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Related Concept Videos

Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

To understand shear on the flat side of a prismatic beam element, consider the vertical and horizontal shearing forces, and the normal forces, acting on the element. The element's upper (U) and lower (L) sections, which are divided by the beam's neutral axis, are examined. The equilibrium of these forces is determined by applying the equilibrium equation, which helps identify the horizontal shearing force. This force is directly related to the bending moments and the cross-section's first...
Beams01:30

Beams

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...
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

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...
Sign Convention01:30

Sign Convention

When analyzing a beam subjected to various loads, it is crucial to understand the internal forces and moments generated within the structure. These internal forces can be broadly classified into normal forces, shear forces, and bending moments. To determine these forces and moments, we use the method of sections and apply a specific sign convention based on their direction and the side of the section being analyzed.
The normal force acts perpendicular to the beam's cross-section and can cause...
Deformation of a Beam under Transverse Loading01:15

Deformation of a Beam under Transverse Loading

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.
The insights from the bending moment diagram extend to...
Deflection of a Beam01:19

Deflection of a Beam

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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Related Experiment Video

Updated: Jun 21, 2026

Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces
09:33

Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces

Published on: June 7, 2019

Directionality of general beams.

Xiaoling Ji1, Xiaoqing Li, Guangming Ji

  • 1Department of Physics, Sichuan Normal University, Chengdu, China. jiXL100@163.com

Optics Express
|July 8, 2009
PubMed
Summary

Researchers studied the directionality of general beams in free space and atmospheric turbulence. They found equivalent general beams can mimic a coherent Gaussian beam

Area of Science:

  • Optics and Photonics
  • Wave Propagation
  • Atmospheric Optics

Background:

  • Understanding beam directionality is crucial for optical communication and remote sensing.
  • Atmospheric turbulence significantly distorts beam propagation, affecting performance.
  • General beams offer flexibility beyond traditional Gaussian beams.

Purpose of the Study:

  • To analyze the directionality of general beams in free space and atmospheric turbulence.
  • To derive analytical expressions for beam width and angular spread.
  • To identify conditions for equivalent beam behavior.

Main Methods:

  • Utilizing partial-coherence theory.
  • Applying the integral transform technique.
  • Deriving analytical expressions for mean-squared width and angular spread.

More Related Videos

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
10:39

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

Published on: October 11, 2016

Related Experiment Videos

Last Updated: Jun 21, 2026

Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces
09:33

Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces

Published on: June 7, 2019

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
10:39

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

Published on: October 11, 2016

Main Results:

  • Mean-squared width and angular spread depend on mode weighting factors and coherence coefficients.
  • Identified conditions for 'equivalent general beams'.
  • These equivalent beams exhibit the same directionality as fully coherent Gaussian beams.

Conclusions:

  • Equivalent general beams can maintain directionality comparable to coherent Gaussian beams.
  • This finding is independent of the specific atmospheric turbulence model.
  • The results have implications for designing robust optical systems in turbulent environments.