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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...
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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.
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...
479
Principal Stresses in a Beam01:11

Principal Stresses in a Beam

746
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...
746
Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

421
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...
421
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

441
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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Updated: Feb 6, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

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Elliptical Airy beam.

Yong Zha, Kaikai Huang, Binjie Liu

    Applied Optics
    |August 22, 2018
    PubMed
    Summary
    This summary is machine-generated.

    Researchers discovered a novel elliptical Airy beam (EAB). This new light beam exhibits unique double focusing and energy flow properties, with potential for future applications in optics.

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    Area of Science:

    • Optics and Photonics
    • Beam Physics

    Background:

    • Airy beams are known for their non-diffracting and self-healing properties.
    • Noncircular symmetrical beams offer unique propagation dynamics and potential applications.

    Purpose of the Study:

    • To introduce and experimentally demonstrate a new type of noncircular symmetrical Airy beam: the elliptical Airy beam (EAB).
    • To investigate the unique propagation characteristics of the EAB, including double focusing and energy flow dynamics.

    Main Methods:

    • Fabrication of a single-pixel checkerboard hologram.
    • Experimental generation of the elliptical Airy beam using the developed hologram.

    Main Results:

    • Successful experimental generation of the elliptical Airy beam (EAB).
    • Observation of the unique double focusing property of the EAB.
    • Identification of energy flow towards the long axis endpoints during propagation.

    Conclusions:

    • The elliptical Airy beam (EAB) represents a novel class of noncircular symmetrical Airy beams.
    • The observed unique properties, such as double focusing, suggest potential applications in various optical fields.