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Combined Beam Column Stresses of Aluminum-alloy Channel Sections
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Buckling tests on eccentrically loaded beam columns
Formulas are obtained for computing the buckling load of rods eccentrically loaded at each end, the computation being extended in particular to the inelastic range. The test results are graphically presented on three sets of curves. Two of these, at least for the elastic range, are independent of the material tested. The third set, which is independent of the material, possesses greater clearness and is therefore used for comparing the test results with the theoretical.
Tables for computing various cases of beam columns
For a better understanding of these tables, the methods by which the cases are computed are discussed first. The importance of the buckling modules is pointed out.
ELASTIC STABILITY CONSIDERATIONS IN AIRCRAFT STRUCTURAL DESIGN
General instability in shell type structures is a relatively infrequent phenomenon. By general instability is meant that a complete section of a structure becomes elastically unstable, as compared with local crippling or buckling. The first step in design is to rough size the structure and determine its compatibility with air vehicle configuration and system instillations. After this step has been completed, it is possible to survey the layouts to determine whether general instability is likely to occur. The general parameters of length, diameter, frame spacing, element stiffness, etc., are than investigated to determine if a general failing stress exists which is less than any local column, beam column, or panel failing stress. In this way, a well-balanced design is determined and general stability failing modes eliminated.
The Influence of the Form of a Wooden Beam on Its Stiffness and Strength III : Stresses in Wood Members Subjected to Combined Column and Beam Action
The general purpose in this study was to determine the stresses in a wooden member subjected to combined beam and column action. What may be considered the specific purpose, as it relates more directly to the problem of design, was to determine the particular stress that obtains at maximum load which, for combined loading, does not occur simultaneously with maximum stress.
Some inconsistencies of the finite element method as applied to inelastic response
The inadequacy of a two noded beam-column element with a linear axial and a cubic transverse displacement field for inelastic analysis is demonstrated. For complete equilibrium satisfaction in the linear elastic range a three noded beam-column element is shown to be consistent. Next, the sensitivity of the inelastic response to numerical solutions of the inelastic response of a cantilever beam resulting from approximate integration of strain energy are brought out and finally, consequences of this on the nonlinear transient response of structures are considered.
Neutron capture measurements at UMass lowell research reactor
A new facility was designed around the thermal column beam port of the 1 MW Research Reactor at the University of Massachusetts Lowell. Thermal neutrons are collimated to a 1-inch diameter beam and incident on samples to induce the radiative neutron capture. New measurements of capture gamma rays are planned for Mn, Cu, Ni, Cr, and Gd samples in the next few years. The experiments will be carried out in close collaboration with the ENSDF (Evaluated Nuclear Structure Data File) evaluation group at Brookhaven National Laboratory. The gamma rays are measured using an array of high-resolution HPGe detectors. Some of the HPGe detectors use active Compton shields that were designed from scintillation detectors and improve significantly the signal-to-background in the measured gamma-ray spectra with HPGe. The experimental spectra will be validated by the GEANT4 simulations of the array and theoretical models of the emission of gamma rays from the compound nucleus. In conclusion, the new experimental results on the capture gamma ray intensities will be incorporated in future ENSDF evaluations.
Structural analysis of bonded honeycomb welded joints.
Structural analysis of welded joints in composite welded panels using beam column concepts
A design procedure for a tension-wire stiffened truss-column
A deployable, tension wire stiffened, truss column configuration was considered for space structure applications. An analytical procedure, developed for design of the truss column and exercised in numerical studies, was based on equivalent beam stiffness coefficients in the classical analysis for an initially imperfect beam column. Failure constraints were formulated to be used in a combined weight/strength and nonlinear mathematical programming automated design procedure to determine the minimum mass column for a particular combination of design load and length. Numerical studies gave the mass characteristics of the truss column for broad ranges of load and length. Comparisons of the truss column with a baseline tubular column used a special structural efficiency parameter for this class of columns.
