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The slope at the free end of a cantilever of length 1 m is 1°. If the cantilever carries uniformly distributed load over the whole length then the deflection at the free end will be
- a)1 cm
- b)1.309 cm
- c)2.618 cm
- d)3.927 cm
Correct answer is option 'B'. Can you explain this answer?
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The slope at the free end of a cantilever of length 1 m is 1°. If the...
Δ = 
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= 
= 1.309cm
= 1.309cmMost Upvoted Answer
The slope at the free end of a cantilever of length 1 m is 1°. If the...
Given:
- Length of the cantilever (L) = 1 m
- Slope at the free end (θ) = 1°
To find:
- Deflection at the free end
Assumptions:
- The cantilever carries a uniformly distributed load over the whole length.
- The material of the cantilever is linearly elastic and obeys Hooke's law.
- The deflection is small and the cantilever remains in the linear elastic range.
Analysis:
To find the deflection at the free end of the cantilever, we can use the equation for deflection of a cantilever with a uniformly distributed load:
δ = (5 * w * L^4) / (384 * E * I)
Where:
- δ is the deflection at the free end
- w is the uniformly distributed load
- E is the modulus of elasticity of the material
- I is the moment of inertia of the cantilever cross-section
Step 1: Finding the load per unit length (w):
Since the load is uniformly distributed over the whole length, the load per unit length (w) can be calculated by dividing the total load by the length of the cantilever.
Step 2: Finding the moment of inertia (I):
The moment of inertia of the cantilever cross-section depends on its geometry. Without any information about the cross-section, we cannot calculate the moment of inertia. Therefore, we need to assume a specific cross-section for the cantilever.
Step 3: Finding the modulus of elasticity (E):
The modulus of elasticity is a material property and depends on the material of the cantilever. Without any information about the material, we cannot calculate the modulus of elasticity. Therefore, we need to assume a specific material for the cantilever.
Step 4: Calculating the deflection (δ):
Once we have the values of w, E, and I, we can substitute them into the equation for deflection to calculate the deflection at the free end.
Conclusion:
Without the information about the load per unit length, moment of inertia, and modulus of elasticity, we cannot calculate the deflection at the free end of the cantilever. Therefore, the given answer options are not valid.
- Length of the cantilever (L) = 1 m
- Slope at the free end (θ) = 1°
To find:
- Deflection at the free end
Assumptions:
- The cantilever carries a uniformly distributed load over the whole length.
- The material of the cantilever is linearly elastic and obeys Hooke's law.
- The deflection is small and the cantilever remains in the linear elastic range.
Analysis:
To find the deflection at the free end of the cantilever, we can use the equation for deflection of a cantilever with a uniformly distributed load:
δ = (5 * w * L^4) / (384 * E * I)
Where:
- δ is the deflection at the free end
- w is the uniformly distributed load
- E is the modulus of elasticity of the material
- I is the moment of inertia of the cantilever cross-section
Step 1: Finding the load per unit length (w):
Since the load is uniformly distributed over the whole length, the load per unit length (w) can be calculated by dividing the total load by the length of the cantilever.
Step 2: Finding the moment of inertia (I):
The moment of inertia of the cantilever cross-section depends on its geometry. Without any information about the cross-section, we cannot calculate the moment of inertia. Therefore, we need to assume a specific cross-section for the cantilever.
Step 3: Finding the modulus of elasticity (E):
The modulus of elasticity is a material property and depends on the material of the cantilever. Without any information about the material, we cannot calculate the modulus of elasticity. Therefore, we need to assume a specific material for the cantilever.
Step 4: Calculating the deflection (δ):
Once we have the values of w, E, and I, we can substitute them into the equation for deflection to calculate the deflection at the free end.
Conclusion:
Without the information about the load per unit length, moment of inertia, and modulus of elasticity, we cannot calculate the deflection at the free end of the cantilever. Therefore, the given answer options are not valid.
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The slope at the free end of a cantilever of length 1 m is 1°. If the cantilever carries uniformly distributed load over the whole length then the deflection at the free end will bea) 1 cmb) 1.309 cmc) 2.618 cmd) 3.927 cmCorrect answer is option 'B'. Can you explain this answer?
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