Sample Midterm Problem 2 edit


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).


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

Solution edit

Part (a) edit

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,






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


Therefore,  , is given by




Part (b) edit