Unified Engineering I
Fall 2003
Problem M17
In question M16. You had a state of strain:
Given a state of plane strain: e11 = -0.000200, e22 = +0.000400, e12 = -0.000200, do the
following:
a) If a strain gauge rosette, with three gauges at 60° to each other was placed with
one of the gauges orientated along the x1 direction. What strains would the
three gauges read?
b) By representing the strains as a matrix calculate the principal strains and
principal directions via the eigenvalue and eigenvectors of the matrix. Show
that this is consistent with the values you calculated in M16.
c) If the state of strain was no longer plane strain, and was now e11 = -0.000200, e22
= +0.000400, e12 = -0.000200, e33 = 0.000300, e23 = 0, e123 = 0. What would the
principal strains now be?
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