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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.

Components of Stress

Components of Stress

Stress analysis under multiple loading conditions is intricate, necessitating a comprehensive grasp of normal and shearing stresses. Consider a small cube at point O, subjected to stress on all six faces, visible or not. Normal stress components σx, σy, σz act perpendicularly to the x, y, and z axes. Shearing stress components τxy and τxz are exerted on faces perpendicular to these axes.
Interestingly, the hidden cube faces also experience these stresses, equal and opposite to those on the...

General State of Stress

General State of Stress

The general state of stress within a material can be accurately depicted using a stress tensor. This tensor encapsulates the internal forces distributed within a material subjected to external forces or deformations.
Specifically, consider a tetrahedral element where one face, labeled XYZ, is perpendicular to the line OA, and the remaining faces align with the coordinate axes with point O as the origin. At any point, such as point O, the stress tensor can be used to determine the stress...

Principal Stresses

Principal Stresses

The graphical depiction of normal and shearing stress equations is represented by a circle, demonstrating the interplay between these stresses under different angular conditions. The center of this circle C, located on the vertical axis, represents the average normal stress, while its radius shows the range of stress variations. At points A and B, where the circle intersects the horizontal axis, the maximum and minimum normal stresses are observed, occurring without shearing stress. These...

Transformation of Plane Stress

Transformation of Plane Stress

Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's faces...

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

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

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.

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Related Experiment Video

Updated: May 9, 2026

In Vitro Reconstitution of Self-Organizing Protein Patterns on Supported Lipid Bilayers

In Vitro Reconstitution of Self-Organizing Protein Patterns on Supported Lipid Bilayers

Published on: July 28, 2018

Self-organization in Pd/W(110): interplay between surface structure and stress.

N Stojić¹, T O Menteş, N Binggeli

¹Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, Trieste I-34151, Italy. IOM-CNR Democritos, Trieste, I-34151, Italy. nstojic@ictp.it

Journal of Physics. Condensed Matter : an Institute of Physics Journal

|August 8, 2013

Summary

Submonolayer palladium (Pd) on tungsten (W(110)) forms ordered stripes. A Pd superstructure, modeled as vacancy lines, is essential for stripe formation, driven by similar physics.

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Published on: January 22, 2014

Area of Science:

Surface science
Materials science
Condensed matter physics

Background:

Submonolayer palladium (Pd) on tungsten (W(110)) exhibits ordered linear mesoscopic stripes at high temperatures.
These stripes possess an internal Pd superstructure with nanoscale periodicity perpendicular to the stripe direction.
This superstructure appears across a broad temperature range below stripe formation.

Purpose of the Study:

Investigate the Pd superstructure on W(110) and its role in mesoscopic stripe formation.
Determine the dependence of the superstructure on temperature and coverage.
Elucidate the underlying physical mechanisms driving both superstructure and stripe formation.

Main Methods:

Combined experimental techniques: low-energy electron diffraction (LEED) and low-energy electron microscopy (LEEM).
Theoretical modeling using density-functional theory (DFT).
Analysis based on continuum elasticity theory.

Main Results:

The Pd superstructure exhibits an unusual dependence on temperature and coverage, deviating from regular surface reconstructions.
DFT modeling identifies the superstructure as periodic vacancy-line configurations.
Calculated surface stresses and anisotropies of vacancy lines, combined with elasticity theory, confirm their prerequisite role in mesoscopic stripe formation.

Conclusions:

The internal Pd superstructure, characterized by vacancy lines, is a necessary precursor for the formation of linear mesoscopic stripes on W(110).
The physical principles governing the formation of the internal superstructure are analogous to those driving the mesoscopic stripe formation.
This study provides quantitative evidence linking nanoscale structural configurations to macroscopic pattern formation in thin films.