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Related Concept Videos

Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

341
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...
341
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...
392
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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Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

463
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 Symmetric Loadings01:15

Beams with Symmetric Loadings

354
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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Beams01:30

Beams

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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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Related Experiment Video

Updated: Dec 27, 2025

Author Spotlight: Advancing Knowledge in Far-From-Equilibrium Materials Through Light-Sheet Microscopy
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The vector Durnin-Whitney beam.

Israel Julián-Macías, Citlalli Teresa Sosa-Sánchez, Omar de Jesús Cabrera-Rosas

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |March 3, 2020
    PubMed
    Summary

    Researchers discovered new exact solutions to Maxwell

    Area of Science:

    • Electromagnetism and Optics
    • Mathematical Physics

    Background:

    • The Maxwell equations govern electromagnetic fields in free space.
    • Previous solutions often involve approximations or specific beam types.

    Purpose of the Study:

    • To derive general, exact solutions to the Maxwell equations.
    • To introduce novel beam types with unique properties.
    • To explore the relationship between beam characteristics and caustics.

    Main Methods:

    • Identified conditions for exact plane wave solutions to Maxwell's equations.
    • Utilized solutions to the eikonal and Laplace equations.
    • Applied the superposition principle to construct new field solutions.

    Main Results:

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  • Established that mutually perpendicular, right-handed field sets and specific scalar functions yield exact solutions.
  • Introduced vector Durnin-Whitney beams with locally stable caustics (fold and cusp types).
  • Derived scalar Durnin-Whitney-Gauss beams and analyzed their associated caustics.

    • Conclusions:

    • Vector Durnin-Whitney beams generalize vector Bessel beams.
    • Caustics of these beams qualitatively map intensity maxima.
    • This framework provides a new method for constructing exact electromagnetic solutions.