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Related Concept Videos

Shearing Stresses in a Beam: Problem Solving01:14

Shearing Stresses in a Beam: Problem Solving

871
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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Distribution of Stresses in a Narrow Rectangular Beam01:11

Distribution of Stresses in a Narrow Rectangular Beam

717
In studying beam stress distribution, examining an elemental section is essential. To determine the average shearing stress on this face, the calculated shear is divided by the surface area. Importantly, shearing stresses on the beam's transverse and horizontal planes mirror each other, indicating a consistent stress distribution along the upper region of the beam. Notably, shearing stresses are absent at the beam's upper and lower surfaces due to the absence of applied forces in these...
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Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

546
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...
546
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

531
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...
531
Elastic Curve from the Load Distribution01:16

Elastic Curve from the Load Distribution

577
The structural behavior of beams under distributed loads is critical for engineering analysis, which focuses on predicting how beams bend and react under such conditions. Different types of beams (e.g., cantilever, supported, or overhanging) behave differently under distributed load conditions.
For all beams, the analysis of the beam's reaction to distributed loads begins by understanding the relationship between a beam's load and the resulting shear forces and bending moments. Initially, this...
577
Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

668
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...
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Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment.

Fei Wang, Chunhao Liang, Yangsheng Yuan

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    A novel generalized multi-Gaussian correlated Schell-model (GMGCSM) beam was developed. This new beam can create specific focal profiles, useful for optical communications and material processing.

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    Area of Science:

    • Optics and Photonics
    • Beam Propagation
    • Coherent Beam Technologies

    Background:

    • Partially coherent beams are crucial in various optical applications.
    • Existing models often lack flexibility in controlling beam profiles.
    • Developing new beam types with tailored correlations is an active research area.

    Purpose of the Study:

    • To propose a new partially coherent beam: the generalized multi-Gaussian correlated Schell-model (GMGCSM) beam.
    • To theoretically analyze the beam's capability to produce specific focal profiles.
    • To experimentally validate the generation and focusing properties of the GMGCSM beam.

    Main Methods:

    • Theoretical formulation of the generalized multi-Gaussian correlated Schell-model (GMGCSM) beam.
    • Analysis of the beam's correlation function and propagation characteristics.
    • Experimental setup for generating and measuring the intensity profile of the GMGCSM beam in the focal plane.

    Main Results:

    • The proposed GMGCSM beam, of the first or second kind, can generate dark hollow or flat-topped beam profiles.
    • Experimental generation and measurement of the focused intensity profile were successfully performed.
    • Experimental results align with theoretical predictions for the GMGCSM beam's behavior.

    Conclusions:

    • The GMGCSM beam offers a novel way to control beam profiles in the focal plane.
    • This new beam type demonstrates practical utility for applications like free-space optical communications.
    • Potential applications include material thermal processing and particle/atom trapping.