Machine Design_slide 3

# Machine Design_slide 3 - ENGR3220MachineDesign...

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ENGR 3220 – Machine Design ENGR 3220 – Machine Design Week 2, Lecture 1 Week 2, Lecture 1 Plane Stress Analysis Plane Stress Analysis

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Plane Stress Plane stress is a two-dimensional state of stress. This 2-D state models well the state of stresses in a flat, thin plate loaded in the plane of the plate. Figure (b) shows the stresses on the x-and y-faces of a differential element. Not shown in the figure are the stresses in the opposite faces and the external forces acting on the material. Since moment equilibrium of the differential element shows that the shear stresses on the perpendicular faces are equal, the 2-D state of stresses is characterized by three independent stress components (σ x , σ y τ xy ). Note that forces perpendicular to the plane can be abbreviated. For example, σ x is an abbreviation for σ xx .
Plane Stress

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In-Plane Principal Stresses In-Plane Principal Stresses
It was demonstrated that at a given point, it is always possible to locate two orthogonal planes in which the shear stress vanishes. These planes in which the normal forces are acting are called the principal planes, while the normal stresses on these planes are the principal stresses. With a similar method, two extreme-value shear stresses are also found:

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## This note was uploaded on 04/16/2011 for the course ENGR 3220 taught by Professor Turro during the Spring '11 term at UOIT.

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Machine Design_slide 3 - ENGR3220MachineDesign...

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