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Beams

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Beams are integral components of structural engineering and construction, designed to support loads applied at various points along their length. These long, straight members can be classified based on geometry, cross-section, support type, and equilibrium condition.
Based on geometry, beams can be straight, tapered, or curved. Straight beams are the most common type and have a constant cross-section throughout their length. Tapered beams, on the other hand, have a varying cross-section along...
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As electron microscopes become more complex and widely used in research labs, it becomes more of a necessity to introduce their capabilities. Focused ion beam (FIB) is an instrument that can be employed in order to fabricate, trim, analyze and characterize materials on mico- and nano-scales in a wide variety of fields from nano-electronics to medicine. FIB...
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Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
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Prismatic Beams: Problem Solving01:15

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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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Principal Stresses in a Beam01:11

Principal Stresses in a Beam

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In prismatic beams subject to arbitrary transverse loading, It is essential to analyze the interaction between shear forces and bending moments in order to understand stress distribution and ensure structural integrity. The highest normal or bending stress occurs at the outer fibers of the beam, decreasing linearly to zero at the neutral axis. In contrast, shear stress peaks at the neutral axis and diminishes toward the outer surfaces.
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Beams with Symmetric Loadings01:15

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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.
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Related Experiment Video

Updated: Jan 19, 2026

Focused Ion Beams FIB-SEM: Milling and Imaging
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Nonparaxial structured vectorial abruptly autofocusing beam: erratum.

Shuhe Zhang, Jinhua Zhou, Min-Cheng Zhong

    Optics Letters
    |September 14, 2019
    PubMed
    Summary

    This erratum corrects a mathematical function in a previously published paper. The correction ensures accuracy in optical physics research and future scientific applications.

    Area of Science:

    • Optics
    • Mathematical Physics

    Background:

    • A previous publication in Optics Letters contained a mathematical error.
    • Accurate mathematical formulations are critical for scientific reproducibility.

    Purpose of the Study:

    • To correct the function z(θ) in equation (7).
    • To ensure the accuracy of the published optical research.

    Main Methods:

    • Identification of the error in the original equation.
    • Correction of the mathematical function z(θ).

    Main Results:

    • The function z(θ) in equation (7) has been corrected.
    • The corrected equation is now accurate for use in optical calculations.

    Conclusions:

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    • The erratum rectifies a specific mathematical error.
    • This ensures the integrity and reliability of the original research findings.