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Circular Shaft - Stresses in Linear Range

Circular Shaft - Stresses in Linear Range

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.

Deformation in a Circular Shaft

Deformation in a Circular Shaft

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...

Shearing Strain

Shearing Strain

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...

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...

Rotational Motion about a Fixed Axis

Rotational Motion about a Fixed Axis

A rigid body's rotation around a fixed axis makes every point within it trace a circular path around a specific line or point. The term given to this type of spinning is defined by the angular position, symbolized by the angle θ. This angle is gauged from a static reference line to the revolving object. From this angular position, any variation is referred to as angular displacement, denoted by dθ. The extent of this displacement can be calculated in degrees, radians, or revolutions, where one...

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 first...

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Related Experiment Video

Updated: Jun 17, 2026

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

Rotational-shearing irnterferometry.

M V Murty¹, E C Hagerott

¹Institute of Optics, University of Rochester, Rochester, New York, USA.

|January 6, 2010

Summary

This summary is machine-generated.

This study reviews rotational-shearing interferometry and presents a novel Jamin-based interferometer. The research details interference patterns from tested optics and analyzes source size effects on coherence.

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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

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Area of Science:

Optics and Photonics
Interferometry

Background:

Lateral- and radial-shearing interferometry are established techniques.
Rotational-shearing interferometry offers unique capabilities for optical testing.

Purpose of the Study:

To review the theory and applications of rotational-shearing interferometry.
To introduce a novel Jamin-based rotational-shearing interferometer.
To investigate the impact of source size on interference pattern coherence.

Main Methods:

Theoretical analysis of rotational-shearing interferometry.
Construction of a Jamin-based rotational-shearing interferometer.
Experimental testing of optical components (lenses, mirrors) using the interferometer.
Analysis of interference patterns and coherence effects.

Main Results:

The Jamin-based interferometer was successfully built and operated.
Interference patterns for lenses and a lightweight mirror were obtained and analyzed.
The effect of source size on the degree of coherence was investigated.

Conclusions:

Rotational-shearing interferometry is a valuable technique for optical analysis.
The developed Jamin-based interferometer provides a practical tool for optical testing.
Source characteristics significantly influence the coherence of interference patterns.