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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.
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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: Feb 22, 2026

Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads
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Practical algorithm for custom-made caustic beams.

Timor Melamed, Amir Shlivinski

    Optics Letters
    |September 29, 2017
    PubMed
    Summary

    We developed a method to design light beams that follow complex paths, including curves. This algorithm enables precise control over beam trajectories for advanced optical applications.

    Area of Science:

    • Optics and Photonics
    • Beam Propagation
    • Computational Electromagnetics

    Background:

    • The Airy beam offers a unique trajectory following a convex caustic.
    • Generalizing beam control beyond simple convex paths is challenging.
    • Existing methods lack flexibility for arbitrary beam trajectories.

    Purpose of the Study:

    • To present a practical algorithm for designing aperture fields.
    • To enable light beams to propagate along predefined generic trajectories with convex and concave sections.
    • To generalize the Airy beam concept to a broader class of 'caustic beams' (CBs).

    Main Methods:

    • Employing the mechanism behind Airy beam formation.
    • Generalizing this mechanism for arbitrary beam trajectories.

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  • Utilizing 'back-tracing' rays from the trajectory to the source aperture.
  • Setting aperture amplitude for uniform beam amplitude along the trajectory.

    • Main Results:

    • A practical algorithm for designing aperture fields for complex beam trajectories.
    • Demonstration of 'caustic beams' (CBs) following generic paths.
    • Numerical examples validating the algorithm's effectiveness.
    • Achieving uniform smooth amplitude for CBs along their paths.

    Conclusions:

    • The developed algorithm provides a robust method for designing beams with complex trajectories.
    • This work extends the concept of self-healing beams to arbitrary paths.
    • The 'caustic beams' offer new possibilities in optical manipulation and delivery systems.