The non-symmetrically laminated beam shown in Figure 7.71 consists of a substrate material having Young's modulus (E_{mathrm{S}})

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The non-symmetrically laminated beam shown in Figure 7.71 consists of a substrate material having Young's modulus \(E_{\mathrm{S}}\) and a coating material having Young's modulus \(E_{\mathrm{C}}\), and both materials are linear elastic, isotropic, and homogeneous. Using a modified laminated beam theory, derive the equation for the flexural modulus \(E_{\mathrm{f}}\) for the beam. Your answer should be in terms of the given parameters. 

Figure 7.71:

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