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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 M = 150 ft-k = = 150 ft-k M = 75 ft-k = ux Muy Figure 4 = 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 M = 150 ft-k = = 150 ft-k M = 75 ft-k = ux Muy Figure 4 = 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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## Structural Analysis of a Braced Frame Member under Combined Loading **Problem Statement:** A member in a braced frame supports an axial compressive load and end moments that cause bending about both axes of the member. The effective length factors for both axes are given as \( K_x = K_y = 1.0 \). The task is to determine whether a W14×82 structural shape (W-shape) is adequate for this scenario. ### Load and Moment Details: - **Axial Compressive Load (\( P \))**: 140 kips (k) - **End Moments at the Upper End**: - About X-axis (\( M_{ux} \)): 150 ft-kips - About Y-axis (\( M_{uy} \)): 150 ft-kips - **End Moments at the Bottom End**: - About X-axis (\( M_{lx} \)): 75 ft-kips - About Y-axis (\( M_{ly} \)): 75 ft-kips - **Member Length**: 16 feet (ft) ### Diagram Illustration: **Figure 4**: This figure presents a simplified schematic of the structural member under combined loading. It features: - An axial compressive load \( P = 140 \) k acting downward. - The upper end moments \( M_{ux} = 150 \) ft-k and \( M_{uy} = 150 \) ft-k acting in opposite directions (opposite ends of the member around their respective axes). - The lower end moments \( M_{lx} = 75 \) ft-k and \( M_{ly} = 75 \) ft-k, also acting in opposite directions. - A notation indicating the member height of 16' between the upper and lower ends. ### Key Factors: 1. **Kx and Ky Values**: The effective length factors for both the X-axis and Y-axis are equal to 1. This implies there is no reduction or increase in the effective length for buckling analysis. 2. **Member Selection**: The shape being evaluated for adequacy is W14×82. ### Evaluation: The adequacy of a structural member considering these loads and moments would typically involve ensuring that the combined stress due to axial load and bending moments does not exceed the allowable limits based on material strength and member properties. This is done using structural design principles and calculations (e.g., LRFD
Transcribed Image Text:## Structural Analysis of a Braced Frame Member under Combined Loading **Problem Statement:** A member in a braced frame supports an axial compressive load and end moments that cause bending about both axes of the member. The effective length factors for both axes are given as \( K_x = K_y = 1.0 \). The task is to determine whether a W14×82 structural shape (W-shape) is adequate for this scenario. ### Load and Moment Details: - **Axial Compressive Load (\( P \))**: 140 kips (k) - **End Moments at the Upper End**: - About X-axis (\( M_{ux} \)): 150 ft-kips - About Y-axis (\( M_{uy} \)): 150 ft-kips - **End Moments at the Bottom End**: - About X-axis (\( M_{lx} \)): 75 ft-kips - About Y-axis (\( M_{ly} \)): 75 ft-kips - **Member Length**: 16 feet (ft) ### Diagram Illustration: **Figure 4**: This figure presents a simplified schematic of the structural member under combined loading. It features: - An axial compressive load \( P = 140 \) k acting downward. - The upper end moments \( M_{ux} = 150 \) ft-k and \( M_{uy} = 150 \) ft-k acting in opposite directions (opposite ends of the member around their respective axes). - The lower end moments \( M_{lx} = 75 \) ft-k and \( M_{ly} = 75 \) ft-k, also acting in opposite directions. - A notation indicating the member height of 16' between the upper and lower ends. ### Key Factors: 1. **Kx and Ky Values**: The effective length factors for both the X-axis and Y-axis are equal to 1. This implies there is no reduction or increase in the effective length for buckling analysis. 2. **Member Selection**: The shape being evaluated for adequacy is W14×82. ### Evaluation: The adequacy of a structural member considering these loads and moments would typically involve ensuring that the combined stress due to axial load and bending moments does not exceed the allowable limits based on material strength and member properties. This is done using structural design principles and calculations (e.g., LRFD
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