Results for “characterization of rare earth elements (REE)” — Page 20

NASA NTRS1992

Monte Carlo modeling of atomic oxygen attack of polymers with protective coatings on LDEF

Characterization of the behavior of atomic oxygen interaction with materials on the Long Duration Exposure Facility (LDEF) will assist in understanding the mechanisms involved, and will lead to improved reliability in predicting in-space durability of materials based on ground laboratory testing. A computational simulation of atomic oxygen interaction with protected polymers was developed using Monte Carlo techniques. Through the use of assumed mechanistic behavior of atomic oxygen and results of both ground laboratory and LDEF data, a predictive Monte Carlo model was developed which simulates the oxidation processes that occur on polymers with applied protective coatings that have defects. The use of high atomic oxygen fluence-directed ram LDEF results has enabled mechanistic implications to be made by adjusting Monte Carlo modeling assumptions to match observed results based on scanning electron microscopy. Modeling assumptions, implications, and predictions are presented, along with comparison of observed ground laboratory and LDEF results.

Bruce A. Banks↗

NASA NTRS1969

Surveyor Project Final Report: Part 1 - Project Description and Performance, Volume 1

The Surveyor Project planned and conducted seven unmanned lunar missions for which spacecraft were launched between May 1966 and January 1968. Each of the spacecraft was successfully launched with the then newly developed Atlas/Centaur vehicle which utilized for the first time a high-specific-impulse, liquid hydrogen/liquid oxygen fueled stage. Five of the spacecraft successfully soft-landed and returned a great quantity of engineering and scientific data on extensive postlanding operations, accomplishing all mission and project objectives. Four of the spacecraft soft-landed at selected mare sites to provide data which were required to support the Apollo Program. The final spacecraft was then successfully used for scientific investigation of a contrasting site in the rugged lunar highlands. Surveyor was a fully attitude-stabilized spacecraft designed to receive and execute a wide variety of earth commands, as well as to perform certain automatic functions including the critical terminal-descent and soft-landing sequences. Significant new and advanced subsystems that were developed and/or used in combination to enable Surveyor to execute the complex terminal phase of flight were: (1) a solid-propellant main retro motor, (2) throttlable liquid-propellant vernier engines (also used for midcourse velocity correction), (3) highly sensitive velocity- and altitude-sensing radars, and (4) an automatic closed-loop guidance and control system. The first Surveyor spacecraft carried a survey television camera which, together with other engineering instrumentation, obtained in-flight and postlanding data. The complement of instruments carried on later missions included various combinations of the following additional devices: (1) a soil mechanics/surface sampler instrument for picking, digging, and handling lunar surface material; (2) an alpha scattering instrument for performing a chemical analysis of the lunar surface material; and (3) magnets attached to the spacecraft for determining magnetic properties of the soil.

Jet Propulsion Laboratory↗

NASA NTRS1969

Surveyor Project Final Report: Part 1 - Project Description and Performance, Volume 2

The Surveyor Project planned and conducted seven unmanned lunar missions for which spacecraft were launched between May 1966 and January 1968. Each of the spacecraft was successfully launched with the then newly developed Atlas/Centaur vehicle which utilized for the first time a high-specific-impulse, liquid hydrogen/liquid oxygen fueled stage. Five of the spacecraft successfully soft-landed and returned a great quantity of engineering and scientific data on extensive postlanding operations, accomplishing all mission and project objectives. Four of the spacecraft soft-landed at selected mare sites to provide data which were required to support the Apollo Program. The final spacecraft was then successfully used for scientific investigation of a contrasting site in the rugged lunar highlands. Surveyor was a fully attitude-stabilized spacecraft designed to receive and execute a wide variety of earth commands, as well as to perform certain automatic functions including the critical terminal-descent and soft-landing sequences. Significant new and advanced subsystems that were developed and/or used in combination to enable Surveyor to execute the complex terminal phase of flight were: (1) a solid-propellant main retro motor, (2) throttlable liquid-propellant vernier engines (also used for midcourse velocity correction), (3) highly sensitive velocity- and altitude-sensing radars, and (4) an automatic closed-loop guidance and control system. The first Surveyor spacecraft carried a survey television camera which, together with other engineering instrumentation, obtained in-flight and postlanding data. The complement of instruments carried on later missions included various combinations of the following additional devices: (1) a soil mechanics/surface sampler instrument for picking, digging, and handling lunar surface material; (2) an alpha scattering instrument for performing a chemical analysis of the lunar surface material; and (3) magnets attached to the spacecraft for determining magnetic properties of the soil.

