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Related Concept Videos

Singularity Functions for Bending Moment01:18

Singularity Functions for Bending Moment

584
Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented using a...
584
Deflection of a Beam01:19

Deflection of a Beam

794
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...
794
Shear and Bending Moment Diagram: Problem Solving01:24

Shear and Bending Moment Diagram: Problem Solving

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When analyzing a beam supporting concentrated loads and a distributed load, drawing the shear and bending moment diagrams is essential. These diagrams help understand the internal forces and moments acting on the beam, which is crucial for designing safe and efficient structures. Follow these steps to create the shear and bending moment diagrams:
Draw a Free-Body Diagram: Start by drawing a free-body diagram of the entire beam, including the concentrated loads, distributed load, and reaction...
3.3K
Unsymmetric Bending - Angle of Neutral Axis01:15

Unsymmetric Bending - Angle of Neutral Axis

913
Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal...
913
Unsymmetric Bending01:18

Unsymmetric Bending

863
Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The...
863
Bending of Material: Problem Solving01:09

Bending of Material: Problem Solving

582
In this lesson, determine the ratio of the maximum bending moments applied to two metal pipes, given that both pipes can withstand a maximum stress of 100 MPa. Both pipes have an outer radius of 1.8 cm. Pipe A has an inner radius of 1.5 cm, and Pipe B has an inner radius of 1 cm. The ratio of the maximum bending moment applied to two metallic pipes, each with a different inner and outer radius, is determined by considering their dimensions. The inner radius of the first pipe is 1.5 cm, and for...
582

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Related Experiment Video

Updated: Feb 20, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

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Self-bending scalar and vector bottle sheets.

F G Mitri

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |October 17, 2017
    PubMed
    Summary

    Researchers generated auto-bending Bessel-Gauss bottle beams in 2D space. These beams circumvent obstacles and can be controlled for various applications, including optical cloaking and particle manipulation.

    Area of Science:

    • Physics
    • Optics
    • Acoustics

    Background:

    • Bessel-Gauss beams are known for their non-diffracting properties.
    • Controlling beam trajectories and shapes is crucial for advanced applications.

    Purpose of the Study:

    • To demonstrate the generation of auto-bending cylindrical/tubular Bessel-Gauss bottle beams in 2D space.
    • To explore the control mechanisms for beam profile, area, and autofocusing spots.

    Main Methods:

    • Angular spectrum decomposition method.
    • Solving the Helmholtz equation and Maxwell's equations under the Lorenz gauge condition.
    • Utilizing intrinsic parameters of illuminating waves and vector potential polarizations.

    Main Results:

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  • Successful generation of auto-bending cylindrical bottle beams with hollow central regions.
  • Demonstrated control over beam profile, area, and autofocusing spot location.
  • Wave fields follow curved trajectories, enabling obstacle circumvention.

    • Conclusions:

    • The demonstrated auto-bending bottle beams offer novel functionalities for manipulating light and sound.
    • Potential applications include optical cloaking, advanced tweezers, and particle sorting devices.