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Calculate the maximum deflection of a simply supported beam if the maximum slope at A is 0.0075 radians and the distance of the centre of gravity of bending moment diagram to support A is 1.33 meters.
- a)9.975 mm
- b)9.5 mm
- c)9.25 mm
- d)9.785 mm
Correct answer is option 'A'. Can you explain this answer?
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Calculate the maximum deflection of a simply supported beam if the ma...
The deflection occurs at support A = A/EI = 0.0075 radians
View all questions of this test
Maximum deflection = Ax/EI = 0.0075 × 1.33
y = 9.975 mm.
Hence, the correct option is (A)
Most Upvoted Answer
Calculate the maximum deflection of a simply supported beam if the ma...
Maximum Deflection of a Simply Supported Beam:
Given:
Maximum slope at A (θ) = 0.0075 radians
Distance of the center of gravity of bending moment diagram to support A = 1.33 meters
To calculate the maximum deflection of a simply supported beam, we can use the following equation:
δ = (θ * L^2) / (8 * D)
where:
δ = maximum deflection
θ = maximum slope at A
L = distance between supports
D = flexural rigidity of the beam
In this case, the beam is simply supported, which means it is supported at both ends and has a fixed support at one end (A) and a roller support at the other end.
Now, let's solve the problem step by step.
Step 1: Calculate the distance between supports (L)
The distance between support A and the center of gravity of the bending moment diagram is given as 1.33 meters.
So, the distance between supports (L) = 2 * 1.33 meters = 2.66 meters
Step 2: Calculate the flexural rigidity of the beam (D)
The flexural rigidity of the beam depends on the material properties and the cross-sectional shape of the beam. It is represented by the product of the modulus of elasticity (E) and the moment of inertia (I) of the beam.
Since the cross-sectional shape and material properties are not given in the question, we cannot calculate the exact value of D. However, we can assume a value for D based on typical values for common materials.
Let's assume a value of D = 1,000,000 Nm^2 for the beam.
Step 3: Calculate the maximum deflection (δ)
Using the equation mentioned earlier:
δ = (θ * L^2) / (8 * D)
Substituting the given values:
δ = (0.0075 * (2.66)^2) / (8 * 1,000,000)
= 0.020006 Nm
Converting the deflection from Newton-meters to millimeters:
δ = 0.020006 * 1000
= 20.006 mm
So, the maximum deflection of the simply supported beam is approximately 20.006 mm.
Therefore, none of the given options (A, B, C, D) matches the correct answer.
Given:
Maximum slope at A (θ) = 0.0075 radians
Distance of the center of gravity of bending moment diagram to support A = 1.33 meters
To calculate the maximum deflection of a simply supported beam, we can use the following equation:
δ = (θ * L^2) / (8 * D)
where:
δ = maximum deflection
θ = maximum slope at A
L = distance between supports
D = flexural rigidity of the beam
In this case, the beam is simply supported, which means it is supported at both ends and has a fixed support at one end (A) and a roller support at the other end.
Now, let's solve the problem step by step.
Step 1: Calculate the distance between supports (L)
The distance between support A and the center of gravity of the bending moment diagram is given as 1.33 meters.
So, the distance between supports (L) = 2 * 1.33 meters = 2.66 meters
Step 2: Calculate the flexural rigidity of the beam (D)
The flexural rigidity of the beam depends on the material properties and the cross-sectional shape of the beam. It is represented by the product of the modulus of elasticity (E) and the moment of inertia (I) of the beam.
Since the cross-sectional shape and material properties are not given in the question, we cannot calculate the exact value of D. However, we can assume a value for D based on typical values for common materials.
Let's assume a value of D = 1,000,000 Nm^2 for the beam.
Step 3: Calculate the maximum deflection (δ)
Using the equation mentioned earlier:
δ = (θ * L^2) / (8 * D)
Substituting the given values:
δ = (0.0075 * (2.66)^2) / (8 * 1,000,000)
= 0.020006 Nm
Converting the deflection from Newton-meters to millimeters:
δ = 0.020006 * 1000
= 20.006 mm
So, the maximum deflection of the simply supported beam is approximately 20.006 mm.
Therefore, none of the given options (A, B, C, D) matches the correct answer.
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Calculate the maximum deflection of a simply supported beam if the maximum slope at A is 0.0075 radians and the distance of the centre of gravity of bending moment diagram to support A is 1.33 meters.a)9.975 mmb)9.5 mmc)9.25 mmd)9.785 mmCorrect answer is option 'A'. Can you explain this answer?
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Calculate the maximum deflection of a simply supported beam if the maximum slope at A is 0.0075 radians and the distance of the centre of gravity of bending moment diagram to support A is 1.33 meters.a)9.975 mmb)9.5 mmc)9.25 mmd)9.785 mmCorrect answer is option 'A'. 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 Calculate the maximum deflection of a simply supported beam if the maximum slope at A is 0.0075 radians and the distance of the centre of gravity of bending moment diagram to support A is 1.33 meters.a)9.975 mmb)9.5 mmc)9.25 mmd)9.785 mmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the maximum deflection of a simply supported beam if the maximum slope at A is 0.0075 radians and the distance of the centre of gravity of bending moment diagram to support A is 1.33 meters.a)9.975 mmb)9.5 mmc)9.25 mmd)9.785 mmCorrect answer is option 'A'. Can you explain this answer?.
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