Consider a beam with boundary conditions, loading, and cross-section given below. In addition to the applied concentrated moment, there is a compressive axial load, P = 5 kips that acts through the centroid of the cross-section. Determine the following: (a) The normal (flexural) stress, o, at D due to the applied moment. (b) The normal stress, o, (c) The total normal stress at D due to both the applied axial load and the applied at D due to the axial load moment.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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### Problem Description

Consider a beam with boundary conditions, loading, and cross-section as shown in the diagram. There is a compressive axial load, \( P = 5 \) kips, acting through the centroid of the cross-section in addition to the applied concentrated moment. Determine the following:

(a) The normal (flexural) stress, \( \sigma \), at D due to the applied moment.  
(b) The normal stress, \( \sigma \), at D due to the axial load.  
(c) The total normal stress at D due to both the applied axial load and the applied moment.

### Diagram Explanation

#### Beam Diagram

- The beam is supported at point A with a triangular support and at point C with a circular support. 
- A 5 kip axial load is applied at both ends of the beam (points A and C).
- A concentrated moment of 144 k-in is applied counterclockwise at point B.
- The entire beam spans 12 ft, with 5 ft from A to B and 8 ft from B to C.
- Point D is located along the beam between points B and C.

#### Cross-section

- The cross-section of the beam at point D is shown as a rectangle.
- The dimensions of the cross-section are 6 inches in width and 8 inches in height.
- Point D is marked as being located central to this section with \( 2 \) inches from the right edge, indicating the location where stress is being evaluated.

This setup allows for the analysis of stresses at point D under the given loading and boundary conditions.
Transcribed Image Text:### Problem Description Consider a beam with boundary conditions, loading, and cross-section as shown in the diagram. There is a compressive axial load, \( P = 5 \) kips, acting through the centroid of the cross-section in addition to the applied concentrated moment. Determine the following: (a) The normal (flexural) stress, \( \sigma \), at D due to the applied moment. (b) The normal stress, \( \sigma \), at D due to the axial load. (c) The total normal stress at D due to both the applied axial load and the applied moment. ### Diagram Explanation #### Beam Diagram - The beam is supported at point A with a triangular support and at point C with a circular support. - A 5 kip axial load is applied at both ends of the beam (points A and C). - A concentrated moment of 144 k-in is applied counterclockwise at point B. - The entire beam spans 12 ft, with 5 ft from A to B and 8 ft from B to C. - Point D is located along the beam between points B and C. #### Cross-section - The cross-section of the beam at point D is shown as a rectangle. - The dimensions of the cross-section are 6 inches in width and 8 inches in height. - Point D is marked as being located central to this section with \( 2 \) inches from the right edge, indicating the location where stress is being evaluated. This setup allows for the analysis of stresses at point D under the given loading and boundary conditions.
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