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A beam is of i-section with flanges 200 mm x 10 mm and web 180 mm x 10 mm. Due to the bending moment applied on the beam section, maximum stress developed in the beam section is 100 MPa, what is the stress developed at inner edge of the flange?
- a)110 MPa
- b)100 MPa
- c)90 MPa
- d)120 MPa
Correct answer is option 'C'. Can you explain this answer?
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A beam is of i-section with flanges 200 mm x 10 mm and web 180 mm x 10...
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A beam is of i-section with flanges 200 mm x 10 mm and web 180 mm x 10...
Given data:
Flanges = 200 mm x 10 mm
Web = 180 mm x 10 mm
Maximum stress developed in the beam section = 100 MPa
To find: Stress developed at the inner edge of the flange.
Solution:
1. Stress distribution in an I-section beam:
The stress distribution in an I-section beam is shown below:
As we can see from the above figure, the maximum stress is developed at the top and bottom flanges of the beam, and the stress gradually reduces towards the neutral axis.
2. Calculation of stress at the inner edge of the flange:
From the stress distribution diagram, we know that the stress at the extreme fiber of the flange is maximum. Therefore, the stress at the inner edge of the flange can be calculated as follows:
Stress at the extreme fiber of the flange = Maximum stress developed in the beam section = 100 MPa
The distance from the neutral axis to the extreme fiber of the flange can be calculated as follows:
Distance from the neutral axis to the extreme fiber of the flange = (200/2) - 10 = 90 mm
Therefore, the stress at the inner edge of the flange can be calculated as follows:
Stress at the inner edge of the flange = Maximum stress developed in the beam section x (Distance from the neutral axis to the extreme fiber of the flange / Distance from the neutral axis to the centroid of the section)
Stress at the inner edge of the flange = 100 x (90/102.5) = 87.8 MPa
Therefore, the stress developed at the inner edge of the flange is 90 MPa (approx).
Hence, option (c) is the correct answer.
Flanges = 200 mm x 10 mm
Web = 180 mm x 10 mm
Maximum stress developed in the beam section = 100 MPa
To find: Stress developed at the inner edge of the flange.
Solution:
1. Stress distribution in an I-section beam:
The stress distribution in an I-section beam is shown below:
As we can see from the above figure, the maximum stress is developed at the top and bottom flanges of the beam, and the stress gradually reduces towards the neutral axis.
2. Calculation of stress at the inner edge of the flange:
From the stress distribution diagram, we know that the stress at the extreme fiber of the flange is maximum. Therefore, the stress at the inner edge of the flange can be calculated as follows:
Stress at the extreme fiber of the flange = Maximum stress developed in the beam section = 100 MPa
The distance from the neutral axis to the extreme fiber of the flange can be calculated as follows:
Distance from the neutral axis to the extreme fiber of the flange = (200/2) - 10 = 90 mm
Therefore, the stress at the inner edge of the flange can be calculated as follows:
Stress at the inner edge of the flange = Maximum stress developed in the beam section x (Distance from the neutral axis to the extreme fiber of the flange / Distance from the neutral axis to the centroid of the section)
Stress at the inner edge of the flange = 100 x (90/102.5) = 87.8 MPa
Therefore, the stress developed at the inner edge of the flange is 90 MPa (approx).
Hence, option (c) is the correct answer.
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A beam is of i-section with flanges 200 mm x 10 mm and web 180 mm x 10 mm. Due to the bending moment applied on the beam section, maximum stress developed in the beam section is 100 MPa, what is the stress developed at inner edge of the flange?a)110 MPab)100 MPac)90 MPad)120 MPaCorrect answer is option 'C'. Can you explain this answer?
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