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Related Concept Videos

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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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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Shearing Stress01:19

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

Shear on the Horizontal Face of a Beam Element

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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...
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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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Mechanical non-reciprocity programmed by shear jamming in soft composite solids.

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Area of Science:

  • Soft matter physics
  • Materials science
  • Mechanical engineering

Background:

  • Mechanical non-reciprocity is traditionally achieved via structural nonlinearities in metamaterials.
  • Continuum solids with inherent non-reciprocal mechanics are underexplored for applications like wave guiding and robotics.
  • Soft composite solids offer potential for novel non-reciprocal functionalities.

Purpose of the Study:

  • To engineer non-reciprocal mechanics in soft composite solids.
  • To explore tunable, direction-dependent asymmetric mechanical responses.
  • To demonstrate programmable non-reciprocal dynamics in soft materials.

Main Methods:

  • Utilizing the shear jamming transition from granular physics.
  • Controlling the interplay between inclusion contact networks and matrix elasticity.
  • Combining responsive magnetic profiles with anisotropic characteristics of shear-jammed systems.

Main Results:

  • Achieved tunable, direction-dependent asymmetry in both shear and normal mechanical responses.
  • Demonstrated programmable non-reciprocal dynamics in static and dynamic regimes.
  • Enabled asymmetric spatiotemporal control over motion transmission in soft materials.

Conclusions:

  • Established a novel strategy for designing non-reciprocal matter in soft composite solids.
  • Bridged granular physics with soft material engineering for mechano-intelligent systems.
  • Opened new avenues for applications in wave guiding, robotics, and adaptive materials.