Search NASASearch

SEARCH · Search NASA

Results for “MECHANICAL PROPERTY”

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.

304 records · Page 5

Structural Mechanics and Dynamics Branch 2002 Annual Report

The 2002 annual report of the Structural Mechanics and Dynamics Branch reflects the majority of the work performed by the branch staff during the 2002 calendar year. Its purpose is to give a brief review of the branch s technical accomplishments. The Structural Mechanics and Dynamics Branch develops innovative computational tools, benchmark experimental data, and solutions to long-term barrier problems in the areas of propulsion aeroelasticity, active and passive damping, engine vibration control, rotor dynamics, magnetic suspension, structural mechanics, probabilistics, smart structures, engine system dynamics, and engine containment. Furthermore, the branch is developing a compact, nonpolluting, bearingless electric machine with electric power supplied by fuel cells for future "more electric" aircraft. An ultra-high-power-density machine that can generate projected power densities of 50 hp/lb or more, in comparison to conventional electric machines, which generate usually 0.2 hp/lb, is under development for application to electric drives for propulsive fans or propellers. In the future, propulsion and power systems will need to be lighter, to operate at higher temperatures, and to be more reliable in order to achieve higher performance and economic viability. The Structural Mechanics and Dynamics Branch is working to achieve these complex, challenging goals.

Stefko, George

Characterization of the Mechanical Trash Compactor Bag Removal Force

Managing trash accumulation is a critical challenge in human space explorations since the trash volume and mass can significantly influence launch cost and operational efficiency. This study aids the development of a Mechanical Trash Compactor (Mpactor) by testing the removal force required to remove a “trash bag” from the Mpactor. To do this, a Pneumatic Pressure Mandrel System was designed to simulate the normal force trash would exerts on the trash bag and subsequently the sidewalls of the Mpactor. For various levels of sidewall normal force, the removal force required to remove the simulated trash bag from the Mpactor compaction chamber was measured. This testing is used to identify optimal bag materials. Additionally, testing was done on both the native stainless steel walls of the compaction chamber as well as the walls after being Teflon lined. Split-plot ANOVA, simple main effects analysis, Holm’s post hoc comparisons for interaction, and sensitivity analyses were conducted to assess the influence of trash bag and sidewall materials on the required removal force. It was found that Teflon reduced the force required to remove the trash bag as well as reduced material-dependent variation in removal force. Testing showed that Teflon reduced the required removal force with a Polyvinylidene Fluoride , an unidentified Ethylene acrylate - Low Density Polyethylene copolymer, and a Polyvinyl Chloride all requiring significantly less removal force than the other materials tested.

pressure mandrel

High Temperature Pressure (HTP) Boron Nitride Nanotube (BNNT): Discovery and Commercialization

Future NASA missions for space exploration require key technological elements that must provide sustainability, survivability and operational envelope in extreme environments, such as the high and low extremes in pressures and temperatures, ionizing radiations, chemical and/or physical corrosion, and hypervelocity particles. Advanced multifunctional materials enable revolutionary design schemes for future aerospace vehicles and structures for the extreme environments of NASA missions. Recent studies of nanocomposite materials have shown the potential for both structural integrity and multifunctional capabilities, such as sensing, actuating, health monitoring, radiation shielding, energy harvesting, thermal management, and thermal protection in extreme environments. After the advent of carbon nanotube (CNT) in 1991, scientists predicted that boron and nitrogen, carbons immediate neighbors on the periodic chart, might also form perfect nanotubes, namely boron nitride nanotubes (BNNTs). The discovery and progress of a new catalyst-free method for synthesizing highly crystalline, very long, and small diameter BNNTs under a high temperature and pressure (HTP) environment have enabled new applications for multifunctional materials. The white color BNNTs offer extraordinary properties including neutron radiation shielding, piezoelectricity, electrostriction, high thermal oxidative stability (>800C in air), not present in CNTs, as well as excellent mechanical strength and toughness, equivalent to CNTs. The characteristics of the BNNTs and their composites along with CNT composites are discussed in this presentation along with their potential aerospace applications in extreme environments.

