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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

692
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...
692
Prismatic Beams: Problem Solving01:15

Prismatic Beams: Problem Solving

447
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...
447
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

389
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...
389
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

415
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...
415

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Related Experiment Video

Updated: Jan 23, 2026

Focused Ion Beam Lithography to Etch Nano-architectures into Microelectrodes
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Sectoral multipole focused beams.

J Olmos-Trigo, M Meléndez, R Delgado-Buscalioni

    Optics Express
    |June 6, 2019
    PubMed
    Summary
    This summary is machine-generated.

    This study identifies "sectoral" multipoles as the only propagating multipole beams under hemispherical illumination. These beams, with defined helicity, offer insights into light-matter interactions in focused beams.

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    Area of Science:

    • Optics and Photonics
    • Electromagnetism
    • Quantum Optics

    Background:

    • Multipole beams are crucial for understanding light propagation and interaction.
    • Defining beam properties like helicity and angular momentum is key in advanced optics.

    Purpose of the Study:

    • To identify and characterize propagating multipole beams with defined handedness.
    • To analyze the properties of these beams, particularly in the focal volume.

    Main Methods:

    • Theoretical analysis of electromagnetic fields.
    • Solving Maxwell's equations for specific beam configurations.
    • Investigating properties like Poynting vector and angular momentum.

    Main Results:

    • Identified "sectoral" multipoles as the sole propagating multipole beams under hemispherical illumination.
    • Demonstrated the equivalence of the sectoral dipole beam to Huygens' sources.
    • Characterized higher-order multipolar beams as vortex beams vanishing on-axis.

    Conclusions:

    • Sectoral multipole beams are exact solutions to Maxwell's equations.
    • Their unique properties in the focal volume aid in modeling light-matter interactions.
    • Provides a foundation for understanding and manipulating light in focused systems.