118,45k 9k ↓ 11' 1k/f 5k in 15,55k

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Draw and label the shear and moment diagrams for the beam below. 

Vmax =_______            Mmax = __________    V =0 @x = __________

**Structural Analysis of a Simply Supported Beam**

This diagram illustrates a simply supported beam subjected to multiple loads. The beam is supported at both ends: a pin support on the left and a roller support on the right. Below, we describe the key elements of the diagram:

1. **Supports:**
   - The left end of the beam (A) is supported by a pin support, which allows rotation but prevents translation in any direction. This support exerts a vertical reaction force of 18.45 kips upwards.
   - The right end of the beam (B) is supported by a roller support, which allows horizontal movement but prevents vertical translation. This support has a vertical reaction force of 15.55 kips upwards.

2. **Loads:**
   - There are two concentrated forces acting downwards on the beam:
     - A 9 kips load is located 4 feet from the left support.
     - A 5 kips load is positioned 5 feet from the right support.
   - Additionally, there is a uniformly distributed load of 1 kip/ft applied over an 11-foot span, starting 4 feet from the left support and ending 10 feet from the right support.

3. **Dimensions:**
   - The total length of the beam is 20 feet.
   - The distance from the left support to the point where the 9 kips load is applied is 4 feet.
   - The portion of the beam subjected to the uniformly distributed load spans 11 feet.
   - The 5 kips load is applied 5 feet from the right support.

Understanding the loading conditions and support reactions will allow for calculating internal forces, shear forces, and bending moments in the beam, which are essential for ensuring the structural integrity and safety of the construction.

For further calculations or examples of similar problems, refer to the module on "Beam Reactions and Internal Forces."
Transcribed Image Text:**Structural Analysis of a Simply Supported Beam** This diagram illustrates a simply supported beam subjected to multiple loads. The beam is supported at both ends: a pin support on the left and a roller support on the right. Below, we describe the key elements of the diagram: 1. **Supports:** - The left end of the beam (A) is supported by a pin support, which allows rotation but prevents translation in any direction. This support exerts a vertical reaction force of 18.45 kips upwards. - The right end of the beam (B) is supported by a roller support, which allows horizontal movement but prevents vertical translation. This support has a vertical reaction force of 15.55 kips upwards. 2. **Loads:** - There are two concentrated forces acting downwards on the beam: - A 9 kips load is located 4 feet from the left support. - A 5 kips load is positioned 5 feet from the right support. - Additionally, there is a uniformly distributed load of 1 kip/ft applied over an 11-foot span, starting 4 feet from the left support and ending 10 feet from the right support. 3. **Dimensions:** - The total length of the beam is 20 feet. - The distance from the left support to the point where the 9 kips load is applied is 4 feet. - The portion of the beam subjected to the uniformly distributed load spans 11 feet. - The 5 kips load is applied 5 feet from the right support. Understanding the loading conditions and support reactions will allow for calculating internal forces, shear forces, and bending moments in the beam, which are essential for ensuring the structural integrity and safety of the construction. For further calculations or examples of similar problems, refer to the module on "Beam Reactions and Internal Forces."
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