colorado). Three alternative designs, typical DDI, and two versions of Super DDI were considered to make a reasonable comparison with the existing Conventional Diamond Interchange (CDI). A comprehensive series of simulation models (192 scenarios with 960 runs) were tested using VISSIM and Synchro to analyze pedestrian operation (travel time, number of stops, and waiting time) in various traffic and pedestrian distributions. As one of the primary contributions in this paper, pedestrian safety was evaluated based on a surrogate performance measure called design flag, introduced by the new National Cooperative Highway Research Program (NCHRP-948) guideline. The results indicated that the proposed new Super DDI designs are relatively safe when compared with CDI and DDI. For example, a pedestrian analysis of one of the most popular alternative interchanges, DDI, showed potential for unsafe pedestrian conditions in all aspects.

An evolutionary computing approach for reducing bias in the dynamic modulus predictive models of hot mix asphalt

Various published literature has indicated significant bias issues with dynamic modulus (E∗) predictive models for the hot mix asphalt. This study proposes Gene Expression Programming (GEP) based approach to reduce such bias. Bias analysis was carried out using database developed during national cooperative highway research program. GEP based predictive models for bias correction factors were developed and subsequently used in conjunction with E∗ predictive models to update E∗ values. Application of correction factors and subsequent statistical analysis showed improvement in the accuracy of predicted E∗ values. The extent of improvement (using sum of squared error) was dependent on model under consideration and ranged between 19 and 36%.

An Improved Neural Network Model for Enhancing Rutting Depth Prediction

Rutting is the main distress form of asphalt pavement, and its prediction accuracy is directly related to the reliability of the designed road. This research developed a neural network model to improve the prediction ability about the rutting of a pavement performance criterion and compared it with the multiple linear regression model and the existing neural network model. The neural network model is developed using the Keras module from the TensorFlow package in Python. Two reports generated by the National Cooperative Highway Research Program project 01-37A and the Long-Term Pavement Performance website records have been used as data sources for training the neural network model, which are reliable data preserved after years of monitoring. The input variables include the pavement thickness, service time, average annual daily traffic of trucks and the deformation of the asphalt concrete layer, granular base layer and subgrade layer. This experiment used 440 samples, of which 352 samples (80%) were used for model training and 88 samples (20%) for testing. The training results of the model reveal that the neural network model is significantly better than the multiple linear regression model, and the newly built neural network model performs better than another similar neural network in predictive performance. For the multiple linear regression model, the correlation coefficient R2 value between the measured and predicted in the testing set increased from 0.265 to 0.712. In contrast, it promotes from 0.867 to 0.902 for the neural network model.

Comparative Evaluation of Pavement Macrotexture Measurements from Different Devices

Ride quality, safety, and tire pavement noise are functional performance measures of concern to highway motorists. Owing to the significant influence of surface macrotexture on wet-weather skid resistance, splash and spray, and highway traffic noise, a need exists for reliable and repeatable methods to measure pavement macrotexture over the road network. To address this need, the National Cooperative Highway Research Program sponsored a project that developed draft protocols for test methods, equipment specifications, and data quality assurance practices for network-level macrotexture measurement. The project conducted three field experiments to evaluate available technologies in regard to repeatability, agreement, and accuracy. This paper focuses on the field experiment conducted at the Texas A&M University RELLIS Campus, which aimed to validate macrotexture measurements from high-speed laser equipped devices suitable for network-level macrotexture data collection and processing. To accomplish this objective, the RELLIS experiment included test speed and laser exposure time in the test matrix, fabricated a measurement beam to collect static reference texture data using a high-resolution laser, and compared texture measurements from different devices with corresponding reference values. This paper presents the findings and conclusions drawn from the RELLIS experiment.

History of Transition From Allowable Stress Design to Load and Resistance Factor Design and Beyond

The Standing Committee on Foundations for Bridges and Other Structures has supported the implementation of the load and resistance factors (LRFD) design philosophy into practice. The committee has contributed by hosting discussions on the advantages, issues, and impact of the implementation of the American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) into foundation design and other related fields. The background and a historical overview of the development of LRFD in bridge foundation design are presented in this paper. Several National Cooperative Highway Research Program (NCHRP) projects have been of paramount importance on this matter. Milestone research projects are described, and a perspective on the future of the field is drawn. This document is intended to be a roadmap through the most useful material to understand reliability analysis and its application to geotechnical engineering. It is intended to be of interest to those engineers charged with performing reliability-based calibration in need of a starting point. The primary literature and steps followed to develop the current AASHTO LRFD specifications are highlighted. This paper aims to contribute to the understanding and future improvement of the LRFD specifications.

