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Related Concept Videos

Distribution of Stresses in a Narrow Rectangular Beam01:11

Distribution of Stresses in a Narrow Rectangular Beam

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In studying beam stress distribution, examining an elemental section is essential. To determine the average shearing stress on this face, the calculated shear is divided by the surface area. Importantly, shearing stresses on the beam's transverse and horizontal planes mirror each other, indicating a consistent stress distribution along the upper region of the beam. Notably, shearing stresses are absent at the beam's upper and lower surfaces due to the absence of applied forces in these...
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Beams01:30

Beams

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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...
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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.
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Proton (¹H) NMR: Chemical Shift01:07

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Organic molecules primarily contain carbon and hydrogen atoms. While all the hydrogen isotopes are NMR-active, protium or hydrogen-1 is the most abundant. It has a significant energy separation between its nuclear spin states due to its large gyromagnetic ratio. As per Boltzmann's distribution, an increase in the energy separation implies a greater excess population of nuclei available for excitation, resulting in a strong NMR absorption signal.
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Prismatic Beams: Problem Solving01:15

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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.
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Principal Stresses in a Beam01:11

Principal Stresses in a Beam

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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.
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Related Experiment Video

Updated: Feb 12, 2026

Functional Characterization of Na+/H+ Exchangers of Intracellular Compartments Using Proton-killing Selection to Express Them at the Plasma Membrane
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Using stable distributions to characterize proton pencil beams.

Frank Van den Heuvel1,2, Ben George1, Niek Schreuder3

  • 1CRUK/MRC Oxford Institute for Radiation Oncology, University of Oxford, Oxford, UK.

Medical Physics
|March 24, 2018
PubMed
Summary

Stable distributions accurately quantify proton pencil beam behavior in media. This method simplifies data needs, allowing interpolation for unmeasured energies and describing asymmetric profiles.

Keywords:
dosimetrylateral scattermodelingprotonprotons

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Area of Science:

  • Medical Physics
  • Radiation Oncology
  • Computational Physics

Background:

  • Proton therapy offers precise dose delivery.
  • Accurate modeling of proton beam transport is crucial for treatment planning.
  • Current methods may require extensive commissioning data.

Purpose of the Study:

  • To introduce and evaluate stable distributions for quantifying proton pencil beam behavior.
  • To develop a robust methodology for modeling proton beam propagation in a medium.
  • To assess the efficacy of stable distributions compared to existing methods.

Main Methods:

  • Monte Carlo simulations (FLUKA) replicated clinical proton pencil beams.
  • Stable distribution methodology characterized beam lateral spread and energy deposition.
  • Parameters (α, γ, β) described beam profiles and their depth variation.

Main Results:

  • Stable distributions showed good quantitative fit, comparable to double Gaussian models, except at highest energies.
  • Meta-parameterization enabled interpolation of unmeasured beam data from limited commissioning.
  • The method successfully described symmetric and asymmetric beam profiles.

Conclusions:

  • Stable distributions are well-suited for describing proton pencil beam propagation.
  • This methodology provides a powerful tool for quantifying beam behavior in various media.
  • The approach can potentially reduce the commissioning effort for proton therapy facilities.