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Related Concept Videos

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

734
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...
734
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

751
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...
751
Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

422
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...
422
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

443
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...
443

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Single-Digit Nanometer Electron-Beam Lithography with an Aberration-Corrected Scanning Transmission Electron Microscope
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Beam Hardening Correction Using Cone Beam Consistency Conditions.

Shiras Abdurahman, Robert Frysch, Richard Bismark

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    This study introduces a novel method to reduce beam hardening artifacts in CT scans. The technique uses cone beam consistency conditions to correct artifacts without needing prior calibration or spectral information.

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    Area of Science:

    • Medical Imaging
    • Image Reconstruction
    • Computational Imaging

    Background:

    • Polychromatic X-ray spectra and energy-dependent material attenuation cause beam hardening artifacts in CT.
    • These artifacts manifest as cupping and streak artifacts, degrading image quality.
    • Current methods rely on projection linearization using polynomial models, often requiring calibration or prior spectral data.

    Purpose of the Study:

    • To present a novel method for correcting beam hardening artifacts in CT.
    • To address the limitations of existing methods that require calibration or prior information.
    • To improve the accuracy and robustness of CT image reconstruction.

    Main Methods:

    • Enforcing cone beam consistency conditions on projection data.
    • Utilizing Grangeat's fundamental relation between cone beam data and the 3-D Radon transform.
    • Iteratively estimating optimal polynomial coefficients by minimizing projection pair inconsistency.

    Main Results:

    • Demonstrated visible reduction of beam hardening artifacts in both simulated and real CT datasets.
    • Showcased the algorithm's robustness against physical measurement and geometrical errors.
    • Validated the method's effectiveness without requiring calibration or prior spectral information.

    Conclusions:

    • The proposed method effectively corrects beam hardening artifacts in CT.
    • It offers a calibration-free and information-independent approach for artifact reduction.
    • Applicable across clinical, pre-clinical, and industrial CT systems for enhanced image quality.