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Stress: General Loading Conditions

Stress: General Loading Conditions

To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes.

Hooke's Law

Hooke's Law

Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.

Temperature Dependent Deformation

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In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added together...

Generalized Hooke's Law

Generalized Hooke's Law

The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...

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

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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.

Saint-Venant's Principle

Saint-Venant's Principle

The principle of Saint-Venant postulates that the stress distribution within a structural member does not rely on the precise method of load application except in the vicinity of the load application points. Consider a scenario where loads are centrally applied on two plates. In this case, the plates move toward each other without any rotation. This movement causes the member to contract in length and expand in width and thickness. Uniform deformation across all elements and maintaining...

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Related Experiment Video

Updated: Jul 23, 2026

Blast Quantification Using Hopkinson Pressure Bars

Blast Quantification Using Hopkinson Pressure Bars

Published on: July 5, 2016

Polymorphs of Alumina Predicted by First Principles: Putting Pressure on the Ruby Pressure Scale

Thomson¹, Wentzcovitch, Bukowinski

¹K. T. Thomson, Department of Chemical Engineering and Materials Science, and Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN 55455, USA. R. M. Wentzcovitch, Department of Chemical Engineering and Materials Science, and Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN 55455, USA, and Instituto de Fisica, Universidade de Sao Paulo, CP 66318, 0 5389-970, Sao Paulo, SP, Brazil. M. S. T. Bukowinski, Department of Geology and Geophysics, University of California, Berkeley, CA 94720, USA.

Science (New York, N.Y.)

|December 13, 1996

Summary

High-pressure calculations reveal aluminum oxide (Al2O3) transforms into a new Rh2O3 (II) structure, potentially impacting ruby fluorescence pressure scales due to similar X-ray spectra.

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Area of Science:

Materials Science
Geophysics
Quantum Mechanics

Background:

Aluminum oxide (Al2O3) is a well-studied material with a known corundum structure.
High-pressure phases of materials are crucial for understanding planetary interiors and developing new technologies.
The ruby fluorescence pressure scale is a standard method for pressure measurement in high-pressure experiments.

Purpose of the Study:

To investigate the high-pressure structural phase transitions of Al2O3 using quantum mechanical calculations.
To predict the X-ray diffraction patterns of these high-pressure phases.
To assess the potential impact of these transitions on the ruby fluorescence pressure scale.

Main Methods:

Fully optimized quantum mechanical calculations were employed.
Phase transitions were simulated at high pressures (up to 223 gigapascals).
Predicted X-ray spectra were compared to known structures.

Main Results:

Al2O3 transforms to the unobserved Rh2O3 (II) structure at approximately 78 gigapascals.
A further transition to the Pbnm-perovskite structure occurs at 223 gigapascals.
The predicted X-ray spectrum of the Rh2O3 (II) structure closely resembles that of the corundum structure.

Conclusions:

The Rh2O3 (II) phase of Al2O3 may be difficult to detect using standard X-ray diffraction techniques.
This structural similarity could lead to misinterpretations in high-pressure experiments using ruby as a pressure sensor.
The thermal history of ruby chips might influence pressure measurements, necessitating careful consideration in high-pressure research.