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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...
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Deformation in a Circular Shaft01:10

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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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Circular Shafts - Elastoplastic Materials01:24

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The study of solid circular shafts under stress shows that within the elastic limit, stress increases directly to the distance from the shaft's center. This relationship holds until the shaft reaches a critical point of stress, beyond which it begins to yield, marking the transition from elastic to plastic deformation. At this crucial juncture, the maximum torque the shaft can endure without permanent deformation is determined, signifying the limit of its elastic behavior.
As torque on the...
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The simplest case of a surface charge distribution is the uniformly charged disk. Calculating its electric field also helps us calculate the electric field of a large plane of charge.
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Consider the elastic torsion formula, which applies to a circular shaft with a consistent cross-section. This formula assumes that the shaft's ends are loaded with rigid plates firmly attached. However, in many cases, torques are applied to the shaft through mechanisms like flange couplings or gears, which are connected by keys inserted into keyways. This application method modifies the stress distribution near the point of torque application, causing it to deviate from the distributions...
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Residual Stresses in Circular Shafts01:10

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In materials that exhibit elastic and plastic behavior, known as elastoplastic materials, residual stresses can accumulate when these materials experience plastic deformation. This deformation arises from either high levels of shearing stress or significant strains. Residual stresses are internal stresses that persist within a material after removing the external force causing deformation. This phenomenon is demonstrated when observing the behavior of a shaft under torque; notably, the...
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Related Experiment Video

Updated: Jun 10, 2025

Analyses of Actin Dynamics, Clutch Coupling and Traction Force for Growth Cone Advance
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Truncated cones from indenting a clamped disk.

Keith A Seffen1

  • 1Advanced Structures Group, Department of Engineering, <a href="https://ror.org/013meh722">University of Cambridge</a>, Cambridge CB2 1PZ, United Kingdom.

Physical Review. E
|October 19, 2024
PubMed
Summary

Thin disks buckle into developable cones (d-Cones) when indented. Clamping the center creates truncated cones (t-Cones), whose number results from optimal shape packaging, matching experimental results.

Area of Science:

  • Solid Mechanics
  • Materials Science
  • Applied Mathematics

Background:

  • Thin disks buckle into developable cones (d-Cones) under central point force.
  • Clamping a central region of the disk alters buckling to truncated cones (t-Cones).

Purpose of the Study:

  • To analyze the kinematics of truncated cones (t-Cones) in clamped disks.
  • To determine the factors influencing the number and distribution of t-Cones.
  • To validate a geometric model against experimental observations.

Main Methods:

  • Geometric analysis of t-Cone folding and synchronous d-Cone vertex behavior.
  • Modeling the optimal 'packaging' of folded shapes in the annular space.
  • Comparison of theoretical predictions with experimental data on saturated t-Cone numbers.

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Last Updated: Jun 10, 2025

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Main Results:

  • Each t-Cone functions as a pair of synchronously folding d-Cone vertices.
  • The number and distribution of t-Cones are governed by optimal spatial packing.
  • The geometric model accurately predicts the saturated number of t-Cones.

Conclusions:

  • The study provides a geometric explanation for t-Cone formation and number in clamped indented disks.
  • Optimal packaging is the key principle determining the buckling pattern.
  • The developed methodology offers a robust framework for predicting buckling behavior.