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Related Concept Videos

Bending of Curved Members - Neutral Surface01:16

Bending of Curved Members - Neutral Surface

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In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
Consider the curved member described in the previous lesson. According to Hooke's law, which relates stress to strain within the...
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Elastic Curve from the Load Distribution01:16

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The structural behavior of beams under distributed loads is critical for engineering analysis, which focuses on predicting how beams bend and react under such conditions. Different types of beams (e.g., cantilever, supported, or overhanging) behave differently under distributed load conditions.
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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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Equation of the Elastic Curve01:23

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The concept of curvature in plane curves, crucial in structural engineering, defines how sharply a beam bends under load. This curvature is determined using the curve's first and second derivatives.
Consider a cantilever beam with a point load at its free end (for instance, a diving board). When analyzing beam deflection with small slopes, the shape of the beam's elastic curve becomes key. The governing equation for this analysis involves the bending moment and the beam's flexural rigidity,...
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Distribution of Stresses in a Narrow Rectangular Beam01:11

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In studying beam stress distribution, examining an elemental section is essential. To determine the average shearing stress on this face, the calculated shear is divided by the surface area. Importantly, shearing stresses on the beam's transverse and horizontal planes mirror each other, indicating a consistent stress distribution along the upper region of the beam. Notably, shearing stresses are absent at the beam's upper and lower surfaces due to the absence of applied forces in these...
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Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

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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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Related Experiment Video

Updated: Apr 3, 2026

Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators
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Spiraling elliptic beam in nonlocal nonlinear media.

Guo Liang, Qi Guo, Wenjing Cheng

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    |September 26, 2015
    PubMed
    Summary

    Spiraling elliptic beams in nonlinear media exhibit unique dynamics. Changes in optical power and orbital angular momentum (OAM) control beam breathing and rotation, offering potential for optical beam control.

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    Area of Science:

    • Nonlinear optics
    • Beam propagation dynamics

    Background:

    • Spiraling elliptic beams carry orbital angular momentum (OAM).
    • These beams exhibit rotational motion perpendicular to their propagation direction.

    Purpose of the Study:

    • To analytically and numerically investigate the dynamical properties of spiraling elliptic beams in nonlocal nonlinear media.
    • To explore the influence of deviations from critical power and OAM on beam behavior.

    Main Methods:

    • Analytical discussion of beam dynamics.
    • Numerical simulations to analyze optical intensity, beam width, and angular velocity.

    Main Results:

    • Deviations from critical power and OAM induce 'breathing' in spiraling elliptic beams.
    • Decreasing OAM or increasing power causes beam contraction, while the reverse leads to diffraction, with distinct behaviors observed.
    • Input optical power and OAM significantly alter the beam's rotating speed.

    Conclusions:

    • Spiraling elliptic beams in nonlinear media display controllable breathing and diffraction patterns.
    • The study demonstrates the potential for manipulating optical beams by controlling power and OAM.
    • Findings may lead to applications in optical beam control technologies.