Cheol Park

Radiation-Conditioned Ti–hBN Coatings for Space Mechanisms: Bridging Tribology and Irradiation Effects from Laboratory to Low-Earth Orbit

The longevity of tribological components in extraterrestrial environments is challenged by abrasive regolith, extreme temperatures, and ionizing radiation. This study evaluates the performance of vacuum plasma sprayed (VPS) Ti-2vol.% hexagonal boron nitride (hBN) coatings applied to joint mechanisms such as rod and slot, ball and socket, and hinge assemblies, fabricated from Al6061 and Ti6Al4V for planetary structures. Coated and uncoated samples were tested under vacuum with lunar regolith simulant (JSC-1A), followed by environmental exposures including electron radiation and thermal cycling. Results show that coated samples consistently outperformed uncoated counterparts across all configurations. Wear depth in coated components was reduced by over 80%, as confirmed by 3D profilometry and surface imaging. SEM analysis revealed severe abrasion and localized plastic deformation in uncoated surfaces, while coated samples retained structural integrity due to synergy of hard protective phases formed during deposition and retained hBN providing solid lubrication in the sliding surface. Coated and exposed samples exhibited smoother actuation profiles and reduced friction, indicating a beneficial "conditioning" effect from environmental exposure. The coatings-maintained performance even on complex geometries with minimal delamination. These findings demonstrate the potential of VPS Ti-hBN coatings to extend the operational life of lunar mechanisms, bridging laboratory-scale tribology with flight-relevant mechanical applications.

tribology

Simulations of Yarn Micro-Mechanics of Woven Heat Shield Materials

Carbon and phenolic fibers are commonly used in ablative thermal protection materials, such as 3-dimensional Mid-Density Carbon Phenolic (3MDCP), a 3D-woven composite comprised of mixed-fiber yarn bundles. Predicting the micro-mechanical response and fracture of twisted yarns composed of brittle and ductile fibers requires a modeling approach that captures per-fiber yielding, fiber fracture, and inter-fiber friction and contact. This work presents an extended bonded particle model (BPM) for discrete element method (DEM) simulation of fiber and yarn mechanics, implemented in LAMMPS. The model builds on the incremental bond formulation of Guo et al. and introduces a piecewise elasto-plastic constitutive law for axial extension, enabling representation of fibers that yield before failure. 3MDCP yarns were constructed using measured fiber radius distributions and helical twist geometry. Tensile simulations of single-ply 3MDCP yarns show good agreement with vender stress–strain results. Fiber breakage models also show details on yarn breakage propagration, centered radially in the yarn. Yarn breakage of multi-ply 3MDCP also matched experimental observations in per-ply breakage; however, predicted yarn breakage strength were found higher than experimental observations.

Discrete Element Method

Simulations of Yarn Micro-Mechanics of Woven Heat Shield Materials (3MDCP)

Carbon and phenolic fibers are commonly used in ablative thermal protection materials, such as 3-dimensional Mid-Density Carbon Phenolic (3MDCP), a 3D-woven composite comprised of mixed-fiber yarn bundles. Predicting the micro-mechanical response and fracture of twisted yarns composed of brittle and ductile fibers requires a modeling approach that captures per-fiber yielding, fiber fracture, and inter-fiber friction and contact. This work presents an extended bonded particle model (BPM) for discrete element method (DEM) simulation of fiber and yarn mechanics, implemented in LAMMPS. The model builds on the incremental bond formulation of Guo et al. and introduces a piecewise elasto-plastic constitutive law for axial extension, enabling representation of fibers that yield before failure. 3MDCP yarns were constructed using measured fiber radius distributions and helical twist geometry. Tensile simulations of single-ply 3MDCP yarns show good agreement with vender stress–strain results. Fiber breakage models also show details on yarn breakage propagration, centered radially in the yarn. Yarn breakage of multi-ply 3MDCP also matched experimental observations in per-ply breakage; however, predicted yarn breakage strength were found higher than experimental observations.

