Let's break down the questions and what you need to provide step by step. --- # Question 1: Maximum Compressive Load ## Step-by-Step Solution ### 1. **Formula for Maximum Compressive Load** The maximum compressive load a column can support (using Euler's formula for buckling, for example) is: \[ P_{cr} = \frac{\pi^2 E I}{(K L)^2} \] Where: - \( P_{cr} \) = Maximum compressive load (kip) - \( E \) = Modulus of elasticity (ksi) - \( I \) = Moment of inertia (in\(^4\)) - \( K \) = Effective length factor (dimensionless) - \( L \) = Unsupported length of column (inches) *Note: Sometimes, the maximum load is limited by yield strength, so compare with \( P_y = F_y \cdot A \), where \( F_y \) is the yield strength and \( A \) is the cross-sectional area.* ### 2. **Plug in Values** Let's assume you are given or have calculated the required values (replace with actual values): - \( E = 29000 \) ksi - \( I = 2.5 \) in\(^4\) - \( K = 1 \) - \( L = 120 \) in Calculate: \[ P_{cr} = \frac{\pi^2 \times 29000 \times 2.5}{(1 \times 120)^2} \] \[ P_{cr} = \frac{3.1416^2 \times 29000 \times 2.5}{14400} \] \[ P_{cr} = \frac{9.8696 \times 29000 \times 2.5}{14400} \] \[ P_{cr} = \frac{9.8696 \times 72500}{14400} \] \[ P_{cr} = \frac{715,072}{14400} \] \[ P_{cr} = 49.7 \text{ kip} \] **Write your answer as:** `49.7 kip` --- # Question 2: Pipe Column Size Selection ## Step-by-Step Solution ### 1. **Check Allowable Stress and Slenderness Ratio** #### a) **Allowable Stress:** Make sure your selected pipe size's allowable load meets or exceeds \( P_{cr} \) from above. #### b) **Slenderness Ratio (SR):** \[ SR = \frac{KL}{r} \] Where \( r = \sqrt{\frac{I}{A}} \) (radius of gyration). Let's assume: - \( K = 1 \) - \( L = 120 \) in - For your chosen pipe: \( r = 2.5 \) in \[ SR = \frac{1 \times 120}{2.5} = 48 \] Assume the requirement is \( SR < 50 \). ### 2. **State Your Selected Pipe Size** For example, assume after calculations you select: **Pipe Size = 2.5" Schedule No. 40** ### 3. **Enter Final Answers** - Pipe Column Size: `2.5" Schedule No. 40` - SR: `48` --- ## **Final Answers (Example)** ### **Question 1:** ``` 49.7 kip ``` ### **Question 2:** ``` 2.5" Schedule No. 40 48 ``` --- **Note:** Replace all example numbers (E, I, L, r, etc.) with your actual values for your specific problem. The process remains the same!