State of stress, strain and hookes law

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SUMMARY

The discussion centers on the application of Hooke's Law to determine the state of stress from a given state of strain. The user employed the formula for stress, incorporating Young's modulus (E = 30 x 10^6) and Poisson's ratio (v = 0.3), to calculate stress components \(\sigma_{xx}\), \(\sigma_{yy}\), and \(\sigma_{zz}\). Despite following the correct methodology, the calculated stress values (\(\sigma_{xx} = -4.6154 \times 10^4\), \(\sigma_{yy} = -1.8462 \times 10^5\), \(\sigma_{zz} = -6.9231 \times 10^4\)) did not match the expected results, leading to confusion about potential errors in the calculations or the source material.

PREREQUISITES
  • Understanding of Hooke's Law and its application in material science.
  • Familiarity with stress and strain tensors in mechanics.
  • Knowledge of Young's modulus and Poisson's ratio.
  • Basic proficiency in mathematical calculations involving engineering formulas.
NEXT STEPS
  • Review the derivation and application of Hooke's Law in three-dimensional stress analysis.
  • Learn about the relationship between shear modulus (G) and Poisson's ratio (v) in material mechanics.
  • Investigate common sources of error in stress-strain calculations and how to verify results.
  • Explore advanced topics in continuum mechanics, particularly regarding isotropic materials.
USEFUL FOR

Students and professionals in engineering, particularly those specializing in materials science, structural engineering, or mechanical engineering, will benefit from this discussion on stress and strain analysis using Hooke's Law.

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in the following question i am asked to find the state of stress given the state of strain.
http://lh6.ggpht.com/_H4Iz7SmBrbk/SwBtHnG3qkI/AAAAAAAAB9M/rFS_orHMbGo/Capture.JPG
i went about solving this using hookes law

\sigmaxx=E[(1-v)\epsilonxx + v(\epsilonyy+\epsilonzz)]/[(1+v)1-2v)]

using the given
E=30*106
v=0.3
\epsilonx=0.001
\epsilonxy=-1.25*10-3
\epsilony=-0.005

i get
\sigmaxx=-4.6154*104
\sigmayy=-1.8462*105
\sigmazz=-6.9231*104

but as you can see these are not the correct answers according to the question.
can anyone see where i have gone wrong ?

also how do i find \tauxy?
 
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\tauxy=G*\gammaxy=-0.0025*(30*106/2(1.3)=-0.0025*11.53846*106=-2.8846*104

from this i already see that the answers are not going to be the same as the answers in the book, and there is nowhere i have gone wrong with the math here,

am i doing something fundamentally wrong or could they be wrong with their answers,??
 

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