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Related Concept Videos

Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

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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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Prismatic Beams: Problem Solving01:15

Prismatic Beams: Problem Solving

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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...
229
Deflection of a Beam01:19

Deflection of a Beam

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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...
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Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

257
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...
257
Elastic Curve from the Load Distribution01:16

Elastic Curve from the Load Distribution

265
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.
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Shearing Stresses in a Beam: Problem Solving01:14

Shearing Stresses in a Beam: Problem Solving

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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...
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Updated: Sep 29, 2025

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Simple beam hardening correction method (2DCalBH) based on 2D linearization.

Cristobal Martinez1,2, Jeffrey A Fessler3, Manuel Desco1,2,4,5

  • 1Dept. BioingenierĂ­a e IngenierĂ­a Aeroespacial, Universidad Carlos III de Madrid, Spain.

Physics in Medicine and Biology
|March 21, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a new method to correct beam hardening artifacts in computed tomography (CT) imaging. The technique accurately restores quantitative image values without needing spectral information or parameter tuning.

Keywords:
CTartifactbeam hardeningcalibrationcuppingpolychromatic

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Area of Science:

  • Medical Imaging
  • Physics

Background:

  • Computed tomography (CT) imaging is susceptible to beam hardening artifacts due to the polychromatic nature of X-ray beams.
  • These artifacts, including cupping and dark bands, lead to inaccurate quantitative values in reconstructed images.
  • Existing correction methods often require knowledge of the X-ray spectrum or suboptimal parameter selection.

Purpose of the Study:

  • To develop and validate a novel post-processing method for correcting beam hardening artifacts in CT images.
  • To restore the quantitative accuracy of CT images without requiring X-ray spectrum information or heuristic parameter tuning.
  • To improve image quality and diagnostic reliability in heterogeneous imaging studies.

Main Methods:

  • The proposed method extends the water-linearization technique using a simple calibration phantom.
  • It characterizes X-ray beam attenuation for soft tissue and bone combinations.
  • Correction is based on bone thickness derived from a preliminary reconstruction, validated with simulations and real phantom data (PMMA and aluminum 6082).

Main Results:

  • Simulated data demonstrated artifact correction and monochromatic value recovery comparable to existing methods.
  • The proposed method significantly outperformed existing techniques on real CT data.
  • The approach successfully restored quantitative accuracy in the presence of beam hardening artifacts.

Conclusions:

  • The developed method effectively corrects beam hardening artifacts in CT imaging.
  • It restores monochromatic attenuation values without spectrum knowledge or parameter tuning.
  • This approach offers a robust and simpler solution for quantitative CT imaging.