lecture08 - Prepared by : Gkhan Karagz 26.10.2009 Lecture...

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Prepared by : Gökhan Karagöz 26.10.2009 Lecture note-8 Generalized Hook’s Law Stres-Strain Relation Generalized Hooke's Law The generalized Hooke's Law can be used to predict the deformations caused in a given material by an arbitrary combination of stresses. The linear relationship between stress and strain applies for where: E is the Young's Modulus n is the Poisson Ratio The generalized Hooke's Law also reveals that strain can exist without stress. For example, if the member is experiencing a load in the y-direction (which in turn causes a stress in the y-direction), the Hooke's Law shows that strain in the x-direction does not equal to zero. This is because as material is being pulled outward by the y-plane, the material in the x-plane moves inward to fill in the space once occupied, just like an elastic band becomes thinner as you try to pull it apart. In this situation, the x-plane does not have any external force acting on them but they experience a change in length. Therefore, it is valid to say that strain exist without stress in the x-plane. ---------------------------------------------------------------------------------------------- http://www.engineering.com/Library/ArticlesPage/tabid/85/articleType/A
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rticleView/articleId/208/Generalized-Hookes-Law.aspx Stress strain curve for low-carbon steel. Hooke's law is only valid for the portion of the curve between the origin and the yield point(2). 1. Ultimate strength 2. Yield strength-corresponds to yield point. 3. Rupture 4. Strain hardening region 5. Necking region. A: Apparent stress (F/A0) B: True stress (F/A) - We need to connect all six components of stres to six components of strain. - Restrict to linearly elastic-small strains. - An isotropic materials whose properties are independent of orientation.
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stres acting. In addition to normal strain there is a lateral contraction ε y = ε z = - ν ε y = - ν . σ x /E There is no shear strain due to normal stres in isotropic materials. γ
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This note was uploaded on 02/28/2011 for the course AEE 361 taught by Professor Daglas during the Spring '11 term at College of E&ME, NUST.

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lecture08 - Prepared by : Gkhan Karagz 26.10.2009 Lecture...

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