Woven

PROTECT: Production and Reuse of Thermally Efficient Ceramic Thermal Protection Systems

PROTECT (Production and Reuse Of Thermally Efficient Ceramic TPS) is a NASA Early Career Initiative focused on developing the next generation of reusable ceramic thermal protection systems (TPS). This project addresses key challenges in TPS design, including temperature capability, thermal stability, and refurbishment time, by integrating novel material development with predictive modeling. Leveraging enhanced capabilities in NASA’s Porous Microstructure Analysis (PuMA) software, PROTECT introduces new modeling tools to predict the thermal and mechanical behavior of fibrous ceramic materials. These tools enable accurate prediction of performance metrics such as thermal conductivity and structural integrity, reducing reliance on costly physical testing. Preliminary advances in these areas will be presented. To support model validation, PROTECT is building a comprehensive database of raw material properties using advanced characterization techniques, including micro computed tomography (CT) scanning in collaboration with the University of Illinois Urbana-Champaign (UIUC). The presentation will detail the sampling workflows and analysis methods used to generate this detailed microstructural data and how it is used to develop improved models in PuMA. This multi-center collaboration, spanning NASA (JSC, ARC, KSC, GRC), Oak Ridge National Laboratory, UIUC, and SpaceX, is developing tailored TPS solutions for LEO, lunar, and Martian missions. By bridging heritage systems with the demands of modern spaceflight, PROTECT contributes to the advancement of reusable TPS technologies for future exploration missions.

Propulsion, Refractory, and Coating Materials

Mechanical Design of Spacecraft

In the spring of 1962, engineers from the Engineering Mechanics Division of the Jet Propulsion Laboratory gave a series of lectures on spacecraft design at the Engineering Design seminars conducted at the California Institute of Technology. Several of these lectures were subsequently given at Stanford University as part of the Space Technology seminar series sponsored by the Department of Aeronautics and Astronautics. Presented here are notes taken from these lectures. The lectures were conceived with the intent of providing the audience with a glimpse of the activities of a few mechanical engineers who are involved in designing, building, and testing spacecraft. Engineering courses generally consist of heavily idealized problems in order to allow the more efficient teaching of mathematical technique. Students, therefore, receive a somewhat limited exposure to actual engineering problems, which are typified by more unknowns than equations. For this reason it was considered valuable to demonstrate some of the problems faced by spacecraft designers, the processes used to arrive at solutions, and the interactions between the engineer and the remainder of the organization in which he is constrained to operate. These lecture notes are not so much a compilation of sophisticated techniques of analysis as they are a collection of examples of spacecraft hardware and associated problems. They will be of interest not so much to the experienced spacecraft designer as to those who wonder what part the mechanical engineer plays in an effort such as the exploration of space.

MARINER SPACE PROBE

Bosch Carbon Catalyst Regeneration in Water I: Bosch Carbon Removal from Reacted Beads Utilizing Mechanical Agitation

The ability to recover oxygen from metabolic carbon dioxide is crucial for crewed long duration missions in which the atmosphere must be recycled. Two physiochemical methods are primarily employed for this purpose: the Bosch process and the Sabatier reaction. This paper focuses on the Bosch process. It utilizes hydrogen in the presence of a catalyst to form water and solid carbon out of metabolic carbon dioxide. The solid carbon product deposits onto the catalyst and eventually causes reactor over pressurization issues. Multiple methods are currently being investigated to regenerate the catalyst’s surface and break up the pressure causing carbon clogs. This paper explores whether water and mechanical abrasion would work to remove Bosch carbon by testing multiple washing conditions. The different washing conditions involved agitation intensity, heating, duration, and volume of water. It was found that it is possible to break up the clumps of carbon formed in the reactor through agitation with room temperature water in one hour and shows promise for completely cleaning the carbon off the beads’ surface.

