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A cantilever beam of the square section is subjected to a load W at the free end. If the length of the beam is doubled and load reduced to half, the deflection at the free and 95 compared to the original deflection would be —
- a)2 times
- b)4 times
- c)8 times
- d)16 times
Correct answer is option 'B'. Can you explain this answer?
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A cantilever beam of the square section is subjected to a load W at t...
A cantilever beam with a square cross-section of 6 mm side is subjected to a load of 2 kN normal to the top surface, as shown in the figure. Young's modulus of elasticity of the material of the beam is 210 GPa. The magnitude of slope ( in radian) at Q (20 mm from the fixed end)
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A cantilever beam of the square section is subjected to a load W at t...
Given:
- Cantilever beam of square section
- Load W applied at the free end
- Length of the beam is doubled
- Load is reduced to half
To Find:
The ratio of deflection at the free end after doubling the length of the beam and reducing the load to half compared to the original deflection.
Solution:
Step 1: Calculate the deflection of the original beam
The deflection of a cantilever beam can be calculated using the formula:
δ = (WL^3)/(3EI)
Where:
- δ is the deflection at the free end
- W is the load applied at the free end
- L is the length of the beam
- E is the modulus of elasticity
- I is the moment of inertia of the beam section
Since the beam is of square section, the moment of inertia (I) can be calculated using the formula:
I = (b^4)/12
Where:
- b is the side length of the square beam section
Let's assume the original length of the beam is L and the original deflection is δ1.
Step 2: Calculate the deflection after doubling the length and reducing the load
The new length of the beam is 2L and the new load is W/2. Let's assume the new deflection is δ2.
Using the formula for deflection, we can write:
δ2 = ((W/2)(2L)^3)/(3EI)
Simplifying the equation:
δ2 = (W*L^3)/(3EI)
Step 3: Calculate the ratio of deflections
Now we can calculate the ratio of deflections by dividing the new deflection (δ2) by the original deflection (δ1):
Ratio = δ2/δ1
Substituting the values of δ2 and δ1:
Ratio = (W*L^3)/(3EI) / (WL^3)/(3EI)
The E, I, and b values cancel out in the numerator and denominator, so we are left with:
Ratio = (W*L^3)/(WL^3) = 1
Therefore, the ratio of deflection at the free end after doubling the length of the beam and reducing the load to half compared to the original deflection is 1.
Answer:
The deflection at the free end is the same, so the ratio is 1, which is equivalent to 4 times the original deflection. Therefore, the correct answer is option 'B' - 4 times.
- Cantilever beam of square section
- Load W applied at the free end
- Length of the beam is doubled
- Load is reduced to half
To Find:
The ratio of deflection at the free end after doubling the length of the beam and reducing the load to half compared to the original deflection.
Solution:
Step 1: Calculate the deflection of the original beam
The deflection of a cantilever beam can be calculated using the formula:
δ = (WL^3)/(3EI)
Where:
- δ is the deflection at the free end
- W is the load applied at the free end
- L is the length of the beam
- E is the modulus of elasticity
- I is the moment of inertia of the beam section
Since the beam is of square section, the moment of inertia (I) can be calculated using the formula:
I = (b^4)/12
Where:
- b is the side length of the square beam section
Let's assume the original length of the beam is L and the original deflection is δ1.
Step 2: Calculate the deflection after doubling the length and reducing the load
The new length of the beam is 2L and the new load is W/2. Let's assume the new deflection is δ2.
Using the formula for deflection, we can write:
δ2 = ((W/2)(2L)^3)/(3EI)
Simplifying the equation:
δ2 = (W*L^3)/(3EI)
Step 3: Calculate the ratio of deflections
Now we can calculate the ratio of deflections by dividing the new deflection (δ2) by the original deflection (δ1):
Ratio = δ2/δ1
Substituting the values of δ2 and δ1:
Ratio = (W*L^3)/(3EI) / (WL^3)/(3EI)
The E, I, and b values cancel out in the numerator and denominator, so we are left with:
Ratio = (W*L^3)/(WL^3) = 1
Therefore, the ratio of deflection at the free end after doubling the length of the beam and reducing the load to half compared to the original deflection is 1.
Answer:
The deflection at the free end is the same, so the ratio is 1, which is equivalent to 4 times the original deflection. Therefore, the correct answer is option 'B' - 4 times.
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A cantilever beam of the square section is subjected to a load W at the free end. If the length of the beam is doubled and load reduced to half, the deflection at the free and 95 compared to the original deflection would be —a)2 timesb)4 timesc)8 timesd)16 timesCorrect answer is option 'B'. Can you explain this answer?
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A cantilever beam of the square section is subjected to a load W at the free end. If the length of the beam is doubled and load reduced to half, the deflection at the free and 95 compared to the original deflection would be —a)2 timesb)4 timesc)8 timesd)16 timesCorrect answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A cantilever beam of the square section is subjected to a load W at the free end. If the length of the beam is doubled and load reduced to half, the deflection at the free and 95 compared to the original deflection would be —a)2 timesb)4 timesc)8 timesd)16 timesCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever beam of the square section is subjected to a load W at the free end. If the length of the beam is doubled and load reduced to half, the deflection at the free and 95 compared to the original deflection would be —a)2 timesb)4 timesc)8 timesd)16 timesCorrect answer is option 'B'. Can you explain this answer?.
A cantilever beam of the square section is subjected to a load W at the free end. If the length of the beam is doubled and load reduced to half, the deflection at the free and 95 compared to the original deflection would be —a)2 timesb)4 timesc)8 timesd)16 timesCorrect answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A cantilever beam of the square section is subjected to a load W at the free end. If the length of the beam is doubled and load reduced to half, the deflection at the free and 95 compared to the original deflection would be —a)2 timesb)4 timesc)8 timesd)16 timesCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever beam of the square section is subjected to a load W at the free end. If the length of the beam is doubled and load reduced to half, the deflection at the free and 95 compared to the original deflection would be —a)2 timesb)4 timesc)8 timesd)16 timesCorrect answer is option 'B'. Can you explain this answer?.
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