Search NASA⌕ Search

SEARCH · Search NASA

Results for “factorization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 541 records · Page 30

Behavioral Health Factors in Long Duration Space Flight: Lessons Learned From Apollo And Their Implications For Artemis

Behavioral health will be a critical factor in future Long Duration Spaceflights (LDSF). As humans venture further from Earth, astronauts will face greater isolation and need to be more autonomous than ever before. Astronauts will face a plethora of stressors, both internally and externally, and it will be mission critical to optimize their mind and bodies to endure and overcome these challenges. Personalities, environmental and physical factors will affect each individual and crew in different ways and it will be important to look at these factors independently and as a whole to maximize the chances of a successful mission. By analyzing environments analogous to space and building upon the lessons learned from the Apollo missions and over 50 years of Low Earth Orbit spaceflight, we hypothesize that a general framework can be developed to optimize crew mental wellbeing.

Nicolas Heft↗

A34F-01: Agricultural Emission Factors from FIREX-AQ

Prescribed fires are a frequent tool for land management, used for both land-clearing and agricultural activities. Determining emissions and subsequent air quality impacts from these fires requires emission factors appropriate for the type of biomass being burned. The NOAA/NASA Fire Influence on Regional to Global Environments and Air Quality (FIREX-AQ) campaign that took place from July to September 2019 provided comprehensive sampling of prescribed fires in the Eastern United States. We calculate emission factors for agricultural and land-clearing activities from FIREX-AQ and the dependence of these emission factors on fuel type/burning characteristics (i.e., modified combustion efficiency).

Katherine R Travis↗

Canadian and Alaskan Wildfire Smoke Particle Properties, Their Evolution and Controlling Factors, From Satellite Observations

The optical and chemical properties of biomass burning (BB) smoke particles greatly affect the impact that wildfires have on climate and air quality. Previous work has demonstrated some links between smoke properties and factors such as fuel type and meteorology. However, the factors controlling BB particle speciation at emission are not adequately understood nor are the factors driving particle aging during atmospheric transport. As such, modeling wildfire smoke impacts on climate and air quality remains challenging. The potential to provide robust, statistical characterizations of BB particles based on ecosystem type and ambient environmental conditions with remote sensing data is investigated here. Space-based Multi-angle Imaging SpectroRadiometer (MISR) observations, combined with the MISR Research Aerosol (RA) algorithm and the MISR Interactive Explorer (MINX) tool, are used to retrieve smoke plume aerosol optical depth (AOD) and to provide constraints on plume vertical extent; smoke age; and particle size, shape, light-absorption properties, and absorption spectral dependence. These tools are applied to numerous wildfire plumes in Canada and Alaska, across a range of conditions, to create a regional inventory of BB particle-type temporal and spatial distribution. We then statistically compare these results with satellite measurements of fire radiative power (FRP) and land cover characteristics, as well as short-term climate, meteorological, and drought information from the Modern-Era Retrospective analysis for Research and Applications (MERRA-2) reanalysis and the North American Drought Monitor. We find statistically significant differences in the retrieved smoke properties based on land cover type, with fires in forests producing the thickest plumes containing the largest, brightest particles and fires in savannas and grasslands exhibiting the opposite. Additionally, the inferred dominant aging mechanisms and the timescales over which they occur vary systematically between land types. This work demonstrates the potential of remote sensing to constrain BB particle properties and the mechanisms governing their evolution over entire ecosystems. It also begins to realize this potential, as a means of improving regional and global climate and air quality modeling in a rapidly changing world.

Katherine T. Junghenn Noyes↗

Measurement Report :Emission Factors of NH3 and NHx for Wildfires and Agricultural Fires in the United States