Agitation

Optical properties of morphologically complex black carbon aerosols: Effects of coatings

Optical properties are computed for fractal-like aggregate black carbon (BC) aerosols coated with different substances. Two models are used for these aerosols: (i) the coated aggregate model (model I), where coating is added to the voids and surroundings of BC fractal-like aggregates; and (ii) the closed-cell aggregate model (model II), where coating is added concentrically to each monomer of BC fractal-like aggregates. Our results favor choosing the coated aggregate model (model I) to simulate scattering and absorption by coated BC aerosols because this model is morphologically more realistic, and because this model yields mass absorption cross section (MAC) and backscattering linear depolarization ratio (LDR) values that are consistent with field measurements. Moreover the corresponding computed degree of linear polarization (DoLP) and LDR values are very sensitive to changes in the coating volume fraction (fvol) and the coating refractive index (m). With the same absorbing BC core, the MAC value increases steadily with increasing fvol and m values. For example, using a density of 1.8 g/cm 3 and BC refractive index 1.95 + i0.79, the calculated MAC values for uncoated BC aggregates range from 6.2 to 6.8 m 2 /g at 0.55 µm. When coating material is applied to the BC aggregates, the calculated MAC values for model I particles increase to between 9.8 and 13.2 m 2 /g (depending on m) when fvol = 87.5%. The backscattering LDR values also tend to increase with the increasing m values for the shapes and sizes considered in our study. For model I particles, the backscattering LDR values span a wide range of 4.2–27.8% at a wavelength of 0.35 µm at fvol = 87.5% when m increases from 1.33 to 1.55. Our results are relevant to analyses of polarimetric and lidar observations of smoke particles, especially when these particles undergo hygroscopic growth.

Black carbon aerosols

Lubricating Properties of Ceramic-Bonded Calcium Fluoride Coatings on Nickel-Base Alloys From 75° to 1900° F

The endurance life and the friction coefficient of ceramic-bonded calcium fluoride (CaF2) coatings on nickel-base alloys were determined at temperatures from 75° to 1900° F. The specimen configuration consisted of a hemispherical rider (3/16-in. rad.) sliding against the flat surface of a rotating disk. Increasing the ambient temperature (up to 1500° F) or the sliding velocity generally reduced the friction coefficient and improved coating life. Base-metal selection was critical above 1500° F. For instance, cast Inconel sliding against coated Inconel X was lubricated effectively to 1500° F, but at 1600° F severe blistering of the coatings occurred. However, good lubrication and adherence were obtained for René 41 sliding against coated René 41 at temperatures up to 1900° F; no blisters developed, coating wear life was fairly good, and the rider wear rate was significantly lower than for the unlubricated metals . Friction coefficients were 0.12 at 1500° F, 0.15 at 1700° F, and 0.17 at 1800° and 1900° F. Because of its ready availability, Inconel X appears to be the preferred substrate alloy for applications in which the temperature does not exceed 1500° F. René 41 would have to be used in applications involving higher temperatures. Improved coating life was derived by either preoxidizing the substrate metals prior to the coating application or by applying a very thin (<0.0002 in.) burnished and sintered overlay to the surface of the coating. Preoxidation did not affect the friction coefficient. The overlay generally resulted i n a higher friction coefficient than that obtained without the overlay. The combination of both modifications resulted in longer coating life and in friction coefficients intermediate between those obtained with either modification alone.

Nickel alloy

Lyotropic Liquid Crystalline Phase Behavior of Boron Nitride Nanotube Aqueous Dispersions

