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Related Concept Videos

Design of Prismatic Beams for Bending01:23

Design of Prismatic Beams for Bending

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 stress...
Distribution of Stresses in a Narrow Rectangular Beam01:11

Distribution of Stresses in a Narrow Rectangular Beam

In studying beam stress distribution, examining an elemental section is essential. To determine the average shearing stress on this face, the calculated shear is divided by the surface area. Importantly, shearing stresses on the beam's transverse and horizontal planes mirror each other, indicating a consistent stress distribution along the upper region of the beam. Notably, shearing stresses are absent at the beam's upper and lower surfaces due to the absence of applied forces in these areas.
Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

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...
Unsymmetric Loading of Thin-Walled Members: Problem Solving01:07

Unsymmetric Loading of Thin-Walled Members: Problem Solving

The shear center of a channel section with uniform thickness, height, and width, is determined by computing the shear force in the member and calculating the moments of inertia of the sections.
To compute the shear forces, find the shear flow at a specific distance from the endpoint using the vertical shear and the moment of inertia values. The total shear force on the flange is calculated by integrating the shear flow from one end of the flange to the other.
Next, calculate the moments of...
Unsymmetric Loading of Thin-Walled Members01:23

Unsymmetric Loading of Thin-Walled Members

Thin-walled members with non-symmetrical cross-sections are vital to engineering structures, offering material efficiency and structural integrity. However, unsymmetrical loading on these members leads to complex stress distributions, resulting in simultaneous bending and twisting can cause deformation or structural failure. The interaction between bending and twisting requires detailed analysis to ensure structural resilience.
The concept of the shear center is crucial in countering the...
Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

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 first...

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Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities
11:08

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

Published on: November 30, 2012

Improved two-dimensional beam-propagation method for three-dimensional integrated-optical waveguide structures having

T Rasmussen, J H Povisen, A Bjarklev

    Optics Letters
    |October 22, 2009
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces an efficient design tool for integrated-optical waveguides using an optimized effective index method and a 2D beam-propagation method. The tool

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    Area of Science:

    • Integrated optics
    • Computational electromagnetics
    • Waveguide design

    Background:

    • Integrated-optical waveguide structures are crucial components in photonic integrated circuits.
    • Efficient and accurate design tools are needed for optimizing waveguide performance.

    Purpose of the Study:

    • To develop an efficient design tool for integrated-optical waveguides with rectangular-core cross sections.
    • To evaluate the accuracy of the proposed design tool.

    Main Methods:

    • Combination of an optimized effective index method with a two-dimensional beam-propagation method.
    • Validation against a full three-dimensional beam-propagation method.

    Main Results:

    • The developed tool provides an efficient method for designing rectangular-core integrated-optical waveguides.
    • The accuracy of the tool is confirmed through comparisons with 3D beam-propagation results.

    Conclusions:

    • The combined method offers an efficient and accurate approach for integrated-optical waveguide design.
    • This tool can facilitate the development of advanced photonic integrated circuits.