During the 2019 Fire Influence on Regional to Global Environments and Air Quality (FIREX-AQ) study, the NASA DC-8 carried out in situ chemical measurements in smoke plumes emitted from wildfires and agricultural fires in the contiguous United States. The DC-8 payload included a modified proton-transfer-reaction time-of-flight mass spectrometer (PTR-ToF-MS) for the fast measurement of gaseous ammonia (NH 3 ) and a high-resolution time-of-flight aerosol mass spectrometer (AMS) for the fast measurement of submicron particulate ammonium (NH 4 + ). We herein report data collected in smoke plumes emitted from 6 wildfires in the Western United States, 2 prescribed grassland fires in the Central United States, 1 prescribed forest fire in the Southern United States, and 66 small agricultural fires in the Southeastern United States. Smoke plumes contained double to triple digit ppb levels of NH 3 . In the wildfire plumes, a significant fraction of NH 3 had already been converted to NH 4 + at the time of sampling (≥2 h after emission). Substantial amounts of NH 4 + were also detected in freshly emitted smoke from corn and rice field fires. We herein present a comprehensive set of emission factors of NH 3 and NH x , with NH x = NH 3 + NH 4 + . Average NH 3 and NH x emission factors for wildfires in the Western United States were 1.86±0.75 g kg −1 and 2.47±0.80 g kg −1 of fuel burned, respectively. Average NH 3 and NH x emission factors for agricultural fires in the Southeastern United States were 0.89±0.58 and 1.74±0.92 g kg −1 , respectively. Our data show no clear inverse correlation between modified combustion efficiency (MCE) and NH 3 emissions. The observed NH 3 emissions were significantly higher than measured in previous laboratory experiments in the FIREX FireLab 2016 study.

Laura Tomsche↗

Transition Modeling Based on the Dual N-factor Method for the CRM-NLF Wind Tunnel Configuration

The dual N-factor method is used to model the boundary-layer transition over the common research model with natural laminar flow (CRM-NLF) aircraft configuration. The flow conditions match selected test conditions from a wind tunnel experiment in the National Transonic Facility at the NASA Langley Research Center. The paper presents a systematic methodology for transition prediction in the presence of a dual shock system and extends the prior capability for iteratively coupled computational fluid dynamics (CFD) predictions to incorporate three-dimensional, transonic wings. The method employs stability computations based on the linear parabolized stability equations (PSE), along with a dual N-factor criterion. The iterative process begins with the fully turbulent Reynolds-averaged-Navier-Stokes (RANS) mean flow solution. For the first iteration, a mean flow solution is calculated with an imposed transition front that aligns with the shock front from the fully turbulent solution. Subsequently, stability computations are performed along a set of streamlines across the wing to calculate the amplification of planar Tollmien-Schlichting (TS) and stationary crossflow (CF) modes. The transition criterion based on the dual N-factor method is used to infer the updated transition front and the process is successively repeated until convergence of the solution. Within three iterations, the predicted fronts for angles of attack of 1.45, 1.98, 2.46 and 2.94 degrees and a mean-aerodynamic-chord Reynolds number equal to 15 million, approach visual convergence in most regions of the studied cases, and the resulting predictions are in good agreement with the transition fronts deduced from measurements of temperature-sensitive paint. Even though surface pressure measurements based on fully-turbulent flow agree well with the measured pressure coefficient distributions, strong viscous-inviscid interaction effects cause significant shifts in the shock locations based on the imposed transition front, underscoring the intrusive nature of static pressure measurements using surface mounted ports on the CRM-NLF configuration.

Boundary Layer Transition↗

Bayesian Symbolic Regression: Addressing Challenges in Estimating Fractional Bayes Factors and Application to Fatigue Crack Growth Modeling

This research pioneers advancements in computational mechanics by integrating Bayesian-based uncertainty quantification into symbolic regression, specifically focusing on the critical task of accurately estimating the fractional Bayes factor for selecting arbitrary equations. In our exploration, we rigorously study two prominent methods—sequential Monte Carlo and the Laplace approximation—employed for computing the fractional Bayes factor. Our findings underscore the limitations of the Laplace approximation, revealing its diminished accuracy in nonlinear and multimodal scenarios. Specifically, the Laplace approximation is shown to underpredict fractional Bayes factor on a wide set of equations associated with a symbolic regression benchmark. This comparative analysis sheds light on the nuanced performance of these techniques, guiding researchers toward more informed choices in uncertainty quantification within symbolic regression. Furthermore, we showcase the practical utility of these enhanced symbolic regression tools through their application to a real-world problem in fatigue crack growth modeling, emphasizing their efficacy in capturing the complexities of mechanical systems.