Boron nitride nanotubes (BNNTs) are gaining significant interest due to their outstanding mechanical and thermal properties, as well as their potential to serve as a model nanorod system. Processing BNNT liquid crystalline (LC) dispersions enables precise control over BNNT orientation in macroscopic assemblies, while their low absorption in the visible spectrum facilitates studying LCs at exceptionally high concentrations. Here, we investigate the behavior of BNNTs in aqueous solutions stabilized by the surfactant sodium deoxycholate (SDC), examining the effect of BNNT purity and BNNT−SDC concentrations on lyotropic LC formation. We disperse up to 15wt% BNNT in SDC solutions and use polarized light microscopy to detail the transition from an isotropic state to a biphasic regime, where isotropic and nematic domains coexist due to phase separation, to a single fully nematic phase. Cryogenic electron microscopy provides direct evidence of BNNT alignment within nematic domains. Our results show that enhanced depletion-induced attractions, driven by increased surfactant concentration, lower the threshold concentration of BNNT required to form nematic domains. In contrast, low surfactant concentrations relative to BNNT result in insufficiently coated nanotube surfaces, leading to poor dispersions and BNNT aggregation. Additionally, we fabricate well-aligned BNNT films from aqueous LC dispersions. Our findings advance the understanding of BNNT LCs, offering insight into controlling their orientation and highlighting their potential for high-performance materials.

Joe Khoury

Mechanisms of Protonic Nonvolatile Memory Device

A nonvolatile memory device based on protonic transport in oxides has been proposed. The mobile H+ ions are introduced into the SiO2 layer by annealing Si/SiO2/Si structures in H2 at temperatures greater than 500 deg C. This effect has only been observed for confined oxides that have been annealed at greater than or equal to 1100 C prior to the hydrogenation anneal. This includes buried oxides such as Unibond and SIMOX as well as thermal oxides annealed with a polysilicon cap. An applied field moves the charge within the oxide and the charge stops moving when the field is removed. In a memory device, the hydrogen-annealed oxide is the gate oxide and the position of the mobile charge is sensed by the shift of the I-V curve. Much is still not understood about the motion of the charge across the buried oxide. Previous work has assumed that H+ transport and the time it takes to traverse the oxide is governed by interactions within the bulk of the oxide. Based on parameters that affect the transport time, we conclude that H+ trapping and detrapping at the Si/SiO2 interface are more important than H+ interactions within the oxide bulk. These parameters include the applied field, the H+ concentration and the oxide thickness. One consequence is that projections of device write-time based on the previous assumptions of H+ transport mechanisms may be overly optimistic.

P J Macfarlane

High Temperature Dielectric Properties and Differential Scanning Calorimetry of Lunar Simulants

To guide development of microwave process technology that could be used during in situ construction on the Moon, we measured the high-temperature basic dielectric properties (εʹ and εʺ) of 17 lunar simulants and related materials. In order to confidently use these data one needs to understand the data’s strengths and weaknesses. Therefore, a goal of this publication is to provide insights into the comparative effects of sample composition, pre-treatments, experimental variables, high temperatures, and other factors on the measured response. The dielectric measurements were performed using the cavity perturbation method over a temperature range between room temperature to 1000 °C, or higher, and provided the real and imaginary components of permittivity at six frequencies. The utility of the original values was limited by the varying density of the pellets used in the measurement. Therefore, all of the εʹ and εʺ measurements at the frequency of 2466 MHz have been scaled to a constant density, 1.75 g/cm 3 . Here the data are presented as graphs chosen to aid analysis within and across simulant groups. To gain additional insight into the processes happening at the elevated temperatures in the dielectric measurements, heat capacity data was obtained using differential scanning calorimetry (DSC) on several of the simulant materials. Our data show that over the frequency range 397 MHz – 2985 MHz a material’s behavior does not greatly change, as compared to the scale of differences observed between lunar mare and highland simulants at high temperatures. For example at 1000 °C, the mare simulant JSC-1A absorbs 10 times more power than the highland simulant NUW-LHT-5M. We observe that as melting temperatures are reached both permittivity and dielectric loss rise non-linearly, helping to explain thermal runaway during microware heating. Our data show that even less than a few weight % of many non-lunar minerals, and the use of mixtures in simulants can affect the dielectric behavior at higher temperatures. A comparison of our results with published dielectric data for Apollo samples and with remote sensing of the Moon supports the conclusion the simulants and lunar material at room temperature have very similar dielectric values.

