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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Chapter 9 - Pre-Flight Tests

Pre-flight testing is critical to the success of any flight test program. Pre-flight tests are performed to measure and evaluate the characteristics of an aircraft in a non-flying environment and to verify that these characteristics are as desired. Since aircraft systems are becoming more and more complex, conducting proper pre-flight testing to help identify system characteristics and deficiencies prior to flight is more important now than ever before. Much flight test time has been lost fixing problems that should have been found and corrected prior to flight. Accidents have occurred because pre-flight tests and verification procedures were not conducted thoroughly enough to identify the aircraft's characteristics properly or to find system discrepancies. Proper pre-flight testing helps ensure that the aircraft is ready to fly and contributes toward an efficient, productive, and safe flight test program. The reader should be aware that this Section is dedicated to the testing that should take place prior to the first flight. There are other "pre-flight" tests that take place prior to each individual flight. These latter tests are not discussed in this Section. The following paragraphs of this Section describe significant tests that are usually accomplished prior to flying a new or highly modified aircraft. Test objectives, descriptions, products, and requirements are provided in the following subsections: 9.1 Wind tunnel tests 9.2 Simulation tests 9.3 Propulsion tests 9.4 Weight and balance tests 9.5 Ground vibration tests 9.6 Structural loads tests 9.7 Gain margin tests 9.8 Verification and calibration tests 9.9 Taxi tests The specific examples given and the test facilities mentioned in this Section will illustrate the approach taken and the techniques used by the US Air Force; however, they are typical of those used by other test organizations.

Paul W Kirsten↗
DOE OSTI1975

Nuclear Safety [Vol. 16, No. 1, January-February 1975]

Nuclear Safety covers significant developments in the field of nuclear safety. The scope is limited to topics relevant to the analysis and control of hazards associated with nuclear energy, operations involving fissionable materials, and the products of nuclear fission and their effects on the environment. Primary emphasis is on safety in reactor design, construction, and operation; however, safety considerations in regard to the entire fuel cycle, including fuel fabrication, spent-fuel processing, nuclear waste disposal, handling of radioisotopes, and environmental effects of these operations, are also treated. Table of Contents for this issue follows. Table of Contents for this issue follows. GENERAL SAFETY CONSIDERATIONS: 1 AEC Working Paper on Population Density Around Nuclear Power-Plant Sites Adapted by J. Ft. Buchanan, 8 Water-Reactor Safety-Research Information Meeting by Wm. B. Cottrell, D. O. Hobson, and G. D. Whitman; ACCIDENT ANALYSIS: 29 Burnout in Boiling Heat Transfer. Part I: Pool-Boiling Systems by A. E. Bergles; PLANT SAFETY FEATURES: 43 Radionuclide Behavior During Normal Operation of Liquid-Metal-Cooled Fast Breeder Reactors. Part 1: Production by C. A. Erdman and A. B. Reynolds; CONSEQUENCES OF EFFLUENT RELEASE: 60 The Control, Monitoring, and Reporting of Radioactivity in Effluents. Part 1: AEC-Owned Facilities by M. B. Biles and F. E. Coffman, 71 The Control, Monitoring, and Reporting of Radioactivity in Effluents. Part 2: AEC-Licensed Facilities by L. B. Higginbotham and J. T. Collins; OPERATING EXPERIENCES: 76 Incident at the Lucens Reactor by J. M. Miller, 79 IAEA Symposium on Experience from Operating and Fueling of Nuclear Power Reactors by William A. Pryor, 87 Recent Occurrences at Nuclear Reactors and Their Causes Compiled by William R. Casto, 98 Summary of Operating U. S. Power Reactors as of Nov. 1. 1974, 101 Selected Safety-Related Occurrences Reported in September and October 1974 Compiled by William R. Casto; CURRENT EVENTS: 104 General Administrative Activities Compiled by Wm. B. Cottrell, 110 Action on Power-Reactor Projects Undergoing Regulatory Review or Consideration Compiled by Wm. B. Cottrell, 119 Action on Nonreactor Projects Undergoing Regulatory Review or Consideration Compiled by Wm. B. Cottrell, 121 Proposed Rule Changes as of Oct. 31, 1974; MISCELLANY: 97 ASTM—Euratom Symposium on Radiation Dosimetry: Developments and Standardization (Announcement), 118 Workshops on In-Pile Filter Testing (Announcement), 119 IAEA Symposium on Radiological Impacts from Releases from Nuclear Facilities into Aquatic Environments (Announcement).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2026