Geoffrey Bomarito↗

Córdoba Wildland Fires: Assessing Fire Risk Factors in Córdoba, Argentina using Earth Observations

In recent years, Córdoba, Argentina has experienced intensified wildfire activity, with fires in 2020 alone scorching over 300,000 hectares within the province. Potential causes for the increased burn area include climate change, the expanding wildland-urban interface (WUI), and inadequate fire management practices. Previous studies have produced fire frequency maps for the region, but gaps remain in understanding the environmental parameters influencing fire behavior and growth. We partnered with the Instituto Nacional de Tecnología Agropecuaria (INTA) to address these gaps by utilizing NASA Earth observing data to analyze key wildfire risk factors. Using a combination of data inputs from Soil Moisture Active Passive (SMAP), Shuttle Radar Topography Mission (SRTM), Global Precipitation Measurement (GPM) Integrated Multi-satellite Retrievals for GPM (IMERG), and Aqua/Terra Moderate Resolution Imaging Spectroradiometer (MODIS), we created a ten-year baseline using environmental variables to determine anomalies that influenced the fires of 2020. Baseline data were used to calculate the statistical significance of the environmental factors as precursors to wildfires. We found that the normalized difference vegetation index (NDVI) and precipitation were the strongest indicators for the September 2020 wildfires. Using the environmental risk factors, we created a wildfire risk map for the province of Córdoba, which can be used to enhance our partner’s fire management strategies and decision-making processes.

wildland fires↗

Risk Characterization Research for Artemis II: Human Factors and Behavioral Performance

BACKGROUND Artemis II will be the first time NASA astronauts go beyond low-Earth orbit (LEO) since the Apollo era, and the first astronauts heading into space in the Orion vehicle. As such, it provides a critical opportunity to refine our understanding of the likelihood and consequences associated with the Behavioral Medicine (BMed), Team, Human System Integration Architecture (HSIA), and Sleep Risks, and prepare for future Moon and Mars missions. However, Artemis II research efforts are uniquely shaped by in-mission data collection constraints. There is currently no in-mission crew time available to complete measures. In-mission data will need to be collected unobtrusively from available data streams (e.g., audiovisual, existing records such as schedules, and actigraphy). Accordingly, the overarching goal of our research is to utilize Artemis II data to further define the likelihood and consequences of these risks, and to create an unobtrusive research infrastructure that can be expanded to include future Artemis missions. This goal spans four aims across three research phases: (1) identify and operationally define key performances metrics and constructs across the four aforementioned risks, (2) develop an unobtrusive methodology and coding scheme for in-mission data collection, (3) characterize performance decrements due to Bmed, Team, HSIA, and Sleep Risks, and (4) develop a data infrastructure for future Artemis missions. The following details results of Phase I efforts in which we address Aims 1 and 2 to develop an unobtrusive measurement plan and coding scheme to capture key constructs, contributing factors, and performance decrements across each risk area. METHOD As part of Phase I, we conducted an interdisciplinary literature review and consulted with SMEs to identify unobtrusive methodologies that leverage text, audio, and/or video data as well as conceptualize key performance metrics, contributing factors, and BMed, Team, HSIA, and Sleep risk constructs related to performance decrements. The Phase I effort resulted in a finalized pre- and post-mission protocol for Artemis II, along with a measurement and coding scheme for in-mission Artemis II data. Phase II will involve data collection from the upcoming Artemis II mission. Phase III will include data processing, coding, depiction, analysis, and report writing of the Artemis II data. RESULTS & DISCUSSION To date, we have completed Phase I efforts. Specifically, we identified BMed, Team, HSIA, and Sleep risk constructs related to performance metrics, summarized how these constructs can be measured using audiovisual data collected during the mission, and worked with NASA’s HFBP Element to finalize a data collection protocol that leverages audiovisual input from the Orion spacecraft system. Our protocol includes novel unobtrusive methodologies that adhere to in-mission data streams and subsequent constraints (e.g., limited storage space on GoPro cameras, ambient noise impeding audio files) to best capture in-mission phenomena across each risk area. We will present our results from Phase I efforts, namely best practices for unobtrusive measurement as identified through literature reviews and SME consultation as well as codebook excerpts for use in Artemis II. We will include a description of planned work as we prepare for Phase II and Phase III of this research plan and the Artemis II mission itself. SUMMARY We describe progress on our Human Factors and Behavioral Performance Research for Artemis II study.

behavioral health↗

Habitability and Human Factors Assessment (iSHORT, SHAQ, and SHU)

