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Related Concept Videos

Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

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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...
260
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

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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...
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Deflection of a Beam01:19

Deflection of a Beam

403
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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Principal Stresses in a Beam01:11

Principal Stresses in a Beam

439
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...
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Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

303
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...
303
Shearing Stresses in a Beam: Problem Solving01:14

Shearing Stresses in a Beam: Problem Solving

327
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...
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Twisted sinc-correlation Schell-model beams.

Yujie Zhou, Weiting Zhu, Daomu Zhao

    Optics Express
    |February 25, 2022
    PubMed
    Summary
    This summary is machine-generated.

    We introduce novel twisted sinc-correlation Schell-model (TSCSM) beams. These beams exhibit unique spectral density and degree of coherence (DOC) rotation and splitting behaviors during propagation.

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    Area of Science:

    • Optics and Photonics
    • Classical Optics
    • Beam Propagation

    Background:

    • Schell-model beams are widely used in optical systems.
    • Understanding beam propagation is crucial for optical applications.
    • Twisted light beams offer unique polarization and coherence properties.

    Purpose of the Study:

    • Introduce a new class of twisted sinc-correlation Schell-model (TSCSM) beams.
    • Analyze the statistical characteristics and propagation behavior of TSCSM beams.
    • Explore the twist effect on spectral density and degree of coherence (DOC).

    Main Methods:

    • Theoretical analysis of TSCSM beam propagation.
    • Investigation of spectral density and DOC distributions.
    • Numerical simulations to demonstrate beam characteristics.

    Main Results:

    • TSCSM beams exhibit a 90-degree rotation in irradiance profile.
    • The degree of coherence (DOC) can show diverse rotational behaviors (unidirectional or non-unidirectional).
    • The twist factor influences spectral density splitting, with beam width and coherence length also playing a role.

    Conclusions:

    • TSCSM beams represent a novel class of optical sources with tunable propagation characteristics.
    • The observed rotation and splitting phenomena offer potential for advanced optical manipulation.
    • Further research can explore applications of TSCSM beams in areas like optical imaging and communication.