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Related Concept Videos

Unsymmetric Bending - Angle of Neutral Axis01:15

Unsymmetric Bending - Angle of Neutral Axis

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Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal...
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Unsymmetric Bending01:18

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Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The...
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Design of Prismatic Beams for Bending01:23

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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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Bending01:10

Bending

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Pure bending is a fundamental concept in structural mechanics, essential for understanding how materials deform under symmetrical loads without direct forces. Pure bending occurs when prismatic members, such as beams, are subjected to equal and opposite moments that induce bending. The phenomenon is crucial as it allows for predicting stress distributions without the influence of axial or shear forces.
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Angle of Twist - Elastic Range01:13

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Consider a cylindrical shaft with a length denoted by L and a consistent cross-sectional radius referred to as r. This shaft undergoes a torque at the free end. The highest shearing strain within the shaft is directly proportional to the twist angle and the radial distance from the shaft axis. When the shaft behaves elastically, this shearing strain can be articulated using variables such as the applied torque, radial distance, the polar moment of inertia, and the modulus of rigidity. By...
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Singularity Functions for Bending Moment01:18

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Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented...
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Ultra-compact multimode waveguide bends with arbitrary bending angles.

Yang Lan, Siwei Liu, Chuang Cheng

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    Researchers developed ultra-compact multimode waveguide bends (MWBs) with arbitrary angles, overcoming the 90° limitation. These novel bends enable more flexible and denser on-chip mode-division multiplexing (MDM) systems.

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    Area of Science:

    • Photonics
    • Integrated Optics
    • Nanotechnology

    Background:

    • On-chip mode-division multiplexing (MDM) requires compact waveguide routing for higher integration and flexible layouts.
    • Existing multimode waveguide bends (MWBs) are limited to 90°, hindering complex on-chip designs.

    Purpose of the Study:

    • To propose and demonstrate ultra-compact multimode waveguide bends (MWBs) with arbitrary bending angles.
    • To enhance design flexibility and integration density in on-chip MDM systems.

    Main Methods:

    • Designed and experimentally demonstrated MWBs with bending angles of 15°, 30°, 45°, and 60° on a silicon-on-insulator (SOI) platform.
    • Employed dual Bezier contours for trajectory optimization of MWBs.
    • Supported the first three transverse electric (TE) modes.

    Main Results:

    • Achieved ultra-compact MWBs with footprints as small as 7.5 × 5.1 µm².
    • Demonstrated insertion losses below 0.417 dB and inter-mode crosstalks below -16.6 dB.
    • Operated across a wide wavelength range of 1500-1600 nm for all three TE modes.

    Conclusions:

    • The proposed arbitrary-angle MWBs significantly advance on-chip MDM capabilities.
    • These MWBs serve as versatile building blocks for complex waveguide layouts and S-bends.
    • Paved the way for ultra-compact and highly integrated on-chip MDM systems.