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Related Concept Videos

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

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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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Principal Stresses in a Beam01:11

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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.
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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.
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Beams with Symmetric Loadings01:15

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Related Experiment Video

Updated: Jun 7, 2025

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Goos-Hänchen shift for an Airyprime beam.

Ze Chen, Shi-Yu Peng, Zhi-Hai Zhang

    Optics Letters
    |November 15, 2024
    PubMed
    Summary
    This summary is machine-generated.

    We present a theory for the Goos-Hänchen (GH) shift of Airyprime beams. A horizontally polarized Airyprime beam exhibits an enhanced spatial GH shift near Brewster's angle.

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    Area of Science:

    • Optics
    • Quantum Optics
    • Photonics

    Background:

    • The Goos-Hänchen (GH) effect describes the transverse spatial shift of a light beam upon reflection.
    • Airy beams and their modified versions (Airyprime beams) exhibit unique propagation dynamics.
    • Understanding GH shifts is crucial for optical sensing and manipulation.

    Purpose of the Study:

    • To develop a comprehensive theory for analyzing the Goos-Hänchen (GH) shift of arbitrarily polarized Airyprime beams.
    • To establish the relationship between the GH shift of Airyprime beams and standard Airy beams.
    • To investigate novel optical phenomena associated with Airyprime beam reflection.

    Main Methods:

    • Derivation of general expressions for spatial and angular GH shifts for Airyprime beams.
    • Analysis of beam polarization effects on the GH shift.
    • Investigation of reflection phenomena near Brewster's angle.

    Main Results:

    • General formulas for spatial and angular GH shifts of Airyprime beams were derived.
    • A direct relationship between the GH shifts of Airyprime and Airy beams was established.
    • A significantly enhanced spatial GH shift and a near-zero angular GH shift were predicted for horizontally polarized Airyprime beams near Brewster's angle.

    Conclusions:

    • The proposed theory provides a robust framework for analyzing GH shifts of Airyprime beams.
    • The findings reveal unique optical behaviors of Airyprime beams, particularly near Brewster's angle.
    • This research contributes to the understanding of light-matter interactions and potential applications in optical devices.