Component of 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.

 

[Valerie Park]

Is my solution correct or am I missing something?Yes, your solution is correct. You can find E12 by rotating the tensor E for 60 and 120 degrees and taking the corresponding E′11 components as the given elongations at 60 and 120 degrees respectively. Then you can calculate E12 from the measured elongations (a,b,c) using the equation E12 = (a + b - 2c)/2.