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Beam A is simply supported at its ends and carries udl of intensity w over its entire length. It is made of steel having Young's modulus E. Beam B is cantilever and carries a udl of intensity w/4 over its entire length. It is made of brass having Young's modulus E/2. The two beams are of same length and have same cross-sectional area. If σA and σB denote the maximum bending stresses developed in beams A and B, respectively, then which one of the following is correct?
- a)σA/σB
- b)σA/σB < 1.0
- c)σA/σB > 1.0
- d)σA/σB depends on the shape of cross-section
Correct answer is option 'D'. Can you explain this answer?
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Beam A is simply supported at its ends and carries udl of intensity w ...
Bending stress 
Shape of cross section 
depends on the shape of cross section
depends on the shape of cross sectionMost Upvoted Answer
Beam A is simply supported at its ends and carries udl of intensity w ...
Solution:
Given parameters:
- Beam A: Simply supported, steel, udl intensity=w, Young's modulus=E
- Beam B: Cantilever, brass, udl intensity=w/4, Young's modulus=E/2
- Both beams: Same length, same cross-sectional area
To find: A/B, where A and B are the maximum bending stresses developed in beams A and B, respectively.
Calculations:
1. Maximum bending stress in beam A:
- For simply supported beam with udl, maximum bending stress occurs at the center.
- Maximum bending moment (M) = wl^2/8, where w=udl intensity, l=length of beam.
- Maximum bending stress (σ) = Mc/I, where c=distance from neutral axis to the edge, I=moment of inertia of cross-section about neutral axis.
- For rectangular cross-section, I=bh^3/12, where b=width, h=height.
- c=h/2
- σ=wLh/8h^3 = wL/8h^2
- Therefore, A=wL/8h^2
2. Maximum bending stress in beam B:
- For cantilever beam with udl, maximum bending stress occurs at the fixed end.
- Maximum bending moment (M) = wL^2/2, where w=udl intensity, L=length of beam.
- Maximum bending stress (σ) = Mc/I, where c=distance from neutral axis to the edge, I=moment of inertia of cross-section about neutral axis.
- For rectangular cross-section, I=bh^3/12, where b=width, h=height.
- c=h/2
- σ=wLh/2h^3 = wL/2h^2
- Therefore, B=wL/2h^2
3. A/B = (wL/8h^2)/(wL/2h^2) = 1/4
Therefore, the correct answer is option D, i.e., A/B depends on the shape of the cross-section.
Given parameters:
- Beam A: Simply supported, steel, udl intensity=w, Young's modulus=E
- Beam B: Cantilever, brass, udl intensity=w/4, Young's modulus=E/2
- Both beams: Same length, same cross-sectional area
To find: A/B, where A and B are the maximum bending stresses developed in beams A and B, respectively.
Calculations:
1. Maximum bending stress in beam A:
- For simply supported beam with udl, maximum bending stress occurs at the center.
- Maximum bending moment (M) = wl^2/8, where w=udl intensity, l=length of beam.
- Maximum bending stress (σ) = Mc/I, where c=distance from neutral axis to the edge, I=moment of inertia of cross-section about neutral axis.
- For rectangular cross-section, I=bh^3/12, where b=width, h=height.
- c=h/2
- σ=wLh/8h^3 = wL/8h^2
- Therefore, A=wL/8h^2
2. Maximum bending stress in beam B:
- For cantilever beam with udl, maximum bending stress occurs at the fixed end.
- Maximum bending moment (M) = wL^2/2, where w=udl intensity, L=length of beam.
- Maximum bending stress (σ) = Mc/I, where c=distance from neutral axis to the edge, I=moment of inertia of cross-section about neutral axis.
- For rectangular cross-section, I=bh^3/12, where b=width, h=height.
- c=h/2
- σ=wLh/2h^3 = wL/2h^2
- Therefore, B=wL/2h^2
3. A/B = (wL/8h^2)/(wL/2h^2) = 1/4
Therefore, the correct answer is option D, i.e., A/B depends on the shape of the cross-section.
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Beam A is simply supported at its ends and carries udl of intensity w over its entire length. It is made of steel having Young's modulus E. Beam B is cantilever and carries a udl of intensity w/4 over its entire length. It is made of brass having Young's modulus E/2. The two beams are of same length and have same cross-sectional area. If σA and σB denote the maximum bending stresses developed in beams A and B, respectively, then which one of the following is correct?a)σA/σBb)σA/σB < 1.0c)σA/σB > 1.0d)σA/σB depends on the shape of cross-sectionCorrect answer is option 'D'. Can you explain this answer?