Jet Propulsion Laboratory↗

NASA NTRS2026

Investigation of Bipropellant Plume-Induced Contamination Effects on Coverglass Materials

Contamination and degradation of external spacecraft materials by unburned and partially combusted species from bipropellant thruster plumes has long been observed as a key component of the induced space environment. Space shuttle flight experiments and returned flight hardware from the International Space Station (ISS) have both experienced microscopic impact features induced by high-velocity thruster plume droplets. Analytical results have shown that droplet impingement angle relative to a receiving surface plays a key role in the surface damage. Although impacts with normal impingement angles contribute more severely to surface degradation than highly oblique angles, surface effects at higher impingement angles should not be dismissed. Thruster plume-induced materials degradation is a complex phenomenon that depends on a variety of parameters, including but not limited to material type, system temperature and pressure, plume composition, and thruster firing specifications such as number of pulses, pulse duration, and sample distance from the thruster. For space applications, attaining the vacuum pressure and temperature conditions necessary for flight-like plume expansion and exposure conditions is not a trivial task. The German Aerospace Center (Deutsches Zentrum für Luft- und Raumfahrt, DLR) is a facility uniquely capable of simulating such conditions. Test coupons were exposed to bipropellant thruster firings under high vacuum at the DLR facility. Percent area coverage (PAC) and droplet size distributions were evaluated for the uncoated and coated solar array coverglass materials over a range of impingement angles (0̊ to 75̊). A post-test imaging workflow was developed that aimed to quantify changes in sample surface morphology obtained from scanning electron microscopy (SEM) images using the Image Processing and Analysis in Java (ImageJ) tool; an opensource image processing software. The goal was to create a framework through which to evaluate the effect of bipropellant-induced PAC and droplet size distribution on solar array coverglass optical transmission losses. Understanding this relationship is important because optical transmission losses are known to lead to current reduction in solar power generation systems. In addition to the development of surface characterization workflows, valuable lessons learned as they pertain to future investigations and experiments will be discussed. The authors hope that sharing these lessons will facilitate more utilization of DLR’s unique capabilities as well as open the conversation for how best to address experimental characterization of flight-like plume expansion and its impacts on materials surface degradation effects.

Gateway↗

NASA NTRS2026

Designing a Propylene-Glycol Coolant Servicer System for Gateway’s Internal Active Thermal Control System

A human spacecraft ATCS—especially one using single-phase coolant loops exposed to cabin atmospheric conditions—requires periodic degassing and refilling to support long-duration missions of 15 to 30 years. During initial fill operations, system maintenance, gas permeation, and quick-disconnect mating or de-mating, small amounts of gas can gradually enter the coolant system over time. This can lead to degraded heat transfer performance, pump cavitation, and potentially pump vapor lock if a significant gas volume accumulates over time. Additionally, system leaks and routine fluid sampling can gradually reduce accumulator volumes to unacceptable levels, requiring periodic refills. In more severe cases, catastrophic changes in fluid composition may necessitate emergency draining, refilling, and degassing to ensure continued system functionality. These risks were identified and mitigated on the ISS ITCS through the development of a dual-membrane degasser ORU and a Fluid Servicer System ORU for coolant refilling. These systems were developed for the fully water-based ISS ITCS Coolant[1]. The Gateway space station, the first permanent human habitat in lunar orbit, uses a propylene-glycol/water coolant mixture, which has significantly different fluid properties compared to pure water. Because microgravity degassing technologies are sensitive to fluid surface tension and viscosity, existing ISS hardware is not suitable for servicing a propylene-glycol-based TCS. Unlike the ISS, the Gateway will operate in a higher-radiation environment and must meet stricter mass constraints due to its location outside of low earth orbit. This Government Furnished Equipment (GFE) flight hardware project aims to develop a lightweight, radiation-resistant Coolant Servicer System (CSS) capable of degassing and refilling Gateway’s propylene-glycol water-based IATCS.