Modeling a Miniaturized Scanning Electron Microscope Focusing Column - Lessons Learned in Electron Optics Simulation
This presentation discusses work done to assess the design of a focusing column in a miniaturized Scanning Electron Microscope (SEM) developed at the NASA Marshall Space Flight Center (MSFC) for use in-situ on the Moon-in particular for mineralogical analysis. The MSFC beam column design uses purely electrostatic fields for focusing, because of the severe constraints on mass and electrical power consumption imposed by the goals of lunar exploration and of spaceflight in general. The resolution of an SEM ultimately depends on the size of the focused spot of the scanning beam probe, for which the stated goal here is a diameter of 10 nanometers. Optical aberrations are the main challenge to this performance goal, because they blur the ideal geometrical optical image of the electron source, effectively widening the ideal spot size of the beam probe. In the present work the optical aberrations of the mini SEM focusing column were assessed using direct tracing of non-paraxial rays, as opposed to mathematical estimates of aberrations based on paraxial ray-traces. The geometrical ray-tracing employed here is completely analogous to ray-tracing as conventionally understood in the realm of photon optics, with the major difference being that in electron optics the lens is simply a smoothly varying electric field in vacuum, formed by precisely machined electrodes. Ray-tracing in this context, therefore, relies upon a model of the electrostatic field inside the focusing column to provide the mathematical description of the "lens" being traced. This work relied fundamentally on the boundary element method (BEM) for this electric field model. In carrying out this research the authors discovered that higher accuracy in the field model was essential if aberrations were to be reliably assessed using direct ray-tracing. This led to some work in testing alternative techniques for modeling the electrostatic field. Ultimately, the necessary accuracy was attained using a BEM/Fourier series hybrid approach. The presentation will give background remarks about the MSFC mini Lunar SEM concept and electron optics modeling, followed by a description of the alternate field modeling techniques that were tried, along with their incorporation into a ray-trace simulation. Next, the validation of this simulation against commercially available software will be discussed using an example lens as a test case. Then, the efficacy of aberration assessment using direct ray-tracing will be demonstrated, using this same validation case. The discussion will include practical error checks of the field solution. Finally, the ray-trace assessment of the MSFC mini Lunar SEM concept will be shown and discussed. The authors believe this presentation will be of general interest to practitioners of modeling and simulation, as well as those with a general optics background. Because electron optics and photon optics share many basic concepts (e.g., lenses, images, aberrations, etc.), the appeal of this presentation need not be restricted to just those interested in charged particle optics.
Towards Construction of a Novel Nanometer-Resolution MeV-STEM for Imaging Thick Frozen Biological Samples
Driven by life-science applications, a mega-electron-volt Scanning Transmission Electron Microscope (MeV-STEM) has been proposed here to image thick frozen biological samples as a conventional Transmission Electron Microscope (TEM) may not be suitable to image samples thicker than 300–500 nm and various volume electron microscopy (EM) techniques either suffering from low resolution, or low speed. The high penetration of inelastic scattering signals of MeV electrons could make the MeV-STEM an appropriate microscope for biological samples as thick as 10 μm or more with a nanoscale resolution, considering the effect of electron energy, beam broadening, and low-dose limit on resolution. The best resolution is inversely related to the sample thickness and changes from 6 nm to 24 nm when the sample thickness increases from 1 μm to 10 μm. To achieve such a resolution in STEM, the imaging electrons must be focused on the specimen with a nm size and an mrad semi-convergence angle. This requires an electron beam emittance of a few picometers, which is ~1000 times smaller than the presently achieved nm emittance, in conjunction with less than 10 -4 energy spread and 1 nA current. We numerically simulated two different approaches that are potentially applicable to build a compact MeV-STEM instrument: (1) DC (Direct Current) gun, aperture, superconducting radio-frequency (SRF) cavities, and STEM column; (2) SRF gun, aperture, SRF cavities, and STEM column. Beam dynamic simulations show promising results, which meet the needs of an MeV-STEM, a few-picometer emittance, less than 10 -4 energy spread, and 0.1–1 nA current from both options. Also, we designed a compact STEM column based on permanent quadrupole quintuplet, not only to demagnify the beam size from 1 μm at the source point to 2 nm at the specimen but also to provide the freedom of changing the magnifications at the specimen and a scanning system to raster the electron beam across the sample with a step size of 2 nm and the repetition rate of 1 MHz. This makes it possible to build a compact MeV-STEM and use it to study thick, large-volume samples in cell biology.
Stability of elastically supported columns
A criterion is developed for the stiffness required of elastic lateral supports at the ends of a compression member to provide stability. A method based on this criterion is then developed for checking the stability of a continuous beam-column. A related method is also developed for checking the stability of a member of a pin-jointed truss against rotation in the plane of the truss.
Buckling of imperfect periodic lattice structures
A simplified buckling analysis is presented for a family of periodic lattice structures such as those proposed for large space structures. A transcendental 6 x 6 matrix of eigenvalues is shown to be sufficient for modeling buckling behavior because member stiffnesses are based on an exact solution of the beam-column equation. Exact stiffnesses are derived for a curved member, thus allowing modeling of imperfect lattice structures. Comparisons of predictions of the lattice model with those available from shell and beam theory underscore the inaccuracies introduced by treating the lattice structure as a continuum. Sample calculations are provided for an isogrid cylinder and a three element double-laced truss.
A variational theorem for creep with applications to plates and columns
A variational theorem is presented for a body undergoing creep. Solutions to problems of the creep behavior of plates, columns, beams, and shells can be obtained by means of the direct methods of the calculus of variations in conjunction with the stated theorem. The application of the theorem is illustrated for plates and columns by the solution of two sample problems.
Mathematical model for predicting human vertebral fracture
Mathematical model has been constructed to predict dynamic response of tapered, curved beam columns in as much as human spine closely resembles this form. Model takes into consideration effects of impact force, mass distribution, and material properties. Solutions were verified by dynamic tests on curved, tapered, elastic polyethylene beam.