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A member in a braced frame supports an axial compressive load and end moments that causes bending about both axes of the member. Kx = Ky = 1.0. Is W14×82 adequate? 140 k 16' Mux Muy = 150 ft-k = 150 ft-k M... = 75 ft-k ux M = 75 ft-k

A member in a braced frame supports an axial compressive load and end moments that causes bending about both axes of the member. Kx = Ky = 1.0. Is W14×82 adequate? 140 k 16' Mux Muy = 150 ft-k = 150 ft-k M... = 75 ft-k ux M = 75 ft-k

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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### Analysis of a Braced Frame Member #### Problem Statement A member in a braced frame supports an axial compressive load along with end moments that induce bending about both principal axes of the member. Given that \( K_x = K_y = 1.0 \), we are tasked with determining whether a W14x82 section is adequate to support the load conditions. #### Load and Moment Details - **Axial Load**: The member is subjected to an axial compressive load of 140 kips. - **End Moments**: There are significant end moments acting about both principal axes at the top and bottom of the member. The magnitudes of these moments are: - At the top of the member: - \( M_{ux} = 150 \) ft-kips - \( M_{uy} = 150 \) ft-kips - At the bottom of the member: - \( M_{ux} = 75 \) ft-kips - \( M_{uy} = 75 \) ft-kips - **Length of Member**: The overall height of the truss member is 16 feet. The provided diagram (Figure 4) visually represents these load conditions: 1. **Axial Load**: A downward axial load of 140 kips is applied at the top of the member. 2. **Moment at Top**: Both the moment about the x-axis (\( M_{ux} \)) and the moment about the y-axis (\( M_{uy} \)) are 150 ft-kips. 3. **Moment at Bottom**: Both the moment about the x-axis (\( M_{ux} \)) and the moment about the y-axis (\( M_{uy} \)) are 75 ft-kips. 4. **Length Specification**: The member length is marked as 16 feet. This data is essential for performing a detailed structural analysis to determine the adequacy of the selected section (W14x82) using methods such as interaction equations or moment magnification factors, considering combined axial and bending loads. **Figure 4: Schematic of the member with axial load and moments** By understanding these loading conditions and performing the appropriate calculations, engineers can ensure the structural integrity and safety of the member within the braced frame system.
Transcribed Image Text:### Analysis of a Braced Frame Member #### Problem Statement A member in a braced frame supports an axial compressive load along with end moments that induce bending about both principal axes of the member. Given that \( K_x = K_y = 1.0 \), we are tasked with determining whether a W14x82 section is adequate to support the load conditions. #### Load and Moment Details - **Axial Load**: The member is subjected to an axial compressive load of 140 kips. - **End Moments**: There are significant end moments acting about both principal axes at the top and bottom of the member. The magnitudes of these moments are: - At the top of the member: - \( M_{ux} = 150 \) ft-kips - \( M_{uy} = 150 \) ft-kips - At the bottom of the member: - \( M_{ux} = 75 \) ft-kips - \( M_{uy} = 75 \) ft-kips - **Length of Member**: The overall height of the truss member is 16 feet. The provided diagram (Figure 4) visually represents these load conditions: 1. **Axial Load**: A downward axial load of 140 kips is applied at the top of the member. 2. **Moment at Top**: Both the moment about the x-axis (\( M_{ux} \)) and the moment about the y-axis (\( M_{uy} \)) are 150 ft-kips. 3. **Moment at Bottom**: Both the moment about the x-axis (\( M_{ux} \)) and the moment about the y-axis (\( M_{uy} \)) are 75 ft-kips. 4. **Length Specification**: The member length is marked as 16 feet. This data is essential for performing a detailed structural analysis to determine the adequacy of the selected section (W14x82) using methods such as interaction equations or moment magnification factors, considering combined axial and bending loads. **Figure 4: Schematic of the member with axial load and moments** By understanding these loading conditions and performing the appropriate calculations, engineers can ensure the structural integrity and safety of the member within the braced frame system.
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