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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...

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...

Beams with Symmetric Loadings

Beams with Symmetric Loadings

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...

Beams with Unsymmetric Loadings

Beams with Unsymmetric Loadings

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.
The first moment-area theorem determines the slope at any point on the beam. This theorem indicates that the change in slope between two points on a beam...

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...

Elastic Curve from the Load Distribution

Elastic Curve from the Load Distribution

The structural behavior of beams under distributed loads is critical for engineering analysis, which focuses on predicting how beams bend and react under such conditions. Different types of beams (e.g., cantilever, supported, or overhanging) behave differently under distributed load conditions.
For all beams, the analysis of the beam's reaction to distributed loads begins by understanding the relationship between a beam's load and the resulting shear forces and bending moments. Initially, this...

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Related Experiment Video

Updated: Mar 21, 2026

Operation of the Collaborative Composite Manufacturing CCM System

Operation of the Collaborative Composite Manufacturing CCM System

Published on: October 1, 2019

Creation operators for Cartesian and circular beams.

Anibal Siguenza-Torres, Julio C Gutiérrez-Vega

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|May 4, 2016

Summary

Fractional order creation operators are introduced to derive general Cartesian and circular beams from Gaussian beams. This method provides a unified approach to finding operators for all special cases of these beam types.

Area of Science:

Physics
Optics
Quantum Optics

Background:

The generation and manipulation of light beams with specific properties are crucial in various optical applications.
Lowest-order Gaussian beams serve as fundamental building blocks for more complex beam structures.

Purpose of the Study:

To introduce and discuss fractional order creation operators for deriving general Cartesian and circular beams.
To establish a generalized method for obtaining creation operators applicable to a wide range of beam types.

Main Methods:

Development of fractional order creation operators.
Application of these operators to a lowest-order Gaussian beam.
Derivation of general Cartesian and circular beam structures.

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Main Results:

Successful introduction of fractional order creation operators.
Demonstration of their capability to derive general Cartesian and circular beams.
Establishment of a general method applicable to all special cases.

Conclusions:

Fractional order creation operators offer a powerful and unified framework for generating complex optical beams.
The presented method simplifies the process of finding creation operators for various beam types, including Cartesian and circular beams.