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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
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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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
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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