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Deflection of a Beam

Deflection of a Beam

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.
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...

Design of Prismatic Beams for Bending

Design of Prismatic Beams for Bending

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...

Bending of Curved Members - Neutral Surface

Bending of Curved Members - Neutral Surface

In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
Consider the curved member described in the previous lesson. According to Hooke's law, which relates stress to strain within the...

Singularity Functions for Bending Moment

Singularity Functions for Bending Moment

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 using a...

Prismatic Beams: Problem Solving

Prismatic Beams: Problem Solving

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.
The design begins with analyzing the beam as a free body to identify moments and force balances, thereby determining support reactions. Next, the...

Beams

Beams

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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Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

Published on: June 24, 2016

Curved singular beams for three-dimensional particle manipulation.

Juanying Zhao¹, Ioannis D Chremmos², Daohong Song³

¹1] The MOE Key Laboratory of Weak-Light Nonlinear Photonics, and TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China [2] CREOL/College of Optics, University of Central Florida, Orlando, Florida 32816 [3] Department of Physics and Astronomy, San Francisco State University, San Francisco, CA 94132 [4] Science and Technology on Solid-State Laser Laboratory, North China Institute of Electronics Optics, Beijing 100015, China.

Scientific Reports

|July 14, 2015

Summary

Researchers created novel singular beams that resist diffraction and follow curved paths. These unique light beams maintain their structure and angular momentum, enabling new applications in optical manipulation and beyond.

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Area of Science:

Physics
Optics
Photonics

Background:

Singular beams carrying angular momentum have diverse applications.
Conventional singular beams propagate linearly and diffract or break up in nonlinear media.

Purpose of the Study:

To design and demonstrate diffraction-resisting singular beams capable of following arbitrary trajectories.
To investigate the properties and applications of these novel curved beams.

Main Methods:

Design of novel optical beams with diffraction-resisting properties.
Demonstration of beams propagating along arbitrary curved trajectories.
Observation of microparticle manipulation using these shaped beams.

Main Results:

Successfully designed and demonstrated diffraction-resisting singular beams.
These beams maintain their central dark core and angular momentum along curved paths.
Observed three-dimensional spiraling of microparticles driven by these dynamical beams.

Conclusions:

Developed a new class of shaped light beams with unprecedented trajectory control.
These beams combine features of optical vortex, Bessel, and Airy beams.
Potential for significant advancements in optical manipulation, microscopy, and communication.