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Related Concept Videos

Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

385
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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Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

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To understand shear on the flat side of a prismatic beam element, consider the vertical and horizontal shearing forces, and the normal forces, acting on the element. The element's upper (U) and lower (L) sections, which are divided by the beam's neutral axis, are examined. The equilibrium of these forces is determined by applying the equilibrium equation, which helps identify the horizontal shearing force. This force is directly related to the bending moments and the cross-section's...
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Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

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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...
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Design of Prismatic Beams for Bending01:23

Design of Prismatic Beams for Bending

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The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and...
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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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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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Related Experiment Video

Updated: Jan 17, 2026

Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces
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Focused axisymmetric spatially chirped beams.

E C Nelson, K J Charbonnet, H H Effarah

    Optics Express
    |September 23, 2025
    PubMed
    Summary

    Researchers characterized focused space-time structures of radially chirped beams, finding their key properties can be mimicked using simpler 1D spatially chirped beam arrays.

    Area of Science:

    • Optics and photonics
    • Laser physics
    • Wave phenomena

    Background:

    • Radially chirped beams exhibit complex space-time structures with tunable properties.
    • Generating ideal radially chirped beams and polarizations presents practical challenges.

    Purpose of the Study:

    • To provide a detailed characterization of focused space-time structures of radially chirped beams.
    • To explore tunable properties including centroid velocity, pulse front symmetry, intensity modulations, and polarization states.
    • To investigate alternative methods for mimicking the characteristics of radially chirped beams.

    Main Methods:

    • Theoretical analysis and simulation of focused radially chirped beam propagation.
    • Examination of tunable parameters: on-axis centroid velocity, pulse front symmetry, transverse intensity modulations, and polarization states.

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  • Comparison of generated beam characteristics with those produced by arrays of 1D spatially chirped beams.

    • Main Results:

    • Detailed characterization of tunable properties of focused radially chirped beams.
    • Demonstration that primary characteristics can be mimicked.
    • Identification of simple arrays of 1D spatially chirped beams as a viable alternative.

    Conclusions:

    • Focused radially chirped beams possess controllable space-time characteristics.
    • Arrays of 1D spatially chirped beams offer a practical approach to replicate key features of radially chirped beams.
    • This finding simplifies the generation and application of beams with desired space-time properties.