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A beam with a rectangular section 120mm × 60mm, designed to be placed vertically is placed horizontally by mistake. The maximum stress is to be limited, the reduction in load carrying capacity would be
- a)1/4
- b)1/3
- c)1/2
- d)1/6
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A beam with a rectangular section 120mm × 60mm, designed to be placed...
So load carrying capacity would be half if placed horizontally by mistake in place of vertically.
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A beam with a rectangular section 120mm × 60mm, designed to be placed...
To understand why the correct answer is option 'C', let's analyze the situation step by step.
Given:
- Beam section: rectangular, 120mm × 60mm
- Beam orientation: placed horizontally instead of vertically
1. Load Carrying Capacity:
The load carrying capacity of a beam is directly related to its moment of inertia (I). When a beam is placed horizontally instead of vertically, its orientation affects the distribution of the load and the calculation of its moment of inertia.
2. Moment of Inertia:
The moment of inertia (I) of a rectangular section about its neutral axis can be calculated using the formula: I = (b * h^3) / 12, where 'b' is the width and 'h' is the height of the section.
3. Calculation of Moment of Inertia:
- For the given beam section placed vertically: I_vertical = (120 * 60^3) / 12 = 8,640,000 mm^4
- For the beam section placed horizontally: I_horizontal = (60 * 120^3) / 12 = 2,160,000 mm^4
4. Comparison of Moment of Inertia:
By comparing the moment of inertia of the beam section in the vertical and horizontal orientations, we can determine the reduction in load carrying capacity.
- Reduction in Moment of Inertia: I_reduction = I_vertical - I_horizontal = 8,640,000 - 2,160,000 = 6,480,000 mm^4
5. Reduction in Load Carrying Capacity:
The reduction in load carrying capacity is directly proportional to the reduction in moment of inertia. Since the moment of inertia is reduced by 6,480,000 mm^4, the load carrying capacity is reduced by the same proportion.
- Reduction in Load Carrying Capacity: Load_reduction = I_reduction / I_vertical = 6,480,000 / 8,640,000 = 0.75
6. Conclusion:
The reduction in load carrying capacity is 0.75 or 75% of the original capacity.
Therefore, the correct answer is option 'C' - 1/2, which represents a reduction in load carrying capacity by half.
Given:
- Beam section: rectangular, 120mm × 60mm
- Beam orientation: placed horizontally instead of vertically
1. Load Carrying Capacity:
The load carrying capacity of a beam is directly related to its moment of inertia (I). When a beam is placed horizontally instead of vertically, its orientation affects the distribution of the load and the calculation of its moment of inertia.
2. Moment of Inertia:
The moment of inertia (I) of a rectangular section about its neutral axis can be calculated using the formula: I = (b * h^3) / 12, where 'b' is the width and 'h' is the height of the section.
3. Calculation of Moment of Inertia:
- For the given beam section placed vertically: I_vertical = (120 * 60^3) / 12 = 8,640,000 mm^4
- For the beam section placed horizontally: I_horizontal = (60 * 120^3) / 12 = 2,160,000 mm^4
4. Comparison of Moment of Inertia:
By comparing the moment of inertia of the beam section in the vertical and horizontal orientations, we can determine the reduction in load carrying capacity.
- Reduction in Moment of Inertia: I_reduction = I_vertical - I_horizontal = 8,640,000 - 2,160,000 = 6,480,000 mm^4
5. Reduction in Load Carrying Capacity:
The reduction in load carrying capacity is directly proportional to the reduction in moment of inertia. Since the moment of inertia is reduced by 6,480,000 mm^4, the load carrying capacity is reduced by the same proportion.
- Reduction in Load Carrying Capacity: Load_reduction = I_reduction / I_vertical = 6,480,000 / 8,640,000 = 0.75
6. Conclusion:
The reduction in load carrying capacity is 0.75 or 75% of the original capacity.
Therefore, the correct answer is option 'C' - 1/2, which represents a reduction in load carrying capacity by half.
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A beam with a rectangular section 120mm × 60mm, designed to be placed vertically is placed horizontally by mistake. The maximum stress is to be limited, the reduction in load carrying capacity would bea) 1/4b) 1/3c) 1/2d) 1/6Correct answer is option 'C'. Can you explain this answer?
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