Understanding and Controlling Hybrid Electric Gas Turbine Engine Transient Dynamics

The electrification of the gas turbine engine is known to increase the flexibility of aircraft architectures by enabling the generation of electrical power to distribute to other electrically based, thrust producing subsystems. It also has potential for direct performance benefits in the gas turbine engine itself, both at steady state and dynamically. Although the design focus of the gas turbine engine performance is primarily at steady state, it is often the instabilities occurring during transients that cause disequilibrium and constrain performance improvements. Instabilities arise due to the disequilibrium of the energy storage mechanisms within the traditional engine system and likewise for the electrified engine system. The primary energy storage mechanisms in the traditional system are the rotational inertia, gas path volumes, the thermal masses that make up the mechanical structure, and now, the electrical power system will provide additional contributions. Understanding the effect each of these energy storage mechanisms has on the others and controlling them appropriately allows for the suppression of state changes within the turbomachinery components to the degree that the components remain near steady state, thus reducing the disequilibrium within the system. The ability to tightly regulate the state changes of turbomachinery components, such as the compressor, minimizes the excursion of the compressor operating point from the operating line (operability), allowing for higher performing, more efficient compressor designs by decreasing the amount of stall margin needed for safe engine power level changes. Preliminary studies with the electrification of the turbine engine have shown that this is possible, and this concept can lead to design trades benefitting engine performance, weight, and volume. This paper explores in detail the energy storage mechanisms and control approaches for coordinating their state changes, and ultimately proposes that a higher performing, more efficient compressor design can result.

transient dynamics↗
DOE OSTI2026

First Wall Design of a Tokamak Pilot Plant Using a Monte Carlo Model for 3-D Heat Flux Deposition

We present a method for calculating the heat fluxes deposited on nonaxisymmetric tokamak first wall components, allowing for a first-of-its-kind model for power handling in the tokamak far scrape-off layer (SOL). The DIV3D Monte Carlo model features strict global power conservation and can calculate the finite cross-field plasma transport into magnetically-shadowed regions, which is significant when dealing with meter-scale shadows introduced by components such as poloidal limiters or antennas. As a case study, we apply the DIV3D model to inform the distribution of first wall poloidal limiters in an ARC-class reactor device. We demonstrate that discrete protection limiters can efficiently reduce peak heat fluxes on recessed breeder wall components in the presence of significant far-SOL plasma fluxes. By varying the toroidal periodicity and radial standoff depth of the limiters, we demonstrate one of the tradeoffs that must be considered in first wall design: more limiters provide greater protection, but at the cost of reduced breeding performance. We also present the impact that radial misalignments between limiters would have on first wall power loading.

Monte Carlo methods↗
NASA NTRS1975

The 1975 GSFC Battery Workshop

The proceedings of the 1975 Goddard Space Flight Center Battery Workshop are presented. The major topics of discussion were nickel cadmium batteries and, to a lesser extent, nickel hydrogen batteries. Battery design, manufacturing techniques, testing programs, and electrochemical characteristics were considered. The utilization of these batteries for spacecraft power supplies was given particular attention.

Source record↗
NASA NTRS1985

Mathematical Storage-Battery Models

Empirical formula represents performance of electrical storage batteries. Formula covers many battery types and includes numerous coefficients adjusted to fit peculiarities of each type. Battery and load parameters taken into account include power density in battery, discharge time, and electrolyte temperature. Applications include electric-vehicle "fuel" gages and powerline load leveling.

