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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...
198
Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

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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...
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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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Linear Momentum in Control Volume01:13

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Newton's second law is applied to obtain the linear momentum in a control volume in a fluid system. According to this law, the rate of change of linear momentum is equal to the sum of external forces acting on the system. When a control volume matches the fluid system at a specific moment, the forces acting on both are identical. Reynolds transport theorem helps explain this by breaking down the system's linear momentum into two components: the rate of change of linear momentum within...
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Load-frequency control

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Load-frequency control (LFC) is vital for maintaining power system stability, ensuring that frequency and power flows remain within acceptable limits during load changes. Turbine-governor control eliminates rotor accelerations and decelerations following load changes. However, a steady-state frequency error persists when the change in the turbine-governor reference setting is zero. In an interconnected power system, each area agrees to export or import a scheduled amount of power through...
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Castigliano's Theorem: Problem Solving01:14

Castigliano's Theorem: Problem Solving

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The deflection of a simply supported beam that carries a central point load can be analyzed using structural mechanics principles, particularly by applying Castigliano's theorem. This theorem relates the displacement at the load application point to the partial derivatives of the strain energy in the structure. The simply supported beam with a point load at its center has symmetric reaction forces at the supports, each bearing half of the load. The bending moment at any point along the beam...
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Related Experiment Video

Updated: Oct 15, 2025

Dynamic Lung Tumor Tracking for Stereotactic Ablative Body Radiation Therapy
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Linac reported steering error insensitive to 6 MV FFF transverse beam position deviations.

Jacob McAloney1, Simon Biggs2, Matthew Sobolewski3,4

  • 1Riverina Cancer Care Centre, Wagga Wagga, Australia. jmcaloney@riverinacancercare.com.au.

Physical and Engineering Sciences in Medicine
|October 25, 2021
PubMed
Summary

Clinically significant beam position deviations occurred with a 6 MV FFF beam, undetected by standard QA. A new method improves steering error sensitivity, ensuring accurate patient treatment delivery.

Keywords:
Beam steeringFFFRadiation field alignment

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Area of Science:

  • Medical Physics
  • Radiation Oncology
  • Quality Assurance

Background:

  • Clinically significant beam position deviations were observed during patient-specific quality assurance (QA) for a 6 MV flattened فیصد (FFF) beam on an Elekta linear accelerator.
  • Routine linear accelerator QA, including the Winston-Lutz test, and machine ion chamber data did not identify these deviations.

Purpose of the Study:

  • To investigate the cause of undetected beam position deviations.
  • To evaluate the impact of small steering errors on beam positioning.
  • To develop and test an alternative method for establishing beam steering error sensitivity.

Main Methods:

  • Investigated beam position deviations using an electronic portal imaging device (EPID).
  • Established test set-points by introducing controlled transverse steering errors.
  • Acquired water tank profiles and EPID images at each set-point.
  • Tested a method to adjust steering error sensitivity based on positional deviations.

Main Results:

  • Small steering errors (<1) resulted in positional deviations greater than 3 mm.
  • Existing vendor protocols for beam steering error may not detect clinically significant positional deviations.
  • A new method for improving steering error sensitivity was implemented.

Conclusions:

  • Current protocols for beam steering error in 6 MV FFF beams can lead to significant positional deviations without triggering interlocks or reporting substantial errors.
  • An alternative method focusing on positional deviations is necessary for accurate QA and safe patient treatment.