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Beam A is simply supported at its ends and carries udl of intensity w over its entire length. It is made of steel having Young's modulus E. Beam B is cantilever and carries a udl of intensity w/4 over its entire length. It is made of brass having Young's modulus E/2. The two beams are of same length and have same cross-sectional area. If σA and σB denote the maximum bending stresses developed in beams A and B, respectively, then which one of the following is correct?a)σA/σBb)σA/σB < 1.0c)σA/σB > 1.0d)σA/σB depends on the shape of cross-sectionCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Beam A is simply supported at its ends and carries udl of intensity w over its entire length. It is made of steel having Young's modulus E. Beam B is cantilever and carries a udl of intensity w/4 over its entire length. It is made of brass having Young's modulus E/2. The two beams are of same length and have same cross-sectional area. If σA and σB denote the maximum bending stresses developed in beams A and B, respectively, then which one of the following is correct?a)σA/σBb)σA/σB < 1.0c)σA/σB > 1.0d)σA/σB depends on the shape of cross-sectionCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Beam A is simply supported at its ends and carries udl of intensity w over its entire length. It is made of steel having Young's modulus E. Beam B is cantilever and carries a udl of intensity w/4 over its entire length. It is made of brass having Young's modulus E/2. The two beams are of same length and have same cross-sectional area. If σA and σB denote the maximum bending stresses developed in beams A and B, respectively, then which one of the following is correct?a)σA/σBb)σA/σB < 1.0c)σA/σB > 1.0d)σA/σB depends on the shape of cross-sectionCorrect answer is option 'D'. Can you explain this answer?.
Beam A is simply supported at its ends and carries udl of intensity w over its entire length. It is made of steel having Young's modulus E. Beam B is cantilever and carries a udl of intensity w/4 over its entire length. It is made of brass having Young's modulus E/2. The two beams are of same length and have same cross-sectional area. If σA and σB denote the maximum bending stresses developed in beams A and B, respectively, then which one of the following is correct?a)σA/σBb)σA/σB < 1.0c)σA/σB > 1.0d)σA/σB depends on the shape of cross-sectionCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Beam A is simply supported at its ends and carries udl of intensity w over its entire length. It is made of steel having Young's modulus E. Beam B is cantilever and carries a udl of intensity w/4 over its entire length. It is made of brass having Young's modulus E/2. The two beams are of same length and have same cross-sectional area. If σA and σB denote the maximum bending stresses developed in beams A and B, respectively, then which one of the following is correct?a)σA/σBb)σA/σB < 1.0c)σA/σB > 1.0d)σA/σB depends on the shape of cross-sectionCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Beam A is simply supported at its ends and carries udl of intensity w over its entire length. It is made of steel having Young's modulus E. Beam B is cantilever and carries a udl of intensity w/4 over its entire length. It is made of brass having Young's modulus E/2. The two beams are of same length and have same cross-sectional area. If σA and σB denote the maximum bending stresses developed in beams A and B, respectively, then which one of the following is correct?a)σA/σBb)σA/σB < 1.0c)σA/σB > 1.0d)σA/σB depends on the shape of cross-sectionCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Beam A is simply supported at its ends and carries udl of intensity w over its entire length. It is made of steel having Young's modulus E. Beam B is cantilever and carries a udl of intensity w/4 over its entire length. It is made of brass having Young's modulus E/2. The two beams are of same length and have same cross-sectional area. If σA and σB denote the maximum bending stresses developed in beams A and B, respectively, then which one of the following is correct?a)σA/σBb)σA/σB < 1.0c)σA/σB > 1.0d)σA/σB depends on the shape of cross-sectionCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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Beam A is simply supported at its ends and carries udl of intensity w over its entire length. It is made of steel having Young's modulus E. Beam B is cantilever and carries a udl of intensity w/4 over its entire length. It is made of brass having Young's modulus E/2. The two beams are of same length and have same cross-sectional area. If σA and σB denote the maximum bending stresses developed in beams A and B, respectively, then which one of the following is correct?a)σA/σBb)σA/σB < 1.0c)σA/σB > 1.0d)σA/σB depends on the shape of cross-sectionCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Beam A is simply supported at its ends and carries udl of intensity w over its entire length. It is made of steel having Young's modulus E. Beam B is cantilever and carries a udl of intensity w/4 over its entire length. It is made of brass having Young's modulus E/2. The two beams are of same length and have same cross-sectional area. If σA and σB denote the maximum bending stresses developed in beams A and B, respectively, then which one of the following is correct?a)σA/σBb)σA/σB < 1.0c)σA/σB > 1.0d)σA/σB depends on the shape of cross-sectionCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Beam A is simply supported at its ends and carries udl of intensity w over its entire length. It is made of steel having Young's modulus E. Beam B is cantilever and carries a udl of intensity w/4 over its entire length. It is made of brass having Young's modulus E/2. The two beams are of same length and have same cross-sectional area. If σA and σB denote the maximum bending stresses developed in beams A and B, respectively, then which one of the following is correct?a)σA/σBb)σA/σB < 1.0c)σA/σB > 1.0d)σA/σB depends on the shape of cross-sectionCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Beam A is simply supported at its ends and carries udl of intensity w over its entire length. It is made of steel having Young's modulus E. Beam B is cantilever and carries a udl of intensity w/4 over its entire length. It is made of brass having Young's modulus E/2. The two beams are of same length and have same cross-sectional area. If σA and σB denote the maximum bending stresses developed in beams A and B, respectively, then which one of the following is correct?a)σA/σBb)σA/σB < 1.0c)σA/σB > 1.0d)σA/σB depends on the shape of cross-sectionCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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