Propylene Glycol Water↗

NASA NTRS2026

Designing a Propylene-Glycol Coolant Servicer System for Gateway’s Internal Active Thermal Control System

A human spacecraft ATCS—especially one using single-phase coolant loops exposed to cabin atmospheric conditions—requires periodic degassing and refilling to support long-duration missions of 15 to 30 years. During initial fill operations, system maintenance, gas permeation, and quick-disconnect mating or de-mating, small amounts of gas can gradually enter the coolant system over time. This can lead to degraded heat transfer performance, pump cavitation, and potentially pump vapor lock if a significant gas volume accumulates over time. Additionally, system leaks and routine fluid sampling can gradually reduce accumulator volumes to unacceptable levels, requiring periodic refills. In more severe cases, catastrophic changes in fluid composition may necessitate emergency draining, refilling, and degassing to ensure continued system functionality. These risks were identified and mitigated on the ISS ITCS through the development of a dual-membrane degasser ORU and a Fluid Servicer System ORU for coolant refilling. These systems were developed for the fully water-based ISS ITCS Coolant[1]. The Gateway space station, the first permanent human habitat in lunar orbit, uses a propylene-glycol/water coolant mixture, which has significantly different fluid properties compared to pure water. Because microgravity degassing technologies are sensitive to fluid surface tension and viscosity, existing ISS hardware is not suitable for servicing a propylene-glycol-based TCS. Unlike the ISS, the Gateway will operate in a higher-radiation environment and must meet stricter mass constraints due to its location outside of low earth orbit. This Government Furnished Equipment (GFE) flight hardware project aims to develop a lightweight, radiation-resistant Coolant Servicer System (CSS) capable of degassing and refilling Gateway’s propylene-glycol water-based IATCS.

Propylene Glycol Water↗

NASA NTRS2026

The Habitable Worlds Observatory Technology Development Plan

The Habitable Worlds Observatory (HWO) is NASA’s next large space telescope, selected by the 2020 Decadal Survey in Astronomy and Astrophysics to search for and characterize habitable exoplanets while enabling a broad range of transformative astrophysics. In August 2024, the HWO Technology Maturation Project Office (TMPO) was formed to begin exploring the HWO science, technology, and mission architectures toward a Mission Concept Review (MCR) at the end of the decade. A primary deliverable of this effort is this technology development plan that identifies critical technologies that enable the mission, defines a process for assessing the readiness of those technologies, and outlines a strategy for developing those technologies to a Technology Readiness Level (TRL) of 5 before the MCR. This document covers technologies organized along three “tracks”: Coronagraph System technologies, Ultra-stable Telescope System technologies, and High-sensitivity Ultraviolet and Visible Instrumentation technologies. Additional emerging and enhancing technologies are also discussed.

technology development↗

NASA NTRS1992

Ruled and holographic experiment (AO 138-5)

The AO 138-5 experiment has been designed, via the French Cooperative Payload (FRECOPA) experiment with the aim to study the optical behavior of different diffraction gratings submitted to space vacuum long exposure and solar radiation. Samples were rules and holographic gratings, masters or replica, and some additional control mirrors with various coatings. The experiment was located on the B3, trailing edge of the Long Duration Exposure Facility (LDEF) and has been protected against atomic oxygen flux. The experienced thermal cycling has been evaluated from -23 C to 66 C during the flight, 34,000 orbits. The analysis has been focused on the triple point characterization including light efficiency, wavefront flatness quality and stray light level. Tests were conducted on control mirrors and gratings loaded but not exposed to cosmic dust or solar irradiations. They did not show any significant variations. Solar exposure has damaged the coating reflectivity in the ultraviolet region, the degradation is higher with the gratings, in terms of efficiency. However, wavefront flatness quality and stray light level tests revealed no additional changes.