Chapman, C. P.↗
DOE OSTI2026

Effects of Composition and Oxidation States on the Structures of Chromium-Containing Sodium Silicate Glasses: Molecular Dynamics Simulations using Machine Learning Interatomic Potentials

Chromium represents a significant challenge for the vitrification of high-level nuclear waste into silicate and borosilicate glasses due to its low solubility and variable oxidation states, which can limit the waste loading due to promotion of crystallization or phase separation during processing. In this study, we modeled chromium containing silicate glasses using molecular dynamics simulations with three machine learning interatomic potentials (MLIPs), MACE, CHGNet, and PFP were employed, to gain insights on glass composition and oxidation states on the structures of these glasses. One of the goals is to evaluate their ability of these MLIPs to accurately represent the general structure of silicate glasses and chromium local environments as a function of chromium oxidation states. Density Functional Theory (DFT) based calculations and experimental data such as neutron structure factors were used to validate the structural models. It was found that the foundation models of all three MLIPs are able to reproduce general structural features of the sodium silicate glass structure consistent with experimental and DFT data, but only CHGNet and PFP can accurately capture the oxidation states and local environment of chromium: tetrahedral for Cr6+ and octahedral for Cr3+. Furthermore, we studied the effect of varying Cr3+/ Cr6+ (Cr3+/Crtotal) ratio and total chromium content using PFP. Our results show that Cr6+ enhances network polymerization by reducing non-bridging oxygens through Na? charge compensation required due to the formation of chromate (CrO42-) species, while Cr³? acts as a network modifier that disrupts connectivity. System size effects on the structural characteristics and chromium environments were also tested using the PFP potential. This work highlights the importance of careful validation on the precision, transferability, and potential of MLIPs for modeling glasses containing transition metal elements that can exist in multiple oxidation states. It is also encouraging to see the foundational models are all three MLFFs are able to reproduce the basic sodium silicate glass structures, while suggesting additional training or refining is needed to improve the description of more complex systems containing transition metals.

Puga, Christina L.↗
NASA NTRS1994

Resistance of Silicon Nitride Turbine Components to Erosion and Hot Corrosion/Oxidation Attack

Silicon nitride turbine components are under intensive development by AlliedSignal to enable a new generation of higher power density auxiliary power systems. In order to be viable in the intended applications, silicon nitride turbine airfoils must be designed for survival in aggressive oxidizing combustion gas environments. Erosive and corrosive damage to ceramic airfoils from ingested sand and sea salt must be avoided. Recent engine test experience demonstrated that NT154 silicon nitride turbine vanes have exceptional resistance to sand erosion, relative to superalloys used in production engines. Similarly, NT154 silicon nitride has excellent resistance to oxidation in the temperature range of interest - up to 1400 C. Hot corrosion attack of superalloy gas turbine components is well documented. While hot corrosion from ingested sea salt will attack silicon nitride substantially less than the superalloys being replaced in initial engine applications, this degradation has the potential to limit component lives in advanced engine applications. Hot corrosion adversely affects the strength of silicon nitride in the 850 to 1300 C range. Since unacceptable reductions in strength must be rapidly identified and avoided, AlliedSignal and the NASA Lewis Research Center have pioneered the development of an environmental life prediction model for silicon nitride turbine components. Strength retention in flexure specimens following 1 to 3300 hour exposures to high temperature oxidation and hot corrosion has been measured and used to calibrate the life prediction model. Predicted component life is dependent upon engine design (stress, temperature, pressure, fuel/air ratio, gas velocity, and inlet air filtration), mission usage (fuel sulfur content, location (salt in air), and times at duty cycle power points), and material parameters. Preliminary analyses indicate that the hot corrosion resistance of NT154 silicon nitride is adequate for AlliedSignal's initial engine applications. Protective coatings and/or inlet air filtration may be required to achieve required ceramic component lives in more aggressive environments.

