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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...

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...

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 stress...

Deformation of a Beam under Transverse Loading

Deformation of a Beam under Transverse Loading

Understanding beam deflection, particularly for indeterminate beams with overhanging segments and multiple concentrated loads, is crucial for ensuring structural integrity and functionality. The process begins with constructing an accurate free-body diagram, which helps identify the forces and moments acting on the beam. This diagram is vital for visualizing how bending moments vary along the beam's length, influencing its curvature.
The insights from the bending moment diagram extend to...

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...

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Related Experiment Video

Updated: May 8, 2026

Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads

Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads

Published on: July 25, 2025

Angular self-reconstruction of petal-like beams.

Igor A Litvin¹, Liesl Burger, Andrew Forbes

¹Council for Scientific and Industrial Research, Pretoria 0001, South Africa. ILitvin@csir.co.za

|August 31, 2013

Summary

Researchers developed a simple equation to predict when Laguerre-Gaussian (LG) beam superpositions self-reconstruct after encountering obstacles. This work clarifies anomalous experimental results and predicts reconstruction dependence on obstacle parameters.

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Area of Science:

* Quantum optics and laser physics.
* Wave propagation and beam dynamics.

Background:

* The self-reconstruction of light fields, particularly superpositions of Laguerre-Gaussian (LG) beams, has been experimentally observed.
* Existing experimental results are anomalous and lack a predictive framework for the conditions under which self-reconstruction occurs.

Purpose of the Study:

* To provide a simple, predictive equation for the self-reconstruction distance of Laguerre-Gaussian (LG) beam superpositions.
* To explain the underlying physics governing the self-reconstruction phenomenon.
* To determine the conditions under which self-reconstruction is not guaranteed.

Main Methods:

* Development of a theoretical equation for predicting self-reconstruction distance.
* Numerical propagation simulations to validate the theoretical model.
* Experimental verification of the predicted self-reconstruction distances and conditions.

Main Results:

* A simple equation accurately predicts the self-reconstruction distance for LG beam superpositions.
* The self-reconstruction process is confirmed to be dependent on obstacle location and size.
* Conditions under which self-reconstruction is not guaranteed have been identified.

Conclusions:

* The developed equation provides a reliable method for predicting LG beam self-reconstruction.
* Understanding the influence of obstacle parameters is crucial for controlling light field reconstruction.
* This work resolves anomalies in previous experimental observations and offers a predictive framework for future studies.