A W10x22 used as a column under axial compression. Use A36 steel. For each column length and end conditions given, calculate the design capacity. (a) L = 8 ft, pinned ends (b) L=8 ft, fixed ends (c) L= 16 ft, pinned ends (d) L = 16 ft, fixed ends (e) L = 16 ft, pinned ends, braced at the midspan in the weak axis direction.

Structural Analysis
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Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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**Column Design Capacity Analysis**

*Objective:* 
Determine the design capacity of a W10x22 column made from A36 steel under axial compression. Assess various lengths and end conditions to see how they influence capacity.

**Column Scenarios:**

1. **Case (a):**
   - Length \( L = 8 \) ft
   - End Condition: Pinned ends

2. **Case (b):**
   - Length \( L = 8 \) ft
   - End Condition: Fixed ends

3. **Case (c):**
   - Length \( L = 16 \) ft
   - End Condition: Pinned ends

4. **Case (d):**
   - Length \( L = 16 \) ft
   - End Condition: Fixed ends

5. **Case (e):**
   - Length \( L = 16 \) ft
   - End Condition: Pinned ends, with bracing at the midspan in the weak axis direction

*Notes:*
- Analyze each condition considering the differences between pinned and fixed ends, which affect the effective length factor and column capacity.
- Midspan bracing affects the buckling resistance in the weak axis, altering the effective length used in calculations.
Transcribed Image Text:**Column Design Capacity Analysis** *Objective:* Determine the design capacity of a W10x22 column made from A36 steel under axial compression. Assess various lengths and end conditions to see how they influence capacity. **Column Scenarios:** 1. **Case (a):** - Length \( L = 8 \) ft - End Condition: Pinned ends 2. **Case (b):** - Length \( L = 8 \) ft - End Condition: Fixed ends 3. **Case (c):** - Length \( L = 16 \) ft - End Condition: Pinned ends 4. **Case (d):** - Length \( L = 16 \) ft - End Condition: Fixed ends 5. **Case (e):** - Length \( L = 16 \) ft - End Condition: Pinned ends, with bracing at the midspan in the weak axis direction *Notes:* - Analyze each condition considering the differences between pinned and fixed ends, which affect the effective length factor and column capacity. - Midspan bracing affects the buckling resistance in the weak axis, altering the effective length used in calculations.
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