{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture08

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

This preview shows pages 1–4. Sign up to view the full content.

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

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

View Full Document
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.
Consider an elment on which there is only one component of normal 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.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 12

lecture08 - Prepared by Gkhan Karagz 26.10.2009 Lecture...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online