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Related Concept Videos

Beams01:30

Beams

1.4K
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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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

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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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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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Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

194
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...
194
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

122
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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Super-Airy beams.

Aly Abdou

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    Summary
    This summary is machine-generated.

    Researchers created super-Airy beams using super-Gaussian beams and cubic phase modulation. These beams significantly extend non-diffracting propagation distances compared to traditional Airy beams, offering enhanced optical control.

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    Area of Science:

    • Optics and Photonics
    • Beam Propagation Physics

    Background:

    • Airy beams exhibit non-diffracting propagation properties.
    • Controlling beam propagation is crucial for optical applications.

    Purpose of the Study:

    • To investigate the formation and propagation of super-Airy beams.
    • To enhance the non-diffracting propagation length of Airy-like beams.

    Main Methods:

    • Numerical simulations of Fourier-transformed super-Gaussian beams with cubic phase modulation.
    • Analysis of beam truncation profiles and curvature effects on propagation.

    Main Results:

    • Super-Gaussian beams with cubic phase modulation form truncated Airy beams.
    • Smaller Airy beam curvature leads to longer non-diffracting propagation.
    • Achieved >350% increase in non-diffracting distance compared to Gaussian beams.

    Conclusions:

    • Super-Airy beams offer significantly improved non-diffracting propagation.
    • Curvature control is key to extending beam stability.
    • This method provides a pathway to enhanced optical beam manipulation.