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A load of 30 kN is applied vertically downward at the free end of a cantilever of span 5 m. If the
elastic modulus of the cantilever is 30 GPa and the section has a width of 0.3 m and a depth of 0.6 m,
then, the elastic deflection (in mm) is ______________
elastic modulus of the cantilever is 30 GPa and the section has a width of 0.3 m and a depth of 0.6 m,
then, the elastic deflection (in mm) is ______________
Correct answer is between '7.65,7.75'. Can you explain this answer?
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Most Upvoted Answer
A load of 30 kN is applied vertically downward at the free end of a ca...
Given data:
- Load applied: 30 kN (vertically downward)
- Cantilever span: 5 m
- Elastic modulus: 30 GPa
- Section width: 0.3 m
- Section depth: 0.6 m
To find:
- Elastic deflection of the cantilever
Assumptions:
- The cantilever is made of a homogeneous and isotropic material.
- The load is applied at the free end of the cantilever.
- The cantilever is subjected to pure bending.
Formula:
The formula for calculating the elastic deflection of a cantilever under pure bending is given by:
δ = (FL^3) / (3EI)
Where:
δ = Elastic deflection
F = Load applied
L = Span of the cantilever
E = Elastic modulus of the material
I = Moment of inertia of the section
Step 1: Calculate the moment of inertia (I):
The moment of inertia (I) for a rectangular section is given by:
I = (b * d^3) / 12
Where:
b = Width of the section
d = Depth of the section
Substituting the given values:
I = (0.3 * 0.6^3) / 12
I = 0.0216 m^4
Step 2: Convert the load to N:
The given load is in kN, so we need to convert it to N:
Load (F) = 30 kN = 30,000 N
Step 3: Calculate the elastic deflection (δ):
Using the formula:
δ = (FL^3) / (3EI)
Substituting the given values:
δ = (30,000 * 5^3) / (3 * 30 * 10^9 * 0.0216)
δ ≈ 7.7 mm
Conclusion:
The elastic deflection of the cantilever is approximately 7.7 mm. Therefore, the correct answer lies between 7.65 mm and 7.75 mm.
- Load applied: 30 kN (vertically downward)
- Cantilever span: 5 m
- Elastic modulus: 30 GPa
- Section width: 0.3 m
- Section depth: 0.6 m
To find:
- Elastic deflection of the cantilever
Assumptions:
- The cantilever is made of a homogeneous and isotropic material.
- The load is applied at the free end of the cantilever.
- The cantilever is subjected to pure bending.
Formula:
The formula for calculating the elastic deflection of a cantilever under pure bending is given by:
δ = (FL^3) / (3EI)
Where:
δ = Elastic deflection
F = Load applied
L = Span of the cantilever
E = Elastic modulus of the material
I = Moment of inertia of the section
Step 1: Calculate the moment of inertia (I):
The moment of inertia (I) for a rectangular section is given by:
I = (b * d^3) / 12
Where:
b = Width of the section
d = Depth of the section
Substituting the given values:
I = (0.3 * 0.6^3) / 12
I = 0.0216 m^4
Step 2: Convert the load to N:
The given load is in kN, so we need to convert it to N:
Load (F) = 30 kN = 30,000 N
Step 3: Calculate the elastic deflection (δ):
Using the formula:
δ = (FL^3) / (3EI)
Substituting the given values:
δ = (30,000 * 5^3) / (3 * 30 * 10^9 * 0.0216)
δ ≈ 7.7 mm
Conclusion:
The elastic deflection of the cantilever is approximately 7.7 mm. Therefore, the correct answer lies between 7.65 mm and 7.75 mm.
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A load of 30 kN is applied vertically downward at the free end of a cantilever of span 5 m. If theelastic modulus of the cantilever is 30 GPa and the section has a width of 0.3 m and a depth of 0.6 m,then, the elastic deflection (in mm) is ______________Correct answer is between '7.65,7.75'. Can you explain this answer?
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A load of 30 kN is applied vertically downward at the free end of a cantilever of span 5 m. If theelastic modulus of the cantilever is 30 GPa and the section has a width of 0.3 m and a depth of 0.6 m,then, the elastic deflection (in mm) is ______________Correct answer is between '7.65,7.75'. 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 A load of 30 kN is applied vertically downward at the free end of a cantilever of span 5 m. If theelastic modulus of the cantilever is 30 GPa and the section has a width of 0.3 m and a depth of 0.6 m,then, the elastic deflection (in mm) is ______________Correct answer is between '7.65,7.75'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A load of 30 kN is applied vertically downward at the free end of a cantilever of span 5 m. If theelastic modulus of the cantilever is 30 GPa and the section has a width of 0.3 m and a depth of 0.6 m,then, the elastic deflection (in mm) is ______________Correct answer is between '7.65,7.75'. Can you explain this answer?.
A load of 30 kN is applied vertically downward at the free end of a cantilever of span 5 m. If theelastic modulus of the cantilever is 30 GPa and the section has a width of 0.3 m and a depth of 0.6 m,then, the elastic deflection (in mm) is ______________Correct answer is between '7.65,7.75'. 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 A load of 30 kN is applied vertically downward at the free end of a cantilever of span 5 m. If theelastic modulus of the cantilever is 30 GPa and the section has a width of 0.3 m and a depth of 0.6 m,then, the elastic deflection (in mm) is ______________Correct answer is between '7.65,7.75'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A load of 30 kN is applied vertically downward at the free end of a cantilever of span 5 m. If theelastic modulus of the cantilever is 30 GPa and the section has a width of 0.3 m and a depth of 0.6 m,then, the elastic deflection (in mm) is ______________Correct answer is between '7.65,7.75'. Can you explain this answer?.
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A load of 30 kN is applied vertically downward at the free end of a cantilever of span 5 m. If theelastic modulus of the cantilever is 30 GPa and the section has a width of 0.3 m and a depth of 0.6 m,then, the elastic deflection (in mm) is ______________Correct answer is between '7.65,7.75'. Can you explain this answer?, a detailed solution for A load of 30 kN is applied vertically downward at the free end of a cantilever of span 5 m. If theelastic modulus of the cantilever is 30 GPa and the section has a width of 0.3 m and a depth of 0.6 m,then, the elastic deflection (in mm) is ______________Correct answer is between '7.65,7.75'. Can you explain this answer? has been provided alongside types of A load of 30 kN is applied vertically downward at the free end of a cantilever of span 5 m. If theelastic modulus of the cantilever is 30 GPa and the section has a width of 0.3 m and a depth of 0.6 m,then, the elastic deflection (in mm) is ______________Correct answer is between '7.65,7.75'. Can you explain this answer? theory, EduRev gives you an
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