Let's solve the problem step by step. --- ## Given Data - Volume fraction of glass fibers, \(V_f = .3\) - Volume fraction of matrix, \(V_m = .7\) (since total is 1) - Elastic modulus of glass fibers, \(E_f = 75\, \text{GPa}\) - Elastic modulus of matrix, \(E_m = 4\, \text{GPa}\) - Applied stress (transverse direction), \(\sigma = 300\, \text{MPa}\) --- ## Step 1: Transverse Loading (Isostrain or Isostress?) **Transverse direction** means **isostress condition** (fibers and matrix experience the same stress). ### Isostress (Transverse) Rule of Mixtures: \[ \text{Transverse Modulus:} \quad \frac{1}{E_c} = \frac{V_f}{E_f} + \frac{V_m}{E_m} \] But, the question asks for the **strain in the fibers**. Under isostress: - \(\sigma_f = \sigma_m = \sigma\) - \(\varepsilon_f = \frac{\sigma}{E_f}\) --- ## Step 2: Calculate Strain in the Fibers Given: - \(\sigma = 300\, \text{MPa} = .3\, \text{GPa}\) - \(E_f = 75\, \text{GPa}\) \[ \varepsilon_f = \frac{\sigma}{E_f} = \frac{.3}{75} = .004 \] --- ## Step 3: Box the Answer - **Correct Option: C) .004** --- ## **Calculation Recap** \[ \varepsilon_f = \frac{\sigma}{E_f} = \frac{.3\, \text{GPa}}{75\, \text{GPa}} = .004 \] --- ### **Final Answer** **C) .004**