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Related Concept Videos

Singularity Functions for Shear01:26

Singularity Functions for Shear

448
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...
448
Shear Diagram01:27

Shear Diagram

1.7K
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...
1.7K
Shearing Stress01:19

Shearing Stress

2.0K
Shearing stress, denoted by the Greek letter tau (Ď„), is stress caused by forces acting transversely on an object. These forces create internal ones within the entity in the plane where the external forces are applied. The resultant of these internal forces is the shear in the section.
The average shearing stress can be calculated by dividing the shear by the area of the cross-section.
2.0K
Shearing Strain01:20

Shearing Strain

1.4K
The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...
1.4K
Normal and Shear Force01:14

Normal and Shear Force

3.3K
When a beam is subjected to different loads, such as weight, pressure, or other external forces, internal forces are generated within the beam. These forces can have a significant impact on the overall stability and strength of the structure. Engineers use various methods to analyze and determine the magnitude and direction of these internal forces. One common technique used to determine internal forces in beams is the method of sections. This method involves considering an imaginary point or...
3.3K
Relation Between the Distributed Load and Shear01:23

Relation Between the Distributed Load and Shear

1.1K
Understanding the relationship between the distributed load and shear force in structural analysis is crucial for analyzing beams subjected to various loading conditions. Consider the case of a beam experiencing a distributed load, two concentrated loads, and a couple moment.
1.1K

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Related Experiment Video

Updated: Feb 2, 2026

Automated 3D Optical Coherence Tomography to Elucidate Biofilm Morphogenesis Over Large Spatial Scales
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Form determination of optical surfaces by measuring the spatial coherence function using shearing interferometry.

Jan-Hendrik Hagemann, Claas Falldorf, Gerd Ehret

    Optics Express
    |November 25, 2018
    PubMed
    Summary
    This summary is machine-generated.

    A novel optical surface measurement technique uses spatial coherence and a shearing interferometer with LED illumination. This method accurately determines surface form through inverse raytracing, offering reliable measurement results.

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    Area of Science:

    • Optical Engineering
    • Metrology

    Background:

    • Accurate form measurement of optical surfaces is crucial for high-performance optical systems.
    • Traditional interferometric methods can be complex and sensitive to environmental factors.

    Purpose of the Study:

    • To introduce a new method for optical surface form measurement.
    • To demonstrate the efficacy of a shearing interferometer combined with LED multispot illumination.
    • To validate the inverse raytracing evaluation approach.

    Main Methods:

    • Utilizing the spatial coherence function for form measurement.
    • Employing a shearing interferometer with LED multispot illumination.
    • Applying an inverse raytracing algorithm for data evaluation.
    • Investigating the convergence and stability of the optimization process.

    Main Results:

    • Successful demonstration of the measurement principle.
    • Presentation of initial measurement results using the inverse evaluation procedure.
    • Validation of the integrated measurement and evaluation system.

    Conclusions:

    • The proposed method provides a viable approach for optical surface form measurement.
    • The inverse raytracing evaluation is effective in connecting measurement data to surface form.
    • The system demonstrates stability and convergence for practical applications.