The \(45^{\circ}\) off-axis test shown in Figure 10.37 is conducted on a 10 in. \(\times 1\) in. \(\times 0.1\) in. \((254 \mathrm{~mm} \times 25.4 \mathrm{~mm} \times 2.54 \mathrm{~mm})\) carbon/epoxy specimen, which deforms as shown under the applied load. It is also known from separate tensile tests that \(E_{1}=32 \times 10^{6} \mathrm{psi}(220 \mathrm{GPa}), E_{2}=1.0 \times 10^{6} \mathrm{psi}(6.89 \mathrm{GPa})\), and \(v_{12}=0.3\). Determine the value of \(G_{12}\) from these test data.

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1 in. L= 10 in. (unloaded) P = 500 lb 0.1 in. L+AL 10.03052 in. (loaded) 45 FIGURE 10.37 Extensional deformation of a carbon/epoxy specimen during a 45 off-axis tensile test.