Nitride↗
NASA NTRS2026

Multi-Agent Swarm State of the Art Report

The Next-Generation Multi-Agent Swarm (NGS) Study conducted by NASA’s Ames Research Center for NASA’s Space Technology Mission Directorate (STMD) will develop a comprehensive understanding of emerging multi-agent swarm capabilities. The study aims to identify existing swarm capabilities and asses their potential for persistent lunar space situational awareness, surface monitoring, and distributed autonomy demonstrations. A key objective is to inform the design of a next-generation multi-agent swarm that can perform autonomous distributed remote sensing, position, navigation, and timing (PNT) services, automated deployment that leverages autonomy, edge computing, and interoperable networking to enable cooperative operations without the need for immediate human operation. This study will address specific shortfalls identified by STMD, including intelligent multi-agent constellations, autonomy, edge computation, position, navigation, and timing for small spacecraft, small spacecraft propulsion, and space situational awareness (1625, 1438, 1433, 1557, 1431, 1430, 1589). The NASA Ames Mission Design Center (MDC) will provide subject matter expertise to support systems engineering trades, while experts in autonomy and spacecraft swarms in NASA’s Intelligent Systems Division will lead the study and focus on identifying emerging next-generation swarm capabilities. The study objectives include: capturing the current state-of-the-art for multi-agent swarm capabilities, evaluating technologies and creating technology roadmaps, and developing at least one new technology demonstration mission concept. This initial NGS study report surveys the current state of the art in technology areas relevant for the next-generation multi-agent swarm design. Our primary focus is on surveying relevant deployed space systems1, supplemented with selective analysis of relevant proposed missions and technology developments that have yet to fly.

agent↗
NASA NTRS2000

In-Orbit Earth Radiation Budget Satellite (ERBS) Battery Switch

A viewgraph presentation outlines the Earth Radiation Budget Satellite (ERBS) power system and battery history. ERBS spacecraft and battery cell failures are listed with the reasons for failure. The battery management decision and stabilization of the batteries is discussed. Present battery operations are shown to be successful.

Ahmad, Anisa↗
NASA NTRS1995

Hubble Space Telescope nickel-hydrogen battery testing: An update

The Marshall Space Flight Center (MSFC) began testing the HST Ni-H2 Six Battery Test and the 'Flight Spare Battery' Tests approximately one year before the launch of the HST. These tests are operated and reported on by the MSFC, but are managed and funded by Goddard Space Flight Center in direct support of the HST program. The HST Ni-H2 batteries are built from Eagle Picher RNH-90-3 cells. The HST EPS (electrical power system) is a direct energy transfer power system. The HST Ni-H2 Six Battery Test is a breadboard of the HST EPS. The batteries in the test are composed of test module cells and packaged into three battery modules identical to the flight modules. This test is the HST EPS testbed. The 'Flight Spare Battery' Test is a simulation of one of the six battery channels on the HST. The cells in the test are from the flight spare lot of cells, which are the same lot of cells that three of the six HST flight batteries are made from. This test is the battery life test for the HST program.

Whitt, Thomas H.↗
DOE OSTI2025

SUDA: A SUrface Dust Analyser for Compositional Mapping of the Galilean Moon Europa

Abstract The Surface Dust Analyser (SUDA) is a mass spectrometer onboard the Europa Clipper mission for investigating the surface composition of the Galilean moon Europa. Atmosphereless planetary moons such as the Galilean satellites are wrapped into a ballistic dust exosphere populated by tiny samples from the moon’s surface produced by impacts of fast micrometeoroids. SUDA will measure the composition of such surface ejecta during close flybys of Europa to obtain key chemical signatures for revealing the satellite’s composition such as organic molecules and salts, history, and geological evolution. Because of their ballistic orbits, detected ejecta can be traced back to the surface with a spatial resolution roughly equal to the instantaneous altitude of the spacecraft. SUDA is a Time-Of-Flight (TOF), reflectron-type impact mass spectrometer, optimized for a high mass resolution which only weakly depends on the impact location. The instrument will measure the mass, speed, charge, elemental, molecular, and isotopic composition of impacting grains. The instrument’s small size of$268 ~\mathrm {mm} \times 250 ~\mathrm {mm} \times 171$ 268 mm × 250 mm × 171 $~\mathrm {mm}$ mm , radiation-hard design, and rather large sensitive area of 220 cm 2 matches well the challenging demands of the Clipper mission.

