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Related Concept Videos

Relation Between the Distributed Load and Shear01:23

Relation Between the Distributed Load and Shear

1.2K
Understanding the relationship between the distributed load and shear force in structural analysis is crucial for analyzing beams subjected to various loading conditions. Consider the case of a beam experiencing a distributed load, two concentrated loads, and a couple moment.
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Shearing Stress01:18

Shearing Stress

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Shearing stress, denoted by the Greek letter tau (τ), is stress caused by forces acting transversely on an object. These forces create internal ones within the entity in the plane where the external forces are applied. The resultant of these internal forces is the shear in the section.
The average shearing stress can be calculated by dividing the shear by the area of the cross-section.
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Shearing Strain01:20

Shearing Strain

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The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...
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Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

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As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
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Shock Waves01:16

Shock Waves

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While deriving the Doppler formula for the observed frequency of a sound wave, it is assumed that the speed of sound in the medium is greater than the source's speed through it. When this condition is breached, a shock wave occurs.
When the source's speed approaches the speed of sound, constructive interference between successive wavefronts emitted by the source occurs immediately behind it. Initially, scientists believed that this constructive interference would result in such high...
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Normal and Shear Force01:14

Normal and Shear Force

4.2K
When a beam is subjected to different loads, such as weight, pressure, or other external forces, internal forces are generated within the beam. These forces can have a significant impact on the overall stability and strength of the structure. Engineers use various methods to analyze and determine the magnitude and direction of these internal forces. One common technique used to determine internal forces in beams is the method of sections. This method involves considering an imaginary point or...
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Related Experiment Video

Updated: May 5, 2026

Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography
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Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography

Published on: September 29, 2019

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Shear shocks in fragile networks.

Stephan Ulrich1, Nitin Upadhyaya, Bas van Opheusden

  • 1Instituut-Lorentz for Theoretical Physics, Leiden University, 2333 CA, Leiden, The Netherlands.

Proceedings of the National Academy of Sciences of the United States of America
|December 7, 2013
PubMed
Summary

Fragile solids exhibit a rigidity transition, losing stiffness at a critical connectivity. Shear front rheology reveals their unique linear and nonlinear responses, with energy dissipation in nonaffine fluctuations and shock waves near the transition.

Keywords:
high damping materialsisostaticityjammingnonaffine responsepolymer networks

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Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography
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Area of Science:

  • Physics
  • Materials Science
  • Rheology

Background:

  • Amorphous solids are modeled as disordered networks of point masses and springs.
  • A critical connectivity value triggers a rigidity transition, marked by vanishing shear modulus and sound speed.
  • Standard oscillatory rheology is the conventional method for studying material viscoelasticity.

Purpose of the Study:

  • Investigate the linear and nonlinear viscoelastic response of fragile amorphous solids.
  • Explore the propagation of shear fronts as an alternative to traditional rheological methods.
  • Characterize the mechanical behavior of these materials near the rigidity transition.

Main Methods:

  • Analytical and numerical investigations of shear front propagation.
  • Development of a "shear front rheology" approach.
  • Analysis of both linear and nonlinear viscoelastic regimes.

Main Results:

  • In the linear regime, shear fronts broaden diffusively, controlled by a shear viscosity diverging at the critical point.
  • Disordered networks behave as if overdamped due to energy dissipation into nonaffine fluctuations.
  • Nonlinear response generates shear shock waves, distinct from compressional waves, leading to superdiffusive broadening.

Conclusions:

  • Shear front rheology offers a novel perspective on the mechanical properties of fragile solids.
  • Energy dissipation mechanisms in disordered networks are crucial for their viscoelastic behavior.
  • Nonlinearities near the rigidity transition create unique shock wave phenomena, preventing quasi-static behavior.