EAS209 L08_Generalized Hookes Law-spring 11

# EAS209 - EAS 209-Spring 2011 Instructors Christine Human EAS 209-Spring 2011 Instructors Christine Human Lecture 8 Generalized Hookes Law To date

This preview shows pages 1–3. Sign up to view the full content.

EAS 209-Spring 2011 Instructors: Christine Human 1/18/2011 1 08-Gen. Hooke’s Law Lecture 8 Generalized Hooke’s Law To date we have looked at the deformation caused by a uniaxial load, and learned that the axial (normal) stress is related to the normal strain through Hooke’s Law E Today’s Objectives: To look at a more general state of loading Poisson’s ratio ( ) Bulk Modulus, k Shear Modulus, G o Shear Strain Generalized Hooke’s Law Today’s Homework EAS 209-Spring 2011 Instructors: Christine Human 1/18/2011 2 08-Gen. Hooke’s Law Poisson’s Ratio ( ) Consider a homogeneous, isotropic, prismatic bar with a uniaxial centric load. Stresses 0 z y x A P Strains 0 , z y x x E Elongation in axial direction is accompanied by shortening in the transverse direction. Poisson’s Ratio is defined as (minus) the ratio of the lateral strain to the axial strain lateral strain () axial strain y z xx nu   ν is constant for a given material and is always positive since the axial and lateral strains have opposite signs.

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

View Full Document
EAS 209-Spring 2011 Instructors: Christine Human 1/18/2011 3 08-Gen. Hooke’s Law Using Hooke’s Law E x x Therefore E x z y  Typical Values For most metals ν =0.25 to 0.35 For concrete ν =0.1 to 0.2 Range of possible values 5 . 0 0 The lower limit is obvious – a negative v would imply that if we stretch a cylinder, the diameter would increase. The upper limit is explained later. No change in lateral imension Constant volume EAS 209-Spring 2011 Instructors: Christine Human 1/18/2011 4 08-Gen. Hooke’s Law Multiaxial Loading (Triaxial Loading) For triaxial loading σ x , σ y and σ z are all non-zero. E E E E E E E E E z y x z z y x y z y x x Does the volume of the material change?
This is the end of the preview. Sign up to access the rest of the document.

## This document was uploaded on 04/08/2011.

### Page1 / 8

EAS209 - EAS 209-Spring 2011 Instructors Christine Human EAS 209-Spring 2011 Instructors Christine Human Lecture 8 Generalized Hookes Law To date

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online