A rossette strain gauge will give you simultaneous readings in two direction but still assumes the the strain normal to the surface is zero. Rosettes are orthogonal strain gauges arranged at 0°, 45° and 90° at one point. Two strain gauges are installed on opposite sides of the structure + Temperature effects are well compensated I do not think you can calculate the Von Mises strain with only one value. Figure 1 illustrates three commonly used strain gage rosette configurations. In the stress analysis with strain gauges usually bridge circuits are used with only one active measurement grid.
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