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Related Concept Videos

Beams01:30

Beams

1.8K
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...
1.8K
Deflection of a Beam01:19

Deflection of a Beam

696
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...
696
Prismatic Beams: Problem Solving01:15

Prismatic Beams: Problem Solving

448
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...
448
Principal Stresses in a Beam01:11

Principal Stresses in a Beam

693
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...
693
Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

390
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...
390
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

417
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...
417

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Related Experiment Video

Updated: Jan 24, 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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Optical trapping below the diffraction limit with a tunable beam waist using super-oscillating beams.

Harel Nagar, Tamir Admon, Doron Goldman

    Optics Letters
    |May 16, 2019
    PubMed
    Summary

    Super-oscillating beams create sub-diffraction optical traps with enhanced particle localization. Optimal trapping occurs when particle size balances beam waist and avoids high-intensity side rings for superior stiffness.

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    Molecular Beam Mass Spectrometry With Tunable Vacuum Ultraviolet VUV Synchrotron Radiation
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    Area of Science:

    • Optical physics
    • Nanotechnology
    • Biophysics

    Background:

    • Super-oscillating beams generate light spots smaller than the diffraction limit.
    • These beams feature a central spot and an adjacent high-intensity side ring.
    • Optical traps utilize focused light to manipulate microscopic particles.

    Purpose of the Study:

    • To investigate the impact of particle-to-beam size ratio on optical trap performance.
    • To analyze the localization and stiffness of traps created by super-oscillating beams.
    • To determine optimal conditions for trapping submicron particles using these beams.

    Main Methods:

    • Generation of super-oscillating beams.
    • Creation of optical traps using the super-oscillating beams.
    • Systematic variation of the ratio between particle size and beam size.
    • Measurement of particle localization accuracy and trapping stiffness.

    Main Results:

    • Super-oscillating optical traps demonstrate superior submicron particle localization compared to conventional traps.
    • Trapping stiffness shows a non-monotonic dependence on the particle-to-beam size ratio.
    • Optimal trapping is achieved when the particle is larger than the beam waist but smaller than the side ring.

    Conclusions:

    • Super-oscillating beams offer enhanced capabilities for optical trapping of submicron particles.
    • Careful control of the particle-to-beam size ratio is crucial for maximizing trapping efficiency and stiffness.
    • These findings advance the application of super-oscillating beams in fields requiring precise particle manipulation.