Upload
aeroamir
View
231
Download
1
Embed Size (px)
DESCRIPTION
stress relations and equilibrium on elasticity
Citation preview
MCE 571 Theory of Elasticity
Chapter 3 Stress and EquilibriumBody and Surface Forces(b) Sectioned Axially Loaded Beam Surface Forces: T(x)S(a) Cantilever Beam Under Self-Weight LoadingBody Forces: F(x)Elasticity Theory, Applications and NumericsM.H. Sadd , University of Rhode Island
1Traction Vector
P1P2P3 p(Externally Loaded Body)FnA(Sectioned Body)Elasticity Theory, Applications and NumericsM.H. Sadd , University of Rhode Island
2Stress Tensor
Traction on an Oblique Plane
xzynTn Elasticity Theory, Applications and NumericsM.H. Sadd , University of Rhode Island
Stress Transformation
Elasticity Theory, Applications and NumericsM.H. Sadd , University of Rhode Island
4Two-Dimensional Stress Transformation
Elasticity Theory, Applications and NumericsM.H. Sadd , University of Rhode Island
5Principal Stresses & Directions
(General Coordinate System)(Principal Coordinate System)
Elasticity Theory, Applications and NumericsM.H. Sadd , University of Rhode Island
Traction Vector Components
Mohrs Circles of Stress
Admissible N and S values lie in the shaded area T nnASNElasticity Theory, Applications and NumericsM.H. Sadd , University of Rhode Island
Example 3-1 Stress Transformation
Elasticity Theory, Applications and NumericsM.H. Sadd , University of Rhode Island
Spherical, Deviatoric, Octahedral and von Mises Stresses
. . . Spherical Stress Tensor. . . Deviatoric Stress Tensor
Elasticity Theory, Applications and NumericsM.H. Sadd , University of Rhode Island
. . . Octahedral Normal and Shear Stresses
. . . von Mises StressStress Distribution Visualization Using2-D or 3-D Plots of Particular Contour LinesParticular Stress ComponentsPrincipal Stress ComponentsMaximum Shear Stressvon Mises StressIsochromatics (lines of principal stress difference = constant; same as max shear stress) Isoclinics (lines along which principal stresses have constant orientation)Isopachic lines (sum of principal stresses = constant)Isostatic lines (tangent oriented along a particular principal stress; sometimes called stress trajectories)
Elasticity Theory, Applications and NumericsM.H. Sadd , University of Rhode Island
Example Stress Contour Distribution Plots Disk Under Diametrical CompressionElasticity Theory, Applications and NumericsM.H. Sadd , University of Rhode Island
PP(a) Disk Problem
(b) Max Shear Stress Contours (Isochromatic Lines)
(c) Max Principal Stress Contours
(d) Sum of Principal Stress Contours (Isopachic Lines)
(e) von Mises Stress Contours
(f) Stress Trajectories (Isostatic Lines)Equilibrium Equations
FT nVSElasticity Theory, Applications and NumericsM.H. Sadd , University of Rhode Island
Stress & Traction Components in Cylindrical Coordinates
Equilibrium Equations
x3x1x2rzdrzrrrzzdElasticity Theory, Applications and NumericsM.H. Sadd , University of Rhode Island
Stress & Traction Components in Spherical Coordinates
Equilibrium Equations
Rx3x1x2RRRElasticity Theory, Applications and NumericsM.H. Sadd , University of Rhode Island