Implementation of Finite Element and Fracture Mechanics Based Reflection Cracking Models for Asphalt Concrete Overlay of Existing Asphalt Concrete Pavement in AASHTOWare Pavement ME Design

The reflection of existing cracks from the underlying pavement is one of the primary modes of failure for rehabilitated asphalt concrete (AC) pavements with AC overlays. The AC overlay design philosophy is to delay the onset of reflection cracking or to eliminate it entirely. In recent years, rehabilitation designs are being optimized not just for cost effectiveness, but also to produce more reliable, sustainable, and environmentally friendly designs that require more detailed and sophisticated methodologies. The new finite element and fracture mechanics based reflection cracking models were developed under National Cooperative Highway Research Program (NCHRP) Project 1-41 to improve design methodology. The new models were generally compatible with the AASHTOWare Pavement ME Design (AASHTOWare) framework. The difference included the computation of critical pavement responses (i.e., stress intensity factors) and others, and thus modified. The modified models were calibrated and validated using Long-Term Pavement Performance projects. The calibration of reflection cracking models produced satisfactory goodness of fit with no significant bias. Thus, the modified reflection cracking models were successfully adapted and deployed in the AASHTOWare software to create a new improved AC overlay of existing AC pavement design methodology. This new methodology represents a paradigm shift from the traditional pavement design procedures. It significantly increases the capability of the pavement design software to simulate all the loadings experienced by AC overlay, estimate pavement responses, and predict reflection cracking based on pavement responses. This paper discusses the implementation of NCHRP 1-41 reflection cracking models for AC overlay of existing AC pavements into AASHTOWare software.

Characteristics of aggregate gradation, drain down and stabilizing agents in stone matrix asphalt mixtures: A state of art review

Over the years stone matrix asphalt (SMA) mixtures have evolved significantly and research works have presented some promising results. This made the paving industries to increase the usage of SMA mixtures in the pavement construction. However, SMA mixtures have certain challenges or setbacks, which require comprehensive understanding. The aim of the review paper is to present some of the challenges in SMA mixtures and their mitigations measures. It is observed that several challenges (i.e., aggregate gradation, stone-on-stone contact, drain down and stabilizing agents) related to SMA mixtures are addressed by the researchers. Many agencies have suggested their own aggregate gradation based on their experience, location, climatic conditions and available manufacturing facilities, and they are working exceptionally. Stone-on-stone contact is achieved with proper aggregate gradation and failure to meet the same will reduce the performance. Drain down is major concern in the SMA mixtures since it controls overall mixture performance. Therefore, researchers shown out the most importance to curtail the same. Several researchers followed ASTM D6390 and National Cooperative Highway Research Program (NCHRP No. 424) procedure to evaluate the drain down and concluded that drain down should be less than 0.3% (by weight of mixture). Apart from that, researchers are trying different stabilizing agents to reduce the drain down. Especially, stabilizing agents such as fibers and polymers have a positive impact. Recently, suitable waste and recycle products are used as stabilizing agent to reduce drain down and environmental pollution. Out of which coconut fiber has shown some promising results, however, comprehensive research is required in this regard. On the other hand, 0.3% of cellulose fiber is working as a good stabilizing agent and can be used without conducting drain down test. The review paper provides a complete knowledge about different stabilizing agents used in SMA mixtures to minimize the drain down.

Correlation of asphalt binder linear viscoelasticity (LVE) parameters and the ranking consistency related to fatigue cracking resistance

Fatigue cracking is a common distress in asphalt pavements. Different cracking parameters obtained from asphalt binder testing have been proposed to measure cracking resistance. In this work, binder tests were conducted on both polymer-modified and unmodified binders, spanning a wide range of binder grades and sources. Linear viscoelastic parameters (i.e., stiffness- or relaxation-based) and binder fatigue damaged-based parameters were both assessed. Test methods included the dynamic shear rheometer (DSR) consisted of temperature-frequency sweep and linear amplitude sweep (LAS) testing, bending beam rheometer (BBR). Parameters selected in this work include |G*|·sinδ (G* is the dynamic shear modulus, δ is the phase angle), Glover-Rowe parameter (GRP), R-value, ΔTc, and number of cycles to failure (Nf) from viscoelastic continuum damage (VECD) analysis. Some calculations, thresholds and fatigue testing temperatures of these parameters are based on the recommendations of the National Cooperative Highway Research Program (NCHRP) Project 9–59. The purpose of this work is to compare different binder parameters that have been proposed as indicators of cracking resistance. The potential changes of intermediate temperature definition are also evaluated. The results show that generally the different stiffness-based binder parameters from the DSR correlate well with each other. A correlation is observed between binder GRP and LAS damage parameters from VECD analysis.

Proposed lump-sum formulas for long-term prestress losses

The current American Association of State Highway and Transportation Officials’ AASHTO LRFD Bridge Design Specifications’ approximate formula for estimating long-term prestress losses is the outcome of the research work presented in National Cooperative Highway Research Program report 496. It is produced by simplifying the detailed method and taking into account the variability of concrete properties and the interaction between the precast concrete girder and cast-in-place deck. This paper presents two detailed parametric studies based on the average con­ditions for the design and construction of commonly used bridge girders. Three spans and, consequently, three levels of prestressing for each section have been considered. The first study establishes the creep multiplier Nc, whereas the second study evaluates the shrinkage multiplier Ns. Both multipliers are used in the lump-sum formulas for estimat­ing long-term prestress losses for different bridge girders. The multipliers produced by these studies are compared with that of the current AASHTO LRFD specifications’ approximate method, and new lump-sum formulas for long-term prestress losses are proposed.