Introduction to Elasticity/Sample midterm 2

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Sample Midterm Problem 2[edit | edit source]

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[edit | edit source]

Part (a)[edit | edit source]

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)[edit | edit source]