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Related Concept Videos

Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

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In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...
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Deformation in a Circular Shaft01:10

Deformation in a Circular Shaft

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One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...
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Transmission Shafts: Problem Solving01:09

Transmission Shafts: Problem Solving

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Designing a solid shaft that transmits power from a motor to a machine tool involves a series of calculations to ensure the shaft can withstand the stresses applied by bending moments and torques. First, calculate the torque exerted on the gear, considering the power transmitted by the shaft and its rotational speed. Following this, compute the tangential forces acting on the gears, which directly relate to the torque and the gear radius.
Next, use bending moment diagrams for the shaft to...
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Torsion of Noncircular Members01:16

Torsion of Noncircular Members

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Circular shafts undergoing torsional stress maintain their cross-sectional integrity due to their axisymmetric nature. This symmetry ensures an even distribution of stress, allowing the shaft to withstand torsion without distorting. In contrast, square bars, lacking this axial symmetry, experience significant distortion across their cross-sections when subjected to torsion, with the exception of along their diagonals and at lines connecting midpoints. A detailed examination of a cubic element...
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Circular Shaft - Stresses in Linear Range01:13

Circular Shaft - Stresses in Linear Range

838
Consider a scenario where a circular shaft is subject to torque that remains within the boundaries of Hooke's Law, avoiding any permanent deformation. So, the formula for shearing strain is revisited. This formula is multiplied by the modulus of rigidity, and then Hooke's Law for the shearing stress and strain is applied. As a result, the equation for shearing stress in a shaft can be derived.
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Screw: Problem Solving01:21

Screw: Problem Solving

769
In mechanical engineering, the interaction between a threaded screw shaft and a plate gear involves analyzing the resisting torque on the plate gear that can be overpowered when a specific torsional moment is applied to the shaft. To better comprehend this concept, consider a generic situation with a threaded screw shaft with a given mean radius and lead and a plate gear with a specified mean radius. The coefficient of static friction between the screw and gear is also provided.
To evaluate the...
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Related Experiment Video

Updated: Mar 28, 2026

Directed Cellular Self-Assembly to Fabricate Cell-Derived Tissue Rings for Biomechanical Analysis and Tissue Engineering
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Directed Cellular Self-Assembly to Fabricate Cell-Derived Tissue Rings for Biomechanical Analysis and Tissue Engineering

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Threading a Ring or Tube onto a Rod: An Entropically Rare Event.

Edith M Sevick1, David R M Williams1

  • 1Research School of Chemistry and ‡Department of Applied Mathematics, Research School of Physical Sciences and Engineering, The Australian National University , Canberra ACT 0200, Australia.

Nano Letters
|December 25, 2015
PubMed
Summary

We calculated the entropy loss for threading rings and tubes onto rods. The fraction of spontaneously threaded items is very small, following power-law relationships with geometric factors.

Keywords:
Threadingnanotubesorientational entropypolymer translocationrotaxanes

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Area of Science:

  • Thermodynamics and Statistical Mechanics
  • Physical Chemistry

Background:

  • Understanding the spontaneous assembly of nanoscale objects is crucial in materials science.
  • Entropy calculations provide insights into the feasibility of self-assembly processes.

Purpose of the Study:

  • To quantify the entropy loss during the threading of circular rings or tubes onto a rod.
  • To determine the fraction of spontaneously threaded components based on geometric parameters.

Main Methods:

  • Derivation of formulas for entropy loss using a partition function.
  • Analysis of geometric parameters including rod length/radius and ring/tube dimensions.

Main Results:

  • Developed formulas to calculate entropy loss for various geometric configurations.
  • Found that the fraction of spontaneously threaded rings/tubes is consistently small.
  • Identified strong power-law dependencies between this fraction and geometric parameters.

Conclusions:

  • The spontaneous threading of rings/tubes onto rods is thermodynamically limited.
  • Geometric parameters significantly influence the likelihood of spontaneous threading.
  • The findings can inform the design of self-assembling nanomaterials.