### Beam Deflection AnalysisThe cantilever beam consists of a rectangular structural steel tube shape \([E = 27000 \, \text{ksi}; \, I = 450 \, \text{in}^4]\). For the loading shown, determine:1. **The beam deflection \(v_B\) at point B.**2. **The beam deflection \(v_C\) at point C.**Assume the following parameters:- \(P = 10.9 \, \text{kips}\)- \(w = 2.9 \, \text{kips/ft}\)- \(L_{AB} = 7.6 \, \text{ft}\)- \(L_{BC} = 4.6 \, \text{ft}\)#### Diagram ExplanationA cantilever beam is illustrated, fixed at one end (point A) and extending horizontally to the right. The beam is subjected to two different types of loads:- A uniformly distributed load \(w\) over the segment \(L_{AB}\).- A concentrated load \(P\) at the end of the beam (point C).The length \(L_{AB}\) is the distance from point A to point B, and \(L_{BC}\) is the distance from point B to point C. These segments are denoted on the diagram as follows:- \(L_{AB} = 7.6 \, \text{ft}\)- \(L_{BC} = 4.6 \, \text{ft}\)#### Graph ExplanationThe diagram illustrates the following:- A vertical arrow pointing downward labeled \(P\) at the end of the beam (point C), indicating the concentrated load.- A series of smaller vertical arrows evenly distributed along the length of \(L_{AB}\), indicating the uniformly distributed load \(w\).### ResultsThe deflection values at points B and C are calculated as follows:- **(a) \( v_B = -0.6016 \, \text{in.} \)**- **(b) \( v_C = -1.2143 \, \text{in.} \)**

Answered: Image /qna-images/answer/367cae22-953a-4885-8050-3e9bd41223ab.jpg

The cantilever beam consists of a rectangular structural steel tube shape [E = 27000 ksi; / = 450 in.4]. For the loading shown, determine: (a) the beam deflection vg at point B. (b) the beam deflection vc at point C. Assume P = 10.9 kips, w = 2.9 kips/ft, LAB= 7.6 ft, LBC = 4.6 ft. "I W ↓↓ B LAB in. A Answers: (a) vg= -0.6016 (b) vc= i -1.2143 in. LBC

The cantilever beam consists of a rectangular structural steel tube shape [E = 27000 ksi; / = 450 in.4]. For the loading shown, determine: (a) the beam deflection vg at point B. (b) the beam deflection vc at point C. Assume P = 10.9 kips, w = 2.9 kips/ft, LAB= 7.6 ft, LBC = 4.6 ft. "I W ↓↓ B LAB in. A Answers: (a) vg= -0.6016 (b) vc= i -1.2143 in. LBC

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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Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

Question

### Beam Deflection Analysis

The cantilever beam consists of a rectangular structural steel tube shape \([E = 27000 \, \text{ksi}; \, I = 450 \, \text{in}^4]\). For the loading shown, determine:

1. **The beam deflection \(v_B\) at point B.**
2. **The beam deflection \(v_C\) at point C.**

Assume the following parameters:
- \(P = 10.9 \, \text{kips}\)
- \(w = 2.9 \, \text{kips/ft}\)
- \(L_{AB} = 7.6 \, \text{ft}\)
- \(L_{BC} = 4.6 \, \text{ft}\)

#### Diagram Explanation
A cantilever beam is illustrated, fixed at one end (point A) and extending horizontally to the right. The beam is subjected to two different types of loads:
- A uniformly distributed load \(w\) over the segment \(L_{AB}\).
- A concentrated load \(P\) at the end of the beam (point C).

The length \(L_{AB}\) is the distance from point A to point B, and \(L_{BC}\) is the distance from point B to point C. These segments are denoted on the diagram as follows:
- \(L_{AB} = 7.6 \, \text{ft}\)
- \(L_{BC} = 4.6 \, \text{ft}\)

#### Graph Explanation
The diagram illustrates the following:
- A vertical arrow pointing downward labeled \(P\) at the end of the beam (point C), indicating the concentrated load.
- A series of smaller vertical arrows evenly distributed along the length of \(L_{AB}\), indicating the uniformly distributed load \(w\).

### Results
The deflection values at points B and C are calculated as follows:
- **(a) \( v_B = -0.6016 \, \text{in.} \)**
- **(b) \( v_C = -1.2143 \, \text{in.} \)**

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