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Related Concept Videos

Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

676
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...
676
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 creating...
881
Singularity Functions for Shear01:26

Singularity Functions for Shear

547
In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the shear...
547
Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

553
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...
553
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

537
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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Deflection of a Beam01:19

Deflection of a Beam

973
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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Related Experiment Video

Updated: May 6, 2026

Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces
09:33

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Optimized shear wave generation using hybrid beamforming methods.

Alireza Nabavizadeh1, James F Greenleaf, Mostafa Fatemi

  • 1Biomedical Informatics and Computational Biology, University of Minnesota-Rochester, Rochester, Minnesota, USA; Department of Physiology and Biomedical Engineering, Mayo Clinic College of Medicine, Rochester, Minnesota, USA.

Ultrasound in Medicine & Biology
|October 22, 2013
PubMed
Summary
This summary is machine-generated.

Hybrid beamforming improves elasticity imaging by combining spherical and axicon focusing. This novel approach enhances the depth of field for accurate shear wave speed measurements in soft tissues.

Keywords:
AxiconDepth-of-fieldHybrid beamformingShear waveShear wave speed

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Area of Science:

  • Medical Imaging
  • Biomedical Engineering
  • Acoustics

Background:

  • Elasticity imaging aids disease diagnosis by measuring tissue elasticity.
  • Shear wave-based ultrasound methods are crucial for soft tissue elasticity measurements.
  • Efficient shear wave generation is vital for the widespread adoption of elasticity imaging.

Purpose of the Study:

  • To develop and evaluate a hybrid beamforming technique for enhanced elasticity imaging.
  • To increase the depth of field (DOF) for shear wave generation and measurement.
  • To improve the accuracy and consistency of shear wave speed measurements in soft tissues.

Main Methods:

  • A linear aperture design combining spherical and axicon focusing was developed.
  • Angular spectrum simulations were used for beam optimization and parametric studies.
  • Experimental validation was performed using two phantoms to assess shear wave speed accuracy and DOF.

Main Results:

  • Hybrid beamforming demonstrated an increased DOF compared to conventional spherical focusing.
  • Accurate shear wave speed measurements were achievable over the extended DOF.
  • The method showed effectiveness across various aperture sizes and focal depths.

Conclusions:

  • Hybrid beamforming offers a significant improvement in DOF for elasticity imaging.
  • This technique enables more reliable and consistent shear wave speed measurements in soft tissues.
  • The findings support the potential for wider clinical application of shear wave-based elasticity imaging.