16: A member having the dimensions shown is to be used to resist an internal bending moment of M = 40 lb-ft. Determine the maximum stress in the member if the moment is applied (a) about the z-z axis, (b) about the y-y axis.
16: A member having the dimensions shown is to be used to resist an internal bending moment of M = 40 lb-ft. Determine the maximum stress in the member if the moment is applied (a) about the z-z axis, (b) about the y-y axis.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![**Problem Statement:**
A member having the dimensions shown is to be used to resist an internal bending moment of \( M = 40 \, \text{lb-ft} \). Determine the maximum stress in the member if the moment is applied (a) about the z-z axis, (b) about the y-y axis.
**Diagram Description:**
The diagram shows a 3D rectangular cross-section oriented along the y, z, and x axes. The member is a box shape with a vertical dimension (height) of 12 inches along the y-axis and a horizontal dimension (width) of 8 inches along the x-axis. The diagram indicates the orientation of the z-z axis perpendicular to the x-y plane.
**Key Dimensions:**
- Height (y-axis): 12 inches
- Width (x-axis): 8 inches
**Analysis:**
For both scenarios (a and b), calculate the section modulus for the respective axis and apply the bending stress formula:
\[ \sigma = \frac{M}{S} \]
where \( \sigma \) is the maximum stress, \( M \) is the bending moment, and \( S \) is the section modulus about the respective axis (z-z or y-y).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79952873-a2a6-4e0e-8058-ca209deee693%2F5c16efbf-f3ef-4d69-a00d-b26b7dd5eb50%2F2ye2ljm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A member having the dimensions shown is to be used to resist an internal bending moment of \( M = 40 \, \text{lb-ft} \). Determine the maximum stress in the member if the moment is applied (a) about the z-z axis, (b) about the y-y axis.
**Diagram Description:**
The diagram shows a 3D rectangular cross-section oriented along the y, z, and x axes. The member is a box shape with a vertical dimension (height) of 12 inches along the y-axis and a horizontal dimension (width) of 8 inches along the x-axis. The diagram indicates the orientation of the z-z axis perpendicular to the x-y plane.
**Key Dimensions:**
- Height (y-axis): 12 inches
- Width (x-axis): 8 inches
**Analysis:**
For both scenarios (a and b), calculate the section modulus for the respective axis and apply the bending stress formula:
\[ \sigma = \frac{M}{S} \]
where \( \sigma \) is the maximum stress, \( M \) is the bending moment, and \( S \) is the section modulus about the respective axis (z-z or y-y).
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