Lecture Notes 2.2

Lecture Notes 2.2 - STRESS We have previously discussed how...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
1 STRESS • We have previously discussed how we can characterize the deformation of a material by the strain in the material. • What happens to the material when we strain it? Undeformed Deformed Strains are the same! But are the forces required to deform these 2 rods the same? Of course not!
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 STRESS Consider the larger rod If the rod is in static eq, and we are applying force to it, then Newton’s 3 rd law says there must be a force to balance it Make a slice through the rod Anywhere you make a slice, there is still that force balance in the new FBD These are “internal” forces We normalize these internal forces to make a geometry- independent measure called stress Normalize by cross sectional area, A F F F F F F A A F = σ
Background image of page 2
3 • If stress is “on-axis”, it is either tensile (positive) or compressive (negative…like pressure). A F = σ Tension Compression Shear A A A If shear stress, typically designate stress as τ
Background image of page 3

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

View Full DocumentRight Arrow Icon
4 Recall this example, where we determined that the block had non-zero shear in the x-y plane and non-zero tension in the y- direction We needed a more complex measure of strain (a tensor) The same can be said for stress
Background image of page 4
5 σ xx zz yy xy yx yz zx zy xz = = = y x yy yx xy xx zz zy zx yz yy yx xz xy xx τ In 3D (note tensor is symmetric). And in 2D.
Background image of page 5

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

View Full DocumentRight Arrow Icon
6 Why do we care about stress? 1. It turns out the the way materials fail most often depends on the level of stress in the material. This could be different for tensile, compressive, and/or shear stresses, and may be defined by some combination of them 2. The level of stress in the material can be related to the amount of strain. Steel Rubber F F Same x-sectional area, same force, same stress, but obviously different strains!
Background image of page 6
7 Constitutive Law • The relationship between stress and strain help define the properties of the material, which allows us to compare one material to another to make design choices, etc… (harken back to skin lab).
Background image of page 7

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

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/30/2012 for the course 125 208 taught by Professor Shreiber during the Spring '08 term at Rutgers.

Page1 / 47

Lecture Notes 2.2 - STRESS We have previously discussed how...

This preview shows document pages 1 - 8. Sign up to view the full document.

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