BACKGROUND As long-duration off-planet habitats become a reality, a consideration of habitability and human factors (HF) is crucial. The habitat is more than just a place to live and work. It is also the crew’s perception of the space, and the psychological impacts of size, layout, and usage over time; all of which can support or strain behavioral health and performance (BHP). A previous International Space Station (ISS) habitability study used the iSHORT (Space Habitability Observation Reporting Tool) to collect detailed data about habitability and human factors and inform NASA Standards. Of the previous iSHORT study, only one of the six ISS subjects had a duration of one year; all other ISS and ground analog subjects had shorter mission durations from one week to six months. It is necessary to collect new data with a focus on long-duration exploration missions of > 6 months and on planetary surface habitat design. New data is also needed to compare the iSHORT to other habitability measures. One measure, the SHAQ (Subjective Habitability and Acceptability Questionnaire), assesses the intersection of psychology and habitability. Another complementary measure, the Scale for Habitat Usability (SHU), is a brief subjective scale that captures how habitat design impacts perceived usability of the built environment in relation to task performance. OBJECTIVE Our study aims to (1) understand how individual well-being and team dynamics may relate to HF concerns over time, (2) capture how habitability and HF change over time, (3) compare the three habitability measures (iSHORT, SHAQ, SHU), (4) assess habitats to capture HF design concerns and related BHP impacts of a planetary habitat, and (5) inform future standards for HF design. METHOD Data are being collected on crews living and working in long-duration spaceflight analogs. Individual-level data collections are repeated at regular intervals throughout the missions on several habitat areas, activities, and key equipment (i.e., points of interest). These points of interest (POIs) include the kitchen/galley, crew quarters, and other work and living areas. Assessments include evaluations of privacy, comfort, convenience, control, efficiency, and social density through the lens of subsequent outcomes like sleep, individual performance, group activities performance, stress, mood, and social interactions. Pre- and post-mission evaluations will also allow comparison with homes, pre- and post-mission hotels, and a retrospective reflection of living and working in a long-duration analog. INITIAL DATA COLLECTIONS In this poster, we will describe the measures and data yield. Since the research protocol was designed, the study team has collected iSHORT Standalone four times, nine collections of SHAQ, and three collections of iSHORT with SHAQ. Data collection is ongoing. SUMMARY A novel assessment suite has been developed to further aid the comparison and complementary understanding of the habitability and human factors measures, which will allow for efficient deployment of these measures in analogs and/or spaceflight in near-term research as well as support well-being and performance through design.

J C W Miller↗

Exemplifying the Usability of NASA Earth Observations to Analyze Potential Risk Factors that Predispose Wildfires in the Rural-Urban Areas of Córdoba, Argentina

In recent years, Córdoba, Argentina has experienced intensified wildfire activity, with fires in 2020 alone scorching over 300,000 hectares within the province. Potential causes for the increased burn area include climate change, the expanding wildland-urban interface, and inadequate fire management practices. Previous studies have produced fire frequency maps for the region, but gaps remain in understanding the parameters influencing fire behavior and growth. This project partnered with the Instituto Nacional de Tecnología Agropecuaria to address these gaps by utilizing NASA’s remote sensing capabilities to analyze key wildfire risk factors. Using a combination of data inputs from Soil Moisture Active Passive (SMAP), Shuttle Radar Topography Mission (SRTM), Global Precipitation Measurement (GPM) Integrated Multi-satellite Retrievals for GPM (IMERG), and Aqua/Terra Moderate Resolution Imaging Spectroradiometer (MODIS), a ten-year baseline was created using environmental variables to determine anomalies that influenced the fires of 2020. Of these anomalies, the baseline data were used to calculate the statistical significance of the environmental factors to the wildfires. This study found that the normalized difference vegetation index (NDVI) and precipitation were the strongest indicators for the September 2020 wildfires. Using the environmental risk factors, this project created a wildfire risk map for the province of Córdoba, which can be used to enhance partner’s fire management strategies and decision-making processes.

Chassety Raines↗

Geometry-aware training of factorized layers in tensor Tucker format

Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during train and inference of large networks. Given its easy implementation and flexibility, one promising approach is layer factorization, which reshapes weight tensors into a matrix format and parameterizes it as the product of two rank-r matrices. However, this family of approaches often requires an initial full-model warm-up phase, prior knowledge of a feasible rank, and it is sensitive to parameter initialization.In this work, we introduce a novel approach to train the factors of a Tucker decomposition of the weight tensors. Our training proposal proves to be optimal in locally approximating the original unfactorized dynamics and stable for the initialization. Furthermore, the rank of each mode is dynamically updated during training.We provide a theoretical analysis of the algorithm, showing convergence, approximation and local descent guarantees. The method's performance is further illustrated through a variety of experiments, showing remarkable training compression rates and comparable or even better performance than the full baseline and alternative layer factorization strategies.

