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Related Concept Videos

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...
Singularity Functions for Shear01:26

Singularity Functions for Shear

In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the shear...
Shear Diagram01:27

Shear Diagram

In the study of beam mechanics, shear diagrams play a crucial role in understanding the distribution of shear forces along the length of a beam. Consider a beam AB that is supported at both ends and subjected to perpendicular loads.
First, a free-body diagram of the beam is drawn, representing all the external forces and internal reactions acting on the beam. One can calculate the reaction forces at each support by employing the equilibrium equations of force and moment. The vertical component...
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...
Interference and Diffraction02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
Shear and Bending Moment Diagram: Problem Solving01:24

Shear and Bending Moment Diagram: Problem Solving

When analyzing a beam supporting concentrated loads and a distributed load, drawing the shear and bending moment diagrams is essential. These diagrams help understand the internal forces and moments acting on the beam, which is crucial for designing safe and efficient structures. Follow these steps to create the shear and bending moment diagrams:
Draw a Free-Body Diagram: Start by drawing a free-body diagram of the entire beam, including the concentrated loads, distributed load, and reaction...

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Related Experiment Video

Updated: Jun 16, 2026

Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography
09:00

Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography

Published on: September 29, 2019

Method for evaluating lateral shearing interferograms.

M P Rimmer

    Applied Optics
    |February 4, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study presents a novel method using orthogonal lateral shear interferograms to accurately describe arbitrary wavefront shapes. This technique simplifies wavefront analysis, offering high precision comparable to measurement accuracy.

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    Area of Science:

    • Optical metrology
    • Wavefront sensing and analysis

    Background:

    • Wavefront shearing interferometers offer advantages by eliminating the need for a reference wavefront.
    • Conventional shearing interferometers present challenges in directly relating fringe patterns to wavefront shape.

    Purpose of the Study:

    • To develop a method for describing arbitrary wavefront shapes using data from two orthogonal lateral shear interferograms.
    • To enable precise wavefront reconstruction from shearing interferometry data.

    Main Methods:

    • Utilizing data from two lateral shear interferograms sheared in orthogonal directions.
    • Employing a least squares criterion for matching measured data to reconstructed shear data on a regular grid.
    • Leveraging sparse matrices solvable by numerical techniques for efficient wavefront definition.

    Main Results:

    • Successfully described wavefronts of arbitrary shapes on a regular grid.
    • Demonstrated that the method is computationally efficient, even for large numbers of points, due to sparse matrices.
    • Error analysis confirmed that the accuracy of the reconstructed wavefront is comparable to the accuracy of the measured data.

    Conclusions:

    • The described method provides an effective way to reconstruct arbitrary wavefronts from orthogonal lateral shear interferograms.
    • The technique offers a computationally efficient and accurate approach to wavefront analysis in optical metrology.