Chapter11EnergyMethods

Chapter11EnergyMethods - Chapter 11 Energy Method --...

Info iconThis preview shows pages 1–14. 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

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 11 Energy Method -- Utilize the Energy Method to solve engineering mechanics problems.-- Set aside the Equations of quilibrium 1. Introduction The relations between forces and deformation : Fundamental concept of We will learn: Strain Ch 2 Strain Energy Ch 11 Stress -- Ch 1 1. Modulus of Toughness 2. Modulus of resilience 3. Castigliano Theorem 11.2 Strain Energy (11.1) dU Pdx = 1 x U Pdx = 1 energy x Strain U Pdx = = (11.2) If the material response is elastic: (11.3) P kx = 1 2 1 1 2 x U kxdx kx = = 1 1 1 2 U P x = 11.3 Strain-Energy Density (11.4) 1 x U P dx V A L = 1 x x U d V = 1 energy density x x Strain u d = = Modulus of Toughness = Toughness = area under the - curve. Modulus of Resilience: (11.5) x x E = 1 2 1 2 x x E u E d = = 2 1 2 u E = 2 2 Y Y u E = (11.6) (11.7) (11.8) 11.4 Elastic strain Energy for Normal Stresses (11.9) lim V U u V = dU u dV = 1 x x u d = 2 2 1 1 1 2 2 2 x x x x u E E = = = (11.9) x x E = 2 2 1 1 1 2 2 2 x x x x u E E = = = 2 2 x U dV E = 2 2 2 P U dV EA = (11.12) (11.11) (11.13) 2 2 2 P U dV EA = 2 2 L P U dx AE = dV Adx = 2 2 P L U AE = 11.5 Elastic Strain Energy for Shearing Stresses (11.18) xy xy xy u d = 2 2 1 1 2 2 2 xy xy xy xy u G G = = = dU u or U udV dV = = 2 2 xy U dV G = (11.19) (11.20) (11.21) Strain Energy in Torsion (11.22) 2 2 2 2 2 2 xy T U dV dV G GJ = = dV dAdx = 2 2 2 2 ( ) L T U dA dx GJ = 2 2 L T U dx GJ = 2 2 T L U GJ = (11.21) (11.19) 11.6 Strain Energy for a General State of Stress (11.25) 1 2 ( ) x x y y z z xy xy yz yz zx zx u = + + + + + 2 2 2 2 2 2 1 1 2 2 2 ( ( )] ( ) x y z x y y z z x xy yz zx u E G = + +- + + + + + (11.26) y z X x y z X y y z X z xy yz zx xy yz zx E E E E E E E E E G G G = +-- = - +- = -- + = = = (2.38) From Eq. (2.38) 2 2 2 2 2 2 1 1 2 2 2 ( ( )] ( ) x y z x y y...
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 / 41

Chapter11EnergyMethods - Chapter 11 Energy Method --...

This preview shows document pages 1 - 14. Sign up to view the full document.

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