Component of a infinitesimal strain tensor

[nikolafmf]

I have the folowing continuum mechanics problem which I can't solve:

The unit elongations at a certain point on the surface of a body are measured experimentally by means of strain gages that are arranged at 60° in the direction of 0°, 60° and 120°. Coordinate system is rectangular Cartesian, defined by e₁ at 0° and e₂ at 90°. If the unit elongations are designated by a, b, c, respectively, what is the strain component E₁₂?

Now I know how to calculate elongation in a certain direction n: it is nEn, where E is written in the coordinate system given above, E is the infinitesimal strain tensor. But what is E₁₂?

Now my idea is to rotate tensor E for 60, or 120 degrees and to take its E'₁₁ component as the given elongation at 60, or 120 degress respectively. From that should be possible to find E₁₂.

 

[BigJDubs]

Am I right? If not, can you explain me how to find E12? Yes, you are right. To find E12, you need to rotate the strain tensor E for 60° or 120° and take its E'11 component as the given elongation at 60° or 120° respectively. Then use the following equation to calculate E12: E12 = a*cos(60°) + b*cos(120°) + c*cos(180°).