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Related Concept Videos

Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

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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.
The M/EI...
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Beams with Unsymmetric Loadings01:17

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Analyzing a supported beam under unsymmetrical loadings is essential in structural engineering to understand how beams respond to varied force distributions. This analysis involves calculating the deflection and identifying points where the slope of the beam is zero, which are crucial for ensuring structural stability and functionality.
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Deflection of a Beam01:19

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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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Design of Prismatic Beams for Bending01:23

Design of Prismatic Beams for Bending

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The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and...
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Different notations are used to represent the three-dimensional structure of molecules on two-dimensional surfaces. One of the most commonly used representations is the dash-wedge formula. The dashed wedges, solid wedges, and the plane lines indicate the groups situated behind the plane, coming out of the plane, and in the plane, respectively.
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Shear on the Horizontal Face of a Beam Element01:16

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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...
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Multi-helix beams generated with binary helico-conical phase patterns.

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    This summary is machine-generated.

    Researchers generated double helico-conical beams (HCBs) and multi-helix beams by binarizing modified helico-conical phase (MHCP) profiles. The number and position of these beams can be precisely controlled for optical applications.

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    Area of Science:

    • Optics and Photonics
    • Beam Shaping
    • Diffractive Optics

    Background:

    • Helico-conical beams (HCBs) are a class of optical beams with unique helical and conical properties.
    • Controlling the generation and arrangement of multiple HCBs is crucial for advanced optical applications.

    Purpose of the Study:

    • To generate and analyze double helico-conical beams (HCBs) and multi-helix beams.
    • To investigate methods for controlling the number and relative positions of these beams.
    • To explore potential applications in optical manipulation and multiplexed holography.

    Main Methods:

    • Binarizing modified helico-conical phase (MHCP) profiles to generate HCBs.
    • Utilizing a blazed grating to adjust the relative positions of double HCBs.
    • Superposing multiple binary MHCPs to create multi-helix beams.
    • Theoretical and experimental analysis of diffraction patterns.

    Main Results:

    • Successfully generated double HCBs and multi-helix beams.
    • Demonstrated arbitrary adjustment of double HCB relative positions using a blazed grating.
    • Showed that the number and position of multi-helix beams can be controlled by the number of superimposed MHCPs and the azimuth factor.
    • Analyzed diffraction patterns theoretically and experimentally.

    Conclusions:

    • The binarization of MHCP offers a flexible method for generating arrayed HCBs.
    • Precise control over beam arrangement is achievable, paving the way for advanced optical systems.
    • Potential applications include optical manipulation and multiplexed holography.