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Related Concept Videos

Deflection of a Beam01:19

Deflection of a Beam

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Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
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Prismatic Beams: Problem Solving01:15

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In the design of a supported timber beam subjected to a distributed load, both the beam's physical dimensions and the timber's characteristics, such as its grade and species, are critical. These factors determine the allowable stress values, which are crucial for calculating the necessary beam depth to ensure structural integrity and safety.
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Deformation of a Beam under Transverse Loading01:15

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Understanding beam deflection, particularly for indeterminate beams with overhanging segments and multiple concentrated loads, is crucial for ensuring structural integrity and functionality. The process begins with constructing an accurate free-body diagram, which helps identify the forces and moments acting on the beam. This diagram is vital for visualizing how bending moments vary along the beam's length, influencing its curvature.
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Shearing Stresses in a Beam: Problem Solving01:14

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A cantilever beam with a rectangular cross-section under distributed and point loads experiences shearing stresses. The analysis begins by identifying the loads acting on the beam. Then, the reactions at the beam's fixed end are calculated using equilibrium equations. The vertical reaction is a combination of the distributed and point loads, while the moment reaction is the sum of their moments. The shear force distribution along the beam, resulting from these loads, is established by creating...
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Principal Stresses in a Beam01:11

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In prismatic beams subject to arbitrary transverse loading, It is essential to analyze the interaction between shear forces and bending moments in order to understand stress distribution and ensure structural integrity. The highest normal or bending stress occurs at the outer fibers of the beam, decreasing linearly to zero at the neutral axis. In contrast, shear stress peaks at the neutral axis and diminishes toward the outer surfaces.
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The analysis of a cantilever beam with a circular cross-section subjected to impact loading at its free end illustrates the conversion of potential energy from a dropped object into kinetic energy, which is then absorbed by the beam as strain energy. This process is crucial for understanding how materials behave under dynamic loads, which is important in fields such as construction and aerospace.
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Understanding Beam-Induced Electronic Excitations in Materials.

David B Lingerfelt1, Panchapakesan Ganesh1, Jacek Jakowski1,2

  • 1Nanomaterials Theory Institute, Center for Nanophase Materials Sciences , Oak Ridge National Laboratory , Oak Ridge , Tennessee 37831 , United States.

Journal of Chemical Theory and Computation
|January 4, 2020
PubMed
Summary

This study introduces new selection rules for electronic excitations in materials using charged particle beams, moving beyond traditional optical spectroscopy. These rules, derived from point charge interactions, offer a novel way to probe material structures with unprecedented spatial resolution.

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Area of Science:

  • Materials Science
  • Quantum Chemistry
  • Spectroscopy

Background:

  • Optical electronic absorption spectroscopy is crucial for understanding material electronic structures.
  • Existing methods often rely on long-wavelength approximations, limiting detailed analysis.

Purpose of the Study:

  • To expand the toolbox of materials science with electron and ion spectroscopies.
  • To formulate and discuss selection rules for electronic excitations induced by charged particle beams.
  • To develop an ab initio framework for probing material structural responses to charged particle irradiation.

Main Methods:

  • Formulating selection rules for electronic excitation by charged particles.
  • Implementing expressions within linear response time-dependent density functional theory (TD-DFT) for transition rates.
  • Validating TD-DFT results with real-time simulations and mapping spatial dependence.

Main Results:

  • Transition probabilities for point charge-induced excitations depend strongly on charged particle position.
  • These probabilities can deviate significantly from the electric dipole approximation.
  • A method was developed to map the spatial dependence of point charge-induced transition rates.

Conclusions:

  • Charged particle beams offer a new regime for manipulating electronic states and material structures.
  • The developed framework enables ab initio probing of structural responses under charged particle irradiation.
  • This work bridges microscopy, spectroscopy, and theoretical calculations for advanced materials analysis.