S'identifier

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 to those on its original perpendicular faces.

The equilibrium equations, formulated by considering only the forces on faces perpendicular to the principal axes (excluding any forces on the triangular faces due to rotation), enable the derivation of new stress components. The normal and shearing stresses are re-expressed in terms of the original stresses.

Equation 1

A new expression for normal stress on the rotated vertical axis is obtained by replacing the rotation angle in a previous expression with a new one.

Equation 2

A notable outcome of this analysis is that the sum of normal stresses does not change regardless of the orientation of the cubic element. This invariance highlights the material's isotropic response to external stresses and is crucial for predicting material behavior under different loading conditions. Understanding how stress components transform with element orientation is vital for predicting material failure modes and designing materials and structures that are more resilient to applied loads.

Tags

Stress TransformationPlane StressStress ComponentsRotation AngleNormal StressShearing StressesEquilibrium EquationsIsotropic ResponseMaterial BehaviorLoading ConditionsMaterial Failure ModesResilient Structures

Du chapitre 23:

article

Now Playing

23.1 : Transformation of Plane Stress

Transformations of Stress and Strain

154 Vues

article

23.2 : Principal Stresses

Transformations of Stress and Strain

145 Vues

article

23.3 : Principal Stresses: Problem Solving

Transformations of Stress and Strain

141 Vues

article

23.4 : Mohr's Circle for Plane Stress

Transformations of Stress and Strain

166 Vues

article

23.5 : General State of Stress

Transformations of Stress and Strain

148 Vues

article

23.6 : Yield Criteria for Ductile Materials under Plane Stress

Transformations of Stress and Strain

121 Vues

article

23.7 : Transformation of Plane Strain

Transformations of Stress and Strain

134 Vues

article

23.8 : Mohr's Circle for Plane Strain

Transformations of Stress and Strain

354 Vues

article

23.9 : Three-Dimensional Analysis of Strain

Transformations of Stress and Strain

160 Vues

article

23.10 : Measurements of Strain

Transformations of Stress and Strain

107 Vues

JoVE Logo

Confidentialité

Conditions d'utilisation

Politiques

Recherche

Enseignement

À PROPOS DE JoVE

Copyright © 2025 MyJoVE Corporation. Tous droits réservés.