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Thin-Walled Hollow Shafts

Thin-Walled Hollow Shafts

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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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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Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.

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Related Experiment Video

Updated: May 10, 2026

Measuring Material Microstructure Under Flow Using 1-2 Plane Flow-Small Angle Neutron Scattering

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Published on: February 6, 2014

Signatures of granular microstructure in dense shear flows

Mueth¹, Debregeas, Karczmar

¹The James Franck Institute and Department of Physics, University of Chicago, Illinois 60637, USA.

|August 10, 2000

Summary

Granular materials form shear bands under stress, unlike fluids. Microstructure, including particle rotation and packing density, dictates flow behavior within these bands.

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Last Updated: May 10, 2026

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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

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

Area of Science:

Physics of granular materials
Rheology of complex fluids

Background:

Granular materials exhibit unique responses to shear stress, forming localized shear bands instead of uniform deformation.
Understanding granular flow, particle rotation, and interparticle slip within shear bands is crucial for industrial, engineering, and geophysical applications.
Limited 3D data exists on granular shear band dynamics and the influence of grain microstructure on flow.

Purpose of the Study:

To investigate the three-dimensional motion within granular shear bands.
To determine the relationship between granular microstructure and shear flow characteristics.
To provide detailed local measurements of particle velocity, rotation, and packing density.

Main Methods:

Utilized a combination of magnetic resonance imaging (MRI), X-ray tomography, and high-speed video particle tracking.
Employed a 3D Couette geometry to simulate shear flow in granular materials.
Obtained local, steady-state measurements of particle dynamics and density.

Main Results:

Characterized the 3D velocity profiles within granular shear bands.
Quantified particle rotation and interparticle slip in dense granular flows.
Identified key microstructural features influencing shear band formation and velocity profiles.

Conclusions:

Granular microstructure significantly determines the macroscopic velocity profiles in shear flow.
Detailed 3D analysis reveals complex particle dynamics within shear bands.
This study enhances the understanding of granular material behavior under shear stress.