Francis Bonnemason↗

NASA NTRS1964

Performance of Solar Reflectors When Applied to Storage of Cryogenic Propellants in Space

An analysis was performed to determine the effectiveness of solar reflectors in reducing heat transfer through the insulation of cryogenic fuel tanks located in deep space. A solar reflector, as used herein, is defined as a surface having a ratio of absorptance with respect to solar radiation to hemispherical emittance (α/ϵ) less than 1.0. This analysis considers the effect of surface coatings with α/ϵ values varying from 0.1 to 1.0 when applied to the external surfaces of bulk insulation or multifoil insulation. Results were obtained in terms of heat leak to two cryogenic propellants, liquid hydrogen and liquid oxygen, when stored at Mars, Earth, and Mercury orbital distances from the sun. The results show that, with sufficiently good insulation and low heat leaks to the propellant, α/ϵ is a reasonable criterion of merit for these coatings, but that, at larger heat leaks, consideration of ϵ (or α) is necessary. It was observed that selective finishes of α/ϵ = 0.1 on a given amount of bulk insulation material can reduce the heat leak to 40 to 55 percent of the heat leak obtained when gray finishes are considered. Or, for equivalent heat leaks, a reduction in bulk insulation material thickness of about one-half is possible with high-quality selective finishes (α/ϵ = 0.1) compared with flat reflectors. Larger benefits may be achieved from selective finishes painted on foils; the analysis shows that heat leak may be reduced tenfold for surfaces with an α/ϵ of 0.1 compared with gray surfaces. Again, consideration of equivalent heat leaks indicates that the use of approximately 10 times fewer foils of emissivity 0.05 is possible when spectrally selective surfaces are employed. The present state of the art in achieving such surfaces is also briefly reviewed.

Propellant Storage↗

NASA NTRS2015

A Battery Certification Testbed for Small Satellite Missions

A battery pack consisting of standard cylindrical 18650 lithium-ion cells has been chosen for small satellite missions based on previous flight heritage and compliance with NASA battery safety requirements. However, for batteries that transit through the International Space Station (ISS), additional certification tests are required for individual cells as well as the battery packs. In this manuscript, we discuss the development of generalized testbeds for testing and certifying different types of batteries critical to small satellite missions. Test procedures developed and executed for this certification effort include: a detailed physical inspection before and after experiments; electrical cycling characterization at the cell and pack levels; battery-pack overcharge, over-discharge, external short testing; battery-pack vacuum leak and vibration testing. The overall goals of these certification procedures are to conform to requirements set forth by the agency and identify unique safety hazards. The testbeds, procedures, and experimental results are discussed for batteries chosen for small satellite missions to be launched from the ISS.

Certification↗

NASA NTRSDate not supplied

Next-Generation Hard X-ray Missions: SuperHERO and HEROIX

High-energy X-ray observations have transformed our understanding of astrophysical systems where non-thermal processes dominate, from shock-accelerated particles in supernova remnants to relativistic jets and hot coronae in active galactic nuclei. NuSTAR’s pioneering focusing images of the hard X-ray sky have demonstrated the immense scientific potential of this band, while also highlighting how limited angular resolution constrains our ability to fully characterize complex physical processes in faint extended sources and resolving faint sources in crowded sky regions. In this presentation, I will discuss a pathway to overcome these challenges through NASA Marshall Space Flight Center’s replicated NiCo full-shell X-ray mirror technology. Specifically, I will discuss the SuperHERO hard X-ray telescope to achieve better than 10-arcsecond half-power diameter (HPD) angular resolution on a balloon flight observing the Crab Nebula, and the High EneRgy Observatory for Imaging X-rays (HEROIX) Medium-Class Mission concept to achieve an integrated effective area of 570 cm2 at 30 keV with 5 arcsec HPD angular resolution.