Astronomy & Astrophysics↗
DOE OSTI2026

EXERGETIC: De-Risking Next-Generation Resilient Geothermal Hybrids via At-Scale Evaluation Using Virtual Emulation Digital Twin Environment for Efficient Operation

The DOE-GTO-funded project, award number 5.1.2.12, entitled "EXERGETIC - De-risking Next Generation Resilient Geothermal Hybrids via at-Scale Evaluation Using a Virtual Emulation Digital Twin Environment for Efficient Operation," advances the solution to these challenges by developing and validating a geothermal co-emulation environment implemented at the National Laboratory of the Rockies (NLR)'s Advanced Research on Integrated Energy Systems (ARIES) platform. This framework enables the de-risking of next-generation geothermal and geothermal hybrid systems through high-fidelity modeling, real-time digital emulation, advanced control strategies, and techno-economic assessment. The project focused on geothermal hybrid configurations that integrate geothermal power plants with concentrated solar power and underground thermal energy storage, enabling enhanced efficiency, flexibility, and grid support capabilities. The main goal of this project was the development of a geothermal digital co-emulation environment to demonstrate the technical and economic value of geothermal hybrid systems and their contribution to grid stability and flexibility. The EXERGETIC framework combined physics-based models, controls, and real assets at ARIES, including digital real-time simulators (DRTS), a 20-MW-scale controllable grid interface (CGI), and a 2-MW conventional generator. Detailed transient models were developed for the key subsystems of a hybrid geothermal plant, including parabolic trough solar collectors, reservoir thermal energy storage (RTES), and a binary Organic Rankine Cycle (ORC) power plant. The ORC model explicitly captured thermal inertia and off-design operation and integrated control strategies to dynamically respond to electric load profiles. The models were validated against published experimental and numerical studies, demonstrating strong agreement and confirming the accuracy and robustness of the modeling approach. The resulting digital twin represents geothermal-solar-storage systems at multiple scales (1 MW to 100 MW) and enables realistic emulation of grid-connected operation. The control architecture allows the geothermal resource to provide stable baseload generation, while solar and stored thermal energy supply flexible, dispatchable support during periods of high demand or variable grid conditions. A key contribution of the EXERGETIC project is the demonstration that geothermal hybrid systems can be designed to be active grid assets rather than passive baseload generators. Using the ARIES platform, the digital twin was evaluated under multiple grid scenarios, including load following, voltage support at the distribution level, and frequency response at the transmission level. Results show that hybrid geothermal systems can respond effectively to dynamic grid conditions, providing inertia-like behavior, primary frequency support, and voltage regulation through coordinated control. In addition to the performance and grid services capability analysis of geothermal and hybrid geothermal systems, the EXERGETIC project also focused on scalability and techno-economic analysis of geothermal hybrid plants. In particular, for the scalability analysis, machine-learning (ML)-based surrogate models were trained using data generated from the geothermal digital twin under different grid-connected scenarios and plant capacities. These ML models demonstrated strong interpolation and extrapolation capabilities across plant sizes, accurately reproducing both steady-state and transient responses with very low errors. Regarding the techno-economic analysis, plant performance results were integrated with cost models for hybrid geothermal systems, and the levelized cost of electricity (LCOE) was used as the main economic metric to evaluate system performance across a range of system capacities, solar shares, solar multiples, and storage durations. Results indicate that economies of scale significantly reduce geothermal LCOE as plant capacity increases, with large-scale systems (25-100 MW) achieving substantially lower costs than small plants. Hybridization with solar thermal energy and storage further improves economic performance by increasing capacity utilization and enabling flexible dispatch. In addition, thermal storage plays a critical role in reducing LCOE by maximizing geothermal, solar, and stored energy resources. In summary, the results from this project demonstrate that geothermal hybrid systems represent a promising alternative for increasing the energy conversion efficiency of geothermal technologies, contributing to the preservation of geothermal resources, and supporting the transition of geothermal plants from traditional baseload resources into flexible, resilient, and cost-competitive energy conversion technologies.

