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The moment of inertia of a beam section which is 500 mm deep is 69.49 × 107 mm4. The maximum stress in the beam is not to exceed 110 N/mm2. The maximum span of the beam is _______ m, when simply supported at the ends and could carry a uniformly distributed load of 50 kN per metre length.
- a)6.99
- b)7.55
- c)8.23
- d)9.01
Correct answer is option 'A'. Can you explain this answer?
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The moment of inertia of a beam section which is 500 mm deep is 69.49...
Section modulus of section,
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z = 27.796 × 105mm3
Let the maximum spam be I metre
∴ Maximum bending moment,
= 62.5 × 103FN−mm
From bending equation, M/z ≤ σmax
⇒ 1 = 6.99m
Most Upvoted Answer
The moment of inertia of a beam section which is 500 mm deep is 69.49...
Given data:
Depth of beam section (d) = 500 mm
Moment of inertia (I) = 69.49 × 107 mm4
Maximum stress (σmax) = 110 N/mm2
Uniformly distributed load (w) = 50 kN/m
We know that the maximum bending moment (Mmax) occurs at the center of the beam when it is simply supported and carries a uniformly distributed load. Therefore,
Mmax = wL2/8
where L is the span of the beam.
Also, we know that the bending stress (σ) in a beam is given by:
σ = My/I
where M is the bending moment, y is the distance from the neutral axis to the point where the stress is being calculated, and I is the moment of inertia of the beam section.
Since the maximum stress (σmax) is given, we can rearrange the above equation to find the maximum bending moment (Mmax) that the beam can withstand:
Mmax = σmax I/y
We need to find the maximum span of the beam (L) such that the maximum bending moment (Mmax) does not exceed the maximum bending moment that the beam can withstand (Mmax = wL2/8). Therefore, we can equate the two expressions for Mmax and solve for L:
wL2/8 = σmax I/y
L2 = 8σmax I/wy
L = √(8σmax I/wy)
Substituting the given values, we get:
L = √(8×110×69.49×107/(50×103×500))
L = 6.99 m (approx.)
Therefore, the maximum span of the beam is 6.99 m (approx.) when simply supported at the ends and could carry a uniformly distributed load of 50 kN per metre length. Hence, the correct answer is option A.
Depth of beam section (d) = 500 mm
Moment of inertia (I) = 69.49 × 107 mm4
Maximum stress (σmax) = 110 N/mm2
Uniformly distributed load (w) = 50 kN/m
We know that the maximum bending moment (Mmax) occurs at the center of the beam when it is simply supported and carries a uniformly distributed load. Therefore,
Mmax = wL2/8
where L is the span of the beam.
Also, we know that the bending stress (σ) in a beam is given by:
σ = My/I
where M is the bending moment, y is the distance from the neutral axis to the point where the stress is being calculated, and I is the moment of inertia of the beam section.
Since the maximum stress (σmax) is given, we can rearrange the above equation to find the maximum bending moment (Mmax) that the beam can withstand:
Mmax = σmax I/y
We need to find the maximum span of the beam (L) such that the maximum bending moment (Mmax) does not exceed the maximum bending moment that the beam can withstand (Mmax = wL2/8). Therefore, we can equate the two expressions for Mmax and solve for L:
wL2/8 = σmax I/y
L2 = 8σmax I/wy
L = √(8σmax I/wy)
Substituting the given values, we get:
L = √(8×110×69.49×107/(50×103×500))
L = 6.99 m (approx.)
Therefore, the maximum span of the beam is 6.99 m (approx.) when simply supported at the ends and could carry a uniformly distributed load of 50 kN per metre length. Hence, the correct answer is option A.
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The moment of inertia of a beam section which is 500 mm deep is 69.49 × 107 mm4. The maximum stress in the beam is not to exceed 110 N/mm2. The maximum span of the beam is _______ m, when simply supported at the ends and could carry a uniformly distributed load of 50 kN per metre length.a)6.99b)7.55c)8.23d)9.01Correct answer is option 'A'. Can you explain this answer?
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The moment of inertia of a beam section which is 500 mm deep is 69.49 × 107 mm4. The maximum stress in the beam is not to exceed 110 N/mm2. The maximum span of the beam is _______ m, when simply supported at the ends and could carry a uniformly distributed load of 50 kN per metre length.a)6.99b)7.55c)8.23d)9.01Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The moment of inertia of a beam section which is 500 mm deep is 69.49 × 107 mm4. The maximum stress in the beam is not to exceed 110 N/mm2. The maximum span of the beam is _______ m, when simply supported at the ends and could carry a uniformly distributed load of 50 kN per metre length.a)6.99b)7.55c)8.23d)9.01Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The moment of inertia of a beam section which is 500 mm deep is 69.49 × 107 mm4. The maximum stress in the beam is not to exceed 110 N/mm2. The maximum span of the beam is _______ m, when simply supported at the ends and could carry a uniformly distributed load of 50 kN per metre length.a)6.99b)7.55c)8.23d)9.01Correct answer is option 'A'. Can you explain this answer?.
The moment of inertia of a beam section which is 500 mm deep is 69.49 × 107 mm4. The maximum stress in the beam is not to exceed 110 N/mm2. The maximum span of the beam is _______ m, when simply supported at the ends and could carry a uniformly distributed load of 50 kN per metre length.a)6.99b)7.55c)8.23d)9.01Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The moment of inertia of a beam section which is 500 mm deep is 69.49 × 107 mm4. The maximum stress in the beam is not to exceed 110 N/mm2. The maximum span of the beam is _______ m, when simply supported at the ends and could carry a uniformly distributed load of 50 kN per metre length.a)6.99b)7.55c)8.23d)9.01Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The moment of inertia of a beam section which is 500 mm deep is 69.49 × 107 mm4. The maximum stress in the beam is not to exceed 110 N/mm2. The maximum span of the beam is _______ m, when simply supported at the ends and could carry a uniformly distributed load of 50 kN per metre length.a)6.99b)7.55c)8.23d)9.01Correct answer is option 'A'. Can you explain this answer?.
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