AGN↗

NASA NTRS2026

Raising TRL of Your Lunar Payload

Preparing payloads for the lunar surface requires rigorous testing that accurately captures the extreme environmental and operational conditions. This presentation provides an overview of the lunar relevant test capabilities at NASA JSC’s Astromaterials Research and Exploration Science (ARES) laboratories as well as the Energy System Test Area (ESTA) Lunar Development and Test Facility. These facilities allow teams to assess hardware performance in dusty vacuum environments, characterize interactions with high fidelity lunar regolith simulants, evaluate mechanical and thermal durability, and understand the effects of micrometeoroid and orbital debris impacts—critical factors for certifying payloads that will operate on the lunar surface or in orbit. While Lunar power challenges such as variable illumination, extreme temperatures, and dust driven degradation will be briefly summarized, the focus of this talk is on how JSC’s test infrastructure enables developers to validate designs, reduce mission risk, and ensure compatibility with CLPS and Artemis objectives. NASA JSC’s expertise and experience help industry, academic, and government teams prepare robust hardware ready for successful delivery and operation on the surface of the Moon.

Lunar Regolith Simulant↗

NASA NTRS2026

Raising TRL of Your Lunar Payload

Preparing payloads for the lunar surface requires rigorous testing that accurately captures the extreme environmental and operational conditions. This presentation provides an overview of the lunar relevant test capabilities at NASA JSC’s Astromaterials Research and Exploration Science (ARES) laboratories as well as the Energy System Test Area (ESTA) Lunar Development and Test Facility. These facilities allow teams to assess hardware performance in dusty vacuum environments, characterize interactions with high fidelity lunar regolith simulants, evaluate mechanical and thermal durability, and understand the effects of micrometeoroid and orbital debris impacts—critical factors for certifying payloads that will operate on the lunar surface or in orbit. While Lunar power challenges such as variable illumination, extreme temperatures, and dust driven degradation will be briefly summarized, the focus of this talk is on how JSC’s test infrastructure enables developers to validate designs, reduce mission risk, and ensure compatibility with CLPS and Artemis objectives. NASA JSC’s expertise and experience help industry, academic, and government teams prepare robust hardware ready for successful delivery and operation on the surface of the Moon.

Laboratories↗

NASA NTRS1995

A review of nickel hydrogen battery technology

This paper on nickel hydrogen batteries is an overview of the various nickel hydrogen battery design options, technical accomplishments, validation test results and trends. There is more than one nickel hydrogen battery design, each having its advantage for specific applications. The major battery designs are individual pressure vessel (IPV), common pressure vessel (CPV), bipolar and low pressure metal hydride. State-of-the-art (SOA) nickel hydrogen batteries are replacing nickel cadmium batteries in almost all geosynchronous orbit (GEO) applications requiring power above 1 kW. However, for the more severe low earth orbit (LEO) applications (greater than 30,000 cycles), the current cycle life of 4000 to 10,000 cycles at 60 percent DOD should be improved. A NASA Lewis Research Center innovative advanced design IPV nickel hydrogen cell led to a breakthrough in cycle life enabling LEO applications at deep depths of discharge (DOD). A trend for some future satellites is to increase the power level to greater than 6 kW. Another trend is to decrease the power to less than 1 kW for small low cost satellites. Hence, the challenge is to reduce battery mass, volume and cost. A key is to develop a light weight nickel electrode and alternate battery designs. A common pressure vessel (CPV) nickel hydrogen battery is emerging as a viable alternative to the IPV design. It has the advantage of reduced mass, volume and manufacturing costs. A 10 Ah CPV battery has successfully provided power on the relatively short lived Clementine Spacecraft. A bipolar nickel hydrogen battery design has been demonstrated (15,000 LEO cycles, 40 percent DOD). The advantage is also a significant reduction in volume, a modest reduction in mass, and like most bipolar designs, features a high pulse power capability. A low pressure aerospace nickel metal hydride battery cell has been developed and is on the market. It is a prismatic design which has the advantage of a significant reduction in volume and a reduction in manufacturing cost.

