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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 designer...

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 stress...

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...

Shear on the Horizontal Face of a Beam Element

Shear on the Horizontal Face of a Beam Element

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 first...

Distribution of Stresses in a Narrow Rectangular Beam

Distribution of Stresses in a Narrow Rectangular Beam

In studying beam stress distribution, examining an elemental section is essential. To determine the average shearing stress on this face, the calculated shear is divided by the surface area. Importantly, shearing stresses on the beam's transverse and horizontal planes mirror each other, indicating a consistent stress distribution along the upper region of the beam. Notably, shearing stresses are absent at the beam's upper and lower surfaces due to the absence of applied forces in these areas.

Shearing Stresses in a Beam: Problem Solving

Shearing Stresses in a Beam: Problem Solving

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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Updated: Jul 3, 2026

Investigating the Potential of Singly Curved Thin Piezoelectric Transducers for Energy Harvesting and Structural Health Monitoring

Investigating the Potential of Singly Curved Thin Piezoelectric Transducers for Energy Harvesting and Structural Health Monitoring

Published on: November 14, 2025

Hollow circular Pearcey beam.

Xingyu Chen, Gefei Zhang, Zijing Zhang

|July 2, 2026

Summary

This summary is machine-generated.

Researchers developed a novel hollow circular Pearcey (HCP) beam for enhanced light focusing. This new beam achieves superior peak intensity contrast, outperforming existing methods for applications like optical manipulation.

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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

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Last Updated: Jul 3, 2026

Investigating the Potential of Singly Curved Thin Piezoelectric Transducers for Energy Harvesting and Structural Health Monitoring

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Published on: November 14, 2025

Active Probe Atomic Force Microscopy with Quattro-Parallel Cantilever Arrays for High-Throughput Large-Scale Sample Inspection

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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Area of Science:

Optics and Photonics
Laser Physics
Nanotechnology

Background:

Abruptly autofocusing (AAF) beams concentrate energy instantaneously, enabling applications in optical manipulation, micro/nano-fabrication, and super-resolution imaging.
Enhancing the focusing performance of light beams is crucial but challenging.

Purpose of the Study:

To introduce a novel hollow circular Pearcey (HCP) beam.
To enhance the focusing performance of light beams by distributing optical fields and concentrating energy precisely.

Main Methods:

Theoretical demonstration of the hollow circular Pearcey (HCP) beam.
Analysis of the beam's focusing properties and intensity contrast.

Main Results:

The HCP beam distributes the optical field over an expanded area.
The HCP beam concentrates energy precisely at a predetermined position.
Achieved a peak intensity contrast of up to 10⁴, exceeding circular Airy beams by two orders of magnitude.

Conclusions:

The novel HCP beam offers superior focusing capabilities compared to existing beams.
This enhanced focusing performance presents a promising approach for bio-compatible optical manipulation.