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A cantilever of length 1.2m carries a concentrated load of 12kN at the free end. The beam is of rectangular cross-section with breadth equal to half the depth. The maximum stress due to bending is not to exceed 100 N/mm2. The minimum depth of the beam should be
- a)120 mm
- b)60 mm
- c)75 mm
- d)240 mm
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A cantilever of length 1.2m carries a concentrated load of 12kN at th...
At point A, Mmax = WL
= (12 × 103)Nm × (1.2)
= 14.4 × 103Nm = 14.4 × 106Nmm
bh2 = 6 × 14.4 × 104
(h / 2) × h2 = 86.4 × 104
h3 = 172.8 × 104
h = 120 mm
Most Upvoted Answer
A cantilever of length 1.2m carries a concentrated load of 12kN at th...
To find the minimum depth of the beam, we need to calculate the maximum bending moment and then use the bending stress formula to determine the minimum depth.
1. Finding the maximum bending moment:
The bending moment at the free end of the cantilever can be calculated using the formula:
M = F * L
Where:
M = Bending moment
F = Concentrated load at the free end (12kN)
L = Length of the cantilever (1.2m)
Substituting the given values:
M = 12kN * 1.2m
M = 14.4kNm
2. Calculating the minimum depth using the bending stress formula:
The bending stress (σ) in a rectangular beam can be calculated using the formula:
σ = (M * y) / (I * c)
Where:
σ = Bending stress
M = Bending moment (14.4kNm)
y = Distance from the neutral axis to the outer fiber (depth/2)
I = Moment of inertia of the cross-section (b * h^3 / 12)
c = Distance from the neutral axis to the extreme fiber (depth/2)
We can rearrange the formula to solve for the depth (h):
h = (12 * M) / (b * σ)
Given that the breadth (b) is equal to half the depth (h/2), we can substitute this value in the formula:
h = (12 * M) / ((h/2) * σ)
Simplifying the equation:
h^2 = (24 * M) / (σ)
h = √((24 * M) / (σ))
Substituting the given values:
h = √((24 * 14.4kNm) / (100N/mm^2))
h ≈ 120mm
Therefore, the minimum depth of the beam should be 120mm, which corresponds to option 'A'.
1. Finding the maximum bending moment:
The bending moment at the free end of the cantilever can be calculated using the formula:
M = F * L
Where:
M = Bending moment
F = Concentrated load at the free end (12kN)
L = Length of the cantilever (1.2m)
Substituting the given values:
M = 12kN * 1.2m
M = 14.4kNm
2. Calculating the minimum depth using the bending stress formula:
The bending stress (σ) in a rectangular beam can be calculated using the formula:
σ = (M * y) / (I * c)
Where:
σ = Bending stress
M = Bending moment (14.4kNm)
y = Distance from the neutral axis to the outer fiber (depth/2)
I = Moment of inertia of the cross-section (b * h^3 / 12)
c = Distance from the neutral axis to the extreme fiber (depth/2)
We can rearrange the formula to solve for the depth (h):
h = (12 * M) / (b * σ)
Given that the breadth (b) is equal to half the depth (h/2), we can substitute this value in the formula:
h = (12 * M) / ((h/2) * σ)
Simplifying the equation:
h^2 = (24 * M) / (σ)
h = √((24 * M) / (σ))
Substituting the given values:
h = √((24 * 14.4kNm) / (100N/mm^2))
h ≈ 120mm
Therefore, the minimum depth of the beam should be 120mm, which corresponds to option 'A'.
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A cantilever of length 1.2m carries a concentrated load of 12kN at the free end. The beam is of rectangular cross-section with breadth equal to half the depth. The maximum stress due to bending is not to exceed 100 N/mm2. The minimum depth of the beam should bea) 120 mmb) 60 mmc) 75 mmd) 240 mmCorrect answer is option 'A'. Can you explain this answer?
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A cantilever of length 1.2m carries a concentrated load of 12kN at the free end. The beam is of rectangular cross-section with breadth equal to half the depth. The maximum stress due to bending is not to exceed 100 N/mm2. The minimum depth of the beam should bea) 120 mmb) 60 mmc) 75 mmd) 240 mmCorrect answer is option 'A'. 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 A cantilever of length 1.2m carries a concentrated load of 12kN at the free end. The beam is of rectangular cross-section with breadth equal to half the depth. The maximum stress due to bending is not to exceed 100 N/mm2. The minimum depth of the beam should bea) 120 mmb) 60 mmc) 75 mmd) 240 mmCorrect answer is option 'A'. 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 A cantilever of length 1.2m carries a concentrated load of 12kN at the free end. The beam is of rectangular cross-section with breadth equal to half the depth. The maximum stress due to bending is not to exceed 100 N/mm2. The minimum depth of the beam should bea) 120 mmb) 60 mmc) 75 mmd) 240 mmCorrect answer is option 'A'. Can you explain this answer?.
A cantilever of length 1.2m carries a concentrated load of 12kN at the free end. The beam is of rectangular cross-section with breadth equal to half the depth. The maximum stress due to bending is not to exceed 100 N/mm2. The minimum depth of the beam should bea) 120 mmb) 60 mmc) 75 mmd) 240 mmCorrect answer is option 'A'. 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 A cantilever of length 1.2m carries a concentrated load of 12kN at the free end. The beam is of rectangular cross-section with breadth equal to half the depth. The maximum stress due to bending is not to exceed 100 N/mm2. The minimum depth of the beam should bea) 120 mmb) 60 mmc) 75 mmd) 240 mmCorrect answer is option 'A'. 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 A cantilever of length 1.2m carries a concentrated load of 12kN at the free end. The beam is of rectangular cross-section with breadth equal to half the depth. The maximum stress due to bending is not to exceed 100 N/mm2. The minimum depth of the beam should bea) 120 mmb) 60 mmc) 75 mmd) 240 mmCorrect answer is option 'A'. Can you explain this answer?.
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