A \(45^{\circ}\) off-axis tensile test specimen has three strain gages attached. Two of the gages are mounted as shown in Figure 2.18 so as to measure the normal strains \(\varepsilon_{x}\) and \(\varepsilon_{y}\), and a third gage is mounted at \(\theta=45^{\circ}\) so as to measure the normal strain \(\varepsilon_{1}\). If the applied stress \(\sigma_{x}=100 \mathrm{MPa}\) and the measured strains are \(\varepsilon_{x}=0.00647, \varepsilon_{y}=-0.00324\), and \(\varepsilon_{1}=0.00809\), determine the off-axis modulus of elasticity \(E_{x}\) the off-axis major Poisson's ratio \(v_{x y \prime}\) and the shearcoupling ratio \(\eta_{x, x y}\).

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FIGURE 2.18 45 x 45 off-axis tensile test specimen Strain gage for measuring & Strain gage for measuring & Ox