A strain rosette consisting of three strain gauges was used to measure the strains at a point in a thin plate of dimensions \(100 \times 20 \times 1 \mathrm{~mm}\). The measured strains in the three gauges are: \(\varepsilon_{A}=0.008, \varepsilon_{B}=0.002\), and \(\varepsilon_{C}=0.008\). Assume \(E=100 \mathrm{GPa}\), and \(v=0.3\).

a. Assuming the plate is in a state of plane stress, determine the complete state of strains and stresses (all six components) at that point.

b. Assuming the state of stress is uniform, calculate the strain energy stored in the plate.

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y X B 120 PA 120