Let's break down the problem into **three steps** with explanations and provide the **final answer** at the end. --- ### **Step 1: Calculate the Required Strength** #### **Explanation:** - The factored load must be calculated for both LRFD and ASD. - For LRFD: \( P_u = 1.2P_D + 1.6P_L \) - For ASD: \( P_{service} = P_D + P_L \) Given: - \( P_D = 85 \) kips - \( P_L = 140 \) kips **Calculations:** - **LRFD:** \( P_u = 1.2(85) + 1.6(140) = 102 + 224 = 326 \) kips - **ASD:** \( P_{service} = 85 + 140 = 225 \) kips --- ### **Step 2: Determine Required Section Strength** #### **Explanation:** Compare the required strengths to the capacities of the suggested W10×68 section: - For LRFD: \(\phi_c P_n = 363\) kips - For ASD: \(P_n / \Omega_c = 241\) kips Compare these to the required strengths from step 1. **Comparison:** - **LRFD:** Required = 326 kips Available = 363 kips **OK** - **ASD:** Required = 225 kips Available = 241 kips **OK** --- ### **Step 3: Check Section Selection and Final Answer** #### **Explanation:** Since the required strengths in both LRFD and ASD are less than the available strengths for the W10×68 section, this section is adequate. --- ## **Final Answer:** ### **W10×68 section is suitable** for both LRFD and ASD. - **LRFD capacity** (\(\phi_c P_n\)) = **363 k** > required 326 k - **ASD capacity** (\(P_n/\Omega_c\)) = **241 k** > required 225 k **Therefore, W10×68 is the correct choice.**