15 GEOTHERMAL ENERGY↗
DOE OSTI2026

Linking international technical specifications for acoustic characterization of marine energy converter sounds with environmental compliance criteria

As new ocean energy technologies emerge and are deployed for testing and operations, sound emissions are a potential concern for environmental effects to marine life. Consistent acoustic measurement and data analysis methods can help promote comparisons of technologies and transferability between project sites. In 2022, acoustic emissions from a prototype scale wave energy converter (WEC) were characterized for a range of environmental conditions and power generation states in the coastal waters off southern California using a set of international technical specifications. Results from the international technical specification analyses were applied to United States regulatory threshold criteria for acoustic impacts to marine mammals and examined in the context of European underwater noise monitoring guidelines. Weighted 24 hour cumulative sound exposure levels SEL24h calculated from the highest power generation state WEC sound pressure levels were often more than 20 dB below threshold criteria for temporary threshold shifts in five relevant marine mammal hearing groups. Following European Union recommendations for analyses and reporting, WEC sound characterization in third octave bands centered at 63 Hz and 125 Hz show clear spatial decay of WEC-generated noise, with more pronounced attenuation at 63 Hz, and a less marked but still detectable gradient at 125 Hz, collectively suggesting a relatively confined acoustic footprint under the observed conditions. The value of the international technical specification approach is highlighted by the isolation of WEC sounds from the surrounding soundscape. This allows for a robust characterization of acoustic emissions through a range of device power generation and sea states. Furthermore, in threshold-based regulatory contexts like the U.S., this facilitates direct evaluation of source contributions, while in broader monitoring frameworks used in the E.U. it provides a reproducible foundation for assessing the contribution of emerging ocean energy technologies to the underwater acoustic environment.

Haxel, Joseph H. (ORCID:0000000273864761)↗
NASA NTRS1997

Galileo Probe Battery System

The conclusions of the Galileo probe battery system are: the battery performance met mission requirements with margin; extensive ground-based and flight tests of batteries prior to probe separation from orbiter provided good prediction of actual entry performance at Jupiter; and the Li-SO2 battery was an important choice for the probe's main power.

Dagarin, B. P.↗
NASA NTRS1994

Nickel cadmium battery operations and performance

The Earth Radiation Budget Satellite (ERBS), Compton Gamma Ray Observatory (CGRO), Upper Atmosphere Research Satellite (UARS), and Extreme Ultraviolet Explorer (EUVE) spacecraft are operated from NASA's Goddard Space Flight Center (GSFC) in Greenbelt, Maryland. On-board power subsystems for each satellite employ NASA Standard 50 Ampere-hour (Ah) nickel-cadmium batteries in a parallel configuration. To date, these batteries have exhibited degradation over periods from several months (anomalous behavior, UARS and CGRO (MPS-1); to little if any, EUVE) to several years (old age, normal behavior, ERBS). Since the onset of degraded performance, each mission's Flight Operations Team (FOT), under the direction of their cognizant GSFC Project Personnel and Space Power Application Branch's Engineers has closely monitored the battery performance and implemented several charge control schemes in an effort to extend battery life. Various software and hardware solutions have been developed to minimize battery overcharge. Each of the four sections of this paper covers a brief overview of each mission's operational battery management and its associated spacecraft battery performance. Also included are new operational procedures developed on-orbit that may be of special interest to future mission definition and development.

Rao, Gopalakrishna↗
NASA NTRS2025

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↗