Zangrando, Emanuele [Gran Sasso Science Institute ↗

Precision Measurement of the Neutron Magnetic Form Factor via the Ratio Method at Jefferson Lab Hall A

Protons and neutrons, collectively known as nucleons, are composed of quarks and gluons. The Sachs electromagnetic form factors encode information about the spatial distributions of charge and magnetization in the nucleon, particularly at low momentum transfer. In particular, the neutron magnetic form factor (GMn) provides crucial information about the distribution of magnetization inside the neutron and helps constrain theoretical models of nucleon structure. Quasi-elastic electron scattering from deuterium was measured up to Q^2=13.5 GeV^2 using the Super BigBite Spectrometer in Hall A at Jefferson Lab. In this work, the neutron magnetic form factor GMn was extracted at Q^2 = 3.0 GeV^2 and Q^2=4.5 GeV^2 using the Ratio Method. These results represent a subset of the full dataset collected in this experiment, which extended to significantly higher Q^2. The extracted GMn values agree with the existing global fit within approximately two standard deviations at Q^2=3.0 and show excellent agreement at Q^2=4.5. The measurements achieved systematic uncertainties of about 2% and statistical uncertainties below 0.5%, among the most precise determinations of GMn at these kinematics. These results demonstrate the robustness of the experimental technique and provide an important validation point for future extractions at higher Q^2, where data remain scarce. In addition, the GRINCH heavy gas Cherenkov detector—a key component of the experimental apparatus—was commissioned and achieved an electron detection efficiency of approximately 97%, supporting reliable particle identification. Together, the analysis presented here advances both our understanding of nucleon structure and the validation of the experimental methods and instrumentation used to access it.

Satnik, Maria [College of William and Mary, Willia↗

How threshold effects in spectroscopic factors influence heavy-ion knockout reactions

A two-decade-old puzzle in heavy-ion one-nucleon knockout reactions is the strong correlation between the reduction factor R S = σ exp /σ t h and the Fermi surface asymmetry ΔS. Theoretical cross sections typically rely on spectroscopic factors (SFs) from shell model (SM) calculations, which neglect continuum coupling effects. Here, we employ the Gamow shell model (GSM), which explicitly incorporates continuum coupling, to compute SFs for p-shell nuclei and predict corresponding theoretical cross sections. Systematic calculations demonstrate that using GSM-derived SFs substantially reduces discrepancies between theoretical and experimental results. This improvement is particularly significant for deeply bound nucleon knockout in nuclei near the dripline, where traditional SM-based calculations fall short. As a result, using GSM SFs, the ratio R s exhibits no pronounced dependence on ΔS. Furthermore, both the ratio of GSM SFs to SM SFs and their corresponding reaction cross sections ratios exhibit a strong ΔS dependence. We have also compared GSM SFs and cross sections with those from the no-core shell model calculations, giving a similar pronounced sensitivity to ΔS. Detailed analysis attributes these correlations to threshold effects for SFs in weakly bound systems. Overall, incorporating continuum coupling via GSM enhances the reliability of SF predictions for exotic, weakly bound nuclei and provides key insights toward resolving the enduring puzzle in heavy-ion knockout reactions from a nuclear structure perspective.

Gamow shell model↗

Nonperturbative aspects of the electromagnetic pion form factor at high energies

The structure of hadronic form factors at high energies and their deviations from perturbative quantum chromodynamics provide insight on nonperturbative dynamics. Using an approach that is consistent with dispersion relations, we construct a model that simultaneously accounts for the pion wave function, gluonic exchanges, and quark Reggeization. In particular, we find that quark Reggeization can be investigated at high energies by studying scaling violation of the form factor.

Form factors↗

Extracellular matrix and growth factors in branching morphogenesis

The unifying hypothesis of the NSCORT in gravitational biology postulates that the ECM and growth factors are key interrelated components of a macromolecular regulatory system. The ECM is known to be important in growth and branching morphogenesis of embryonic organs. Growth factors have been detected in the developing embryo, and often the pattern of localization is associated with areas undergoing epithelial-mesenchymal interactions. Causal relationships between these components may be of fundamental importance in control of branching morphogenesis.

