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Related Concept Videos

Prismatic Beams: Problem Solving01:15

Prismatic Beams: Problem Solving

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 designer...
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...
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...
Internal Loadings in Structural Members: Problem Solving01:28

Internal Loadings in Structural Members: Problem Solving

When designing or analyzing a structural member, it is important to consider the internal loadings developed within the member. These internal loadings include normal force, shear force, and bending moment. Engineers can ensure that the structural member can support the applied external forces by calculating these internal loadings.
To illustrate this, let's consider a beam OC of 5 kN, inclined at an angle of 53.13° with the horizontal and supported at both ends. Determine the internal loadings...
Distributed Loads: Problem Solving01:21

Distributed Loads: Problem Solving

Beams are structural elements commonly employed in engineering applications requiring different load-carrying capacities. The first step in analyzing a beam under a distributed load is to simplify the problem by dividing the load into smaller regions, which allows one to consider each region separately and calculate the magnitude of the equivalent resultant load acting on each portion of the beam. The magnitude of the equivalent resultant load for each region can be determined by calculating...
Shearing Stresses in a Beam: Problem Solving01:14

Shearing Stresses in a Beam: Problem Solving

A cantilever beam with a rectangular cross-section under distributed and point loads experiences shearing stresses. The analysis begins by identifying the loads acting on the beam. Then, the reactions at the beam's fixed end are calculated using equilibrium equations. The vertical reaction is a combination of the distributed and point loads, while the moment reaction is the sum of their moments. The shear force distribution along the beam, resulting from these loads, is established by creating...

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Related Experiment Video

Updated: Jun 11, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
12:14

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Analytic solution for the three-layer multiple beam interferometer.

R G Horn, D T Smith

    Applied Optics
    |June 29, 2010
    PubMed
    Summary
    This summary is machine-generated.

    We derived an analytic solution for light interference in a three-layer interferometer. This model accounts for metallic coatings and enables precise thin-film thickness measurements using chromatic order fringes.

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    Last Updated: Jun 11, 2026

    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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    Published on: August 12, 2013

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    Area of Science:

    • Optics and Photonics
    • Materials Science
    • Thin Film Analysis

    Background:

    • Interferometry is crucial for optical measurements.
    • Understanding light interference in multi-layer systems is complex.
    • Accurate thin-film characterization is vital in various scientific fields.

    Purpose of the Study:

    • To develop a simple analytic solution for constructive interference in a three-layer interferometer.
    • To investigate the impact of metallic coatings on optical interference.
    • To provide a method for precise measurement of thin film thickness.

    Main Methods:

    • Developed an analytic model for light transmission through three transparent layers.
    • Incorporated empirical expressions for phase changes due to metallic coatings (silver on silica, sapphire, mica).
    • Applied the model to analyze fringes of equal chromatic order.

    Main Results:

    • A straightforward analytic solution for constructive interference conditions was established.
    • Empirical formulas were derived for phase shifts caused by silver coatings on common substrates.
    • The method demonstrates high precision for measuring extremely thin films.

    Conclusions:

    • The presented analytic solution simplifies the analysis of multi-layer interferometers.
    • The inclusion of metallic coating effects enhances the model's applicability.
    • This technique offers a precise and accessible method for thin-film metrology.