Differential Scanning Calorimetry

Thermal Cycling and Isothermal Deformation Response of Polycrystalline NiTi: Simulations vs. Experiment

A recent microstructure-based FEM model that couples crystal-based plasticity, the B2<-> MB190 phase transformation and anisotropic elasticity at the grain scale is calibrated to recent data for polycrystalline NiTi (49.9 at.% Ni). Inputs include anisotropic elastic properties, texture and differential scanning calorimetry data, as well as a subset of recent isothermal deformation and load-biased thermal cycling data. The model is assessed against additional experimental data. Several experimental trends are captured - in particular, the transformation strain during thermal cycling monotonically increases and reaches a peak with increasing bias stress. This is achieved, in part, by modifying the martensite hardening matrix proposed by Patoor et al. [Patoor E, Eberhardt A, Berveiller M. J Phys IV 1996;6:277]. Some experimental trends are underestimated - in particular, the ratcheting of macrostrain during thermal cycling. This may reflect a model limitation that transformation-plasticity coupling is captured on a coarse (grain) scale but not on a fine (martensitic plate) scale.

Phase Transformations

PROTECT: Production and Reuse of Thermally Efficient Ceramic Thermal Protection Systems

PROTECT (Production and Reuse Of Thermally Efficient Ceramic TPS) is a NASA Early Career Initiative focused on developing the next generation of reusable ceramic thermal protection systems (TPS). This project addresses key challenges in TPS design, including temperature capability, thermal stability, and refurbishment time, by integrating novel material development with predictive modeling. Leveraging enhanced capabilities in NASA’s Porous Microstructure Analysis (PuMA) software, PROTECT introduces new modeling tools to predict the thermal and mechanical behavior of fibrous ceramic materials. These tools enable accurate prediction of performance metrics such as thermal conductivity and structural integrity, reducing reliance on costly physical testing. Preliminary advances in these areas will be presented. To support model validation, PROTECT is building a comprehensive database of raw material properties using advanced characterization techniques, including micro computed tomography (CT) scanning in collaboration with the University of Illinois Urbana-Champaign (UIUC). The presentation will detail the sampling workflows and analysis methods used to generate this detailed microstructural data and how it is used to develop improved models in PuMA. This multi-center collaboration, spanning NASA (JSC, ARC, KSC, GRC), Oak Ridge National Laboratory, UIUC, and SpaceX, is developing tailored TPS solutions for LEO, lunar, and Martian missions. By bridging heritage systems with the demands of modern spaceflight, PROTECT contributes to the advancement of reusable TPS technologies for future exploration missions.

Propulsion, Refractory, and Coating Materials

First-Principles Investigation of Phase Transitions in RuNb, RuTa, and Ru-Nb-Ta Ultrahigh Temperature Shape Memory Alloys

Ultrahigh temperature shape memory alloys (UHT-SMAs) have transition temperatures above 600 C, and they have found applications for sensing and actuating devices in aerospace industry. Among very few such UHT-SMAs currently known are Ru-based alloys such as RuNb and RuTa, whose martensite structures and phase transitions are totally different from those of NiTi-based SMAs and were poorly understood. In this work, we carried out a systematical study of RuNb using first-principles total energy calculations and molecular dynamics (MD) simulations. The transition paths and mechanisms in cubic → tetragonal →monoclinic transitions are revealed. and the transition sequence and martensitic transition temperatures are determined (MTTs) by evaluating the Gibbs free energies using thermodynamic integration. The calculated MTTs are in very good agreement with the experimental data. We found that the monoclinic phase at the second transition has the 𝑃21/m symmetry instead of experimentally identified 𝑃2/m. Our calculations demonstrate that RuTa has very similar phase transitions to those of RuTa. Furthermore, we studied the Ru0.5Nb0.25Ta0.25 ternary. Our results can explain the measured significant drop of MTT (~ 200 C) in the second transition for Ru0.5Nb0.25Ta0.25 compared with those of RuNb and RuTa, while in the first transition its MTT is between MTTs of RuNb and RuTa. The insights gained by this study and the verified ab initio methods for accurate MTT calculations can be applied to fast screen and quantitatively design novel UHT-SMAs having similar properties with desirable MTTs and much reduced cost.

Zhigang Wu

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