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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.
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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Deformations in a Transverse Cross Section01:21

Deformations in a Transverse Cross Section

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When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
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Singularity Functions for Shear01:26

Singularity Functions for Shear

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In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the shear...
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Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

674
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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Deformation of a Beam under Transverse Loading01:15

Deformation of a Beam under Transverse Loading

968
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...
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Beams01:30

Beams

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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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Updated: May 1, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Accelerating light beams with arbitrarily transverse shapes.

Adrian Ruelas, Jeffrey A Davis, Ignacio Moreno

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    |March 26, 2014
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    Summary
    This summary is machine-generated.

    Researchers demonstrate a new method to create custom-shaped accelerating beams, which maintain their form along curved paths. This breakthrough offers enhanced versatility for applications in optics and laser technology.

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    Area of Science:

    • Optics and Photonics
    • Wave Phenomena

    Background:

    • Accelerating beams are specialized wave packets known for maintaining shape during curved propagation.
    • They have existing applications in optical micromanipulation, plasma generation, and laser micromachining.

    Purpose of the Study:

    • To develop a general method for generating accelerating beams with arbitrarily chosen transverse shapes.
    • To demonstrate the theoretical and experimental feasibility of this method in both paraxial and nonparaxial regimes.

    Main Methods:

    • Utilizing the spectral representation of accelerating beams for a compact description.
    • Developing a general construction method for arbitrary transverse beam shapes.
    • Experimental validation of beam propagation in the paraxial regime.

    Main Results:

    • Successful theoretical and experimental generation of accelerating beams with user-defined transverse shapes.
    • Demonstration of beam propagation maintaining shape along curved trajectories.
    • The spectral representation provides a powerful tool for beam characterization.

    Conclusions:

    • The presented method enables on-demand generation of versatile accelerating light patterns.
    • This offers new possibilities for existing applications and opens doors for novel uses.
    • The technique enhances the adaptability of accelerating beams in scientific and industrial contexts.