1-13 - CHAP 1 Stress-Strain Analysis 37 13 Consider the...

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CHAP 1 Stress-Strain Analysis 37 13. Consider the following displacement field in a plane solid: ( , ) 0.04 0.01 0.006 ( , ) 0.06 0.009 0.012 u x y x y v x y x y (a) Compute the strain components xx , yy , and xy . Is this a state of uniform strain? (b) Determine the principal strains and their corresponding directions. Express the principal strain directions in terms of angles the directions make with the x -axis. (c) What is the normal strain at Point O in a direction 45 o to the x -axis? Solution: (a) Strain components: 0.01 xx u x   0.012 yy v y 0.009 0.006 0.015 xy v u x y Yes, this is a state of uniform strain, because the strains are independent of position x,y,z . (b) Principal strains and principal directions. 1 0.0075 2 xy xy 0.01 0.0075 0.0075 0.012 xx xy xy yy
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