A strain rosette consisting of three strain gauges was used to measure the strains at a point in a thinwalled plate. The measured strains in the three gauges are: \(\quad \varepsilon_{A}=0.001, \varepsilon_{B}=\) -0.0006 , and \(\varepsilon_{C}=0.0007\). Note that gauge \(\mathrm{C}\) is at \(45^{\circ}\) with respect to the xaxis. Assume the plane stress state.

a. Determine the complete state of strains and stresses (all 6 components) at that point. Assume \(E=70 \mathrm{GPa}\), and \(v=0.3\).

b. What are the principal strains and their directions?

c. What are the principal stresses and their directions?

d. Show that the principal strains and stresses satisfy the stressstrain relations.

Transcribed Image Text:

y X B C A