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Related Concept Videos

Beams01:30

Beams

1.9K
Beams are integral components of structural engineering and construction, designed to support loads applied at various points along their length. These long, straight members can be classified based on geometry, cross-section, support type, and equilibrium condition.
Based on geometry, beams can be straight, tapered, or curved. Straight beams are the most common type and have a constant cross-section throughout their length. Tapered beams, on the other hand, have a varying cross-section along...
1.9K
Deflection of a Beam01:19

Deflection of a Beam

728
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.
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...
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Prismatic Beams: Problem Solving01:15

Prismatic Beams: Problem Solving

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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.
The design begins with analyzing the beam as a free body to identify moments and force balances, thereby determining support reactions. Next, the...
472
Principal Stresses in a Beam01:11

Principal Stresses in a Beam

732
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.
Analyzing principal stresses is crucial, especially in...
732
Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

420
The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
The M/EI...
420
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

438
Analyzing a supported beam under unsymmetrical loadings is essential in structural engineering to understand how beams respond to varied force distributions. This analysis involves calculating the deflection and identifying points where the slope of the beam is zero, which are crucial for ensuring structural stability and functionality.
The first moment-area theorem determines the slope at any point on the beam. This theorem indicates that the change in slope between two points on a beam...
438

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Related Experiment Video

Updated: Feb 2, 2026

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
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Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

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Three-beam convergent-beam electron diffraction for measuring crystallographic phases.

Yueming Guo1, Philip N H Nakashima1, Joanne Etheridge1,2

  • 1Department of Materials Science and Engineering, Monash University, Victoria 3800, Australia.

Iucrj
|November 17, 2018
PubMed
Summary
This summary is machine-generated.

A new method extracts phase information from electron diffraction patterns. This technique directly measures three-phase invariants in convergent-beam electron diffraction (CBED) patterns, aiding crystal structure determination.

Keywords:
convergent-beam electron diffractioncrystallographic phase problemdynamical studiesenantiomorph ambiguitymultiple scatteringnanocrystalsstructure determinationthree-phase invariants

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Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Area of Science:

  • Crystallography
  • Materials Science
  • Electron Microscopy

Background:

  • Electron diffraction patterns inherently contain phase information of structure factors.
  • Extracting this phase information is challenging due to the strong interaction of electrons with matter.
  • No universal method currently exists for direct phase information extraction.

Purpose of the Study:

  • To derive analytical expressions for intensity distribution in three-beam convergent-beam electron diffraction (CBED) patterns.
  • To develop a direct method for extracting three-phase invariants from CBED patterns.
  • To demonstrate the method's applicability in determining crystal structures.

Main Methods:

  • Derivation of analytical expressions for intensity distribution in three-beam CBED patterns.
  • Identification of specific features within CBED patterns for direct three-phase invariant extraction.
  • Experimental validation using silicon (Si) and gallium arsenide (GaAs) samples.

Main Results:

  • Simple analytical expressions for three-beam CBED intensity distribution were derived.
  • Features in CBED patterns allowing direct extraction of three-phase invariants were identified.
  • The octant of the three-phase invariant was determined with an uncertainty of ±22.5°.

Conclusions:

  • A direct method for measuring three-phase invariants from CBED patterns has been established.
  • This method eliminates the need for iterative refinement processes.
  • The approach provides direct measurements that can enhance *ab initio* phasing methods in structure determination.