Elasticity/Sample midterm 2

Sample Midterm Problem 2

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Given:

A strain gage rosette provides the following data

 

where the   and   directions are perpendicular to each other and   is the extensional strain of a line element at an angle of   to the   axis (in the counterclockwise direction).

Find:

  • (a) Compute  .
  • (b) Is the result valid if the material is anisotropic ?

Solution

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Part (a)

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From the previous problem, for an angle of rotation of 30 , the rotation matrix   is

 

Therefore, the components of strain in the rotated co-ordinate system are given by

 

Since we are given  , we will calculate the value of this strain in terms of the original components of strain. Thus,

 

Therefore,

 

Hence,

 

Next, for an angle of rotation of 60 , the matrix   is

 

Therefore,  , is given by

 

Therefore,

 

Part (b)

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