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Related Concept Videos

Equation of the Elastic Curve01:23

Equation of the Elastic Curve

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,...
Deformation of a Beam under Transverse Loading01:15

Deformation of a Beam under Transverse Loading

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...
Deformations in a Transverse Cross Section01:21

Deformations in a Transverse Cross Section

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...
Elastic Curve from the Load Distribution01:16

Elastic Curve from the Load Distribution

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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Impact Loading on a Cantilever Beam01:13

Impact Loading on a Cantilever Beam

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Deflection of a Beam01:19

Deflection of a Beam

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Related Experiment Video

Updated: Jun 8, 2026

Direct Imaging of Laser-driven Ultrafast Molecular Rotation
10:52

Direct Imaging of Laser-driven Ultrafast Molecular Rotation

Published on: February 4, 2017

Geometric bowing effect of a laser beam.

Y Kafri, O Kafri

    Applied Optics
    |October 14, 2010
    PubMed
    Summary

    When a laser beam is projected skyward at a shallow angle, an optical effect causes it to bend downwards. This atmospheric optics phenomenon makes the laser beam appear to curve toward the ground.

    Area of Science:

    • Atmospheric optics
    • Laser physics

    Background:

    • Laser beams are typically expected to travel in straight lines.
    • Atmospheric conditions can influence light propagation.

    Purpose of the Study:

    • To describe and analyze a downward bending effect of laser beams projected at shallow angles.
    • To investigate the optical principles behind this observed atmospheric phenomenon.

    Main Methods:

    • Observation of a laser beam projected toward the sky at a shallow angle.
    • Analysis of the beam's apparent propagation path from an observer's perspective below.

    Main Results:

    • The laser beam appears to bend and propagate towards the ground.
    • The observed bending deviates from the expected upward trajectory.

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    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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    High-speed Particle Image Velocimetry Near Surfaces
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    High-speed Particle Image Velocimetry Near Surfaces

    Published on: June 24, 2013

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    Last Updated: Jun 8, 2026

    Direct Imaging of Laser-driven Ultrafast Molecular Rotation
    10:52

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    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
    12:14

    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

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    High-speed Particle Image Velocimetry Near Surfaces

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    Conclusions:

    • A notable optical effect occurs when lasers are projected at low elevation angles.
    • Atmospheric interactions cause a visible downward curvature in laser beam paths.