Non-NASA Center↗

Selected Contribution: Skeletal muscle focal adhesion kinase, paxillin, and serum response factor are loading dependent

This investigation examined the effect of mechanical loading state on focal adhesion kinase (FAK), paxillin, and serum response factor (SRF) in rat skeletal muscle. We found that FAK concentration and tyrosine phosphorylation, paxillin concentration, and SRF concentration are all lower in the lesser load-bearing fast-twitch plantaris and gastrocnemius muscles compared with the greater load-bearing slow-twitch soleus muscle. Of these three muscles, 7 days of mechanical unloading via tail suspension elicited a decrease in FAK tyrosine phosphorylation only in the soleus muscle and decreases in FAK and paxillin concentrations only in the plantaris and gastrocnemius muscles. Unloading decreased SRF concentration in all three muscles. Mechanical overloading (via bilateral gastrocnemius ablation) for 1 or 8 days increased FAK and paxillin concentrations in the soleus and plantaris muscles. Additionally, whereas FAK tyrosine phosphorylation and SRF concentration were increased by < or =1 day of overloading in the soleus muscle, these increases did not occur until somewhere between 1 and 8 days of overloading in the plantaris muscle. These data indicate that, in the skeletal muscles of rats, the focal adhesion complex proteins FAK and paxillin and the transcription factor SRF are generally modulated in association with the mechanical loading state of the muscle. However, the somewhat different patterns of adaptation of these proteins to altered loading in slow- vs. fast-twitch skeletal muscles indicate that the mechanisms and time course of adaptation may partly depend on the prior loading state of the muscle.

NASA Discipline Musculoskeletal↗

Skeletal unloading induces resistance to insulin-like growth factor I

In previous studies with a hindlimb elevation model, we demonstrated that skeletal unloading transiently inhibits bone formation. This effect is limited to the unloaded bones (the normally loaded humerus does not cease growing), suggesting that local factors are of prime importance. IGF-I is one such factor; it is produced in bone and stimulates bone formation. To determine the impact of skeletal unloading on IGF-I production and function, we assessed the mRNA levels of IGF-I and its receptor (IGF-IR) in the proximal tibia and distal femur of growing rats during 2 weeks of hindlimb elevation. The mRNA levels for IGF-I and IGF-IR rose during hindlimb elevation, returning toward control values during recovery. This was accompanied by a 77% increase in IGF-I levels in the bone, peaking at day 10 of unloading. Changes in IGF binding protein levels were not observed. Infusion of IGF-I (200 micrograms/day) during 1 week of hindlimb elevation doubled the increase in bone mass of the control animals but failed to reverse the cessation of bone growth in the hindlimb-elevated animals. We conclude that skeletal unloading induces resistance to IGF-I, which may result secondarily in increased local production of IGF-I.

NASA Center ARC↗

Mechanics of Preloaded Bolt Tensile Loading With Focus on Load Introduction Factor

The bolt tensile and joint separation loads are directly influenced by the locations at which the external loads enter the clamped members of a preloaded bolted joint (PBJ) and the associated load-paths through the joint. This physical load introduction mechanism affecting the bolt tensile loading is typically represented in the bolt tensile load equation, in part, by a load introduction factor (LIF), which was shown by H.M. Lee of Marshall Spaceflight Center to be a natural product of the bolt tensile load equation using a linear spring stiffness model. This LIF, being a function of load-path stiffness, has subsequently been denoted as the stiffness-based LIF (SBLIF), providing a framework to calculate the LIF using whatever load-path stiffness approximations are appropriate. Expanding upon the work of Lee, it is shown that the SBLIF and the joint stiffness factor are functions of the stiffnesses of the same load-paths and regions within a PBJ, and thus they should not be treated as independent variables. Mathematical expressions for the SBLIF are presented. Comparisons are shown between the analytically calculated SBLIF, the analytically calculated geometric LIF (GLIF), which is a simple clamped-member thickness ratio, the experimentally derived LIF, and the LIF determined by finite element analysis (FEA). Using experiment and FEA as a benchmark, the SBLIF, using traditional load-path stiffness approximations, enables a more accurate prediction of bolt tensile loading than the GLIF, although it can be unconservative near joint separation. The GLIF generally attributes more of the externally applied tensile load to the bolt than does the SBLIF, potentially resulting in heavier and/or more costly bolted joints. Mathematical relationships between the SBLIF and the GLIF are developed. Supplemental material is provided in the appendixes where the historical practice of using the joint compressive stiffness in place of the joint tensile stiffness is evaluated. The appendixes include step-by-step examples demonstrating the calculation of the SBLIF using traditional stiffness approximations and conclude with the development of the joint diagram in terms of the SBLIF, culminating into formulas for the key features of a joint diagram, which is useful for programming.

Load Path↗