Introduction to Elasticity/Sample midterm 2
Sample Midterm Problem 2 
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 ?
Part (a) 
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