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

Principal Stresses in a Beam

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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.
Analyzing principal stresses is crucial, especially in...
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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...
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Mixtures of Gases: Dalton's Law of Partial Pressures and Mole Fractions03:03

Mixtures of Gases: Dalton's Law of Partial Pressures and Mole Fractions

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Unless individual gases chemically react with each other, the individual gases in a mixture of gases do not affect each other’s pressure. Each gas in a mixture exerts the same pressure that it would exert if it were present alone in the container. The pressure exerted by each individual gas in a mixture is called its partial pressure.
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Updated: Jan 23, 2026

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
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Self-steering partially coherent vector beams.

Haidan Mao, Yahong Chen, Chunhao Liang

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

    Researchers developed self-steering partially coherent vector optical beams. These beams exhibit controllable intensity and polarization, enabling applications like microparticle trapping and novel surface wave excitation.

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    Area of Science:

    • Optics and Photonics
    • Quantum Optics
    • Laser Physics

    Background:

    • Partially coherent vector beams are crucial in optical manipulation and imaging.
    • Controlling the spatial dynamics of light's polarization and intensity is an active research area.
    • Existing methods often lack flexibility in steering beam properties.

    Purpose of the Study:

    • To introduce and characterize a novel class of self-steering partially coherent vector optical beams.
    • To demonstrate the experimental realization and control of these beams.
    • To explore potential applications in microparticle trapping and surface wave generation.

    Main Methods:

    • Utilized a generalized complex Gaussian representation for theoretical analysis.
    • Employed experimental setups to generate and propagate the novel vector beams.
    • Investigated the free-space propagation dynamics of intensity and polarization distributions.

    Main Results:

    • Introduced cylindrically correlated partially coherent (CCPC) vector beams with inhomogeneous statistics.
    • Demonstrated mobile guiding centers for intensity and polarization distributions.
    • Achieved controllable steering of beam intensity and polarization, with adjustable far-field polarization patterns.

    Conclusions:

    • The developed self-steering CCPC vector beams offer unprecedented control over optical properties.
    • These beams can generate far-field polarization arrays and exhibit tunable polarization.
    • Potential applications include advanced optical trapping and the excitation of exotic surface waves.