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Beams01:30

Beams

1.9K
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...
1.9K
Deflection of a Beam01:19

Deflection of a Beam

756
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...
756
Prismatic Beams: Problem Solving01:15

Prismatic Beams: Problem Solving

481
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...
481
Principal Stresses in a Beam01:11

Principal Stresses in a Beam

758
In prismatic beams subject to arbitrary transverse loading, It is essential to analyze the interaction between shear forces and bending moments in order to understand stress distribution and ensure structural integrity. The highest normal or bending stress occurs at the outer fibers of the beam, decreasing linearly to zero at the neutral axis. In contrast, shear stress peaks at the neutral axis and diminishes toward the outer surfaces.
Analyzing principal stresses is crucial, especially in...
758
Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

432
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...
432
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

450
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...
450

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Related Experiment Video

Updated: Feb 13, 2026

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

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Double wedge prism based beam deflector for precise laser beam steering.

Krzysztof Tyszka1, Marek Dobosz1, Tomasz Bilaszewski1

  • 1Institute of Metrology and Biomedical Engineering, Warsaw University of Technology, Św. A. Boboli 8, 02-525 Warsaw, Poland.

The Review of Scientific Instruments
|March 3, 2018
PubMed
Summary

We developed a novel double wedge-prism laser beam deflector for enhanced stability in interferometric measurements. This system offers precise, low-noise beam steering, improving active laser stabilization.

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Last Updated: Feb 13, 2026

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Area of Science:

  • Optics and Photonics
  • Precision Engineering

Background:

  • Interferometric measurements demand high laser beam pointing stability.
  • Existing beam deflection systems often face limitations in stability and noise reduction.

Purpose of the Study:

  • To design and validate a novel laser beam deflector for active laser beam stabilization systems.
  • To achieve high-resolution, linear beam steering with minimal noise influence.

Main Methods:

  • Design of a double wedge-prism system with a piezo-driven tilting platform.
  • Theoretical analysis for wedge-prism selection and performance prediction.
  • Experimental validation of the deflector's steering range, resolution, and noise characteristics.

Main Results:

  • Achieved linear beam steering with sub-microradian resolution over a 100-microradian range.
  • Demonstrated significantly reduced noise influence compared to mirror-based deflectors (deflection ratio < 0.1).
  • Experimental results align with theoretical predictions, confirming system efficacy.

Conclusions:

  • The presented double wedge-prism system effectively enhances laser beam pointing stability.
  • This design offers a superior alternative for active laser stabilization in precision measurements.
  • The theoretical framework provides guidance for optimizing wedge-prism selection.