Beam loading: 0.4 m R₁ 800 N 12 mm Beam cross-section: 30 mm 0.9 m 0.8 m- A 400 N 600 N +0.3 B -|-0.3 m-/- -0.5 0.5 m Determine the Maximum Bending Stress in the beam. m-0.2 m- R₂ 200 N 0.4 m C
Beam loading: 0.4 m R₁ 800 N 12 mm Beam cross-section: 30 mm 0.9 m 0.8 m- A 400 N 600 N +0.3 B -|-0.3 m-/- -0.5 0.5 m Determine the Maximum Bending Stress in the beam. m-0.2 m- R₂ 200 N 0.4 m C
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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![### Beam Loading and Cross-section Analysis
#### Beam Loading:
The diagram represents a beam subject to various point loads and supports. The key details are as follows:
- **Loads:**
- 800 N applied at a distance of 0.4 m from the left end.
- 400 N applied 0.8 m from the first load (1.2 m from the left end).
- 600 N applied 0.3 m from the second load (1.5 m from the left end).
- 200 N applied 0.3 m from the third load (1.8 m from the left end).
- **Supports:**
- Support \(R_1\) located 0.9 m from the left end.
- Support \(R_2\) located 0.2 m from the right end (or equivalently 0.7 m from 600 N load, or 2.3 m from the left end).
#### Beam Cross-section:
The beam's cross-sectional dimensions are:
- Height: 30 mm
- Width: 12 mm
Given the cross-section, the moment of inertia (I) can be calculated using the formula for a rectangular section:
\[ I = \frac{1}{12} \times \text{width} \times (\text{height})^3 \]
\[ I = \frac{1}{12} \times 12 \, \text{mm} \times (30 \, \text{mm})^3 \]
\[ I = \frac{1}{12} \times 12 \times 27000 \]
\[ I = 27000 \, \text{mm}^4 \]
#### Task:
Determine the Maximum Bending Stress in the beam:
Maximum Bending Stress (\(\sigma_{max}\)) can be determined using the bending stress formula:
\[ \sigma = \frac{M \cdot y}{I} \]
Where:
- \( M \) = Maximum moment
- \( y \) = Distance from the neutral axis to the outermost fiber (half of the height for a rectangular section)
\[ y = \frac{30 \, \text{mm}}{2} = 15 \, \text{mm} \]
- \( I \) = Moment of inertia
Please calculate the maximum moment \( M \) from the bending moment diagram, then substitute the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a28b893-91ec-4064-8fee-f9f0d1fd8200%2Fdffa2098-2ae6-438c-bdd3-7e075f0e6448%2Flcnnmz_processed.png&w=3840&q=75)
Transcribed Image Text:### Beam Loading and Cross-section Analysis
#### Beam Loading:
The diagram represents a beam subject to various point loads and supports. The key details are as follows:
- **Loads:**
- 800 N applied at a distance of 0.4 m from the left end.
- 400 N applied 0.8 m from the first load (1.2 m from the left end).
- 600 N applied 0.3 m from the second load (1.5 m from the left end).
- 200 N applied 0.3 m from the third load (1.8 m from the left end).
- **Supports:**
- Support \(R_1\) located 0.9 m from the left end.
- Support \(R_2\) located 0.2 m from the right end (or equivalently 0.7 m from 600 N load, or 2.3 m from the left end).
#### Beam Cross-section:
The beam's cross-sectional dimensions are:
- Height: 30 mm
- Width: 12 mm
Given the cross-section, the moment of inertia (I) can be calculated using the formula for a rectangular section:
\[ I = \frac{1}{12} \times \text{width} \times (\text{height})^3 \]
\[ I = \frac{1}{12} \times 12 \, \text{mm} \times (30 \, \text{mm})^3 \]
\[ I = \frac{1}{12} \times 12 \times 27000 \]
\[ I = 27000 \, \text{mm}^4 \]
#### Task:
Determine the Maximum Bending Stress in the beam:
Maximum Bending Stress (\(\sigma_{max}\)) can be determined using the bending stress formula:
\[ \sigma = \frac{M \cdot y}{I} \]
Where:
- \( M \) = Maximum moment
- \( y \) = Distance from the neutral axis to the outermost fiber (half of the height for a rectangular section)
\[ y = \frac{30 \, \text{mm}}{2} = 15 \, \text{mm} \]
- \( I \) = Moment of inertia
Please calculate the maximum moment \( M \) from the bending moment diagram, then substitute the
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