Smithrick, John J.↗

NASA NTRS2026

Experimental Study of Aeropropulsive Interactions for Electric Ducted Fans on a Wing

The Adaptable Distributed Electric Propulsion Testbed (ADEPT)Wing was tested in the NASA Langley 12-Foot Low-Speed Tunnel to investigate electric propulsion technologies for commercial transport aircraft. The purpose of the test was to study the aeropropulsive effects across angle of attack and fan speed variations for several propulsor placements and array sizes, and to investigate how distributed electric propulsion (DEP) can be leveraged for augmented lift and vehicle control. Six electric ducted fan (EDF) array placements were tested by positioning the fans along the leading and trailing edges on the top and bottom surfaces, as well as centered on the chord line in front of and behind the wing. Each fan placement configuration was tested with an array of one, three, and five EDFs to characterize an aeropropulsive extrapolation effect, and the bare wing was tested separately to provide baseline aerodynamic measurements. The results compare the longitudinal forces and moments for each configuration by analyzing the combined aeropropulsive interaction effects, and offer valuable insight into considerations for fan placement along a wing to enable the benefits of DEP integration.

Rose Weinstein↗

NASA NTRS2026

Controlled Parametric Forcing During Directional Solidification of a Bulk Organic Alloy Under Microgravity

The response of dendritic microstructures to step-like pulling velocity conditions is investigated using microgravity directional solidification experiments conducted on DECLIC-DSI combined with phase-field simulations. Under a constant pulling velocity of 1.5 µm/s, the evolution toward steady-state growth is characterized in terms of primary spacing, dendrite drift, and tip dynamics. For the first time, side-view observations enabled direct measurement of tip radius and sidebranching frequency. When step-like oscillations of the pulling velocity are imposed, the dendritic array exhibits a strongly period-dependent response: short periods lead to rapid tip adaptation, whereas longer periods induce a phase lag between tip position and morphology, resulting in progressive tip flattening and, above a critical period, interface destabilization and dendrite splitting. Quantitative phase-field simulations, including a realistic thermal field and stochastic noise, reproduce the experimental observations and provide insight into the governing mechanisms, highlighting the role of characteristic relaxation times, sequence-dependent effects, and the irreversible reorganization of the microstructure following splitting.

Microgravity↗

NASA NTRSDate not supplied

Development of an Additively Manufactured Subscale Secondary Sealed Container for the NASA FROSTE Project

This presentation details the development of an additively manufactured (AM) subscale test article for the secondary sealed container (SSC) as part of the NASA FROSTE project. FROSTE is focused on the collection of regolith samples from shadowed regions of the Moon and the preservation of those samples at cryogenic temperatures for return to Earth. Our team was integrated into the FROSTE program to leverage innovative design approaches and additive manufacturing capabilities in support of a scalable development strategy, where the subscale configuration serves as the development path toward a full-scale SSC. Scalmalloy was selected as the primary material for all AM components due to its favorable strength-to-weight ratio, thermal conductivity, and demonstrated performance in aerospace applications. Its aluminum-based composition supports robust mechanical behavior at cryogenic temperatures while enabling efficient heat transfer and control of thermal gradients within the containment system. The SSC architecture consists of an outer container assembly that houses a phase change material (PCM) tank, which in turn contains primary containers holding the regolith. Thermal management relies on controlled conductive and radiative heat transfer, including a thermal connection assembly that interfaces the PCM tank to an external cryocooler via a thermal strap, and IMLI surrounding the PCM tank to inhibit radiative heat transfer. The outer container assembly incorporates sealing interfaces, thermal connection ports, and I/O feedthroughs, with PTFE spring seals used at critical interfaces to maintain containment integrity. The PCM tank is manufactured as a single monolithic Scalmalloy component and incorporates an integral lattice structure to minimize thermal gradients, internal channels for thermocouple routing, and interface features for thermal connection assembly integration. The tank is centrally suspended within the outer container using support rings, with G10 insulating components employed to inhibit thermal leaks. This work describes the design methodology, AM approach, and key considerations used to inform the design.

regolith↗

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↗