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Related Concept Videos

Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

385
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...
385
Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

374
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...
374
Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

493
To understand shear on the flat side of a prismatic beam element, consider the vertical and horizontal shearing forces, and the normal forces, acting on the element. The element's upper (U) and lower (L) sections, which are divided by the beam's neutral axis, are examined. The equilibrium of these forces is determined by applying the equilibrium equation, which helps identify the horizontal shearing force. This force is directly related to the bending moments and the cross-section's...
493
Deflection of a Beam01:19

Deflection of a Beam

653
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...
653
Shearing Stresses in a Beam: Problem Solving01:14

Shearing Stresses in a Beam: Problem Solving

592
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 creating...
592
Prismatic Beams: Problem Solving01:15

Prismatic Beams: Problem Solving

418
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...
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Related Experiment Video

Updated: Jan 10, 2026

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
10:39

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Quantitative evaluation of a beam-matching procedure using one-dimensional gamma analysis.

Jan Hrbacek1, Tom Depuydt, An Nulens

  • 1Department of Oncology and Experimental Radiation Oncology, University of Leuven, Belgium.

Medical Physics
|September 8, 2007
PubMed
Summary

This study quantitatively evaluated Varian Medical Systems' beam matching, finding good agreement in 70% of profiles using a novel 1D gamma analysis. Measurement errors limit perfect beam interchangeability despite meeting vendor criteria.

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Area of Science:

  • Medical Physics
  • Radiation Oncology

Background:

  • Accurate beam matching is crucial for radiation therapy consistency.
  • Varian Medical Systems' beam matching procedures require quantitative evaluation.

Purpose of the Study:

  • To quantitatively evaluate the Varian Medical Systems beam matching procedure.
  • To assess the level of agreement between matched beams using a customized 1D gamma analysis.

Main Methods:

  • Developed a customized 1D gamma analysis with local fitting to minimize noise and discreteness effects.
  • Utilized criteria of 1 mm distance-to-agreement and 1% dose difference.
  • Performed relative point and profile measurements on Varian Clinac 2100C/D photon and electron beams.

Main Results:

  • 70% of matched beam profiles completely passed the defined agreement criteria (1 mm, 1%).
  • The novel 1D gamma analysis showed good agreement for most matched beams.
  • Measurement errors were identified as a limiting factor for the remaining 30% of profiles.

Conclusions:

  • The evaluated beam matching quality allows treating beams as identical and using reference data for new units.
  • Vendor acceptance criteria may be met without ensuring full beam interchangeability.
  • A customized 1D gamma analysis provides a robust evaluation of beam matching accuracy.