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Related Concept Videos

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...
381
Principal Stresses in a Beam01:11

Principal Stresses in a Beam

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In prismatic beams subject to arbitrary transverse loading, It is essential to analyze the interaction between shear forces and bending moments in order to understand stress distribution and ensure structural integrity. The highest normal or bending stress occurs at the outer fibers of the beam, decreasing linearly to zero at the neutral axis. In contrast, shear stress peaks at the neutral axis and diminishes toward the outer surfaces.
Analyzing principal stresses is crucial, especially in...
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Distribution of Stresses in a Narrow Rectangular Beam01:11

Distribution of Stresses in a Narrow Rectangular Beam

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In studying beam stress distribution, examining an elemental section is essential. To determine the average shearing stress on this face, the calculated shear is divided by the surface area. Importantly, shearing stresses on the beam's transverse and horizontal planes mirror each other, indicating a consistent stress distribution along the upper region of the beam. Notably, shearing stresses are absent at the beam's upper and lower surfaces due to the absence of applied forces in these...
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Residual Stresses in Bending01:18

Residual Stresses in Bending

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In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...
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Elastic Curve from the Load Distribution01:16

Elastic Curve from the Load Distribution

329
The structural behavior of beams under distributed loads is critical for engineering analysis, which focuses on predicting how beams bend and react under such conditions. Different types of beams (e.g., cantilever, supported, or overhanging) behave differently under distributed load conditions.
For all beams, the analysis of the beam's reaction to distributed loads begins by understanding the relationship between a beam's load and the resulting shear forces and bending moments. Initially, this...
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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

388
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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Dynamics of Stress-Driven Two-Phase Elastic Beams.

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  • 1Department of Structures for Engineering and Architecture, University of Naples Federico II, Via Claudio 21, 80125 Naples, Italy.

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Summary

This study introduces a nonlocal continuum mechanics model to analyze micro- and nano-beams, offering a computationally efficient alternative to atomistic methods for designing micro- and nano-electro-mechanical systems (M/NEMS). The model accurately predicts beam dynamics, aiding in M/NEMS optimization.

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Area of Science:

  • Solid Mechanics
  • Continuum Mechanics
  • Nanotechnology

Background:

  • Investigating the dynamic behavior of micro- and nano-beams is crucial for advanced applications.
  • Atomistic methods for nanoscale simulations are computationally intensive.
  • Continuum mechanics offers a more computationally feasible approach.

Purpose of the Study:

  • To develop and validate a nonlocal continuum mechanics model for micro- and nano-beam dynamics.
  • To incorporate size effects into the mechanical analysis of slender beams.
  • To provide a computationally convenient method for M/NEMS design.

Main Methods:

  • Formulating nonlocal equations of motion for slender beams.
  • Integrating these equations using an analytical approach.
  • Modeling size effects via an integral mixture of local and nonlocal phases.

Main Results:

  • The nonlocal model provides well-posed structural problems.
  • Analytical solutions were obtained for beam dynamics.
  • Validation against the classical strain gradient model shows good agreement in natural frequencies.

Conclusions:

  • The proposed nonlocal continuum mechanics approach is effective for analyzing micro- and nano-beam dynamics.
  • This methodology facilitates the design and optimization of micro- and nano-electro-mechanical systems (M/NEMS).
  • The model offers a computationally advantageous alternative to atomistic strategies.