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A beam having the cross section shown is subjected to a couple that acts in a horizontal plane. Determine the largest permissible value of the moment Mo of the couple if the maximum stress in the beam is not to exceed 13 ksi.

A beam having the cross section shown is subjected to a couple that acts in a horizontal plane. Determine the largest permissible value of the moment Mo of the couple if the maximum stress in the beam is not to exceed 13 ksi.

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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A beam having the cross-section shown is subjected to a couple that acts in a horizontal plane. Determine the largest permissible value of the moment \( M_0 \) of the couple if the maximum stress in the beam is not to exceed 13 ksi. Given: - \( I_y = I_z = 11.3 \, \text{in}^4 \) - \( A = 4.75 \, \text{in}^2 \) - \( k_{\text{min}} = 0.983 \, \text{in} \) **Diagram Explanation:** The diagram shows an L-shaped section with dimensions as follows: - The vertical and horizontal parts both have a width of 0.5 in. - The total height of the vertical section is 5 in. - The horizontal section extends 5 in. from the corner \( C \). - The dimension from the bottom of the vertical section to the top surface of the horizontal section is 1.43 in. - The couple \( M_0 \) acts at point \( C \) about the z-axis. - The centroid \( B \) is marked at the intersection where the section bends. The largest permissible value of the moment \( M_0 \) is ________ kip-in.
Transcribed Image Text:A beam having the cross-section shown is subjected to a couple that acts in a horizontal plane. Determine the largest permissible value of the moment \( M_0 \) of the couple if the maximum stress in the beam is not to exceed 13 ksi. Given: - \( I_y = I_z = 11.3 \, \text{in}^4 \) - \( A = 4.75 \, \text{in}^2 \) - \( k_{\text{min}} = 0.983 \, \text{in} \) **Diagram Explanation:** The diagram shows an L-shaped section with dimensions as follows: - The vertical and horizontal parts both have a width of 0.5 in. - The total height of the vertical section is 5 in. - The horizontal section extends 5 in. from the corner \( C \). - The dimension from the bottom of the vertical section to the top surface of the horizontal section is 1.43 in. - The couple \( M_0 \) acts at point \( C \) about the z-axis. - The centroid \( B \) is marked at the intersection where the section bends. The largest permissible value of the moment \( M_0 \) is ________ kip-in.
Expert Solution
Step 1: Determining extreme fibre distance from neutral axis


Civil Engineering homework question answer, step 1, image 1

z = 1.43 in ( from left side )

z = 5 - 1.43

  =  3.57 in ( from right side )

Iy = 11.3 in4

Maximum bending stress = 13 ksi

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