Chapter7TransformationsofStressandStrain

Chapter7TransformationsofStressandStrain - Chapter 7...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 7 Transformations of Stress and Strain 7.1 Introduction General State of Stress 3 normal stresses 3 shearing stresses-- xy , yz , and zx-- x , y , and z Goals: determine: 1. Principal Stresses 2. Principle Planes 3. Max. Shearing Stresses 2-D State of Stress Plane Stress condition Plane Strain condition A. Plane Stress State: B. Plane Stress State: z = 0, yz = xz = yz = xz = 0 z 0, xy z = 0, yz = xz = yz = xz = 0 z 0, xy Examples of Plane-Stress Condition: Thin-walled Vessels In-plane shear stress Out-of-plane shear stress Shear stress Max. x & y Max. xy (Principal stresses) 7.2 Transformation of Plane Stress ' ' : ( cos )cos ( cos )sin ( sin )sin ( sin )cos x xy x x y xy F A A A A A = - - - - = ' ' ' : ( cos )sin ( cos )cos ( sin )cos ( sin )sin x xy y x y y xy F A A A A A = + - - + = 2 2 2 ' cos sin sin cos x y xy x = + + 2 2 ' ' ( )sin cos (cos sin ) x y xy x y = -- +- 2 2 2 2 2 sin sin cos , cos cos sin = =- After rearrangement: (7.1) (7.2) 2 2 1 2 1 2 2 2 cos cos cos , sin +- = = Knowing 2 2 2 2 ' cos sin x y x y xy x +- = + + 2 2 2 ' ' sin cos x y xy x y - = - + 2 2 2 2 ' cos sin x y x y xy y +- =-- Eqs. (7.1) and (7.2) can be simplified as: (7.5) (7.6) ' y Can be obtained by replacing with ( + 90 o ) in Eq. (7.5) (7.7) 1. max and min occur at = 0 2. max and min are 90...
View Full Document

This note was uploaded on 12/03/2011 for the course EMA 3702 taught by Professor Wu during the Fall '11 term at FIU.

Page1 / 54

Chapter7TransformationsofStressandStrain - Chapter 7...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online